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Relationship OCD is a subtype of obsessive-compulsive disorder (OCD) characterized by a preoccupation with their partner’s appropriateness as a mate, reports an article from the OCD Center of Los Angeles. The disorder causes intrusive, unwanted, and distressing thoughts about the strength, quality, and “true nature” of their love for their partner and often leads the affected person to question their partner’s overall level of attractiveness, sexual desirability, or long-term compatibility. Relationship OCD is less visible than other forms of OCD and often goes unnoticed or is misdiagnosed by professionals. Relationship OCD is different from normal relationship doubts, as doubts are inconsistent with their true feelings and tend to cause extreme distress. Relationship OCD is treatable through a combination of psychoeducation, cognitive restructuring, exposure and response prevention (ERP) and mindfulness skills training. To read this article in its entirety, click here.
Intercultural Teaching Competence Workshop Series Workshop 1: Facilitating Learning in the Intercultural Classroom Nanda and Aisha led experiential activities and shared examples to demonstrate strategies effective in facilitating learning in a diverse classroom. In the workshops, students 1. identified the effects of assumptions on GTA-student relationship and the implication for teaching; 2. explored facilitation strategies for students with diverse communication styles; 3. identified differences in giving feedback across cultures; and, 4. designed activities that promote interaction among students Workshop Materials: Workshop 2: Presenting your Research to Diverse Audience Aisha guided GTAs through the analysis of some contestants’ performance in the 3-minute speech competition to identify what makes an effective presentation to diverse audience. In the workshop, students 1. identified differences between presenting for disciplinary vs inter-disciplinary audiences; 2. analyzed skills through sample presentations to prepare and organize speeches for interdisciplinary audiences; and, 3. applied strategies to present their own research ideas. Workshop Materials:
Wednesday, September 03, 2008 Natural Gas Limelight A decade ago, natural gas looked like the certain winner of a shift to lower-emission energy sources, as concerns about greenhouse gas emissions grew. The path to that outcome has been much bumpier than expected, however. Rising natural gas prices and supply concerns coincided with another shift, this one among environmentalists who identified gas as a key element of a "carbon economy" they were driven to transform, rather than the least-emitting fossil fuel. These dynamics are shifting again, and the future again looks positive for the US gas industry, thanks in part to the increased visibility created by the Pickens Plan and a new industry PR campaign. Its improved supply outlook and relative pricing against oil are helping, as well. Since 1998 demand for natural gas in the power sector has grown by 50%, and gas-fired turbines now account for 41% of US generating capacity and 21% of net generation. But by 2004 US gas production had dipped by about 5% from its recent high in 2001--a slump that was deepened in 2005 and 2006 by the lingering effects of Hurricane Katrina. As a result, natural gas prices are running at about four times their 1998 level of around $2 per million BTUs, and winter spikes to $10 or higher have become the norm. As recently as a couple of years ago, many analysts saw natural gas as the country's quiet energy crisis, with our import dependence beginning to mirror that of oil. Today, that perspective has been dramatically altered by the success of the US gas industry in tapping unconventional sources, including coal-bed methane and the shale plays that are driving the success of companies such as Chesapeake Energy. BP is purchasing a 25% interest in Chesapeake's Fayettville Shale assets. Although it comes too late to save many of the gas-intensive industries that moved offshore in search of lower input costs, and while I'm skeptical of claims that the US might become a net natural gas exporter, the resurgence in US gas production could not come at a better time, given our intertwined concerns about energy security and climate change. The greenhouse gas advantage of natural gas for power generation looks significant, compared to coal. In 2000 the average US gas-fired power plant emitted nearly 40% less CO2 per kilowatt-hour than the average coal-fired plant. But with wind and solar power booming, this glass was increasingly viewed by environmentalists as 60% full, rather than 40% empty. That did not stop gas from gaining market share at the expense of coal, but its green image hasn't held up as well as its supporters expected. Some of that luster is being restored by the attention generated by Mr. Pickens, who casts gas as an environmentally-friendly bulwark of US energy security. Recent remarks by Speaker Pelosi and Senator Obama suggest that this approach is working. It also helps that the Pickens Plan focuses on increasing natural gas consumption in transportation, where its emissions benefits and cost savings align nicely. A natural gas vehicle emits about 25% less CO2 per mile, measured from "well-to-wheels", than the comparable gasoline car, and it appears to be slightly greener than a flexible-fuel vehicle running on E85. Factor in the substantial price discount for compressed natural gas, compared to gasoline, and this ought to be a winning proposition for consumers, particularly if legislation to provide incentives for buying or converting a car to run on compressed natural gas passes. Let's put all of this in perspective. Higher US natural gas production should provide economic and environmental benefits for the entire country, even if it doesn't result in a gas glut, but it is still no panacea. At 23 trillion cubic feet (TCF) per year and growing, US gas consumption still exceeds the highest previous level of US production, 22.6 TCF in 1973. And with US electricity demand having grown by 78 million MWh last year--a multiple of the additions from wind and solar power--and with new coal-fired plants being canceled left and right, natural gas consumption in the power sector seems likely to increase, not decrease, at least for the next several years. That means that in order for gas use for transportation to grow large enough to have an impact on US greenhouse gas emissions, it must compete for its share of growing production, or rely on imports, undermining its perceived energy security benefit. Moreover, politicians tempted to nudge the market in the direction of more natural gas cars should keep in mind that much of the nation's gas is consumed in ways that would have a large and fairly direct impact on consumers' wallets, should increased competition for it drive up its price. No comments:
Detecting CPU Speed From OSDev Wiki Jump to: navigation, search This article's tone or style may not reflect the encyclopedic tone used throughout the wiki. See Wikipedia's article on tone for suggestions. What is CPU Speed There are several different things that could be called "CPU speed": 1. how quickly it can execute code (e.g. instructions per second) 2. how fast its clock is running (e.g. cycles per second) How quickly a CPU can execute code is important for determining the CPU's performance. How fast a CPU's clock is running is only useful for specific cases (e.g. calibrating the CPU's TSC to use for measuring time). There are also several different measurements for these different "CPU speeds": 1. best case 2. nominal case 3. average case 4. current case 5. worst case For example, if you look at a modern Core i7 CPU (with turbo-boost, power management and hyper-threading), the best case instructions per second would occur when there's no throttling/power saving at all, only one logical CPU is running (turbo-boost activated and hyper-threading not being used), you're executing simple instructions with no dependencies in a loop that fits in the CPU's "loop buffer", there are no branch mispredictions, and there are no accesses to memory (no data being transferred to/from caches or RAM). The worst case instructions per second would be the exact opposite; and may be several orders of magnitude worse (e.g. a best case of 4 billion instructions per second and a worst case of 100 million instructions per second). The nominal instructions per second is an estimation of "normal" - e.g. the normal average instructions per second you'd expect (note: "nominal cycles per second" is used more often). All of these things are fixed values - a specific CPU always has the same best case, worst case and nominal case, and these values don't change depending on CPU load, which instructions are/were executed, etc. The current instructions per second is the instructions per second at a specific instant in time and must be somewhere between the best and worst cases. It can't actually be measured, but can be estimated by finding the average instructions per second for a very short period of time. The average case is something that has to be measured. Both the current instructions per second and the average instructions per second depend heavily on the code that was running. For example, the average instructions per second for a series of NOP instructions may be much higher that the average instructions per second for a series of DIV instructions. General Method In order to tell what's the CPU speed, we need two things: 1. being able to tell that a given (precise) amount of time has elapsed. 2. being able to know how much 'clock cycles' a portion of code took. Once these two sub-problems are solved, one can easily tell the CPU speed using the following : prepare_a_timer(X milliseconds ahead); while (timer has not fired) { inc iterations_counter; cpuspeed_mhz = (iteration_counter * clock_cycles_per_iteration)/1000; Note that except for very special cases, using a busy-loop (even calibrated) to introduce delays is a bad idea and that it should be kept for very small delays (nano or micro seconds) that you must comply when programming hardware only. Also note that PC emulators (like BOCHS, for instance) are rarely realtime and that you shouldn't be surprised if your clock appears to run faster than expected on those emulators. Waiting for a given amount of time There are two circuits in a PC that allows you to deal with time: the PIT (Programmable Interval Timer, 8253 iirc) and the RTC (Real Time Clock). The PIT is probably the better of the two for this task. The PIT has two operating mode that can be useful for telling the cpu speed: 1. the periodic interrupt mode (0x36), in which a signal is emitted to the interrupt controller at a fixed frequency. This is especially interesting on PIT channel 0 which is bound to IRQ0 on a PC. 2. the one shot mode (0x34), in which the PIT will decrease a counter at its top speed (1.19318 MHz) until the counter reaches zero. Whether or not an IRQ is fired by channel0 in 0x34 mode should be checked Note that theoretically, _one shot_ mode could be used with a _polling_ approach, reading the current count on the channel's data port, but I/O bus cycles have unpredictable latency and one should make sure the timestamp counter is not affected by this approach. Knowing how many cycles your loop takes This step depends on your CPU. On 286, 386 and 486, each instruction took a well-known and deterministic amount of clock cycles to execute. This allowed the programmer to tell exactly how many cycles a loop iteration took by looking up the timing of each instruction and then sum them up. Since the multi-pipelined architecture of the Pentium, however, such numbers are no longer communicated (for a major part because the same instruction could have variable timings depending on its surrounding, which makes the timing almost useless). It is possible to create code which is exceptionally pipeline hostile such as: xor eax,edx xor edx,eax xor eax,edx xor edx,eax A simple xor instruction takes one cycle, and it's guaranteed that the processor cannot pipeline this code as the current instructions operands depend on the results from the last calculation. One can check that, for a small count (tested from 16 to 64), RDTSC will show the instruction count is almost exactly (sometimes off by one) the cycles count. Unfortunately, when making the chain longer you'll start experiencing code cache misses, which will ruin the whole process. E.g. looping on a chain of 1550 XORs may require a hundred of iterations before it stabilizes around 1575 clock cycles on a AMDx86-64, and I'm still waiting it to stabilize on my Pentium3 Despite this inaccuracy it gives relatively good results across the whole processor generation given a reasonably accurate timer but if very accurate measurements are needed the next method should prove more useful. A Pentium developer has a much better tool to tell timings: the _Time Stamp Counter_: an internal counter that can be read using RDTSC special instruction rdtscpm1.pdf explains how that feature can be used for performance monitoring and should provide the necessary information on how to access the TSC on a Pentium RDTSC Instruction Access The presence of the Time Stamp Counter (and thus the availability of RDTSC instruction) can be detected through the [CPUID] instruction. When calling CPUID with eax=1, you'll receive the features flags in edx. TSC is the bit #4 of that field. Note that prior to use the CPUID instruction, you should also make sure the processor support it by testing the 'ID' bit in eflags (this is 0x200000 and is modifiable only when CPUID instruction is supported. For systems that doesn't support CPUID, writing a '1' at that place will have no effect) In the case of a processor that does not support CPUID, you'll have to use more eflags-based tests to tell if you're running on a 486, 386, etc. and then pick up one of the 'calibrated loops' for that architecture (8086 through 80486 may have variable instruction timings). Working Example Code There is a Real Mode Intel-copyrighted example in the above-mentioned application note ... Here comes another code submitted by DennisCGC that will give the total measured frequency of a Pentium processor. Some notes: • irq0_count is a variable, which increases each time when the timer interrupt is called. • in this code it's assumed that the [PIT] is programmed to 100 hz (of course, I give the formula about how to calculate it • it's assumed that the command CPUID is supported. ;first do a cpuid command, with eax=1 mov eax,1 test edx,byte 0x10 ; test bit #4. Do we have TSC ? jz detect_end ; no ?, go to detect_end ;wait until the timer interrupt has been called. mov ebx, ~[irq0_count] cmp ebx, ~[irq0_count] jz wait_irq0 rdtsc ; read time stamp counter mov ~[tscLoDword], eax mov ~[tscHiDword], edx add ebx, 2 ; Set time delay value ticks. ; remember: so far ebx = ~[irq0]-1, so the next tick is ; two steps ahead of the current ebx ;) cmp ebx, ~[irq0_count] ; Have we hit the delay? jnz wait_for_elapsed_ticks sub eax, ~[tscLoDword] ; Calculate TSC sbb edx, ~[tscHiDword] ; f(total_ticks_per_Second) = (1 / total_ticks_per_Second) * 1,000,000 ; This adjusts for MHz. ; so for this: f(100) = (1/100) * 1,000,000 = 10000 mov ebx, 10000 div ebx ; ax contains measured speed in MHz mov ~[mhz], ax See the intel manual (see links) for more information. - bugs report are welcome. IM to DennisCGC Without Interrupts I'd be tempted to say 'yes', though I haven't gave it a test nor heard of it elsewhere so far. Here is the trick: disable() // disable interrupts (if still not done) outb(0x43,0x34); // set PIT channel 0 to single-shot mode outb(0x40,0); // program the counter will be 0x10000 - n after n ticks long stsc=CPU::readTimeStamp(); for (int i=0x1000;i>0;i--); long etsc=CPU::readTimeStamp(); outb(0x43,0x04); // read PIT counter command ?? byte lo=inb(0x40); byte hi=inb(0x40); Now, we know that • ticks=(0x10000 - (hi256+lo)) periods of 1/1193180 seconds have elapsed at least and no more than ticks+1. • etsc-stsc clock cycles have elapsed during the same time. Thus (etsc-stsc)1193180 / ticks should be your CPU speed in Hz ... As far as i can say, 0x1000 iterations lead to 10 PIT ticks on a 1GHz CPU and a bit less than 0x8000 ticks on the same CPU running BOCHS. This certainly means that on very high speed systems, the discovered speed may not be accurate at all, or worse, less than 1 tick could occur ... This technique is currently under evaluation in [the forum\|Forum:5849] - hope you like my technique /PypeClicker Asking the SMBios for CPU speed The SMBios (System Management BIOS) Specification addresses how motherboard and system vendors present management information about their products in a standard format by extending the BIOS interface on Intel architecture systems. The information is intended to allow generic instrumentation to deliver this information to management applications that use DMI, CIM or direct access, eliminating the need for error prone operations like probing system hardware for presence detection. SMBios Processor Information A Processor information (type 4) structure describes features of the CPU as detected by the SMBios. The exact structure is depicted in section 3.3.5 (p 39) of the standard. Within that information you will find the processor type, family, manufacturer etc. and also: • the External Clock (bus) frequency, which is a word at offset 0x12, • the Maximum CPU speed in MHz, which is a word at offset 0x14 (e.g. 0xe9 is a 233MHz processor), • the Current CPU speed in MHz, (word at offset 0x16). Getting the SMBIOS Structure SMBios provide a _Get SMBIOS Information_ function that tells you how many structures exists. You can then use _Get SMBIOS Structure_ function to read processor information. As an alternative, you can locate the _SMBIOS Entry Point_ and then traverse manually the SMBIOS structure table, looking for type 4. All this is depicted in 'Accessing SMBIOS Information' structure of the standard (p 11). The SMBIOS Entry Point structure, described below, can be located by application software by searching for the anchor-string on paragraph (16-byte) boundaries within the physical memory address range 000F0000h to 000FFFFFh. This entry point encapsulates an intermediate anchor string that is used by some existing DMI browsers. 00-03 Anchor String (_SM_ or 5f 53 4d 5f) 04 Checksum 05 Length 06 major version 07 minor version 08-09 max structure size 0A entry point revision 0B-0F formatted area 10-14 _DMI_ signature 15 intermediate checksum 16-17 structure table length 18-1B structure table (physical) address 1C-1D number of SMBIOS structures 1E SMBIOS revision (BCD) I don't feel like re-explaining the PnP calling convention etc. as chances are it will be useless in Protected Mode ... Related threads in the forum • Forum:5849 • Forum:767 • Forum:922 • Forum:8949 featuring info on bogomips, how linux does it and durand's code. Other resources especially section 12: "Operating Frequency" on page 29 of 24161815.pdf Regarding SMBIOS Personal tools
Tag Archives: causes of diabetes Type 1 Sugar Diabetes. Causes of Type 1 Sugar Diabetes Truth in a nutshell, nobody knows what causes Type 1 sugar diabetes. There is no definite points of development for Type 1 sugar diabetes. Unfortunately, Type 1 sugar diabetes is averagely diagnosed well after all the major damage was already done. As many other thyroid disorders, Type 1 diabetes is an autoimmune disorder. Same as in other similar disorders, such as lupus, multiple sclerosis, or rheumatoid arthritis, the immune ssytem wrongfully tags healthy parts of the body as alien and therefore attack them, destroying cells. In sugar di abetes, the person’s immune system attacks and destroys the very important insulin-producing beta cells in the pancreas. Scientists don’t know why does it happen or how to prevent it from happening. But they identified two main causes behind this abnormal autoimmune response. » Read more Share This:
Goats Milk A dairy Products with Special Properties? In many developed countries the consumption of traditional cows milk is plateauing or even declining, even though milk and related dairy products are very good sources of calcium and protein. However, a very fast growing product in the dairy case these days is goats milk. It has been estimated that, on a world wide basis, there are more people who drink the milk of goats than of any other single animal. Over 440 million goats (world wide) produce an estimated 4.8 million tons of milk consumed mostly locally, or processed into various types of cheeses. Goats milk has a long way to go to catch up to cows milk, but there may be several reasons why consumers are turning to goats milk. Goats milk has a reputation as being a highly digestible dairy product. This is due in part to the composition and structure of the lipid (fat) portion of goats milk and in part to the way the protein in goats milk reacts in the stomach as it starts to be digested. Perhaps the most interesting aspect of goats milk is its hypo-allergenicity properties. It has often been found that infants that are not able to tolerate mothers milk or cows milk are able to eat goats milk. It is estimated that up to 7.5 % of infants are not able to eat cows milk. It is not clear at this time why goats milk can be eaten by these sensitive children, but it may be due to the structure of the milk proteins found in goats milk. The amino acid content of goats milk differs from that of cows milk and this may be one reason why goats milk is an alternative for cows milk intolerant babies. The goat industry in North America is a very small one at the present time. However, the ability of small farms to produce "organic" goats milk together with research into the unique composition and properties of goats milk mean that this dairy product may become more in demand in the future. Table 1: Cows vs goats milk Differences Between Cows milk and goats milk ** Digestibility - goats milk considered more easily digested Milk fat globule -smaller in goats milk than cows milk Calcium content - higher in goats milk than cows milk Iron content -lower in goats milk than cows milk Vitamin C content -about the same in both milks Vitamin D content -about the same in both milks Short chain fatty acid content -higher in goats milk than cows milk 1. Further information 2. Nutritional Information1 3. milk allergy2 1Julia - Wed, 08 Oct 2003 01:33:07 I would like to know where is your company? and how can I order goat milk for my family? (I’m living in Scarborough, Ontario of Canada )Thank you 2 Mike - Wed, 8 Oct 2003 15:51:09 Medicinal Food News is located in Ottawa, Ontario. We do not sell, market or endorse any products. I suggest you contact your local dairy for information. You might also try 3 Ontario Goat Milk Producers’ Association which provides a list of processors (3 located in the Toronto area). Other articles on milk § < previous \| index \| next > External Link Index 1 - http://www.meyenberg.com/?action=facts 2 - http://allergysa.org/milk.htm 3 - http://www.ontariogoatmilk.org/milk_processors.htm
Name: Mojoceratops ‭(‬Mojo horned face‭)‬. Phonetic: Mo-jo-seh-ra-tops. Named By: Nicholas R.‭ ‬Longrich‭ ‬-‭ ‬2010. Synonyms: Possibly Eoceratops,‭ ‬canadensis,‭ ‬Chasmosaurus kaiseni. Classification: Chordata,‭ ‬Reptilia,‭ ‬Dinosauria,‭ ‬Ornithoschia,‭ ‬Ceratopsia,‭ ‬Ceratopsidae,‭ ‬Chasmosaurinae. Species: M.‭ ‬perifania‭ (‬type‭)‬. Diet: Herbivore. Size: Uncertain due to incomplete fossil material,‭ ‬but possibly up to‭ ‬5‭ ‬-‭ ‬6‭ ‬meters long based upon comparison to Chasmosaurus‭ ‬-‭ ‬refer to main text for details. Known locations: Canada,‭ ‬Alberta‭ ‬-‭ ‬Dinosaur park Formation. Time period: Campanian of‭ ‬the Cretaceous. Fossil representation: Eight partial skeletons. Mojoceratops was discovered by a close examination of some skulls that had been assigned to the more well Chasmosaurus.‭ ‬The more the skulls were studied the more differences were discovered,‭ ‬resulting in the creation of a new genus.‭ ‬The palaeontologists who were looking the skulls over initially came up with name Mojoceratops when they were brainstorming ideas.‭ ‬However when they realised that a mojo is actually a charm for attracting members of the opposite sex they found the name to be very fitting as ceratopisan most probably used their frills for that exact purpose.‭ ‬Additionally the frill dips in the middle making the two halves form a structure that loosely resembles a heart shape. Further reading - Mojoceratops perifania, A New Chasmosaurine Ceratopsid from the Late Campanian of Western Canada. - Journal of Paleontology 84 (4): 681–694. - Nicholas R. Longrich - 2010. Random favourites
This year’s hurricane season in the Arabian Sea was already one for the books, thanks to just one storm, Cyclone Chapala, which last week became one of the strongest ever recorded there and the first hurricane-strength storm known to hit Yemen. Now the arid country has had an unprecedented back-to-back strike, as Cyclone Megh made landfall near the major port city of Aden early Tuesday morning. This marked the first time storms in such quick succession have been recorded in the Arabian Sea at this time of year. The unheard-of activity may have received a boost from El Niño and recent research has suggested that both changing levels of air pollution and climate change could alter tropical cyclone activity in the region. cyclone megh This infrared image of Cyclone Megh was taken by the Suomi NPP satellite's VIIRS instrument around 1005Z on November 9, 2015. While Megh wasn’t as strong as Chapala when it made landfall, having weakened to tropical storm strength, it was still expected to dump considerable rains on the region. As the up to 24 inches of rain Chapala dumped in some areas made clear, such rains can lead to extensive, dangerous flooding in such a dry landscape. Megh formed just two days after Chapala slammed into Yemen, a considerable surprise given how few storms the Arabian Sea region typically sees. The basin may only see one or two tropical cyclones in a whole year, compared to other basins, which range from five to more than 20 in an average season. (Tropical cyclone is the generic term for hurricanes, typhoons and cyclones, all different names for the same phenomena.) Cyclones are less common in the Arabian Sea than in other ocean basins because, despite very warm waters that would otherwise provide ample fuel for storm convection, winds in the region are generally hostile, cutting off storm formation and development. If storms do form, they tend to do so before or after the summer monsoon season, when wind shear — winds moving at different directions at different levels of the atmosphere — is at its worst. So the timing of Chapala and Megh isn’t unusual, but the short time between one storm and the other hasn’t been seen in the historical record, with high-quality data going back to 1990. “In the historical record we’ve never seen two [tropical cyclones] spin up, especially one after the other, during this time of year,” Amato Evan, an atmospheric scientist at the Scripps Institution of Oceanography, said in email. chapala rains before and after Before and after images show the impact of Chapala's rains. At its peak strength, Chapala had winds of about 155 mph, equivalent to a Category 4 hurricane. By wind speed, it was the second strongest storm ever recorded in the region, behind Cyclone Gonu in 2007. (By another measure, which takes into account a storm’s winds over its entire lifetime, Chapala was the strongest.) Chapala was able to reach such heights because it happened to encounter a particularly favorable environment, with wind patterns that actually encouraged its development. That let the storm take advantage of ocean waters with unusually high temperatures, even for the always-warm Arabian Sea. Megh has also benefited from this conducive environment, though waters along its path weren’t quite as warm, thanks to the relatively cooler waters Chapala left in its wake, and it topped out a Category 3 strength. One reason winds may have been so favorable for both storms could be El Niño, the force that seems to behind so many trends this year. Monsoon winds in the region tend to be weaker during an El Niño, Suzana Camargo, a hurricane researcher at Columbia University’s Lamont-Doherty Earth Observatory, said in an email. “It's not clear, though, if we can obviously blame [these storms] on El Niño, as it would be important to do a more in-depth analysis, but that's my suspicion,” she said. These same conditions have also allowed for the development of another storm, in the Bay of Bengal. The last time there were storms in both areas simultaneously was 2010, hurricane researcher Philip Klotzbach, of Colorado State University, told Forbes. Megh took a slightly more southerly path than Chapala, brushing the coast of Somalia as it headed toward landfall. That interaction with land, as well as dry air from the Arabian Peninsula, weakened the storm before it hit Yemen. Reports about damage in the Aden area will likely take time to fully emerge, though the reinsurance firm Aon Benfield cited reports of widespread flooding and damage and at least two deaths on the island of Socotra, which was also hit hard by Chapala. Rain and flooding are major concerns again with Megh as Yemen typically only sees about 2 inches of rain in a year. Chapala’s rains caused severe flooding in and around Mukalla — the impact was visible from satellites observing from space, which saw floodwaters near the coast and numerous wadis, or ephemeral streams, flush with water. Compounding the threat is the conflict between Houthi rebels and forces fighting for the president-in-exile that have left many citizens displaced and with severe food shortages. While Chapala hit away from the main area of fighting, Megh has hit a major battle area and one which has a larger population. Arabian Sea cyclone activity has generally received much less attention from researchers than busier basins, but this season could change that. “This year will probably raise my interest in this area again,” Camargo, who along with Evan conducted a survey of activity in the region in 2011, said. Of the research that has been done, there are some potential forces that could be at play to allow for stronger Arabian Sea storms. Another study that involved Evan suggested that increased aerosol pollution could be allowing for more intensification of Arabian Sea storms. “In the paper we speculated that the very thing we have right now (very strong [cyclone]s occurring during the post-monsoon season) would be possible in the future as a result of increased pollution and lower [wind] shear,” Evan said. Other research has suggested that climate change could lead to an increase in cyclone activity in the Arabian Sea, but a decrease in the Bay of Bengal. But the research on such potential links is limited and requires further study, Camargo said.
Sunday, July 6, 2014 2011. Photograph: Don Emmert/AFP/Getty Images Open Source is a powerful concept, its given us Wikipedia and the computer operating system Linux. Its not without flaws however. In my discussions with Caleb, we discussed how frequently open source software encryption and networking software has been compromised by intelligence agencies because while the source code can be inspected by anyone, in truth it often isn't, because that takes constant work and vigilance, and people tend towards being lazy unless there's value in not being lazy. So we see many cases of where code has been injected into open source networking software to introduce vulnerabilities such in Open VPN. Where in the case of commercial software vendors they are often paid directly to introduce such vulnerabilities, but at least can be publicly embarrassed when exposed by researchers. In the case of Wikipedia, various companies have arisen that remove data from Wikipedia by cleverly using multiple IDs to make it look like a consensus has been reached about data in a Wikipedia article when in fact it is one group trying to remove data or inject false or sanitized data on a subject or person. These are not insurmountable issues, but it requires a means to identify people more accurately when it comes to being responsible for data stewardship, and to create value incentives for maintaining and inspecting Open Source code, designs and data for accuracy and removal of flaws. Open Source is still an evolving concept. But it can be quite useful tool in expanding the general wealth of all humanity. -AK The open source revolution is coming and it will conquer the 1% - ex CIA spy
It seems the sky is falling… Imagine driving in your car on a lovely Friday morning and seeing a flaming ball of death streaking across the sky and coming, as best you can tell, right at you. This view from a Russian dashboard camera shows a terrifying view of the fireball as the meteoroid entered the atmosphere and hurtled over the city of Chelyabinsk. Credit: Discovery News That’s what terrified citizens in the lovely Russian city of Chelyabinsk experienced on the morning of Friday, February 15. The multitude of videos and photos of this meteor are simply horrifying since many of them give the impression that this huge chunk of flaming interplanetary death is about to smash right into the camera. Not only did this fireball make a scary visual impression, but it packed a very literal punch as well. As the meteoroid hurtled through the atmosphere at 40,000 mph, the heat and pressure it felt caused it to break apart with a huge amount of energy, the equivalent of 470 kilotons of TNT (or 30-40 times the power of the atomic bomb dropped on Hiroshima). The deposition of that huge amount of energy into the sky caused a pressure wave that blasted the city. Over 1,000 people were injured by the blast, mostly due to cuts and scrapes from glass as windows shattered. Scientists have now come to the conclusion that the initial object was only 17 meters wide– that’s about the size of a tractor trailer. That’s pretty small cosmically speaking. Imagine the damage that could have been inflicted if something larger had hit the atmosphere. The last time a meteor had significant large-scale impact was in 1908, again in Russia. This impact, known as the “Tunguska event“, is the largest impact ever recorded- 20-30 times larger than the one that happened this month. This meteoroid, which is estimated to have been about 100 meters wide (the size of a football field), blew up in the air and released 10-15 megatons of energy, leveling 830 square miles of trees. Witnesses to the event said that the heat and pressure from the explosion made their skin feel like it was on fire. The 1908 Tunguska event, the largest impact near or on Earth ever recorded, leveled trees over 830 square miles. Credit: Luckily the 2013 Russian meteor was much smaller, so windows got knocked out but buildings weren’t leveled. The object was actually so small that astronomers didn’t even see it coming. NASA has a whole division of people who track objects that could potentially come close to Earth, it’s known as the Near-Earth Object Program. Unfortunately, for scientists to be able to see an object it needs to be large enough to reflect an observable amount of light. That didn’t happen here. The meteor also came as a bit of a shock since scientists were so focused on another Near-Earth Object called 2012 DA14. This 45-meter wide asteroid was scheduled for a flyby of Earth on the same day, February 15. This relatively small piece of space rock flew closer to the Earth than any other celestial body. It was 17,200 miles away at its closest approach, that’s closer than satellites in geosynchronous orbit and much, much closer than the Moon. Although scientists were certain that DA14 wouldn’t impact the Earth, they were very excited to use the close flyby as an opportunity to study the asteroid. This collage of 72 individual radar-generated images of asteroid 2012 DA14 was created using data from NASA’s 230-foot Deep Space Network antenna at Goldstone, CA. Credit: NASA Of course it was ironic that after weeks of assuring the public that there was no threat of an impact from DA14 another huge impact happened in Russia the same day. Scientists from NASA’s Meteoroid Environment Office concluded that the Russian meteor and DA14 were totally unrelated, having come from two very distinct trajectories/orbits. This means it was a huge cosmic coincidence that they just happened to occur on the same day…weird. This plot of the orbits of the Russian meteor and asteroid 2012 DA14 show that the two bodies came from very different parts of the solar system and were unrelated. The Russian meteoroid most likely originated from the Asteroid Belt out past Mars. Credit: NASA/ The Cosmic Distance Ladder, part 1… For the past few months, I’ve been spending a lot of time in my position as Manager of the UNH Observatory, in helping to prepare for the 2012 New England Fall Astronomy Festival. The event, lovingly known as NEFAF, is a family-friendly astronomy-related event that will be hosted by the UNH Physics Department in partnership with the New Hampshire Astronomical Society. As you can imagine, this is quite an undertaking, but in an incredibly exciting turn of events, we just found out that Dr. Alex Filippenko, noted astronomer from UC-Berkeley and member of the research team that won the 2011 Nobel Prize in Physics, will be giving the keynote talk at NEFAF 2012! In addition to being a highly acclaimed professor, Filippenko is also the co-author of an extremely popular astronomy textbook and a frequent contributor to the documentary series The Universe on The History Channel. Dr. Alex Filippenko, the newly announced keynote speaker for the 2012 New England Fall Astronomy Festival to be held at the UNH Observatory. That extremely exciting news has inspired me to do a couple of posts about the expansion of the universe, the area of research that Dr. Filippenko works on. But before we can really get into talking about that, we need to cover a very basic aspect of astronomy, but something that most non-astronomers don’t really know about. I was at a public session at the Observatory this weekend when a guest who had never studied astronomy before asked me what she thought might be an “ignorant” question: she wanted to know how exactly astronomers knew the distances to objects in space. This is by no means an ignorant question, in fact it’s a very fundamental and very involved question that really gets at the very nature of astronomy. Astronomy by definition is an observational science. Unlike many other scientific disciplines, astronomers can’t really do experiments in a laboratory (although some do). But the stereotypical astronomer can’t throw his subject (a star or galaxy) on a lab bench and dissect it or set up an experiment to test it, so astronomers need to observe and record data. Okay, so we observe light, that tells us what something looks like, where it is, and how bright it is. Big deal, is that really that helpful scientifically. Well, not really. So we have to come up with ways to get more information from observing the light. The main way we do that is by breaking the light up in a spectrometer, an instrument that breaks light down into a spectrum of colors. This breakdown of light can reveal an abundance of new information including what the object is made up of, how hot it is, how fast and in what direction it’s moving, how old it is, and more. The question of how astronomers calculate the distance to an astronomical object varies depending on how far away the object is. Because most of these techniques only work up to a certain distance, there is actually a progression of different approaches that astronomers use to measure distance to celestial objects. This list of methods of measuring astronomical distances is known as the Cosmic Distance Ladder (or less poetically, the extragalactic distance scale). A graphical representation of the distance-measuring techniques that make up the Cosmic Distance Ladder. “1 A.U.” is 1 astronomical unit or approximately 93 million miles, the distance from the Earth to the Sun. A “pc” is a parsec, equal to 3.2 lightyears (206,265 A.U.) or about 20 trillion miles. “Mpc” stands for “Megaparsec” or millions of parsecs. Credit: University of Rochester In our solar system The first step in our exploration of the universe was to our own celestial neighborhood. The first step was precise measurement of the size scale of the solar system, which started with the determination of the distance between the Earth and the Sun. As I’ve explained before, this measurement was originally calculated via observations of transits of the planet Venus across the disk of the Sun. Early on in the 20th century, observations of asteroids also played an important role in this measurement. But today the distance from the Earth to the Sun, defined as 1 Astronomical Unit or “AU”, is measured with high precision using radar ranging. By bouncing a radar beam off another planet, usually Venus, and measuring the time that beam takes to return to Earth, scientists can very accurately determine the difference in the size of the two planets’ orbits. Using that difference and the ratio of the two orbital sizes, we can very easily calculate the distance the Earth must be from the Sun. We use a similar process even closer to home. During the Apollo missions of the late 1960s-early 1970s, astronauts deployed the lunar laser ranging experiments, arrays of mirrors that allowed scientists to measure the distance to Earth’s only natural satellite with extreme precision using lasers. This radar ranging is how we’ve calculated the distance to most of the objects in our solar system. More recently, we can also use spacecraft in orbit around other planets as a tape measure by measuring the time it takes for a signal to travel from the spacecraft to its controllers on Earth. Another way we can get measure the distance to the planets and to nearby stars is a phenomenon known as stellar parallax. This method is less accurate than radar ranging for planets, but is very good for stars in our local stellar neighborhood. Parallax is something you experience almost every day. Hold your thumb up at arm’s length. Close one eye, then open that one and close the other. Notice how your thumb appears to shift with respect to the objects far off in the distance? That’s parallax! Astronomers take measurements of a planet or star a two points in Earth’s orbit (6 months apart) and measure the angular shift of an object with respect to the background stars between those two measurements. Then, because we know the distance the Earth is from the Sun, we can use some basic geometry to calculate the distance to that star or planet in the foreground. This diagram shows how parallax is used to find the distance to planets in our solar system and nearby stars. Scientists make two observations 6 months apart, measuring the angle that an object (the red dot) makes with regard to the background stars between the two observations. Then using the distance from the Earth to the Sun (1 A.U.) and some simple geometry, the distance to the object (d) can be calculated. Credit: Hyperphysics It was using parallax, that Italian astronomer Giovanni Domenico Cassini was able to roughly calculate the distance to Mars in 1672. His calculation was a little bit off though, because instead of taking two measurements 6 months apart, he sent his colleague to Cayenne, French Guiana (on the northern coast of South America) to make observations while he stayed in Paris. Then Cassini could make the same parallax calculation using the known distance between the two observation points (~4400 miles) instead of the distance from the Sun to the Earth. This single direct measurement of the distance to Mars, which is now easily calculated and heavily used by missions such as Curiosity, actually allowed for the calculation of the distances to all the planets. Since geometry and Kepler’s Laws governed the basic ratios the Sun-planet distances, you only needed to measure one Earth-planet distance to be able to easily calculate them all. This major contribution and several others in planetary science (including the discovery of four of Saturn’s moons and joint discovery of Jupiter’s Great Red Spot) prompted NASA to name the Saturn-bound spacecraft mission after the him. Giovanni Domenico Cassini [To be continued…] Related Posts: Curiosity did not kill the cat… So as I’m sure you’ve all heard, NASA’s Curiosity rover successfully landed on the surface of Mars in the early hours of yesterday morning (east coast time). In an earlier post, I relayed the video by NASA of the harrowing entry that Curiosity needed to go through to reach the Martian surface safely and highlighted that the entire elaborate landing procedure was 100% automated since it takes double the time the landing would take to occur for information to be relayed back to Earth. And all the taxings of a mission so complicated, despite all the finesse and delicacy needed to execute such a bold attempt, and despite all the things that could go wrong, the scientists and engineers at NASA succeeded. Honestly, if you watch the 7 Minutes of Terror video, realize that scientists built and programmed a machine that could do that all automatically, millions of miles away from Earth (352 million to be exact) while moving at thousands of miles per hour and have it work flawlessly, and aren’t awed and impressed, then well you should probably check your pulse. The Mars Science Laboratory’s mission is to investigate the interior of the Gale Crater for signs of microbial life. Top left: A profile of Curiosity’s landing site, Gale Crater. Top Right: A simulation of Curiosity’s proposed mission. Bottom: A map showing the distribution of NASA’s missions to the Martian surface. Credit: BBC News In addition to being the largest rover we’ve ever sent to another world, twice as long (about 10 feet) and five times as heavy as NASA’s twin Mars Exploration RoversSpirit and Opportunity, launched in 2003, Curiosity also has new equipment that allows it to gather samples of rocks and soil, process them, and then distribute them to various scientific instruments it carries for analysis; that internal instrument suite includes a gas chromatograph, a mass spectrometer, and a tunable laser spectrometer with combined capabilities to identify a wide range of organic (carbon-containing) compounds and determine the ratios of different isotopes of key elements. There’s clearly a reason why the mission is called the Mars Science Laboratory. This illustration from NASA shows the size and instrumentation of Curiosity that will help it to investigate the possibility of microbial life on Mars. (A) Six independent wheels allowing the rover to travel over the rocky Martian surface. (B) Equipped with 17 cameras, Curiosity will identify particular targets and then zap them with a laser to probe their chemistry. (C) If the signal is significant, Curiosity will swing over instruments on its arm for close-up investigation. (D) Samples drilled from rock, or scooped from the soil, can be delivered to two hi-tech analysis labs inside the rover body. (E) The results are sent to Earth through antennas on the rover deck. Return commands tell the rover where it should drive next. Credit: BBC News According to NASA, Curiosity carries with it “the most advanced payload of scientific gear ever used on Mars’ surface, a payload more than 10 times as massive as those of earlier Mars rovers.” All that gear will be important as Curiosity investigates its main science objective: whether or not there is evidence of microbial life (past or present) in Martian rocks. Although both Spirit and Opportunity listed the search for life as among their scientific goals, neither rover was really equipped to search for microbial life; the twin early generation rovers were more specifically looking for water or the evidence of past water on the Martian surface and then whether that water could sustain life. Curiosity, on the other hand, is specifically equipped to look for microbial life (or evidence of it) in the rocks and soil of the Red Planet. More than just the roving explorer that its forebears were, Curiosity is for all intents and purposes a laboratory on wheels. This image of Curiosity descending to the Martian surface with its parachute was taken by the High-Resolution Imaging Science Experiment (HiRISE) camera on the Mars Reconnaissance Orbiter. The rover is descending toward the etched plains just north of the sand dunes that fringe Aeolis Mons. Credit: NASA And it’s not just the instrumentation that Curiosity is equipped with that make NASA rover 2.0 better than previous generations, but the technology it used to get to the Martian surface is leaps and bounds ahead of how Spirit and Opportunity landed. If you watch this NASA movie that highlights the landing process for the Mars Exploration Rovers (which only had six minutes of terror), you’ll notice that most of the landing procedure seems similar to Curiosity’s. Extremely high-speed entry into the Martian atmosphere, heat shield, parachute, rocket thrusters, etc. Until you get to the last step, when Spirit and Opportunity wer basically dropped onto the Martian surface at nearly 60 mph, surrounded by huge air bags, and allowed to bounce three or four times until they settled. Compared to the fine precision placement of the Curiosity rover earlier this week, the previous rovers’ landings were downright barbaric, like trying to hunt a deer by throwing rocks. This image, one of the first returned by Curiosity, shows the rover’s shadow on the Martian surface and one of the main targets of its mission, Aeolis Mons, on the distant horizon. Credit: CNN Rather than violently smashing the $2.6 billion rover into the surface and hoping for the best, this descent involved a sky crane and the world’s largest supersonic parachute, which allowed the spacecraft carrying Curiosity to target the specific landing area that NASA scientists had meticulously chosen. That landing area is roughly 12 km (7.5 miles) from the foot of the Martian peak previously known as Mount Sharp. Aeolis Mons, as it’s now known, is the 18,000-foot (5,500-meter) peak at the center of Gale Crater, previously known as Mount Sharp. The stratified composition of the mountain could give scientists a layer-by-layer look at the history of the planet as Curiosity attempts its two-year mission to determine whether Mars ever had an environment capable of supporting life. Possibly the biggest piece of the NASA Curiosity puzzle has been the enormous PR campaign that NASA has thrown behind the rover. Not only has the rover and it’s 7 Minute of Terror video been all over the internet, TV news, newspapers, and other media outlets, but NASA has even gone out of its way to get high-level stars in the fold. Last week they released this video (above) of William Shatner, most famously known as Capt. James Tiberius Kirk of Star Trek, narrating a preview of Curiosity’s “Grand Entrance” to Mars. There was also another video featuring narration by Wil Wheaton (Wesley Crusher from Star Trek: The Next Generation). Related Posts: 7 Minutes of Terror… Related Posts: Getting your rocks off… Hello all you loyal readers out there, sorry for the lack of posts this summer, but it’s just so nice outside and it’s hard to see with the sunlight reflecting off my screen. In any case there’s a lot going on down in Washington regarding budgets and debt and all that good economics stuff (read: things that I don’t really understand or care to), so I figure I’ll just ignore that and talk about some fun space stuff! • First off, as this blog has been (or attempting to) chronicling for most of the summer, NASA finally ended the Space Shuttle program after the successful return of the final mission of Atlantis on July 21. The shuttle ran an amazing 30 year history and is still to this day the most sophisticated vehicle ever constructed by man. NASA and the U.S. government now have to wait and hope (with bated breath and some hard finger crossing) that private companies quickly ramp up the development and advancement of private launch capabilities. Several big-time frontrunners in the commercialization of space exploration (SpaceX, Orbital Sciences, etc.) have hit major setbacks, failures, and are going way over budget. • Next up, here is a very cool picture from the Opportunity rover on Mars. Yes, that’s right Opportunity found metal on Mars! How cool is that!??!! But yeah, not the giant pieces of scrap metal that are in the background, NASA is actually interested in that strange metallic-looking rock in the foreground to the left. That’s the real prize. The scrap metal (which I half expected to see wrecked R2-D2 and C-3PO somewhere near…) is not some failed attempt at Martians to reach space, it’s actually Opportunity‘s own heat shielding that was abandoned during the rover’s descent back in 2004. The rock though, found to be made mostly of dense metals iron and nickel, is thought to be just as alien to Mars as Opportunity‘s heat shielding. Scientists believe the rock to be a meteorite much like the vast number found in Antarctica here on Earth. It’s not the scrap metal here that interests scientists, but the small metallic rock in the left foreground. Credit: APOD • In a news story that is too weird to be made up, a man recently released from jail, is finally having the story told of how he stole moon rocks from NASA (similar to the NJ heist?). A new book, Sex on the Moon: The Amazing Story Behind the Most Audacious Heist in History by Ben Mezrich (the author of the books Bringing Down the House and The Accidental Billionaires, the movies behind 21 and The Social Network respectively), focuses on the story of then-24-year-old Thad Roberts, a former Mormon from Utah, who stole an entire safe full (not just the rocks in the safe, but the ENTIRE safe) of moon rocks from a lab at NASA’s Johnson Space Center in Houston back in 2002. Why, you ask, would the wanna-be astronaut pull off such an audacious crime? For the love of a girl he’d met only three weeks prior…so he claims. In any case the article and book detail the robbery and how the couple celebrated the crime on the 33rd anniversary of first moon walk by being intimate ON the rocks (hence the pun of this post’s title). The short summary is, people are weird, but this book HAS to be a page-turner. Related Posts: %d bloggers like this:
Online Writings Online writings (90 Points – 2 x 45) In order to advance our discussions, to push reflection and dialogue, and to otherwise foster engagement, this class will use our course blog space to expand upon course issues. There will be a particular focus on diversity and the ways in which inequality, differential access to opportunity/privilege, and history defines diversity within the United States. Every two weeks, I will post a different question. It will be your responsibility to respond to the question at hand and also respond to at least one peer comment. You will be responsible for responding to at least 2 prompts. The key to success here is both self-reflection and engagement with course materials. TO RECEIVE FULL CREDIT, YOU MUST INTEGRATE SPECIFICS FROM COURSE MATERIALS AND READINGS. The questions will, thus, connect to course materials but also push you to think about your own experiences. Below you will see examples of types of questions you may find throughout the course 1. Does race matter? 2. How has racism impacted your life? 3. Is colorblindness the same as equality? 4. Are all “whites born into privilege”? Are all men born into privilege? Are all heterosexual born into privilege. Write down and reflect on some examples? Over the next several days keep a log of unearned advantages/privileges that you experience 5. If you identify as white, what does it mean to you to be white? If you do not identify as white, what does whiteness mean to you in this society and/or beyond it? Using readings, film, course discussions, and your own personal experiences, please focus on racialization and the connections between whiteness, privilege, and white supremacy. 6. Describe in detail the racial and ethnic make-up of either your hometown and/or your high school. How is racism visible within these spaces? How might it impact this community without being visible? 7. What are the important facts, historical events, legal and political issues, court cases, etc., that you think are important in the larger history of race in America? Which of these events are still relevant today? 8. Do people of color in the United States have more in common with people of color from other parts of the world or with whites in America? 9. How does guilt function within conversations about race? 10. Who do you represent? 11. Do you have memories of family or friends challenging racism during your life? Impact here? What examples of anti-racist activist did you learn about in school? 12. What experiences have shaped and impacted your views about race and racism? 13. What are the pictures, feelings, smells, sounds, and words that come to mind when you read the word “restaurant” or “restaurant worker”? 2 comments on “Online Writings • When I read the word restaurant I think of a place with a quite atmosphere. I typically think of it as a somewhat special event because I don’t go out to actual restaurants all that often so I associate it with special dates or birthdays or something of that nature. When I read the word restaurant worker the feeling sort of changes. I think of someone who is outgoing and energetic but also young and poor. I usually think of a college student who is working there to pay for school or rent but not really there for a career. After witnessing the way people can treat restaurant workers I have a new respect for them and picture them as someone who has to be able to deal with a lot and have the ability to keep going. The video taught me a lot about the struggles in the restaurant business and the lack of pay and benefits that accompany that struggle. There is no being sick, and no day’s off. Job security is something that is nearly impossible to accomplish In the restaurant industry because even if you do put your heart into it looks have a lot to do with whether or not you keep your job there. Many restaurant’s want to keep a young workforce which is easy to do with the abundance of young college kids looking for “pass-through” work. I have never worked in the restaurant business and this lesson has made me glad that I haven’t but I do have a whole new level of respect for those who are working in that field. It made me understand that there is a whole other world that happens behind the scenes of the restaurant. There are hazards and accidents that occur every year and leave people with hefty medical bills that they cannot afford due to the lack of health insurance provided through work. • November Online Writing, # 1 My hometown of Kingston Washington is really as simple and cliche as it gets. A progressive, laid back little town on the water with the vast majority being white people. Close by are a couple of Indian Reservations that blend in well with the community (not like the Native Americans in the video in class). Not to mention the minority black, Hispanic and Asian descents that seem to fit in as well. I am not trying to say that race is not a problem in my community because as we know, different races encounter different instances of racism along with the severeness of the incident. I feel like in my community, I haven’t witnessed much racial encounters. Maybe its because everyone has a respect for one another and when a slight joke is said with un-harmful intentions, its not seen as as racism, but rather a joke that can build bonds and friendships inter racially. I not only feel like the white kids are blessed with privilege, but the minorities have privileges as well because they live in a functional community that is lower middle class. People know their place and don’t try to hard to be classy and prove a point. My town could be described as being ‘colorblind racism”, but as long as we don’t see it that way, I don’t think there will ever be a major problem in the liberal town of Kingston, Washington. • Leave a Reply You are commenting using your account. Log Out / Change ) Twitter picture Facebook photo Google+ photo Connecting to %s %d bloggers like this:
Self-Determination of Nations ... Ayn Rand The right of “the self-determination of nations” applies only to free societies to societies seeking to establish freedom; it does not apply to dictatorships Just as an individual’s right of free action does not include the “right” to commit crimes (that is, to violate the rights of others), so the right of a nation to determine its own form of government does not include the right to establish a slave society (that is, to legalize the enslavement of some men by others). There is no such thing as “the right to enslave.” A nation can do it, just as a man can become a criminalbut neither can do it by right. It does not matter, in this context, whether a nation was enslaved by force, like Soviet Russia, or by vote, like Nazi Germany. Individual rights are not subject to a public vote a majority has no right to vote away the rights of a minority the political function of rights is precisely to protect minorities from oppression by majorities and the smallest minority on earth is the individual. Whether a slave society was conquered or chose to be enslaved, it can claim no national rights and no recognition of such “rights” by civilized countries—just as a mob of gangsters cannot demand a recognition of its “rights” and a legal equality with an industrial concern or a university, on the ground that the gangsters chose by unanimous vote to engage in that particular kind of group activity. A nation, like any other group, is only a number of individuals and can have no rights other than the rights of its individual citizens. Such a nation has a right to its sovereignty (derived from the rights of its citizens) and a right to demand that its sovereignty be respected by all other nations. A nation that violates the rights of its own citizens cannot claim any rights whatsoever. In the issue of rights, as in all moral issues, there can be no double standard. A nation ruled by brute physical force is not a nation, but a horde—whether it is led by Attila, Genghis Khan, Hitler, Khrushchev or Castro. Dictatorship nations are outlaws. Any free nation had the right to invade Nazi Germany and, today, has the right to invade Soviet Russia, Cuba or any other slave pen. Whether a free nation chooses to do so or not is a matter of its own self-interest, not of respect for the non-existent “rights” of gang rulers. It is not a free nation’s duty to liberate other nations at the price of self-sacrifice, but a free nation has the right to do it, when and if it so chooses. from Ayn Rand : The Virtue of Se4lfishness - Collectivized Rights ; The Voice of Reason : Global Balkanisation
The Cobb salad and the Caesar salad were the first ‘main course’ salads. Word Origin for Robert Cobb, the owner of Hollywood’s Brown Derby restaurant where the salad was created Read Also: • Cobb syndrome Cobb syndrome (kŏb) n. A syndrome caused by vascular abnormality of the spinal cord and resulting in neurologic symptoms and cutaneous angiomas. Also called cutaneomeningospinal angiomatosis. • Cob-coal noun 1. coal in large round lumps. • Cobden [kob-duh n] /ˈkɒb dən/ noun 1. Richard, 1804–65, English manufacturer, merchant, economist, and statesman. /ˈkɒbdən/ noun 1. Richard. 1804–65, British economist and statesman: with John Bright a leader of the successful campaign to abolish the Corn Laws (1846) • Cobelligerent [koh-buh-lij-er-uh nt] /ˌkoʊ bəˈlɪdʒ ər ənt/ noun 1. a state or individual that cooperates with, but is not bound by a formal alliance to another in waging war. /ˌkəʊbɪˈlɪdʒərənt/ noun 1. a country fighting in a war on the side of another country
Proclamation to the Wisest Man (Blog post 2) In Plato’s “The Apology”, he portrays Socrates as a humble person who knows the extent of his own knowledge. I believe he does so in order to show his readers that Socrates has died an unjustified death, since ultimately in the end he did not harm anyone or anything but he was executed because those in his society feared his philosophies. This ties me in with my theory that Plato names his excerpt “The Apology” as a pun, being both a defense mechanism that Socrates used (since the word “apology” meant ‘a speech made in defense’ during his times) to explain himself when he was in trial, and as an actual apology for Socrates since his execution was poorly justified. Plato also describes Socrates as a devoted person; when people did things, he wanted to know the reasons that they did them; he wanted to know their true intentions. This curiosity of his also portrayed him as a pest to his community because no one was able to quench Socrates’ thirst for knowledge with a thorough legitimate answer. Plato probably puts in these additional characterizations for Socrates as naturally curious and devoted in order to emphasize Socrates’ rapturous passion for knowledge. Despite being someone people would turn to for his wisdom, his thirst for knowledge and curious personality did in fact give him some opponents. His top three opponents were Metelus (the primary man responsible for Socrates being accused) and other accusers, Lycon and Anytus. Socrates was being accused of corrupting the youth and not conforming to common beliefs (religious). Socrates highly valued virtue and knowledge. In his quest for knowledge, he is ultimately accused and sentenced to death, but his life virtues allow him to accept his death as shamelessly as possible. He says that “I ought not to do anything common or mean in the hour of danger: nor do I now repent of the manner of my defence, and I would rather die having spoken after my manner, than speak in your manner and live. For neitherin war nor yet at law ought any man to use every way of escaping death.” Meaning that he would rather die being falsely accused than to live and conform to what his society thinks is okay. This event also characterizes Socrates as a brave man who stands by his words. An oracle describes Socrates as the most “wisest man”, which is ironic because Socrates declared himself as not wise during his search for a wiser man. When he would meet a person that other people during his time period thought of as wise, Socrates would question and analyze that person and realize that they’re not wise at all, but are merely people who take on the title of being wise. I believe that the oracle states that Socrates is the wisest man because Socrates is the only man who is humble and modest enough to believe that there is someone who is more wise than he is, despite him being adequately wise himself. By denying himself as being wise, Socrates emphasizes his thirst for knowledge. • Apryl Berney • October 5th, 2011 1. No trackbacks yet. Leave a Reply You are commenting using your account. Log Out / Change ) Twitter picture Facebook photo Google+ photo Connecting to %s %d bloggers like this:
, , , Venus of Willendorf The Venus of Willendorf has been a widely discussed piece of art from the prehistoric art era since its discovery by Josef Szombathy in 1908. The small, four-inch, figurine was carved by hand from a fine porous oolitic limestone; which is not found in Willendorf, Austria, where it was found. The artist carved this voluptuous looking woman with the breasts and pubic area having an exaggerated look. This woman figure has very big curves for a woman of this time period. Historians believe that women of this time would have been skinnier, since most tribes members were hunters and gatherers; so they were constantly on the move not letting them be heavy in weight. With this in mind, some historians believe that this figurine could be of a woman of importance; one who had others hunt and gather for her. The name of the artwork does not fit it justly. The name Venus of Willendorf was given to this piece of art by Szombathy when he discovered her. Many believe this name to be an insult or a joke since its origin comes from the Roman and Greek goddess Venus, who was a young beautiful woman with a thin slender body. The differences between these two Venuses are extreme. The goddess Venus is usually depicted as a young nkaed attractive woman that tends to cover her breasts and pelvic areas; where the Venus of Willendorf has big breasts and inflated pubic area, which are exposed for everyone to see. Venus of Willendorf also has no face, leading some to believe that it was not modeled after someone specific but more of a charm of some sort. The figurine’s lack of facial features leads historians to believe the figurine is more symbolic than the depiction of a specific woman. This figure seems to have a sense of beauty, or at least what the artist thought of beauty. Many historians believe that this figurine could be a fertility charm, one that brings good luck to a woman trying to bare a child. Based on this theory, the figurine may resemble the beauty of a pregnant woman, emphasizing the breasts and pubic areas because of the idea of a fertility figurine. When I look at this piece of artwork, my first reaction is that it looks heavy, and without knowing the actual size of this figure, I would say it looks like a large sculpture of a heavy woman. With the knowledge that this artwork is small enough to fit in my hand, it changes my whole perspective of this piece. I can see the beauty and delicacy in this piece of art. I can see that the artist took his or her time with it and that it had some significant value. I feel that if I was able to hold this in my own hands that I could feel the smooth edges and the elegance that the piece seems to have. It may seem offensive or vulgar for the piece to be fully nude as well as to have exaggerated breasts and a pubic area; however without those key factors, this piece would not be a hot topic for historians to keep discussing. It would not have the impact on people that is does now. I personally like this small figurine and find the thoughts and feeling that art historians have on this piece to be very insightful and interesting. I agree with the art historians that debate Venus of Willendorf to be a symbolic figurine of fertility or some significance in that nature for the person who owns it. I believe this to be true because of the elegance that it possesses in the way it looks. I also believe it to be of someone with importance, maybe some kind of goddess that would bring the person baring it good luck in its purpose. I don’t think it is to depict the way women looked back then, but to be a symbolic charm or small statue to give praise to an important woman from that time.
( SS64 ) Oracle Syntax SQLPlus commands The following commands can be issued in SQLPlus (in addition to the standard SQ L commands.) Run (START) an SQL Script @MyScript.sql parameter1 parameter2 parameter3 In the SQL-Script, refer to the parameters as &1, &2, and &3. @ScriptName.sql will call sub-scripts from the current working di rectory of SQLPlus. @C:\work\oracle\ScriptName.sql will call a sub-script from a spec ific directory. @@pathname Run (START) an SQL Script @@ will call a sub-script from the same directory as the main scr ipt. @variable A substitution variable @pathname @@variable A substitution variable valid for the session / ACCEPT Execute (or re-execute) commands in the SQLPlus buffer does not list commands before running User input ACC[EPT] variable [NUM[BER]\|CHAR\|DATE] [FORMAT format] [DEFAULT default] [PROMPT text\|NOPROMPT] [HIDE] Add text to the end of the current line in the buffer. A[PPEND] text_to_add Specify where and how formatting will change. BREAK ON {column\|expr\|ROW\|REPORT} action Place and format a title at the bottom of each page. BTITLE printspec [text\|variable] BTITLE [OFF\|ON] Change text on the current line. C /oldval/newval Clear the SQLPlus screen and the screen buffer. CLEAR {BREAKS\|BUFFER\|COLUMNS\|COMPUTES\|SCREEN\|SQL TIMING} Change display width of a column. Calculate and display totals. Connect to a database as a specified user. connect username/password@SID Copy data from a query into a table (local or remote) User variables: DEFINE varName = String function procedure.display buffer lines n to m For all lines . logoff and exit (n = error code) EXIT SQL.SQLCODE Retrieve a previously stored command file HELP topic Topic is an SQL PLUS command or HELP COMMANDS HOST INPUT LIST n m Execute a host operating system command HOST CD scripts Edit sql buffer .Display a user variable DEFINE varName Display all variables DEFINE DEL Delete the current line in the SQL buffer DESC[RIBE] Describe a table. column.add line(s) to the buffer Edit sql buffer . By default. DISCONNECT Logoff (but don't exit) EDIT EXECUTE EXIT [n] GET file Load the SQLPlus buffer into an editor. synonym.BUF Run a single PLSQL statement EXEC :answer := EMP_PAY. view.BONUS('SMITH') Commit. saves the file to AFIEDT. package or package contents.specify m as LAST Wait for the user to hit RETURN PAUSE message PRINT variable List the value of a bind variable or REF Cursor (see VARIABLE / SHOW) PROMPT message Echo a message to the screen REMARK RUN RUNFORM SAVE file SET SHOW REMARK comment or --comment-.or /* comment / Execute (or re-execute) commands in the SQLPlus buffer Lists the commands before running Run a SQLForms application Save the contents of the SQLPlus buffer in a command file SAVE file [CRE[ATE] \| REP[LACE] \| APP[END]] Display or change SQLPlus settings List the value of a system variable (see PRINT) SHUTDOWN [ABORT\|IMMEDIATE\|NORMAL\|TRANSACTIONAL] SPOOL file Store query results in file . Related: Editing SQL scripts in SQLPlus SQL-Plus.sql (this tip r equires Oracle 10g or greater) Client Servers were a tremendous mistake and we are sorry that we sold it to you. instead of just SQL> SET sqlprompt '&_user:&_connect_identifier > ' Add the line above to the file: $ORACLE_SID/sqlplus/admin/glogin.SPOOL OFF SQLPLUS STA[RT] Turn off spooling SPOOL OUT sends file to printer Start SQLPlus and connect to a database. Instead of applications running on the desktop and data sitting on the server. PRINT myRefCursor EXECUTE somePackage. Run an SQL Script (see @) STARTUP [NoMOUNT\|MOUNT\|OPEN] TIMING TTITLE UNDEFINE ) VARIABLE Define a bind variable (Can be used in both SQLPlus and PL/SQL) VAR[IABLE] [variable {NUMBER\|CHAR\|CHAR(n)\|REFCURSOR}] Record timing data TIMING {START \| SHOW \| STOP} see CLEAR TIMING Define a page title Delete a user/substitution variable UNDEFINE varName (see DEFINE A RefCursor bind variable can be used to reference PL/SQL cursor variables in stored procedures.Larry Ellison. CEO. Oracle Corp.com . WHENEVER OSERROR Exit if an OS error occurs WHENEVER SQLERROR Exit if an SQL or PLSQL error occurs SQLPlus Prompt: To display the currently connected UserName and SID.SQL*Plus Tutorial Back to the Top © Copyright SS64. everything will be Internet based .com 1999-2013 Some rights reserved .someProcedure(:myRefCursor) VARIABLE on its own will display the definitions made. Sign up to vote on this title UsefulNot useful
The news site of Miami Palmetto Senior High School The Panther The Inaccurate Portrayal of Mental Health in Television Kalia Richardson, News Editor Every case is different. The chances of an individual morphing into a reptilian like beast with rhinoceros tusks and abducting young girls, presents an unlikely case. With reference to the recently released movie “Split” the main character experiences 23 personas as a result of Dissociative Identity Disorder. The hit Netflix series “13 Reasons Why” features a fictional character who hangs herself and mysteriously leaves 13 tapes explaining why she killed herself. Examples of such dramatized media exist solely for entertainment. Actors, screenwriters, directors all make a living off of the attention span of the audience. Their reaction equates to big buck salaries. The audience must comprehend that they want to produce attention grabbing material. Through the insertion of touchy subjects recurring through news outlets, they can drag in an eager audience. In today’s day and age, many children at the start of middle school have smartphones, meaning Wi-Fi capabilities meaning access to just about any movie and TV show through the internet. Preteens and teenagers have access to mature content, unsupervised by adults and only discussed in social circles at school and between other young watchers. Watchers visualize the aftermath of fatal events, drawing them to consider the result of suicidal thoughts. Additionally, seeking help from trustworthy figures is left bluntly out of the question as the exposure to violence grows. The major issue revolving around this exploitation remains the poor portrayal of mental illness. Some critics see the message in “13 Reasons Why” as glorifying the concept of suicide, through the accounts of its protagonist Hannah, an ignored and bullied teen. Oftentimes, those diagnosed with the disorder appear as monsters, as seen in “Split,” when in reality they are normal people who may unfortunately struggle with the basic procedures of life. These so-called creatures are normal human beings seeking help. The help they receive appears either distant or insufficient. Psychologists and therapists portrayed as careless and the patient’s characterize them as invaluable and an embarrassment. In the T.V. show, “American Crime” the protagonist, Taylor, dreads the occasional counselor visit in order to discuss his sexual orientation and a social media scandal (Pictures of him unconscious after being drugged and assaulted at a school party surface the internet). The discomfort towards a therapist produces a negative air in the minds of curious and learning youth. In extreme cases, they’re placed in psychiatric wards, left to rot, with no hope for cures or rehabilitation. As seen in the film “A Cure for wellness,” sick patients sent to a health center in Switzerland cease to progress. In an even more dramatic light, episodes and movies conclude on eerie and unexpected notes–all in order to keep the audience on their toes, clawing for a sequel. Every single person with a diagnosis does not experience an inevitable death or inescapable rehabilitation center, many situations exist where they seek help and recover. Excluding such a valuable step in the process of battling a disorder proves that the producers are not creating a movie in the effort to help those in need. A film and a mystical plot reign superior. When it comes to concluding on this topic, recognizing the disorder and exposing it to the audiences demonstrates that such disorders exist. Maybe not to such extreme degrees, but there are individuals out there that suffer with mental illness. As seen in “Split” “13 Reasons Why” “A Cure for Wellness,” etc… they project characters in a negative light leaving out ways to recuperate. The right resources need to be recognized either during or after the show, if they’d like to halt their streak of miserably portraying mental illness. Print Friendly, PDF & Email Leave a Comment The news site of Miami Palmetto Senior High School The Inaccurate Portrayal of Mental Health in Television
Dried hot peppers are, simply put, hot peppers that have been dried to preserve the vegetable for off season use. In some cases the peppers are first roasted or smoked and then dried. The texture and flavor undergo dramatic changes, and dry peppers must be handled very differently than fresh ones. To use, dry chiles must be ground or chopped, boiled or soaked. Dry chiles are a staple in Mexican cuisine, and are an integral part of many Caribbean, African and Mediterranean dishes.
Thursday, February 4, 2010 Sifting Through the Rubble: Facts and Myths in Earthquake Safety What is the right thing to do when the ground starts shaking? Ask this question to a room full of people and you’ll get a variety of answers. “Stand in the doorway” is a common one. That option is easily debunked if the room has one doorway and you do a quick test of how many people in the group can fit in that doorway. If there are engineers or architects in the room they might point to certain structural strong points in the building and make a case for heading towards those. Some might also mention the Triangle of Life theory. This comes from a viral e-mail/internet message that recommends a complicated system for identifying where the void spaces will be in a structural collapse. Here are the problems with all these ideas. First, they are based on the assumption of structural collapse. While there are no guarantees, building codes in the United States, especially in earthquake-prone areas like the Pacific Northwest, go a long way to minimize the potential for building collapse. Second, these theories fail to recognize that most injuries and deaths in U.S. earthquakes result from falling or flying furniture, equipment, lighting fixtures, and so on. Lastly and most importantly, none of these are quick solutions. When the ground starts shaking, all of that furniture and equipment could start flying in seconds. You won’t have time think, let alone call your engineer friend and ask him to recommend the choicest spot. Emergency managers, public safety officials, and earthquake experts are unanimous in their recommendation for what to do: when the ground starts shaking (don’t wait for the official earthquake announcement!) drop, cover, and hold. Dropping, covering your head under a table, desk, or other sturdy furniture, and holding onto the furniture offers the best protection in most situations. Visit for more information. Sadly, even after discussing this topic, if the ground actually starts shaking our room full of people are likely to follow their instincts. They’ll make a run for it. We’ve seen it time and again. Just look at Youtube videos of just about any earthquake. Unless you make a decision now to drop, cover, and hold and, better yet, you actually practice it, the fight or flight reaction is going to take over and you may get hurt. No comments:
Modern Compiler Implementation in C Andrew W. Appel, Maia Ginsburg Mentioned 7 Describes all phases of a modern compiler, including techniques in code generation and register allocation for imperative, functional and object-oriented languages. More on Mentioned in questions and answers. Preferred languages: C/C++, Java, and Ruby. I am looking for some helpful books/tutorials on how to write your own compiler simply for educational purposes. I am most familiar with C/C++, Java, and Ruby, so I prefer resources that involve one of those three, but any good resource is acceptable. The Dragon Book is definitely the "building compilers" book, but if your language isn't quite as complicated as the current generation of languages, you may want to look at the Interpreter pattern from Design Patterns. The example in the book designs a regular expression-like language and is well thought through, but as they say in the book, it's good for thinking through the process but is effective really only on small languages. However, it is much faster to write an Interpreter for a small language with this pattern than having to learn about all the different types of parsers, yacc and lex, et cetera... I think Modern Compiler Implementation in ML is the best introductory compiler writing text. There's a Java version and a C version too, either of which might be more accessible given your languages background. The book packs a lot of useful basic material (scanning and parsing, semantic analysis, activation records, instruction selection, RISC and x86 native code generation) and various "advanced" topics (compiling OO and functional languages, polymorphism, garbage collection, optimization and single static assignment form) into relatively little space (~500 pages). I prefer Modern Compiler Implementation to the Dragon book because Modern Compiler implementation surveys less of the field--instead it has really solid coverage of all the topics you would need to write a serious, decent compiler. After you work through this book you'll be ready to tackle research papers directly for more depth if you need it. I must confess I have a serious soft spot for Niklaus Wirth's Compiler Construction. It is available online as a PDF. I find Wirth's programming aesthetic simply beautiful, however some people find his style too minimal (for example Wirth favors recursive descent parsers, but most CS courses focus on parser generator tools; Wirth's language designs are fairly conservative.) Compiler Construction is a very succinct distillation of Wirth's basic ideas, so whether you like his style or not or not, I highly recommend reading this book. I concur with the Dragon Book reference; IMO, it is the definitive guide to compiler construction. Get ready for some hardcore theory, though. If you want a book that is lighter on theory, Game Scripting Mastery might be a better book for you. If you are a total newbie at compiler theory, it provides a gentler introduction. It doesn't cover more practical parsing methods (opting for non-predictive recursive descent without discussing LL or LR parsing), and as I recall, it doesn't even discuss any sort of optimization theory. Plus, instead of compiling to machine code, it compiles to a bytecode that is supposed to run on a VM that you also write. It's still a decent read, particularly if you can pick it up for cheap on Amazon. If you only want an easy introduction into compilers, Game Scripting Mastery is not a bad way to go. If you want to go hardcore up front, then you should settle for nothing less than the Dragon Book. Big List of Resources: • ¶ Link to a PDF file • $ Link to a printed book This is a pretty vague question, I think; just because of the depth of the topic involved. A compiler can be decomposed into two separate parts, however; a top-half and a bottom-one. The top-half generally takes the source language and converts it into an intermediate representation, and the bottom half takes care of the platform specific code generation. Nonetheless, one idea for an easy way to approach this topic (the one we used in my compilers class, at least) is to build the compiler in the two pieces described above. Specifically, you'll get a good idea of the entire process by just building the top-half. Just doing the top half lets you get the experience of writing the lexical analyzer and the parser and go to generating some "code" (that intermediate representation I mentioned). So it will take your source program and convert it to another representation and do some optimization (if you want), which is the heart of a compiler. The bottom half will then take that intermediate representation and generate the bytes needed to run the program on a specific architecture. For example, the the bottom half will take your intermediate representation and generate a PE executable. Some books on this topic that I found particularly helpful was Compilers Principles and Techniques (or the Dragon Book, due to the cute dragon on the cover). It's got some great theory and definitely covers Context-Free Grammars in a really accessible manner. Also, for building the lexical analyzer and parser, you'll probably use the *nix tools lex and yacc. And uninterestingly enough, the book called "lex and yacc" picked up where the Dragon Book left off for this part. The quickest approach is through two books: 1990 version of An Introduction to Compiling Techniques, a First Course using ANSI C, LeX, and YaCC by JP Bennett - a perfect balance of example code, parsing theory and design- it contains a complete compiler written in C, lex and yacc for a simple grammar Dragon Book (older version) - mostly a detailed reference for the features not covered in the former book How do you evaluate publications? Im currently searching for a CS research topic and reading various papers. My dilemma on reading a paper usually is - is it really worthwhile continuing research in this topic? what are the indicators of impact of research? btw, im currently interested in - Liveness analysis. what do you think of it? The highest impact papers are those that are cited most. Citeseer and the ACM will show you how often a paper is cited. Really influential papers are cited long after they cease to actually be useful. Everyone cites papers they haven't read because they are certain that the paper is the definitive reference. The definitive way to know the good papers is to have looked at everything in the area, but the question really is where to start. A good strategy I've found is to start in textbooks, as they will sometimes cite the most important work at the time they are written. Obviously, use a recent text. Liveness comes under compilers, so try Cooper/Torczon, Muchnick, or Appel. Look at the end of the chapters, where there are often mini-literature surveys. (I don't usually recommend the Dragon Book. I just checked it though, and there's nothing useful.) Finally, look for others to do the work for you. Look at the comments on the top of source files in gcc or LLVM. Look for survey papers. Look for papers that you already know the content of who touched on the topic, and follow the citation trail. Example: Lets take a quick example. I remember a few papers that use liveness. One is Sam Guyer's 2006 PLDI paper, "Free Me". And I did a bit of work on SSA recently, and people use liveness a lot with SSA. I don't remember a specific recent paper, but I expect that Briggs' semi-pruned SSA probably talks about liveness, so that's somewhere to go second. So looking at Guyer's paper, I went to the bibliography, and there were maybe two papers that mentioned liveness: • M. Hirzel, A. Diwan, and J. Henkel. On the usefulness of type and liveness accuracy for garbage collection and leak detection. ACM TOPLAS • H. Inoue, D. Stefanovi´c, and S. Forrest. Object lifetime prediction in Java. Technical Report TR-CS-2003-28, University of New Mexico, May 2003. TOPLAS is a quality journal, so I'd look there first. And so on... I'm planning to write a simple interpreter ( like TI-BASIC language for TI-89 ) or compiler ( C compiler ) using C++. I'm currently taking a course about programming languages, and learning the basic of BNF, EBNF. I wonder is it good enough to start on this project? In addition, could anyone know some good books about this area? Any feedback would be greatly appreciated. Everyone I know rants and raves about Modern Compiler Construction in C, although the Java version usually gets more credit. However if you want a more C++ focused book you can't go wrong with Writing Compiler and Interpreters. I want to build a lexer in C and I am following the dragon book, I can understand the state transitions but how to implement them? Is there a better book? The fact that I have to parse a string through a number of states so that I can tell whether the string is acceptable or not! If you're looking for a more modern treatment than the dragon book(s) : Andrew W. Appel and Maia Ginsburg, Modern Compiler Implementation in C, Cambridge University Press, 2008. Chapter 2 is focused on Lexical Analysis : Lexical tokens, Regular expressions, Finite automata; Nondeterministic Finite Automata; Lexical analyzer generators Look at the Table of Contents Big List of Resources: ¶ Link to a PDF $ Link to a printed book A compiler is a program which translates one language into another. Compiler construction is the process of creating a compiler. The tag should be applied to questions concerning the programming of compilers or for questions about the detailed inner workings of compilers. One language to another? I thought they made executables! The notional, garden variety compiler does exactly that: it translates a human readable computer programming language (like fortran or c++ or java) into a machine executable format. Or not. In fact many real world compilers translate a high level language into assembly code which is subsequently assembled by a separate program. The standard java compiler translate java code into JVM bytecode, which must be run by a dedicated program (the Java execution environment) which may include a Just In Time (JIT) compiler that translates the bytecode into chip native machine instructions on the fly. The earliest versions of the language that became c++ were called cfront and were compiled to c. And so on. Big List of Resources:
Please Enter Your Search Term Below: Websearch Directory Dictionary FactBook Wikipedia: Freeware Wikipedia: Freeware From Wikipedia, the free encyclopedia. Freeware is computer software which is made available free of charge. Typically freeware is distributed without source code. Freeware usually carries a license that permits redistribution but may have other restrictions, such as limitations on its commercial use. The term was coined by Andrew Fluegelman when he wanted to distribute a communications program named PC-TALK that he had created but for which he did not wish to use traditional methods of distribution because of their cost. Previously, he held a trademark on the term "freeware" but this trademark has since been abandoned. Commercial vendors often release freeware as a loss leader to attract customers to other services or products available for a fee. Others release freeware because other methods of distribution are unlikely to make a profit or because the software is outdated and is no longer worth selling. Freeware is distinct from the following categories of software: • Free software and open-source software. The word "free" in "free software" refers to freedom, not price; specifically, it refers to software whose license terms permit its use, modification and redistribution, with or without charge. The word "free" in "freeware" refers only to price. The word "gratisware" as a synonym for "freeware" makes this distinction clearer, but is not in common use. • Crippleware, Shareware. Shareware is distributed similarly to freeware except that it requires payment after some trial period or for more features (the "full version"), in the case of crippleware. • Adware. Adware is distributed similar to freeware, but it requires the user to view advertisements to use the software. • Donationware. The authors of donationware ask that anyone using their software make a donation to the authors or to some third party such as a charity. Because the donation is optional, donationware may also be freeware or fall into some other category. • Public domain software. Software in the public domain has no copyright and therefore may be distributed without charge. Freeware is usually copyrighted and its license may restrict certain activities. • Abandonware. Abandonware is commercial software that has not been sold for a long time or whose copyright holder is defunct; it has been "abandoned". The licenses of most such software forbid redistribution or require payment, so distributing it violates the author's copyright (though there may be no author around to enforce it). "Legal abandonware" is a misnomer for commercial software that has been re-released by the copyright holder as freeware.] • Postcardware. The software is essentially freeware, however the author requests that you send him a post card expressing thanks and enabling him to provide feedback to users. External links Freeware archives From Wikipedia, the free encyclopedia. Modified by Geona
By: Karla Gutierrez Print this Page July 8th, 2014 Studies Confirm the Power of Visuals in eLearning eLearning design \| visual communication \| visual design \| eLearning We are now in the age of visual information where visual content plays a role in every part of life. As 65 percent of the population is visual learners, images are clearly key to engaging people in eLearning courses. Moving and still images have been included in learning materials for decades, but only now has faster broadband, cellular networks, and high-resolution screens made it possible for high-quality images to be a part of eLearning visual design. Graphic interfaces made up of photos, illustrations, charts, maps, diagrams, and videos are gradually replacing text-based courses. In this post, we will dig deep into some statistics and facts to further convince of why eLearning developers should embrace visuals when creating their courses. the power of visuals in elearning 1. Visuals Stick in Long-Term Memory Both the short-term and long-term memory store information in chunks, but the former is limited. One of the easiest ways to ensure that learners store information in their long-term memory is to pair concepts with meaningful images. Research has found that this tactic increases recall better than when courses deliver information through aural or textual form. Visuals help people make sense out of the content and direct attention, increasing the possibilities that the learners will remember. According to Dr. Lynell Burmark, education consultant who writes and speaks about visual literacy: “…unless our words, concepts, ideas are hooked onto an image, they will go in one ear, sail through the brain, and go out the other ear. Words are processed by our short-term memory where we can only retain about seven bits of information (plus or minus 2) […]. Images, on the other hand, go directly into long-term memory where they are indelibly etched.” Furthermore, this effect increases over time. One study found that after three days, a user retained only 10-20 percent of written or spoken information but almost sixty five percent of visual information. Another study showed that an illustrated text was nine percent more effective than text alone when testing immediate comprehension and 83 percent more effective when the test was delayed. 2. They Transmit Messages Faster According to the Visual Teaching Alliance: • The brain can see images that last for just 13 milliseconds. • Our eyes can register 36,000 visual messages per hour. • We can get the sense of a visual scene in less than 1/10 of a second. • 90% of information transmitted to the brain is visual. • Visuals are processed 60,000X faster in the brain than text. • 40 percent of nerve fibers are linked to the retina All this indicates human beings process visual information more efficiently than text. Just see it yourself: visual eLearning Image source: Uberflip Blog Taking all these into consideration, eLearning developers can use this knowledge in their visual designs to their advantage by including well-timed graphics or a sequence graphics to aid instant understanding as well as to reduce explanation time and content. Think about it: What content would be better structured as an image or a video, rather than a bullet-list? 3. ...And Improve Comprehension Visuals have been found to improve learning by up to 400 percent. Also, they affect learners on a cognitive level and stimulate imagination, therefore, enabling users to process the information faster. Stanford University's Robert E. Horn, explained this relationship clearly "When words and visual elements are closely entwined, we create something new and we augment our communal intelligence ... visual language has the potential for increasing ‘human bandwidth'—the capacity to take in, comprehend, and more efficiently synthesize large amounts of new information." Other studies have found that visuals such as graphic organizers improve performance in areas including: • Reading comprehension • Student achievement • Organizing and communicating ideas • Finding patterns and relationships This infographic shows how our brains are pre-wired to automatically interpret relationships between objects, allowing for almost instant comprehension with minimal effort: visuals in eLearning 4. Visual Cues Trigger Emotions Visuals cause a faster and stronger reaction than words. They help users engage with the content, and such emotional reactions influence information retention. This is because the visual memory is encoded in the medial temporal lobe of the brain, the same place where emotions are processed. The brain is set up in a way that visual stimuli and emotional response is easily linked, and together the two form memories. Negative visual depictions are particularly useful for leaving a strong emotional impression. Even abstract concepts can benefit from images, when course creators use visual metaphors. Including visual metaphors in their eLearning course help express emotions to trigger a similar emotional response in students. See this example: visualsImage Source: Visual Rhetoric Blog 5. Visuals Motivate Learners Around 40 percent of learners respond better to visual information than text alone. Simply seeing a picture allows users to recreate the experience in their mind. eLearning professionals can benefit from this by telling stories in their courses through entrancing images and compelling videos. 6. But Wait... Incorrect Use of Visuals Can Also Deter Learners It is important to note that graphics can also negatively impact learning if they are used inappropriately. When off-topic graphics appear on the screen, such as those used for purely decorative purposes, learners will subconsciously try to figure out the message and reason for the image. The following are examples of images that course creators should always avoid in eLearning visual design: • Pictures that are obviously stock photographs. • Generic graphics that display a clear lack of imagination. • Poor quality images that are pixelated, low-resolution, over-compressed, or badly resized. On the other hand, well-selected images can improve comprehension and insight when developers strategically place such graphics within a course. Unlike text, pictures have the power to enrich communication and stimulate emotional response. In order to utilize visuals in a way that will reinforce course material and facilitate learning, it is necessary to use images that: • Represent actual objects, people, or places. • Simplify complex or abstract ideas. • Bridge already learned materials with the unfamiliar. eLearning designers should only use images that have a clear value, otherwise they are distractions at best and, at worst, give learners the wrong impression. This means omitting anything that does not directly support learning goals. visual design crash course About Karla Gutierrez • Connect with Karla Gutierrez
Cardiovascular Medicine - Education Center Aortic valve and vessel abnormalities: Aortic stenosis In aortic stenosis, left ventricular outflow is reduced and a pressure load on the left ventricle is imposed by the significant narrowing of the aortic valve. A harsh mid-systolic murmur is usually heard maximally over the aortic area and it frequently extends to the carotid arteries as well. Causes include degenerative calcific aortic stenosis (usually in elderly patients), calcification usually on a congenital bicuspid valve and rheumatic heart disease. Aortic stenosis in wav format Aortic stenosis in real audio format Aortic regurgitation Aortic regurgitation is caused by an incompetent aortic valve that allows regurgitation of blood from the aorta into the left ventricle as long as the aortic diastolic pressure exceeds the left ventricular diastolic pressure. The murmur is usually high-pitched and tends to merge into S2 - as in this case. Aortic regurgitation may be acute or chronic. Acute aortic regurgitation may be due to infective endocarditis or aortic root dilatation due to Marfan's syndrome, aortic aneurysm or hypertension. Chronic aortic regurgitation can be due to valvular causes such as rheumatic heart disease, congenital (bicuspid valve or ventricular septal defect) or seronegative arthropathy (especially ankylosing spondylitis) or aortic root dilatation due to Marfan's syndrome, aortitis (syphilis, Marfan's syndrome, seronegative arthropathies, rheumatoid arthritis, etc) or aortic aneurysm. Aortic regurgitation in wav format Aortic regurgitation in real audio format Coarctation of the Aorta This is a congenital narrowing of the aorta just distal to the origin of the left subclavian artery. The etiology appears related to the abnormal position of tissues involved in closure of the ductus arteriosus. It is also associated with Turner's syndrome and the bicuspid aortic valve. Coarctation of the Aorta in wav format Coarctation of the Aorta in real audio format Return to the IMC Main Lobby
Voyagers expedition The Voyagers have enjoyed studying about Leicester’s past and present. They have been especially curious about the concept of one room schoolhouses. They visited the Shelburne Museum to learn about life in the past and had an opportunity to practice life in the Vergennes Schoolhouse now located on the museum grounds. They bowed and curtsied to the teacher when arriving at school. They practiced standing up and saying, “Yes, ma’am” when called on. They sat in the old desks, used slates, and took part in a spelling bee. They were amazed to see the woodstove in the center of the schoolroom and learned that the older students would help keep it going. Subpages (1): Old Schoolhouses
Friday, December 28, 2012 Turing's Revolution In my post Alan Turing Year, I discussed how it's important for people to be aware of Turing's intellectual contributions to math and computer science, as well as his war efforts and tragic death. It's time to live up to my own call and do my part. In this post I'll talk about Turing's impact, from his best known contributions to his lesser known, but important ones. I should note that the content of this post is largely stolen from answers to a question I asked on the StackExchange (SE) cstheory site, where I sought to gather a compendium of Turing's less known results. The answers made a collection of impressive contributions, some of which I wasn't familiar with. Some of his contributions turned out to be surprisingly modern. They also introduced us to viewing the world through an algorithmic lens. Without further ado, here they are: 1. Defining Turing Machines and Showing the Existence of UTMs (1936): A Turing machine is a universal computing device that forms the basis of how we think about computing. A Universal Turing machine is a fixed machine that can simulate any other Turing machine -- most relevant to our current computers. (SE link) a Lego Turing Machine, photo from wikipedia 2. The Church-Turing Thesis (1939): The idea that the Turing Machine (and Lambda calculus) captures all of computation, and is therefore worth studying. This hypothesis cannot be proven, but everyone believes it nonetheless. (wiki link 3. Solving the Halting problem (1936): A version of this was posed by Hilbert. Turing showed that telling whether a program will Halt is undecidable. (wiki link 4. The Turing Test and Introducing AI (1950): Turing gave an objective test that decides whether a computer exhibits intelligence. The idea is to say that a computer is intelligent if it can fool humans into thinking it is also human. Accepting this idea is a way to avoid many philosophical arguments about the nature of intelligence. (wiki link 5. Introducing Oracles and Relativization into Computability Theory (1939): Oracles are incredibly useful for all sorts of analysis -- for example the famous Baker-Gill-Solovay result that says P vs NP cannot be separated any technique that relativizes (holds for relative to any oracle), eg diagnolization. It was part of the paper "Computing machinery and intelligence" that launched AI. (SE link 6. The Bombe (1950): Also called the Turing-Welchman Bombe, for breaking the German enigma machine in WW2 and introducing tools to cryptanalysis. (SE link) the Bombe, from 7. Randomized Algorithms (1950): Turing observed the potential advantage an algorithm can gain from having access to randomness. (SE link) 8. The First Artificial Neural Network (1948): This idea is an important one in AI and machine learning. Turing's design predated Rosenblatt's preceptron. (SE link 9. The Chemical Basis of Morphogenisis (1952): In his most cited paper, he began to tackle the question of how a symmetric embryo develops into an assymetric organism using symmetry perserving chemical reactions. This started to introduce algorithmic thinking into biology. (SE link 10. Good-Turing Estimator (1953): For estimating an unseen fraction on a population when given past data. (SE link 11. One of the First Chess Algorithms (1952): Before we had computers, we had paper chess algorithms. (SE link Deep Blue, photo form wikipedia 12. Checking a Large Routine (1949): The idea of using invariants to prove properties of programs and "well-foundedness" to prove termination. (SE link 13. LU-Decomposition (1947): A method for factorizing a matrix as the product of a lower triangular matrix and an upper triangular matrix. Now commonly studied in Linear Algebra. (SE link) 14. Turing's Method for Computational Analysis of a Function (1943): Invented for studying the of the Riemann zeta-function but is more widely applied. (SE link) I'm sure there are more. Any one of these is an impressive achievement for a scientist -- the first couple are revolutionary. That Turing did all of these and more shows his remarkable contributions to our field. Update (12/31/12): Alan Richmond points out another important work of Turing's, which I added as # 14. Also, my wording for the Turing test proved a bit controversial, so I've changed it to better reflect reality. Friday, December 07, 2012 UIC's MCS Program Seeking Graduate Students As I'd posted before, UIC has two departments interested in computer science. We have a computer science department in the engineering school. And the math department in the school of liberal arts and sciences, where I have an appointment, has a smaller program in "mathematical computer science" (MCS). The MCS program is more focused on the mathematical aspects of computing and less on systems, databases, etc. It is similar to the ACO programs at CMU and Georgia Tech. We recently updated our website, where you can learn more about the program and the affiliated faculty. More importantly, if you're a student looking to get a Ph.D. in a mathematical area of computing, consider applying to our program -- we're looking for strong applicants. a screenshot of the new MCS website Tuesday, August 07, 2012 Diamond Forever Recently, the academic community started to fight back against traditional academic publishers, who earn large profits without any longer providing many clear services. The internet has been a great tool for taking care of such inefficiencies, and it's quickly disrupting the publishing market as well. Having thought a bit about these issues myself, I wanted to summarize my views of some of the various publishing models (as described by Tim Gowers) under consideration, as well as the pros and cons of each. It's possible, even likely, that I am missing something, so feel free to point it out in the comments. The Systems screenshot, after I tried to access a paper from system: Researchers send manuscripts to publishers. Publishers have volunteer editorial boards consisting of researchers who decide whether to accept/reject manuscripts. Accepted manuscripts are published but cannot be accessed without a paid subscription to the given journal. Authors lose most (or all) rights to their own work. who wins: publishers, by charging for access who loses: university libraries and therefore scientists who pay for it with overhead; the public, who doesn't get access to the research their taxes likely funded; authors, who cannot easily have their research read and used. opinion: This system made some sense before the internet era, where there were few other good ways to disseminate research. The publishers used to have to work hard for their profits by doing serious formatting/printing/publishing work. With the internet, all of this is now done by the authors, and the closed-access system no longer makes sense. system: Same as closed-access, except that authors are allowed to put their accepted manuscripts on their websites and onto online repositories such as the arXiv. who wins: publishers, by charging for access; researchers who put their papers online who loses: basically same as closed-access, except for the authors who put their papers online opinion: This is the system most journals are now on, or at least they usually don't go after scientists who keep their papers online. This is strictly better than closed-access, but doesn't go far enough. Too many scientists do not put their papers on their websites or arXiv. There is still no guarantee that science will be public, as it should be. a screenshot of the new gold-access math journal system: Researchers send manuscripts to publishers. Publishers have volunteer editorial boards consisting of researchers who decide whether to accept/reject manuscripts. Authors of accepted manuscripts pay to have their work published but published manuscripts are freely accessible to everyone online. who wins: the public, who can access research for free. the publishers, who still get paid (but not as much) who loses: the authors, who have to pay (usually large sums) to have their work published. universities, which might need to subsidize the fees. quality (see below). opinion: I think adopting this system would be a mistake. First, scientists are the ones doing the work, the editing, and the main contributions -- it seems unfair to make them pay as well. Researchers without grants or university support would have to use their personal funds. Moreover, I think this would seriously impact paper quality. In this system, journals would make money by accepting more papers as opposed to getting more readers, and some authors may have incentives to pad their CVs. I cannot see how this wouldn't go wrong. the journal of machine learning research, image from their website system: Researchers send manuscripts to publishers. Publishers have volunteer editorial boards consisting of researchers who decide whether to accept/reject manuscripts. Authors of accepted manuscripts have their work published for free and published manuscripts are freely accessible to everyone online. who wins: scientists, who can publish for free and have their papers read. the public, who can access research freely. universities, who do not have to pay for journal access. research quality. who loses: publishers, who cannot any longer charge for anything opinion: This is the best of all worlds. Everyone seems to win, and research quality especially wins because nobody makes a profit from publishing bad results. The only problem is that the publishers lose, and why would anyone run a journal without making a profit? A Solution Diamond-access is the best system for everyone, except for the publishers. However, publishers need incentives to run a journal, which they wouldn't have in a diamond access system. Now, becoming a publisher would involve operating at a loss. So who should take the hit? One obvious solution is for universities to publish (or pay for publishing) journals. They would make a sacrifice in maintaining the journals for free, but what would they win? Quite a lot actually. Were we do switch to this system, university libraries would no longer have to pay subscription fees to journals, and the university professors wouldn't have to pay to have their work published. And the quality of publications wouldn't suffer. Some of this cost could even be handled by overhead. Yale's library (from wiki), where I not once went to do research during my Ph.D. But what is the cost of running a diamond access publication? Well, it turns out to be very small. With pdfs online, there's really no need to publish paper proceedings. I don't think I've ever gone to a library to find an article on paper -- pretty much nobody does these days. So, all you need to do is register a domain and pay for some maintenance and hosting. The rest of the work is done by volunteers. Looking at the financial statement (of which I learned from Google+) of the Journal of Computational Geometry, it could take as little as $10 per year. Heck, we don't really need universities to pay for it. Yes, it really costs very little to run a journal these days if you do it right. There's no need for readers, or authors, to pay huge sums to middle-men. Monday, May 07, 2012 Atlanta, Northward When you accept a postdoctoral position, you know you probably can't stay indefinitely. Psychologically, it means you have to prepare yourself for having to switch jobs, coworkers, offices, etc., and I, as a postdoc, have been ready for this foreseeable consequence with Georgia Tech, where I've enjoyed being part of a strong and lively department the last two years. Unfortunately, when you take a postdoc in a city like Atlanta, where there isn't as high a concentration of universities and research labs as some other places, you not only have to leave your job, but likely also the city. And even though it was in the back of my mind that I'd probably have to move, I didn't expect to love Atlanta as much as I have come to. Atlanta's botanical garden Atlanta has sunny, warm weather, really friendly people, lots of trees, amazing restaurants, nice parks, museums, a symphony, theaters, and everything you could want in a city (except, perhaps, a waterfront). It's also very livable -- the population density is fairly low, so you're not elbow-to-elbow every time you leave your house, and you can live in really nice suburbs right in the middle of the city. Because of the large influx of new residents, it's mostly new and clean, yet the cost of living is quite low. And you can reach great hiking with a 20 minute drive and reach a beautiful national park in 3 hours. It's certainly a place I wouldn't mind living in again at some point in my life. Smoky Mountains National Park But while I'm sad to have to leave Atlanta, but I am also excited to begin a new phase in my career. In a couple months, I'll be joining the University of Illinois at Chicago (UIC) as an Assistant Professor in the Math department, actually called "Mathematics, Statistics, and Computer Science." The department is quite strong, but unlike most math departments, UIC's is expressly concerned with Computer Science (so, yes, I'm remaining a computer scientist). Additionally, UIC has another entire standard Computer Science department, where I'll also have a courtesy appointment. Between the two departments, there are quite a few great faculty members working on various aspects of machine learning -- I'm looking forward to joining them. And with Northwestern, UChicago, and TTI-C nearby, Chicago should be quite an exciting place to work. Chicago, reflected in "the bean" But because this post started with Atlanta, I should say something about the city of Chicago. While I don't yet know Chicago well, it also looks like a beautiful, livable place, on the shores of a (literally) great lake. The people seem friendly, and there is a lot to do. I just hope that, after being spoiled by Atlanta, I can get used to Chicago's cold winters. Friday, April 27, 2012 Computing Conceptions From Georgia Tech, many of us have been closely and concernedly watching our southern neighbors at the University of Florida, where budget cuts and a seemingly hostile dean conspired in an attempt to decimate their well-respected computer science department. Dismantling the department, at a time when computer science research is so critical, would be a laughably bad decision on the part of the university. I don't claim to fully understand the rationale behind this plan. However, I have a feeling that part of the reason such an idea was even being seriously considered has to do with a couple misconceptions of what computer science research is, and I fear that such misconceptions extend beyond the state of Florida. And I don't just mean that the average person doesn't understand computer science; that's to be expected. I mean that many academics, even scientists, don't understand the basics of what computer science is about and therefore tend to devalue it, especially as an academic discipline. First, many people seem to assume that computer science is just programming or fixing computers. As a graduate student at Yale, where computer science is a small department, I was often asked by other Ph.D. students why computer science even has a Ph.D. program. They didn't view it as an academic pursuit, but more as a trade skill. I fear that many scientists view computer science as limited to programming or getting computers to work, probably because that's the way most, say, physicists use computers. They have little understanding of the beautiful, deep results and insights that computer science has brought the world. Viewing it as an instrumental non-academic field, people think it would be okay to kill-off computer science research and leave the professors to teach programming (which, admittedly, is an important part of a computer science department's job). (clip art from here) something computer scientists do not normally do The other, very related, misconception, one that was clearly in play at the University of Florida, is that the computer science department was somewhat redundant because the electrical and computer engineering department already has the word "computer" in it. Their reasoning sounded more sophisticated than that, but only superficially. But computer science and electrical engineering are very far in their central concerns. Computer science, for the most part, is divorced from concerns about electricity, physical media, or anything of that sort. Whether you work on operating systems, machine learning, or the theory of computation, you mostly don't really care about the underlying hardware, whereas electrical engineers do. Greg Kuperberg, writing on Scott Aaronson's great blog post on this issue, puts it better than I could: "Apparently from (Florida engineering dean) Abernathy’s Stanford interview, and from her actions, she simply takes computer science to be a special case of electrical engineering. Ultimately, it’s a rejection of the fundamental concept of Turing universality. In this world view, there is no such thing as an abstract computer, or at best who really cares if there is one; all that really exists is electronic devices. [...] Yes, in practice modern computers are electronic. However, if someone does research in compilers, much less CS theory, then really nothing at all is said about electricity. To most people in computer science, it’s completely peripheral that computers are electronic. Nor is this just a matter of theoretical vs applied computer science. CS theory may be theoretical, but compiler research isn’t, much less other topics such as user interfaces or digital libraries. Abernathy herself works in materials engineering and has a PhD from Stanford. I’m left wondering at what point she failed to understand, or began to misunderstand or dismiss, the abstract concept of a computer." (image from here) something usually not of research interest to computer scientists It looks like a disaster in Florida has so far been avoided. And with each passing year, more scientists will have, at the very least, taken some basic computer science in college -- it is part of our job to teach the important concepts in our introductory courses. I'm hoping this will improve the perceptions of our field. But in the meanwhile, it has become apparent that we have much more PR to do to. (image from here) now we're talking! Sunday, January 22, 2012 Alan Turing Year I am excited that 2012, the centenary of Alan Turing’s birth, will see many celebrations of his life and legacy. It is hard to think of a scientist who has had more impact both on science and on our lives, but who still remains as unknown to the public, so I am glad Turing will be getting some much-deserved attention this year. Alan Turing, photo copyright held by National Portrait Gallery in London Alan Turing laid out the foundations of the study of computer science (in the process of solving Hilbert’s Entscheidungsproblem – no small feat on its own), contributed fundamentally to our understanding computation in nature, envisioned the future of intelligent machines, and saved millions of lives by helping shorten the length of World War 2. Yet upon discovering Turing was gay (and convicting him for "indecency"), the British government took away his job, kept many of his contributions secret, and chemically castrated him, driving him to suicide. After some long-overdue outrage, Gordon Brown issued an apology on Britain's behalf, albeit decades too late. Now there are new petitions, asking for the British Government to grant Turing a pardon. I have nothing against these efforts, but how Turing was treated is to our collective shame, and we should remember that these efforts are to make us, not him, feel better. Turing knew he wasn't doing anything wrong and never needed condescending “pardoning” from politicians, nor does he need them any more after his death. If the pardon is to send an apology to the homosexual community for their mistreatment, I’m sure the British government can think of something a little more direct. I think a better way of honoring Turing is to make sure people know about his work – like we do of KeplerGalileoNewtonDarwinEinstein, and many of the other great scientists who revolutionized our world-views. Unfortunately there’s a lot of work to be done: even well-meaning articles trying to popularize Turing’s work mainly describe him as an accomplished code-breaker and World War 2 hero. Turing did break codes, most notably the German Enigma machine, but calling Turing a code-breaker without mentioning his scientific impact is akin to calling Isaac Newton a treasurer, given his years as England's Master of the Mint. So, this year, we academics will celebrate Turing’s great accomplishments by holding conferencesawards, and lectures in his honor. There will be documentaries released about his life. I’m sure an op-ed or two will be written in the newspapers. But I also hope that reporters, lecturers, and especially teachers, will help the the public at large learn about this pioneer of the information age.
Let’s talk about the word delincuente and vocabulary related to crime and criminals. In English, the noun ‘delinquent’ often refers to young lawbreakers, ‘juvenile delinquents’. In Spanish, delincuente is more general, refering to someone of any age who is engaged in criminal activity, a criminal. (The word ‘criminal’ does exist in Spanish but it is less commonly used than its English counterpart.) Crimes are delitos. (Again, crímenes exists but is less used than its English counterpart.) A felony, a crime with serious legal consequences, would be a delito grave. When speaking of crime in general and not of specific incidences, use delincuencia. High rates of crime, altos niveles de delincencia. An asalto is a mugging or a hold-up, so it doesn’t work as a general translation for the English word ‘assault’. Esto es un asalto. This is a stick-up. Me asaltaron en la calle. I got mugged. An asaltante is an attacker. Atracar is another common verb for ‘attack’ criminally. A ratero is a garden-variety thief or robber. I’ve also heard ratero applied disparagingly to white-collar offenders engaged in corruption. Speaking of corruption, the noun ‘bribe’ is mordida, literally ‘bite’, or more formally, soborno. The corresponding verbal forms are dar una mordida and sobornar.
]> HyperText Markup Language Request For Comments Format Cisco Systems, Inc. RFC Editor This document defines the HTML format that should be used for the production of Internet-Drafts and RFCs. The HTML output will include a default CSS to enable page layout, and the HTML itself includes semantic information only. This format will be rendered from the canonical XML format for an RFC. The RFC Series has been in existence for over 40 years. During much of that time, the limitations of character set, line and page length, and graphics restrictions of RFC documents met the most immediate needs of the majority of authors and readers. As technology changed, new formats that allowed for a richer set of edit, search and display features came in to use, and tools were created to convert the plain ASCII documents to other desired formats such as HTML, PDF, and Microsoft Word. While the converted versions of the RFCs are widely available, the canonical display format remains the plain text, ASCII, line-printer structured one. In 2013, after a great deal of community discussion, the decision was made to shift from the plain text, ASCII-only canonical format to XML . Several different publication formats will be rendered from that canonical XML, including HTML, PDF, TXT, and EPUB. This memo describes an HTML format that will be used as one of the publication formats for the RFC Series. It defines a strict subset of HTML appropriate for Internet-Draft and RFC Series documents, and serves as a comprehensive example of all of the HTML elements that are permissible. The CSS that defines the visual layout, while included in the HTML file, will be described in a separate document . The HTML itself will represent semantic information only. The HTML has to render correctly on the following: the latest released versions of Chrome, Firefox, and IE running on Windows 8 in November 2013 the latest released versions of Chrome, Firefox, and Safari running on Mac OS X 10.9 in November 2013 the latest released versions of Chrome and Safari running on iOS 7 in November 2013 the latest released versions of Chrome and Firefox running on Ubuntu 13.10 in November 2013 the latest released versions of Chrome and Firefox running on Android 4.1 in November 2013 These requirements are expected to change in the future to reflect the expectation that HTML rendering will be required for current versions of browsers and platforms, while ideally continuing to render correctly on earlier versions. The HTML document must preserve all semantic information that is in the canonical XML document. One use case is that preformatted text that has different tags in the XML will also be differentiable in the HTML, making it trivial to extract all of the (for example) ABNF in an RFC with a simple program. Another use case is that someone who wants to write programs that will extract information from an RFC can do so equally well with the XML and HTML, and can choose the tool that uses one or the other format for input. The HTML document must come with a default, internal set of CSS formatting. This will allow for a mostly-consistent display of RFCs across browsers. It will also allow for the HTML file to be moved over different transports (such as e-mail) and have the result look the same. The HTML must display adequately in at least one text-based browser. Any use of javascript must not negatively impact the ability to read the document. The HTML document must allow easy local override of the default CSS formatting. This will allow users who have a different visual style that they prefer to make RFCs display with that style without having to alter the contents of the HTML document. This might also be valuable for allowing people with specific accessibility needs to have custom CSS. No HTML tags in the document may have style information. All style information must be done through "class" and "id" attributes, with the style for those represented in the CSS alone. Exceptions can be made for formatting that is not possible in any other way in HTML5 , such as table column widths. The HTML must make it easy to separate chunks into separate files. This will make creating EPUB documents easier in the future. The output needs to be HTML5. Language extensions might be acceptable after further discussion. The RFC Editor will use an automated validating tool before publishing the HTML. This requirement is not important for viewing with browsers, but is important for programs that will use the HTML format as input for processing. The HTML must not have any Javascript or other active code in <script> or <object> tags. All section, subsections, figures, and paragraphs should have stable numbered link anchors. Additionally, anchors expressed in the source XML should be exposed as anchors in the HTML as well. The abstract must be marked up or tagged in a way that search engines will extract it as summary. Normative information must be easily accessible to the following consumers: People with impaired vision, including those that use large fonts and those that use screen readers People with difficult;y distinguishing between colors People who use devices with small screens, such as cell phones Other groups TBD Specific instances where these goals are important in the design choices of the format have been called out in the text. The HTML document does not require the inclusion of non-semantic information such as comments and processor instructions. NOTE: designing for these consumers does not preclude the use of features they cannot use, but does require that key semantic data is not lost when read using the tools and settings that are required by a given constituency. The format specified here is a subset of HTML, deemed to be widely-implemented by common browsers at the time that the specification was created, likely to continue to be widely-implemented in the future, and unlikely to cause security issues. The following rules SHALL be enforced: The HTML source MUST be encoded as UTF-8, as specified in RFC3629. Note that RFC3629 forbids "surrogate" codepoints in the range U+D800 to U+DFFF. The document MUST be valid HTML5. Single quotes (U+0027 APOSTROPHE: ') MUST be used to quote attribute values. Unquoted attribute values MUST NOT be used. Each logical line MUST be terminated solely with a \n (U+000A: LINE FEED), otherwise known as "Unix-style" line endings. Other than \n (U+000A: LINE FEED), code points less than " " (U+0020: SPACE) (otherwise known as "control characters") MUST NOT be used. Any character references that would generate these code points (e.g. ) MUST NOT be used. NOTE: this rule explicitly forbids \t (U+0009: CHARACTER TABULATION), \f (U+000C: FORM FEED), and \r (U+000D: CARRIAGE RETURN) from appearing in the source. Each text-containing element such as headings (<h1>-<h6>), paragraphs (<p>), or list items (<li>), MUST be serialized as a single line without wrapping. The contents of <pre> elements MUST NOT be modified by processing tools. The following rules apply to all elements except for <pre>: HTML SHALL be indented using spaces (not tabs). Each child element SHALL be indented two spaces more than its parent element, unless the child element is mixed with non-whitespace-only text children of the same parent element. NOTE: none of these rules affect the rendered output of the HTML, but are intended to increase the chance that multiple tools that process the format will generate identical syntax. In turn, this will make difference tools that operate on the HTML source easier to write. The HTML comprising the document MUST be valid according to the latest version of the HTML specification at the time of publishing, starting with the version commonly known as HTML5. Although the HTML specification mandates several of syntax and structure rules in this document, they are called out here for emphasis. The DOCTYPE of the document MUST be "html", which declares that the document is compliant with HTML5. The document will start with exactly this string: The SYSTEM 'about:legacy-compat' portion MAY be dropped in the future if the tooling chosen to produce this format does not require it. The root element of the document MUST be <html>. This element SHOULD include a lang attribute, whose value is a RFC5646 language tag describing the natural language of the document. For documents submitted to the RFC Series or Internet-Draft Series, the language tag MUST be 'en', meaning "English". If the lang attribute is not present, its value should be taken to be 'en'. In order to be correctly processed by browsers that load the HTML using a mechanism that does not provide a valid MIME content-type or charset, the HTML <head> element MUST contain a <meta> element, with charset attribute with value 'utf-8'. This will look like: The <head> SHOULD contain an embedded CSS stylesheet in a <style> element. The styles in the stylesheet are to be set consistently between documents by the RFC Editor, according to the best practices of the day. The RFC Editor SHALL choose a stylesheet that does not modify the meaning of the normative text of the document. The RFC Editor SHALL make the stylesheet available via a standard protocol (e.g. HTTP or HTTPS) for ease of authorship. However, when a document is submitted, external stylesheets (other than "local.css" as specified below) are NOT ALLOWED. The stylesheet itself MUST NOT be considered as normative information. To ensure consistent formatting, individual style attributes SHOULD NOT be used in the main portion of the document source except in highly exceptional circumstances; each use MUST be individually justified. Different readers of a specification will desire different tweaks to the stylesheet. To facilitate this, the <head> SHOULD include a <link> to a stylesheet in the same directory as the HTML file, named "local.css", after the embedded stylesheet. Note that this "local.css" file will not exist for most users; browsers will correspondingly ignore this <link>. For example: Words or phrases may be emphasized using the <em> element, usually rendered as italics. Strong emphasis may be donated with the <strong> element, which is usually rendered as boldface. Underlining MUST NOT be used except for links, to avoid visual confusion. Text-only emphasis such as "bold" MUST NOT be used. The RFC Editor will set a policy that reflects the current feelings of the community as to whether this emphasis markup is allowed in documents that are submitted for publication in the RFC series. HTML comments will not be generated by the rendering agent from the canonical XML. Each section of the document SHALL be formatted as a <div> tag, with a class attribute with value 'section'. A document-unique id attribute SHOULD be assigned to each section <div>. NOTE: HTML5 requires id attributes to be unique across an entire document. Each section <div> MUST contain a header tag (<h2>-<h6>) of the appropriate depth, with top-level sections getting an <h2> tag, and each nested section getting the next higher header level. If more than five levels of headers are required, <h6> MUST be used for each deeper-nested section. However, nesting sections more than five levels deep is NOT RECOMMENDED. The text in each header tag MUST begin with the section number. Section numbers MUST begin at "1.", and MUST increment by one for each successive section at the same level. Subsections MUST be numbered by appending the subsection number to the parent section number. It is RECOMMENDED that the section number be wrapped in an <a> element, whose href attribute points to the corresponding section div with a local relative reference. This <a> element SHOULD have the CSS class self-ref. Within a section, each "normal" paragraph MUST be surrounded by a <p> element. For example: 1.Example Section This is a description of the example 1.1. Nested Section This is a description of the nested section. This is the second description paragraph. Parent sections that contain child sections MUST NOT contain "normal" paragraphs after a sub-section. For example, the following is invalid: 1. Example Section This is a description of the example 1.1.Nested Section This is a description of the nested section. Appendices are special cases of top-level sections. Each appendix of the document SHALL be formatted as a <div> tag, with a class attribute with value 'appendix'. A document-unique, id attribute SHOULD be assigned to each section <div>. The id MAY be human-readable or generated. Each appendix <div> MUST contain an <h2> element containing text that describes the purpose of the appendix. Appendices are identified to the reader with Latin capital letters A-Z, in order. It is NOT RECOMMENDED to have more than 26 appendices, but if required, appendices "AA.", "AB.", etc. follow Appendix Z. Inside the appendix, subsections MUST be formatted per Sections, numbered sequentially. For example, the first subsection of "Appendix A." is "Appendix A.1.". For example: Appendix A. Acknowledgements The author gratefully acknowledges the contributions of... Appendix A.1. Contributors These people contributed text... Paragraphs MUST be contained in a section <div> or an appendix <div>. A document-unique, id attribute SHOULD be assigned to each <p>. The id will usually be machine-generated, but MAY be human-readable if desired. It is RECOMMENDED that each paragraph be kept relatively small compared to a "page" in previous RFC formats, so that references to each paragraph are at least as valuable as page references have been in previous formats. Lists may be used inside a section <div>, and may nest in other lists as needed. However, lists MUST NOT be nested inside a <p> element. Unordered lists (<ul>) and ordered lists (<ol>) may both be used. For example: Unordered list An explanation: • One • Two 1. Two.1: (this one is numbered) Reference format must follow the guidance in the RFC Style Guide . Non-trivial direct quotes from other documents SHOULD use the <blockquote> element. If the quote needs a citation, wrap the <blockquote> in a <figure> and add a <figcaption> element that contains text (and possibly links) that describe the quote. For example, this code: Here a blockquote element is used in conjunction with a figure element and its figcaption to clearly relate a quote to its attribution (which is not part of the quote and therefore doesn't belong inside the blockquote itself): Sample Quote from HTML5, section 4.5.4 ]]> Would render as: This section describes how to format several types of information that occur regularly in documents for the Internet-Draft and RFC Series which are not descriptive text. The RFC2119 keywords in the document will be set off with special markup. They MUST be surrounded with a <span> element containing the CSS class rfc2119. For example: They <span class='rfc2119'>MUST</span> be surrounded The table of contents for the document MUST appear in a <div> element, which SHOULD precede any of the sections of proper document content. The <div> element MUST have an id attribute with value 'toa'. The <div> element SHOULD contain an <h2> element containing the string Table of Contents, followed by nested <ul> and <li> elements describing the structure of the document, with links to each of the sections mentioned. For example: Table of Contents NOTE: the Table of Contents SHOULD NOT be considered meta-data for the document. The sections themselves SHOULD contain all of the data that is required. SVG can be included directly in the HTML source, surrounded by a <figure> element and succeeded by a <figcaption> element, as described in Section . The root <svg> element MUST contain a <title> or <desc> element that fully describes the diagram for accessibility to screen readers; this is similar to the alt; attribute on images. See "SVG Drawings for RFCs: SVG 1.2 RFC" for details on the appropriate SVG profile for use in RFCs . Use the <code> element to set aside literal references to code or protocol elements in the middle of a paragraph. If desired, the language of the code or protocol can be declared using a class attribute starting with language-. For example: Use the <code class='language-html'><;code>;</code> element Larger sections of code or protocol can be included using a <pre> element with a class attribute of code. If desired, the language of the code or protocol can be declared using a further class value starting with 'language-' (multiple class values are separated by spaces in HTML). The text inside the <pre> element will be rendered in a monospace font, with whitespace maintained. For example: <html> < /> </html> ]]> Will be rendered as: < /> ]]> Depending on author style, blocks of code MAY be enclosed in a <figure> element, with a <figcaption> element that describes the block. For example, see . A code block wrapped in a figure. ASCII art is still preferred by some authors in preference to an image or SVG. The RFC Editor may decide to prefer SVG, or may decide to prohibit ASCII art in the future, depending on the needs of the community at the time of publishing. Until that time, to include ASCII art, wrap a <pre> element with class='ascii' in a <figure> along with a <figcaption>, as if the <pre> element were an Section 3.3.4 image. For example: \| original \| <+ \| \| \| nit \| edit v \| nit (no-op) +-----------+ \| \| \| canonical \| \| Sample ASCII art Packet format descriptions can be encoded as a <table> element wrapped in a <figure> along with a <figcaption>, as if the <pre> element were an image, as specified in Section . For consistent formatting, the <table> element should have class pdu. For example: Sample packet format [table describing the packet] Metadata for the document SHOULD be easily extractable from the document by tools that ordinarily process HTML. Typically, the class and id attributes can be used to query the document using CSS-style selectors. The metadata scheme SHOULD be designed such that the element name is not required in order to select a given piece of data. Instead, any element that can contain text can be used for a given class or id to be selected. The value of the data contained by the selected element(s) consists of the concatenation of all of the text from all of the child nodes of the selected element or elements, with each run of consecutive whitespace Unicode codepoints [codepoints with the White_Space property, such as U+0020 (SPACE), U+0009 (CHARACTER TABULATION), U+000A (LINE FEED), U+000C (FORM FEED), U+000D (CARRIAGE RETURN), U+00A0 (NON-BREAKING SPACE), and U+2029 (PARAGRAPH SEPARATOR)] compressed to a single U+0020 (SPACE). The metadata scheme MUST allow unambiguous selection. The id attribute is used to identify pieces of data that are guaranteed to be unique across the document. Any element with an id attribute can also be used as a fragment target in a URI by starting with the base URI of the document, then appending "#" (U+0023: NUMBER SIGN) and the value of the id attribute. In CSS, the element with a given id attribute value is selected by prepending the value with '#' (U+0023: NUMBER SIGN). For example, the following HTML in a document with the URI http://example.com/index.html: Important Text ]]> Can be targeted directly with the URL http://example.com/index.html#example, and the CSS selector #example. The class attribute is a catch-all tagging mechanism for everything in the document that might not be unique. Multiple classes may be defined on a single element by setting the class attribute to a space-separated list of classes. All of the elements with a given class name can be selected in CSS by prepending the class name with "." (U+002E: FULL STOP). Information about the document as a whole. The <div> element with id='document' SHOULD be the first child element of the HTML. For example: Network Working Group Standards Track J. Hildebrand Cisco Systems, Inc. More details for this format will be included in future drafts of this document. The title of the document MUST appear in an <h1> element, which SHOULD follow directly after the Document Information. The <h1> element MUST have an id attribute with value 'title'. For example: HTML RFC Format ]]> The abstract for the document MUST appear in a <div> element, which SHOULD follow directly after the Title. The <div> element MUST have an id attribute with value 'abstract'. The <div> element SHOULD contain an <h2> element containing the word Abstract, and MUST contain one or more <p> elements containing text that describes the document succinctly. For example: This document defines an HTML format... The IPR boilerplate for the document MUST appear in a <div> element, which SHOULD follow directly after the Abstract. The <div> element MUST have an id attribute with value 'ipr' and a CSS class of the name of the relevant IPR ruleset. The only valid values for the IPR ruleset class are trust200902, noModificationTrust200902, and noDerivativesTrust200902 at this time. The contents of the <div> element are to be set correctly for the given ruleset, based on guidance from the IETF trust. For example: Status of this Memo Copyright Notice This section will be augmented with normative text when an approach is decided upon. A quick example (as an existence proof) can be found in . Joe Hildebrand Cisco Systems, Inc. 1899 Wynkoop St, Suite 600 Denver, CO 80202 United States This draft itself is a good example of how to use the format. Please view-source. int main(int argc, char *argv) { printf("Hello, IETF\n"); return 0; } ]]> Include an image tag with class='sequence', where the alt; text is the WebSequenceDiagrams.com source for the diagram. Before publication, this approach will be replaced by something more well-specified and not requiring third-party software. A sample sequence diagram title Authentication Sequence Alice->Bob: Authentication Request note right of Bob: Bob thinks about it Bob->Alice: Authentication Response ]]> Augmented Backus-Naur Form is a way of describing formal syntax, described in RFC5234. Include ABNF (without extra indentation) in a <pre> element, with CSS class 'code' and "language-abnf". For example: label = top-level 4section-num top-level = section-num / appendix-let section-num = 1DIGIT "." appendix-let = 1CAP "." CAP = %x41-5A ; A-Z DIGIT = %x30-39 ; 0-9 ]]> Is rendered as: label = top-level 4section-num top-level = section-num / appendix-let section-num = 1DIGIT "." appendix-let = 1*CAP "." CAP = %x41-5A ; A-Z DIGIT = %x30-39 ; 0-9 Since RFCs are sometimes exchanged outside the normal Web sandboxing mechanism (e.g. rsync to a mirror) then loaded from a local file, more care must be taken with the HTML than is ordinary on the Web. In particular, the intent with the format is to forbid any embedded code such as JavaScript as well as all mechanisms that could be used to execute code outside of the browser such as plugins or non-static media (such as video). This section collects all of the elements that are allowed in the HTML RFC format. Each element is listed with a set of allowed attributes, and a list of the parent elements in which the element may be placed. The attributes class, id, and lang are allowed on all elements. All other elements, attributes, and nesting approaches MUST NOT be used. Element Attributes Parents a href, title address, div, figcaption, h2, h3, h4, h5, li, p, span, td address div blockquote figure html br td, th code blockquote, li, p, td div address, , div, li em p, span figcaption figure figure div h1 h2 div h3 div h4 div h5 div head html html img alt;, height, src, width figure li 1, 1.0, 1.1, 10, 10646-1, 16, 2, 2026, 2026., 206, 2119., 2418., 2739., 3.2, 329, 3978, 4, 4748, 495, 617, 79, a, abbrev, abnf, abnf., about, additional, all, alpha, also, alt;o, among, an, analyzer, and, any, applications, are, as, at, audio, augmented, authors, available, backus-naur, balances, bcp, be, been, beginning, benefit, best, between, bnf, both, box, but, by, called, can, capitalized., cases, channel., character, characteristic, checking, chromaticity, color, common, communities, community, compactness, compatibility, compatible, concerning, constraints, contributions, contributors, core, coyote, creation, current, data, data-xml, day, define, defines, definitions, delivery, depths, described, describes, designed, desirable, details, detection, developed, development, differences, discussion, display, document, document:, documents, documents., email, encoding, encodings, encompasses, ensure, entities, errors., exchanging, extensible, extensions, file, follow, for, force, form, formal, format, formatted, from, full, fullname, fully, gamma, gif, graphics, groups, guidelines, has, have, heterogeneous, hill, holders., how, identifying, iec, ietf, ietf., image, images, images., improved, in, including, incorporate, indicate, individuals, information, initials, integrity, intellectual, intended, interchange., internet, interpreted, involve, ipr, is, iso, it, key, language, large, led, legitimate, level, lexical, made, many, markup, mass., matching, may, media, meet., memo, memo., modified, month, most, much, mult;iple, must, name, naming, near, need, network, not, note, object, object., objectives, obsoletes, octets, of, often, on, online, option., optional, originally, other, over, palo, paragraph, parsers, participants, patent, patent-free, permitting, phrase, plus, png, policies, popular, possible., power., practices, preserving, private, progressive, property, proposal, proposed, provide, provides, providing, public, range, ranges., raster, reasonable, recommended, reference, register, related, relative, rely, replace, replacement, replaces, representational, representing, requests, required, requirement, requirements, research, respecting, retain, revision, rfc, rfc2083, rfc2119, rfc2397, rfc3629, rfc3979, rfc5234, rfc5378, rfc5646, rfc6350, rfcs, rights, rule, s, sample, section, semantics, set, several, shall, sheets, should, signify, simple, simplicity, so, software, specification, specification., specifications, specifications., specifications:, specifies, standard, standards, storage, store, streamable, structured, style, such, suggestions, supplies, surname, syntax, syntax., systems., tags, target, technical, technologies, technology, telephone, that, the, their, these, they, this, tiff., to, track, transformation, transmission, transparent, truecolor, type, universal, updates, url, us-ascii, use, used, used., user-defined, uses, utf-8, value, values, variety, vcard, vector, version, viewing, well, well-compressed, were, where, which, while, who, wide, with, within, words, work, worked, working, world, writing, year ol, ul meta charset, content, name head ol div p div, li, td pre div, figure span address, div, li, p, span strong p, pre svg height, viewbox, width figure table div, figure t table td colspan tr th colspan tr thead table title head tr t, thead ul div, li, td, ul Although the author can add class information to any element, the following class names have special meaning in an HTML RFC: Class Meaning adr appendix ascii author authors code company country-name date docName edge email expires family-name figref fn given-name graph hidden identifiers initial initials invalid languag-hmtl language-abnf language-c language-html locality n nickname node note org pdu postal-code published ref reflinks region rfc2119 rfceditor-remove section sectref self-ref sequence series series-info status street-address surname title toc todo trust200902 vcard version workgroup Although the author can add an id attribute to any element, the following id values SHOULD NOT be used except for the role defined for each below: ID Meaning document Data about the document, including dates, name, version, etc. title The title of the document, usually applied to a <h1> element. abstract The abstract for the document, usually applied to a <div> element that contains a heading and paragraphs of text. ipr The Intellectual Property Rights associated with the document. The class attribute of the same element will contain a machine-readable IPR statement name from this list: trust200902: This is appropriate for most drafts, where the entire content of the draft is written by the draft's authors, or all authors of other material have given explicit permission to use their work. noModificationTrust200902: This is appropriate for drafts where the authors wish to place the additional condition that if the draft is published as an RFC, it must have no changes other than formatting. An example might be a document published by another organization that permits copying but not modification. noDerivativesTrust200902: This is appropriate for drafts not intended to be published as RFCs. pre5378Trust200902: This is appropriate for drafts that include material submitted to the IETF prior to RFC 5378 (10 Nov 2008), where the authors of that material have not given explicit permission to use their work in this draft. An example might be a draft using material from an RFC whose author has died or cannot be located, or who thinks your draft is stupid. The element with this id will contain all of the IPR and status boilerplate text Note: an IANA registry may be required for this attribute in the future. venue The venue for discussion. Inside the element tagged with this id will be one or more <a> elements that describe the discussion venue for Internet-Drafts. toc The Table of Contents references The section containing bibliographical data, including sections for normative and informative references. normative The section containing normative document references. informative The section containing informative document references. authors The section containing data about the authors of the document. security The section containing the Security Considerations for the document. iana The section containing the IANA Considerations for the document. acknowledgments The section containing the author's acknowledgments. The author gratefully acknowledges the contributions of: Patrick Linskey &RFC2119; &W3C.CR-html5-20130806; &W3C.REC-CSS2-20110607; &I-D.brownlee-svg-rfc; &I-D.iab-styleguide; &I-D.hoffman-xml2rfc;
Friday, May 1, 2009 10 Amazing Facts & 1 Naked truth about Water – Very interesting, Very useful. 1)Approximately 85% of your brain, 80% of your blood and 70% of your muscle is water. 2)The water you drink has been circling around in the water cycle for millions of years - that means the same water exists now as when dinosaurs were on the Earth 3)97% of the worlds water is salty or otherwise undrinkable, 2% is stored in glaciers and the ice caps, the remaining 1% is left for humanity's needs. 4)In the time it took you to read these first three facts another child has just died in the developing country from unsafe drinking water. 5)Water expands by 9% when it freezes, making it less dense, which is why ice floats on water. 6)You could live for a month without food, but you would be dead after a week without water. 7)According to NASA the natural rotation of the Earth has been altered slightly by some 10 trillion tons of water stored in reservoirs over the past 40 years. 8)If a person aboard a ship is suffering from thirst, he may be tempted to drink ocean water. But ocean water is salt water, and salt water won't help put water in the body's cells — instead it will help the cells lose the water they already have. This happens because of a natural process called osmosis, which makes liquids pass through the thin walls of body cells. Normally, the water that reaches the cells is lighter than the salty water inside the cells, so it passes through the cell walls and enters the cells. But salt water is heavier than" the water inside the cells. When it reaches the cells, the water inside the cells passes through the walls to join the salt water outside the cells. So a person who drinks salt water actually makes his body more thirsty!. A famous line of poetry reads: Water, water, everywhere, nor any drop to drink." And that's exactly what happens when a sailor is suffering from thirst — there's water everywhere, but he can't drink a drop of it! 9)There is enough water in the atmosphere, that if it all fell as rain at the same time, it would cover the entire surface of the Earth with 2.5 cm (1 in) of water. 10)If the amount of water in your body is reduced by just 1%, you'll feel thirsty. If it's reduced by 10%, you'll die. You have read the 10 facts but due you know 1 naked truth India also falls in the fourth fact of the above, Are you sure that you are drinking Pure water . Now see these pics : 1) A Snapshot taken by Daily thanthi Reporter (A Daily Tamil leading News paper in India, Tamil Nadu) shows CocoRoach in Packaged Drinking Water. 2) Packaged Water Cans Stored Near Drainage Point . 3) A Worker Unloading Drinking water cans after finding Tadpoles in water. 4) Drinking Water Cans stored in Ugly Dangerous Junkyards. 5) A photo taken from a water filling unit showing EarthWorms in Packed Drinking water. 6) A Pic showing Labour filling unprocessed water directly from tap(Mixing processed and unprocessed water) to meet the Market demand for Drinking water. 7) A Stunning Picture showing a Gecko ( A small wall creeping creature of Lizard family) in Packed water can ready for Despatch. 8) Fully Contaminated Drinking water poured in a bucket in a lab - Report shows the water is full of dreadful disease causing bacteria and viruses. Sample water E-coli -seen in Microscope Salmonella-Under Microscope 9) A News in THE HINDU (India's National Newspaper) Dated : Sunday, August 12, 2007 Says 227 samples of branded packaged water analysed and found contaminated with E. coli and coliform bacteria(Usually found in Sewage). 10) Due you know that GOOGLE pulls more than 2,57,000 Results for : Deaths due to contaminated Drinking water, Some samples are here : A. B. Do you Know that by today’s technology you can set up your own Mini Drinking Water Plant at a very reasonable cost (cost per litre-Damn cheaper than any Can, bubble top or bottled water), just click the link below to be sure you drink pure . For Camparison chart showing your SAVINGS in setting up the Mini- Reverse Osmosis plant click the link below : *Water Elixir of life* Issued in Public Interest from Water Sparks A unit of Venus Createch Solutions. N. B :By the time you read this if you feel thirsty you suffer from Selective Schizophrenic De-Hydration.
Aeroseal - A patented sealing process; the most effective, affordable, and viable method of sealing the central heating and cooling ductwork in your home. AFUE - Annual Fuel Utilization Efficiency, a rating that reflects the efficiency of a gas furnace in converting fuel to energy. A rating of 80 means that approximately 80 percent of the fuel is utilized to provide warmth to your home, while the remaining 10 percent escapes as exhaust. BTU - British Thermal Unit. In scientific terms, it represents the amount of energy required to raise one pound of water one degree Fahrenheit. One BTU is the equivalent of the heat given off by a single wooden kitchen match. For your home, it represents the measure of heat given off when fuel is burned for heating or the measure of heat extracted from your home for cooling. CFM - Cubic feet per minute, a standard of airflow measurement. A typical system produces 400 CFM per ton of air conditioning. Capacity - The output or producing capability of a piece of cooling or heating equipment. Cooling and heating capacity are normally referred to in BTUs. Compressor - The heart of an air conditioning or heat pump system. It is part of the outdoor unit that pumps refrigerant. The compressor maintains adequate pressure to cause refrigerant to flow in sufficient quantities in order to meet the cooling requirements of the system. Condenser Coil or Outdoor Coil - Located in the outdoor unit, the coil dissipates heat from the refrigerant, changing the refrigerant from vapor to liquid. Downflow Furnace - A furnace that pulls in return air from the top and expels warm air at the bottom. Ductwork - Pipes or channels that carry air throughout your home. Evaporator Coil - The coil that is inside your house in a split system. In the evaporator, refrigerant evaporates and absorbs heat from air passed over the coil. Heat Exchanger - A device for the transfer of heat energy from the source to the conveying medium. Horizontal Furnace - A furnace that lies on its side, pulling in return air from one side and expelling warm air from the other. Humidifier - A device that injects water vapor into heated air as the air is expelled from the furnace. Humidity - The amount of moisture in the air. Air conditioners remove moisture for added comfort. HSPF - Heating Seasonal Performance Factor. Refers to the efficiency of the heating mode of heat pumps over an entire heating season. The higher the number, the more efficient the unit. HVAC - Heating, ventilation and air conditioning. ICM - Integrally Controlled Motor. A specially engineered, variable-speed motor used in top-of-the-line indoor units. ICM motors are more than 90 percent efficient versus 60 percent efficiency for conventional motors. Continuous comfort, quiet operation and ultimate system efficiency are the benefits of the indoor products graced with the ICM motor. Packaged System - A piece of air conditioning and heating equipment in which all components are located in one cabinet. Used occasionally in residential applications, the packaged unit is installed either beside or on top of the home. Refrigerant - A substance that produces a refrigerating effect while expanding or vaporizing. Refrigerant Lines - Set of two copper lines connecting the outdoor unit and the indoor unit. SEER - Seasonal Energy Efficiency Ratio, a rating that measures the cooling efficiency of a heat pump or air conditioner. The higher the number, the more efficient the unit. Split System - Refers to a comfort system configuration consisting of components in two locations. Common examples include an outside unit, such as an air conditioner, and an indoor unit, such as a furnace and coil. Switchover Valve - A device in a heat pump that reverses the flow of refrigerant as the system is switched from cooling to heating. Also called a reversing valve or four-way valve. Thermostat - A temperature control device, typically found on a wall inside the home. It consists of a series of sensors and relays that monitor and control the functions of a heating and cooling system. Programmable thermostats allow you to program different levels of comfort for different times of the day. Upflow Furnace Zoning - A method of dividing a home into zones, which enables you to control the amount of comfort provided to each.
The Forbidden City is in the heart of Beijing In the heart of Beijing lies the largest palace in the world, The Forbidden City. For five hundred years, it served as the home of the almighty Emperors of China along with their wives, concubines, and entourages of tens of thousands of eunuchs and civil servants. But the Forbidden City is more than an imperial residence; it is the center of the universe, a unique complex of structures revealing a hierarchy of power both imperial and divine. Many of the largest building blocks of the Forbidden City came from a quarry about 43 miles (70 kilometers) away from the site. People in China had been using the spoked wheel since about 1500 B.C., so it was commonly thought that such colossal stones would’ve been transported on wheels, not by something like a sled. Over the hundreds of years since it was first built, most parts of the Forbidden City have been rebuilt many times. In modern times, The Forbidden City has been renamed the Palace Museum and is open to the general public. The Forbidden City is also a treasure trove of movable cultural relics; it is the seat of the National Palace Museum. It has over 1.8 million movable cultural relics, including more than 1.68 million pieces of precious relics. In 2012, the highest single-day passenger flow volume of Forbidden City exceeded 180,000 people, and annual passenger flow volume exceed 15 million people. It can be regarded as the busiest museum in the world.
Neanderthals: Support for Evolution? Dear hijas, Are Neanderthals support for evolution? For many years they were proclaimed as such. The truth of the matter however, bears some interesting details. The bones of what would be labeled ‘Neanderthal’ were first discovered in 1856 from the quarrying of limestone in a valley about 10 miles east of Düsseldorf, Germany. The valley was named after Joachem Neander, an evangelical (Lutheran) theologian and school rector who lived in the late 1600’s. He loved to take walks in this valley, and as he strolled along he would compose hymns and sing them in praise to God. He was there so often, the valley became known as the Neanderthal–the Neander Valley (tal or thal in Old German means “valley”, the h being silent). It was a couple hundred years later that the valley was owned by a Herr von Beckersdorf, and as owner of the valley his workmen quarrying the limestone found a cave. The cave was known as Feldhofer Grotto, and it was there that a skullcap, some ribs, part of the pelvis, and some limb bones were discovered. These bones were taken and analyzed by several different individuals in the ensuing years , and it was William King, professor of anatomy at Queen’s College, Galway, Ireland, who reading an evolutionary history into the bones, gave them their first scientific name, Homo neanderthalensis. This is significant, because King believed the bones represented a person so primitive that he didn’t even belong to the same species as modern humans. neanderthal range map More fossils were found in later years in different places, and today, because of the richness of the Neanderthal fossil record we have a general idea of what they looked like. In fact, there is a distinct Neanderthal morphology: large cranial capacity; skull shape low, broad, and elongated; rear of the skull pointed with a bun; large heavy browridges; low forehead, etc. They do differ somewhat from a typical modern human, but they also overlap. What we come to find out is that they should have never been placed in a separate taxonomic status. They are completely human, descended from Adam and Eve as our first parents, just like we are. The same can be said about Cro-Magnon man. Neanderthals were ‘otherized’, but they shouldn’t have been. They buried their dead with distinct mortuary practice, butchered and quartered their prey animals in the hunt for food, used stone and bone tools (purposeful chipping at stone like a sculptor would), created rock art and musical instruments from bone, and have a record of tender care for debilitated individuals. In life and death they were so very human. What must be remembered, mis hijas, is that ever since Darwin, evolutionists have sought to discover the path by which humans arose from their alleged primate ancestors. Coupled with this is the attempt at an explanation of the path that our own species, Homo sapiens, arose. Neanderthals were supposed to be on that path. Today, there are a couple of views in evolutionary circles about the Neanderthals. Evolutionists have changed their story and now mostly believe that they were an isolated side branch of the family tree. But what about the “dating”, you might ask? “Neanderthals are supposed to be several hundred thousand years old, becoming extinct some 30,000-35,000 years ago”, you might say. “What about that, nuestros padre?” Ah, yes, the “dating” game. Stay tuned mis hijas. Vaya con Dios mis hijas, Dear ol’ Dad Frauds in the Rise of the Apemen Dear hijas, Have you ever heard of Piltdown Man? Piltdown Man Perhaps you studied him at university in your anthropology classes or in your high school biology textbooks in the sections on evolution. Turns out he was a hoax, a fraud. Perpetuated for over 40 years as a ‘missing link’ in the human evolutionary chain it was a very successful hoax indeed; a combination of ape and human bones labeled Eoanthropus dawsoni after Charles Dawson the medical doctor and amateur paleontologist who in 1912 discovered a mandible (lower jaw) and part of a skull in a gravel pit in Piltdown, England. Piltdown man 1912 Here’s the story. The jawbone was apelike but had teeth that showed similar wear to that of humans. The skull, on the other hand, was very humanlike. The two specimens were combined, together with other pieces of skull, and later a canine tooth in the Piltdown gravel pit and surrounding area, and this combination was called ‘Dawn Man’. He was calculated to be 500, 000 years old. Turns out the whole thing was an elaborate hoax. The skull was indeed human (but only about 500 years old), the jawbone was that of an orangutan whose teeth had been obviously filed down to crudely resemble the human wear pattern, and the canine tooth discovered 3 months later had been filed down so far it had exposed the pulp chamber, which was then filled in to hide the mischief. The fraud was likely committed by only one or two persons, (a dozen different individuals have been named as the likely culprit or culprits) whether Dawson or someone else, nobody knows, but the fascinating thing is that the hoax lasted for over 40 years! It was only in 1982 that the mandible and canine tooth were determined conclusively, by collagen reactions, to be those of an orangutan. The literature produced on Piltdown Man was huge. Perhaps as many as 500 doctoral dissertations were written on Piltdown. Thinking they were writing and perhaps seeing actual fossils of their evolutionary ancestors ‘proving’ the human evolutionary chain, they were really writing and looking at a hoax. Sir Arthur Keith, perhaps one of the greatest anatomists of the twentieth century, and writing about Piltdown more than anyone (see his The Antiquity of Man), was completely conned. Keith had put his faith in Piltdown. At 86 years old he was at home when he was told that the fossil he had trusted in for more than 40 years was a fraud. His Autobiography tells of his attending evangelistic meetings and seeing students make a public profession of faith in Jesus Christ, and often feeling ‘on the verge of conversion.’ Sadly, he had rejected the gospel in large part to faith in a phony fossil and the human evolutionary chain it supposedly was part of. The widespread myth, mis hijas, is that science is a superior worldview because of its self-correcting nature. In reality, it’s not all that self-correcting in any meaningful way as the Piltdown Hoax has demonstrated. Science as a tool, practiced in light of God’s revelation in Scripture, is very powerful to explain the means that our Creator upholds and sustains His Creation; science as practiced by unregenerate men and women looking to explain their origins apart from God, is fraught with hoaxes, frauds, and errors. As always, I remain, Dear ol’ Dad Vaya con Dios mis hijas Rise of the Apemen: The Australopithecines Lucy She's No Lady Dear hijas, The supposed human evolutionary chain starts with the fossil apes. Evolutionary paleoanthropologists in accordance with their evolutionary assumptions begin with the presupposition that man has, in fact, evolved from apes. The only question paramount in their thinking is “From which apes did man evolve?” They are looking for any anatomical feature that looks ‘intermediate’ between that of apes and that of man in the fossil record. Fossil apes having such features are declared to be ancestral to man and are called hominids. Any similarity between what is found in the ground as a fossilized extinct ape and the bones of living men, are then proclaimed as “proof” of our ape ancestry. ape to man 2 But what is the evidence? Is there an unbroken and identifiable progression of development in the fossil record from the australopithecines like “Lucy” through Homo habilis through Homo erectus through early Homo sapiens (and/or Neanderthals) to anatomically modern Homo sapiens? Evolutionists like to think so, but what are we really looking at? In the case of “Lucy”, we’re looking at an extinct ape, most likely an extinct chimpanzee. There is nothing in Lucy’s bones that indicate she is a transition between apes and humans. She has an obvious ape skull, obvious ape pelvis, and obvious ape hands and feet. Her long arms are common to knuckle-walkers with locking wrists. Her feet, like her hands, are long, curved, and heavily muscled, much like those of living tree-dwelling primates. If humans evolved from a chimp-like animal such as “Lucy”, it is obvious that we had to pass through a number of stages on this long evolutionary journey. We are classified as Homo sapiens. Lucy is classified as Australopithecus afarensis. Not only are we said to come from some form that was not our species, but we are said to come from some form that was not even our genus. Theoretically, the progression (from Australopithecus afarensis or Australopithecus africanus through to modern Homo sapiens) looks tidy, but it is anything but. Lucy is dated by evolutionists at 3 million years. Homo habilis at 2 to 1.5 million years. Homo erectus at 1.6 to 0.4 million years, with early Homo sapiens and anatomically modern Homo sapiens in the last hundred thousand years or so. This sequencing implies genus to species and species to species development that could take up to 1 million years between the classifications. Since the evolution of one genus to species, or one species to another would require many favorable genetic mutations (the existence of a ‘favorable’ mutation has yet to be conclusively demonstrated), it becomes obvious that evolution requires vast periods of time even on the species level and even “if” several advantageous genes were being dispersed throughout the population at the same time. If evolution were true, we have the right to expect that the hominid fossil record would faithfully follow the time and morphology sequence set forth by evolutionists, don’t we? We are supposed to have evolved from something very similar to Lucy, something very dissimilar to what we are today, so we have the right to expect that very modern-looking fossils would not embarrass the evolutionist by showing up in ancient times and that primitive or archaic fossils would not embarrass the evolutionist by showing up in modern times. We also have the right to expect that if a significant number of fossils are so rude to show up at the wrong time, the evolutionist would be honest enough to admit that his theory of human evolution has been falsified, correct? In actuality, many fossils have been that rude, and evolutionists have been less than intellectually honest. Vaya con Dios mis hijas, Dear ol’ Dad The Rise of the Apemen: Support for Evolution? ape to man Dear hijas, People are fascinated by the story of their origins. We want to know where we came from, how we got to be who we are. On the one hand is the evolution myth, that humans find their origin in an unidentified apelike creature that lived millions of years ago and this from tracing a lineage back to a single-celled organism that allegedly lived billions of years ago. On the other hand is the Creator God Himself, who has revealed to us in propositional form (the Scriptures) that He created everything that exists, out of nothing (ex nihilo), including man, and that man was made in the very image of God. This propositional revelation tells us that we are not apes who have evolved over time, but a special creation of the Creator, the altogether grand other, the infinite, omnipotent, and sovereign Elohim. A man’s own nature tells him that this God exists, and he is held accountable for accepting or rejecting this knowledge within and about him. Does what you believe about who you are (your origins) influence the way you live and view those around you? Do you think that if you view yourself as nothing more than an intelligent ape, kicked up slowly over millions of years from the primordial pond scum, that you might act like an ape (animal) in daily living? That this belief (that we are no more than an intelligent animal), might express itself in lawless animal behavior? (An interesting side-note is what the Nazi’s did based on this belief, but we’ll save that for later). For years we’ve been taught that human evolution is fact and that the human evolutionary chain contains “links” of fossil skulls and fragments of bone that “prove” our progression from a supposed apelike creature several million years ago. We’ve heard accounts that “Lucy” and “Ida”, and others, are the missing links, now found, that show how this is true. We’ve watched TV documentaries like the BBC Walking with Cavemen (2003), or National Geographic’s The Journey of Man: A Genetic Odyssey (2003), or The Mystery of Us (2005). But what is the real evidence for human evolution? What evidence are we not hearing? Are these purported claims of presumed ape ancestry “proof” of evolution? Far from it, and what we will see as we examine the details is that anthropologists are either making man out of a monkey, or making monkeys out of men. The evidence will point to the conclusion that man is a unique creation of God, and made in His image. Vaya con Dios mis hijas, Dear ol’ Dad Short and Long-Period Comets: Support for Evolution? Dear hijas, What do you know about comets? Dirty snowballs or hairy stars, perhaps? They have been observed for millennia and are often considered quite mysterious. Wikipedia describes them as: an icy small Solar System body (SSSB) that, when close enough to the Sun, displays a visible coma (a thin, fuzzy, temporary atmosphere) and sometimes also a tail. These phenomena are both due to the effects of solar radiation and the solar wind upon the nucleus of the comet. Comet nuclei range from a few hundred meters to tens of kilometers across and are composed of loose collections of ice, dust, and small rocky particles. Comets have been observed since ancient times. What do you know about their orbital period; the time it takes them to make one revolution around the sun? Astronomers put this orbital period into two categories: short-period comets (less than 200 years), and long-period comets (longer than 200 years). Halley’s Comet, for example, has an orbital period of 75-76 years. It was last seen in 1986 and won’t return again until 2061 or 2062. Halley's comet Each time a comet passes the Sun, they lose some of their mass. We can observe that this is happening in the ‘coma’ and ‘tail’ of the comets. Since comets consist of dust and ‘ice’, and this ice is not just frozen water, but frozen ammonia, methane and CO2, some of the ‘ice’ evaporates at it makes this close pass. This observed loss rate combined with a comet’s maximum orbital period means comets could not have been orbiting the sun for the supposed billions of years that evolution requires. Remember, evolution is a three-stranded cord: cosmological, geological, and biological. Or think of a three-legged stool. You knock one of the legs out, the stool falls over. Biological evolution is seriously eroded , and indeed, a non-starter, if cosmological or geological evidences within the universe indicate that it can’t possibly be billions and millions of years old. “But wait, we’re missing something here,” you might say. “You haven’t given us all the information.” “What if both short and long-period comets have a natural source that is consistent with billions of years?” Ah, yes, that’s a good question. Comets are assumed to be primordial. They are assumed to be leftovers from the Big Bang 13.8 billion years ago, and specifically to the formation of our solar system 4.6 billion years ago. Astronomers have long seen the continued existence of comets today as a problem. They should have all burned out by now. So, what is an evolutionist to do? She doesn’t want any of the legs of her stool to fall over, so she postulates an ad-hoc, unobserved, and theoretical source of those comets we see today from the Oort Cloud. Jan Oort, a Dutch astronomer, proposed a large spherical cloud of comet nuclei that formed early in the history of the Solar System. This Oort cloud is supposed to be at a large distance from the Sun, putting the comet nuclei too far away to be observed. Theoretically, the Solar System is 4.6 billion years old, thus comets formed at that time and currently residing in this Oort Cloud are supposedly and occasionally knocked and bumped by gravitational effects of other stars into an orbit that takes them around the Sun. But here’s the problem; this Oort Cloud is only theoretical. It’s never been observed. It has no empirical observational proof of its very existence and is completely ad-hoc (for a specific purpose only; lacking justification). “But what about the Kuiper Belt”, you say. “Astronomers have discovered objects, called Kuiper Belt Objects (KBO’s) beyond the orbits of Neptune and Pluto, and this could be the source of comets consistent with a billions of years old universe.” Well, yes, evolutionary astronomers, who assume the solar system is billions of years old, must propose a ‘source’ that will supply new comets as old ones are destroyed. The Kuiper Belt is one such proposed source for short-period comets. But there are a couple of things to keep in mind. One, an estimated billion icy cores in the Kuiper Belt would be needed to replenish the solar system’s supply, whereas only ‘several hundred’ KBO’s have actually been observed, and two, the KBO’s that have been observed have nuclei that are far larger than comet nuclei. This calls into question whether these KBO’s are actual precursors of short-period comets at all. Bottom line, mis hijas, comets are powerful testimony to a universe that is not billions and millions of years old. They can’t possibly be losing material for the supposed billions and millions of years that the evolutionary timeframe requires, and the supposed sources are either ad-hoc, or seriously in question. Be sure to tell your Momma and I’s grandkids and great- grandkids in 2061 when you see Halley’s comet again what a wondrous Creator we serve, and what amazing testimony a comet truly is! For further study, please see here:, and As always, I remain, Dear ol’ Dad Vaya con Dios mis hijas! Bioluminescence: Support for Evolution? bioluminescent marine animals Dear hijas, Though research on bioluminescence recently garnered a Nobel Prize, the phenomenon is still poorly understood, according to a new paper reviewing recent discoveries about bioluminescence’s benefits, its evolution, and the surprising diversity of ways plants and animals generate glowing substances. The above quote is from a National Geographic article on bioluminescence. Notice the phrase “the phenomenon is still poorly understood”. What? I thought evolution was supposed to be able to explain it all. How did an organism ‘evolve’ the ability to produce its own light? Answer: scientists poorly understand it. What an understatement. 2 Darwin Tree of Life The reason they ‘poorly understand it’, and what they don’t tell you, is that they can’t make their supposed ‘tree of life’ work very well from a supposed common ancestor who first evolved bioluminescence and then supposedly should have passed it along. They assume a tree of life and assume there should be a natural pattern that can be detected, but what they find is that bioluminescence is scattered haphazardly among dozens of totally different life forms. The list of bioluminescent creatures includes bacteria, fungi, jellyfish, sea worms, sea slugs, clams, squid, roundworms, beetles, isopods (an order of crustacean that includes woodlice and pillbugs), ostracods (a class of crustacean sometimes known as seed shrimp), copepods (small crustaceans found in the sea and nearly every freshwater habitat), shrimp, centipedes, millipedes, sea stars, crinoids (sometimes called ‘sea lilies’), fish, sharks, tunicates (marine filter feeders), and many other less familiar living things. Evolutionists organize all of these basic forms into the preconceived tree of life, yet admit that: The distribution of bioluminescence across the major taxonomic groups does not appear to follow any obvious phylogenetic or oceanographic constraint. (Haddock, S.H.D., M.A. Moline, and J.F. Case. 2010. Bioluminescence in the Sea. Annual Review of Marine Science. 2 (2010): 443-493) There is a huge mismatch between theory and reality here. They must cling to the unlikely conclusion that bioluminescence has evolved 40-50 times among extant organisms. A question that immediately comes to mind is “If bioluminescence evolved so often in the past, then why is it not evolving today?” What better explanation, in remembering the Creator-creature distinction, that it was the Creator who built bioluminescence into just those creatures He wished. It is Christ Himself in His work of creation (John 1:3, Colossians 1:16) who should get the credit, and not the non-directed blind chance of evolution. For further study please see here: Vaya con Dios mis hijas, Dear ol’ Dad C-14 Decay: Support for Evolution? Dear hijas, Take C-14 for example. C-14 or radiocarbon is a perfect example of a physical aspect of our universe that is scientifically determined and analyzed. From your chemistry classes you remember that the element carbon comes in three isotopes: C-12, C-13, and C-14. The carbon atom has 6 protons, but it is the number of neutrons that determine the isotope. C-12 then has 6 protons and 6 neutrons, C-13 has 6 protons and 7 neutrons, C-14 has 6 protons and 8 neutrons. During life both plants and animals, including you and I, are gaining and losing C-14; plants chiefly through CO2 in the air, animals chiefly through eating the plants. When an organism dies, it no longer gains C-14, but only loses it. The production of C-14 in the universe follows an ordered principle or law whereby cosmic rays trigger a process in the atmosphere that changes atmospheric nitrogen into C-14. This carbon in the atmosphere mostly becomes attached to oxygen formed carbon dioxide (CO2) . The CO2 includes the stable, common isotope C-12 and a very tiny amount of the unstable C-14; only about 1 in a trillion carbon atoms is a C-14 atom. Carbon dioxide is then ingested by plants and animals and is incorporated into their biological structures, and it stops at the time of death of the organism. It can be seen in the chart below: C-14 production Unlike C-12 and C-13, C-14 is unstable and eventually decays back into nitrogen. Once a plant or organism dies it no longer takes in new carbon, and the amount of C-14 in the tissue of the plant or animal begins to decrease. This decay rate can be measured as the ratio of the isotopes C14/C12. It is expressed in terms of a half-life, which is the amount of time for half of any given sample of C-14 to decay back into nitrogen. Thus, after one half-life, 50% of the original C-14 atoms will remain in the sample. After two half-lives, 25% of the original C-14 atoms will remain, three half-lives 12.5%, 4 half-lives 6.25%, and so on. The scientifically measured half-life today of C-14 is 5730 years. So how does this support evolution and its millions and millions of years? It doesn’t; C-14 decay actually supports just the opposite. It supports a relatively young (thousands, not billions and millions) age for the dead organisms found in the rock layers of the earth, thus eliminating the vast long ages required for evolution to even happen. We can see this in a number of examples. We must remember the half-life, right? C-14 half-life = 5730 years. After 18 half-lives, or a little more than 100,000 years, the percentage of C14/C12 in any given sample is undetectable by our most sensitive scientific instruments. The implications here are huge! Since each half-life is 5730 years, this means that no C-14 at all would be detectable in a specimen that is older than 18 X 5730 = 103,140 years. But what if we did find C-14 in, let’s say, a dinosaur bone, or coal, or seashells? These are formerly living organisms. Dinosaurs supposedly went extinct 65 millions years ago. Coal is thought to be hundreds of millions of years old. Some seashells supposedly date back even further. Wouldn’t detectable C-14 in these specimens tell us these things couldn’t possibly be older than 100,000 years? It certainly suggests it, doesn’t it? But, not only that, what if we found detectable C-14 in something supposedly billions of years old? How could something supposedly billions of years old have any C-14 left? It shouldn’t, except that we do find detectable C-14 even in diamonds supposedly billions of years old. These examples throw the whole dating system upon which evolution is based into a futile exercise of whack-a-mole. The actual, detectable C-14 in specimens supposedly millions and billions of years old keeps popping up to disprove the old dates they’ve been given by the evolutionists. C-14 decay is a valuable tool in our arsenal, mis hijas, and is just one of many proofs to disembowel long evolutionary ages. For further study I encourage you to visit:,,, Vaya con Dios mis hijas, Dear ol’ Dad Evolution and Millions and Billions of Years: A three-stranded braid 1 Darwin's Tree of Life Dear hijas, We must remember in our discussions here, that Darwinian evolution and millions of years go together. Evolution, as it is defined today, would not be possible without the vast ages of time for slow and gradual step-by-step modification from one species to the next through many, many transitions; all happening by non-directed blind chance through death and struggle. Evolution and an old earth, or the necessity for an old earth, are two sides of the same coin. The biological side of the coin representing the millions and millions of year of biodiversity of life, and the geological side of the coin representing millions and millions, in fact ‘billions’, of years of earth development in the rocks. But we cannot forget the cosmological side of things, can we?. Think of a braid. When hair or rope is braided, it is common to take three sections and weave them together into one, isn’t it? This is exactly the picture we must think of when talking about evolution; a three-stranded braid or cord. One section of the braid is the cosmological side with it’s billions of years of star and planet formation, another section is the geological side with its billions of years of strata development in the rocks of the earth, the last section is the biological side with its millions of years of plant and animal development from lower to higher forms through mutation and natural selection, death and struggle. 3-ply braided rope So it is with an old universe (billions of years), an old earth (billions of years), and evolution (millions of years). Evolution needs an old earth. An old earth needs an old universe. They are inseparably linked. We must not forget this. If it turns out that the universe and earth are relatively young (thousands not billions of years), evolution as it is currently defined, would not be possible, and would fall dead on arrival; it would not have even been proferred let alone gained any traction in the minds of men. Whether speaking with a non-Christian, (or Christian who has accepted the claims of evolution; theistic evolutionist), we must remember the implicit acceptance of the millions and billions of years associated with an old universe and old earth behind the actual claims of the biological development of life on earth. It is critical that we not forget this. The evolutionary system of thought should always be thought of as a three-stranded braid or cord; cosmological, geological, and biological. Thus, in what is to follow in future posts, we will be dealing with not only the biological side of evolution, but its cosmological and geological sides as well. Vaya con Dios mis hijas, Dear ol’ Dad Did God Create or Evolutiate? Dear hijas, Your sister has suggested I start a series on creation vs. evolution; specifically the evidences from the natural world that show scientifically how evolution is a non-starter and can’t possibly be true. You’ll notice I coined an imaginary word in the title: evolutiate. For purposes of our discussion, I mean by this term, in contrast to create, that God used the process of evolution to bring about the universe and all of the biodiversity of life on this planet. Thus specifically, did God create ex nihilo (out of nothing) and de novo (afresh, from the beginning), or did He evolutiate stars and planets from a singularity and life from non-life over billions and millions of years? This last view is called theistic evolution. Darwin's Tree of Life Evolutionist D.J. Futuyma has clearly stated the issue here: Creation and evolution, between them, exhaust the possible explanations for the origin of living things. Organisms either appeared on the earth fully developed or they did not. If they did not, they must have developed from pre-existing species by some process of modification. If they did appear in a fully developed state, they must have been created by some omnipotent intelligence. (D. J. Futuyma, ‘Science on Trial’, Pantheon Books, New York, 1983). To move our discussion along, we must have a proper definition of evolution. Evolution as we will use it is the “descent with modification”, or “descent from a common ancestor” model. Starting with single-celled organisms, life supposedly followed a chain of development from marine invertebrates, to chordates, to fish, to early reptiles and amphibians, to various stages of mammals, and finally through various hominids to modern Homo sapiens. This enormous chain of development was brought about by time, chance, struggle, and death, without any help from a supernatural ‘god’ or an ‘intelligent designer’. Mutation and natural selection accomplished everything. We must remember that the evolutionary system arose and was elaborated on by those wishing to replace the Christian concept of special creation. Evolution is a replacement paradigm. It sought, in its original objective, to do away with Christianity once and for all. In this it is more of a philosophical system than a scientific one; a faith-based belief system with religious dogma like any other system of thought. Dr. Michael Ruse, one of evolution’s chief spokesmen has candidly admitted the following: Evolution is promoted by its practitioners as more than mere science. Evolution is promulgated as an ideology, a secular religion–a full-fledged alternative to Christianity, with meaning and morality. I am an ardent evolutionist and an ex-Christian, but I must admit that in this one complaint…the literalists are absolutely right. Evolution is a religion. This was true of evolution in the beginning, and it is true of evolution still today. (Michael Ruse, ‘Saving Darwin from the Darwinians’, National Post, May 13, 2000, as quoted in John Morris and Frank Sherwin, ‘The Fossil Record: Unearthing Nature’s History of Life’, Institute for Creation Research, Dallas, TX 2010) With that as backdrop to our discussion, we will compare and contrast the claims of evolution with that of a special creation ex nihilo by God. We will run the gamut of cosmological, geological, and biological claims by evolution that God has nothing to do with our existence, doesn’t even exist in and of Himself, and has no claims on how we live our lives here on earth. We will touch on the compromising and accommodationist positions of those within the Church whose views distort and twist the clear meaning of Scripture on its foundational doctrine of creation. We will see how God’s revelation to man on how He did it is paramount to the gospel we preach to fallen sinners. As always, I remain, Dear ol’ Dad Vaya con Dios mis hijas
Over-pronation, or flat feet, is a common biomechanical problem that occurs in the walking process when a person?s arch collapses upon weight bearing. This motion can cause extreme stress or inflammation on the plantar fascia, possibly causing severe discomfort and leading to other foot problems.Over Pronation It is important to identify the cause of overpronation in order to determine the best treatment methods to adopt. Not all treatments and preventative measures will work equally well for everyone, and there may be a little trial and error involved to get the best treatment. A trip to a podiatrist or a sports therapist will help you to establish the cause of overpronation, and they will be able to tell you the best treatments based on your specific degree of overpronation and the cause. Overpronation has many causes, with the most common reasons for excessive pronation listed, low arches, flexible flat feet, fallen arches, gait abnormalities, abnormal bone structure, abnormal musculature, bunions, corns and calluses. Because pronation is a twisting of the foot, all of the muscles and tendons which run from the leg and ankle into the foot will be twisted. In over-pronation, resulting laxity of the soft tissue structures of the foot and loosened joints cause the bones of the feet shift. When this occurs, the muscles which attach to these bones must also shift, or twist, in order to attach to these bones. The strongest and most important muscles that attach to our foot bones come from our lower leg. So, as these muscles course down the leg and across the ankle, they must twist to maintain their proper attachments in the foot. Injuries due to poor biomechanics and twisting of these muscles due to over-pronation include: shin splints, Achilles Tendonitis, generalized tendonitis, fatigue, muscle aches and pains, cramps, ankle sprains, and loss of muscular efficiency (reducing walking and running speed and endurance). Foot problems due to over-pronation include: bunions, heel spurs, plantar fasciitis, fallen and painful arches, hammer toes, and calluses. Non Surgical Treatment Overpronation is usually corrected with orthotics and/or strengthening exercises for the tibialis posterior. Massage treatment can relieve myofascial trigger points in the tibialis posterior, and other muscles, and address any resulting neuromuscular dysfunction in the leg or foot. Biomechanical correction of overpronation might require orthotics, neuromuscular reeducation, or gait retraining methods, as well. Stretching the gastrocnemius and soleus muscles will reduce hypertonicity in these muscles and also is essential for effective treatment. Because of impacts throughout the remainder of the body, the detrimental effects of overpronation should not be overlooked. Surgical Treatment Hyperpronation can only be properly corrected by internally stabilizing the ankle bone on the hindfoot bones. Several options are available. Extra-Osseous TaloTarsal Stabilization (EOTTS) There are two types of EOTTS procedures. Both are minimally invasive with no cutting or screwing into bone, and therefore have relatively short recovery times. Both are fully reversible should complications arise, such as intolerance to the correction or prolonged pain. However, the risks/benefits and potential candidates vary. Subtalar Arthroereisis. An implant is pushed into the foot to block the excessive motion of the ankle bone. Generally only used in pediatric patients and in combination with other procedures, such as tendon lengthening. Reported removal rates vary from 38% – 100%, depending on manufacturer. HyProCure Implant. A stent is placed into a naturally occurring space between the ankle bone and the heel bone/midfoot bone. The stent realigns the surfaces of the bones, allowing normal joint function. Generally tolerated in both pediatric and adult patients, with or without adjunct soft tissue procedures. Reported removal rates, published in scientific journals vary from 1%-6%.
How to Create an Accessible Garden Everyone knows that spending time in a garden renews body and mind. Whether you work in it, move through it, or sit it, a garden engages the senses and restores the soul. It’s easy to make a garden that anyone can enjoy. Accessible gardens are gardens for everyone; they eliminate barriers to enjoying gardens, providing spaces for people of all ages and abilities. Accessible Garden Paths Unusual Garden Pathway Garden paths that are level, smooth, and firm provide good traction, making being in the garden safer and easier for everyone. A grade of between five and eight percent is ideal. Direct routes through the garden make the space easier to navigate. To accommodate the turning radius of a wheelchair, one-way paths need to be at least five-foot wide and two-way paths at least seven feet wide. Rigid edging helps people who have difficulty walking and people with visual disabilities stay on the paths. Various paving materials have advantages and disadvantages. Consider who will use the paths and how much wear and tear they will get before deciding on materials. Asphalt is relatively inexpensive, but it absorbs heat, making it hot in summer. Paths made from wood are attractive, but slippery when wet. Brick paths are expensive to buy and install. Crushed gravel is readily available; it’s good for people in wheelchairs, but not for people on crutches. Neither wheelchairs nor crutches can be easily used on turf grass or woodchips. Concrete is expensive, but easy for most users. Raised Beds Raised beds For people who cannot get down to the garden, why not raise the garden up to them? Raised beds elevate the garden so gardeners can work without much bending or reaching. People who use wheelchairs can also tend the plants in raised beds. Gardens for the Senses Design your accessible garden for all the senses. Beautiful colours and shapes appeal to the eyes. Feeling textured and fuzzy leaves brings tactile enjoyment. The scents of herbs and flavours add the element of fragrance to the garden. Wind chimes and flowing water bring the pleasure of sound, and can help people with limited visibility orient themselves in the garden. Easy Watering Dragging hoses around and filling watering cans can discourage even the most avid gardeners. To make watering easy install soaker hoses or drip irrigation in garden plots or raised beds and leave them in place. Vertical Gardens Colourful Vertical Garden Gardens that grow up are easy to enjoy, tend, and harvest. Vines such as sweet peas, clematis, and morning glory present flowers at different levels. Crop plants like peas and pole beans are natural climbers, while tomatoes, cucumbers, and squash need only a little encouragement to climb up poles or trellises. Tools to Use Tools with long or retractable handles make it easier to reach across garden beds without stretching or bending. Gardening tools with large diameter handles are easier to hold onto without straining muscles and joints. When you make a garden accessible, everyone can enjoy it. Image Credits: Image 1 , Image 2 , Image 3 , Image 4 Please Post Your Comments & Reviews We'd love to hear from you. Your name is required. Your comment is required. Waterproof Cushions
5 Facts About Ticks And Fleas That You Should Know Email to Your Friends No matter how many times you give your pets a bath or how hard you try and protect them from parasites, fleas and ticks somehow manage to find their way onto their skin. Your pet’s skin is the perfect place for pests to thrive because their fur makes the environment warm and their blood is like an all-you-can-eat buffet! When fleas and ticks feed on your pet’s blood, not only does it cause severe itching but also infections, allergies, and diseases. Ticks and fleas are common during warm months, but you should take steps to protect your furry friend throughout the year. These pests are quite dangerous and here are a few things you should know about them. 1. Fleas And Ticks Can Cause Anemia A female flea is an egg-producing machine. It can lay up to 20 eggs a day and out of those eggs, half will be female. At this rate, by the end of 60 days, you will have around 20,000 fleas in your pet’s fur. As for ticks, a female tick can lay up to several thousand eggs at a time. And each tick can drink up to 20 times its body weight. When all these pests constantly drink your pet’s blood, it causes immense blood loss, resulting in anemia. If your pet constantly scratches itself and is not as active as it used to be, you can check its fur for signs of pests such as red rashes, black specks which are droppings, or white specks which are eggs. 2. Fleas And Ticks Infect Humans Too Just because you don’t have fur, does not mean that you are safe from fleas and ticks. Fleas can jump 110 times their length, meaning that they can easily jump onto your skin. When eggs fall on the carpet, they target you and your pet after they hatch. You need to keep carpets as dry as possible by vacuuming regularly. Ticks cannot jump, but they can crawl up onto your skin like they do on your pet’s skin. 3. Flea And Tick Shampoos Are Very Specific As a pet owner, you have to be very careful about what you are dealing with, fleas or ticks. In many instances, some shampoos that kill fleas don’t affect ticks. Since shampoos are mainly used to get rid of existing pests, they are not particularly useful in preventing them. Your pet can still get ticks and fleas when it goes outside. You also have to be careful about the kind of shampoo you get. Dogs and cats need different types of shampoos depending on the type of their fur. 4. Ticks Need To Be Removed With Extra Caution Though fleas are much more mobile than ticks, it is easier to get rid of them. Shampoos, flea collars, and even oral tablets help get rid of fleas as they do not latch onto your pet’s skin. In the case of ticks, they attach themselves onto your pet by drilling their mouth deep into the skin or by secreting cement-like substances that help them glue themselves on your pet’s skin. When removing ticks, use fine-tipped tweezers. Hold the part of the tick that is closest to the skin and pull upward with a steady pressure. Be careful not to twist or jerk as it may cause the mouth part to break, making it difficult to remove it. Also, do not squeeze the inflated part of the tick as the infected blood may flow back into your pet’s system. If you feel you cannot remove the ticks on your own, head to the veterinarian. In certain cases, your pet may experience muscle paralysis due to the saliva secreted by the tick, which will get better once the tick is removed. 5. Prevention Is Always Better Than Cure Since it is very difficult to get rid of a flea and tick infestation, you should do your best to prevent your pet from getting infected in the first place. You can use collars which are known to ward off these pests. These collars contain chemicals that protect your pet from both fleas and ticks. If you have a puppy or kitten, you will need to use a collar with a lower dose of chemicals. Always read the labels and follow instructions carefully. Do not let your children play with the collar and always wash your hands with soap after handling it. Regular grooming also prevents pests from infesting your pet’s skin to a certain extent. It is best to take your pet to the vet on a regular basis to get it checked for ticks and fleas. Do not use chemicals or medicines without consulting the vet first as it may worsen your pet’s skin condition if it has rashes and scabs. Email to Your Friends
When Mexicans Could Play Ball: Basketball, Race, and Identity in San Antonio, 1928–1945 (Hardcover) By Ignacio M. Garcaia University of Texas Press, 9780292753778, 292pp. Publication Date: January 6, 2014 In 1939, a team of short, scrappy kids from a vocational school established specifically for Mexican Americans became the high school basketball champions of San Antonio, Texas. Their win, and the ensuing riot it caused, took place against a backdrop of shifting and conflicted attitudes toward Mexican Americans and American nationalism in the WWII era. Only when the Mexicans went from perennial runners-up to champs, Garcia writes, did the emotions boil over. The first sports book to look at Mexican American basketball specifically, When Mexicans Could Play Ball is also a revealing study of racism and cultural identity formation in Texas. Using personal interviews, newspaper articles, and game statistics to create a compelling narrative, as well as drawing on his experience as a sports writer, Garcia takes us into the world of San Antonio's Sidney Lanier High School basketball team, the Voks, which became a two-time state championship team under head coach William Carson Nemo Herrera. An alumnus of the school himself, Garcia investigates the school administrators project to Americanize the students, Herrera's skillful coaching, and the team's rise to victory despite discrimination and violence from other teams and the world outside of the school. Ultimately, Garcia argues, through their participation and success in basketball at Lanier, the Voks players not only learned how to be American but also taught their white counterparts to question long-held assumptions about Mexican Americans.
Types of Menus Used in Restaurants Restaurants such as Ruby Tuesday offer various cuisines, price ranges and customs, and this is reflected by the menu style they use. Simply put, the menu is a restaurant’s face, and the way it reaches out to patrons like you. Not only are there different kinds of restaurants, but the menus they use vary as well. The Cycle Menu Cycle_Menu_RestaurantMealPricesA cycle menu is a list of menu items or dishes that is changed each day during the cycle and repeated. These menus are usually found in institutional facilities, schools and cafeterias, although some restaurants use them as well. The cycles can last for a month or a week, depending on the number of menu items displayed. The purpose of this menu is to make the items easier to prepare and promote. Du Jour Menu Du-Jour-Menu_RestaurantMealPricesDu Jour means “of the day’ so salad du jour means “salad of the day”. Du jour menus are changed frequently and concentrate on seasonal ingredients, and emphasis is on preparing food as fresh as possible. Though many restaurants offer specials every day, all the items listed on a du jour menu are special. Du jour menus are sometimes called chalkboard menus because they used to be written there, and most of the highlights are on vegetables and fish that are freshly available the time of the year it is being displayed. Because they’re seasonal, once a du jour menu is changed it will take time before you can see the menu item again. Prix-Fixe Menu Prix-Fixe-Menu_RestaurantMealPricesThe prix-fixe menu offers you numerous courses for a fixed price tag. Depending on the restaurant the options may include courses for dessert, meat, seafood, intermezzo, soup, salad, appetizer and bouche. While a prix-fixe menu may be costly, at least you get a lot of food options. Prix-fixe menus are usually found only in fine dining restaurants and the ingredients change often as the items are seasonal. A prix-fixe menu is also called the “degustation menu” or the “chef’s tasting menu”. A la Carte Menu Carte Menu_RestaurantMealPricesAn a la carte menu is more pricing than a menu type, as the form is determined by what you order. For instance, the main dishes are not organized with side items for a single price, as you can order vegetable, meat and starch separately and pay separately. What makes a la carte menus popular is you can have a lot of variety in your food, and it can be customized in some restaurants. Static Menus Static-Menu_RestaurantMealPricesStatic menus are the traditional menus served in restaurants and are laminated or printed. They’re frequently used in diners, fast food chains and casual diners, with the categories divided into salads, soups, appetizers, sides, desserts and entrees. Because people are very familiar with the layout, they’re used very often, making it easy for the patron to find what he or she wants. So the next time you visit Ruth’s Chris Steakhouse or another diner, take a good look at their menu, and you’ll see that there’s more to these menus that you might have thought, as it says a lot about the restaurant itself. Category: Healthy Food Show Buttons Hide Buttons Restaurant Meal Prices
Sun September 06, 2009 By: plz explain Expert Reply Wed September 09, 2009 Homologous chromosomes are a pair of chromosomes, one inherited from each parent, that have corresponding gene sequences and that pair during meiosis. Each chromosome pair contains genes for the same biological features, such as eye color, at the same locations (loci) on the chromosome. Each chromosome pair can contain the same gene (both genes for blue eyes) or different genes (one gene for blue eyes and one gene for brown eyes) for each feature. Homologous chromosomes are two pairs of sister chromatids that have gone through the process of crossing over and meiosis. In this process the homologous chromosomes cross over (not the sister chromatids)each other and exchange genetic information. This causes each final cell of meiosis to have genetic information from both parents, a mechanism for genetic variation. The homologous chromosomes are similar in length. kIndly post each of the remaining questions individually as separate queries. Related Questions Home Work Help
American Flags Store Ary KY 41712 Proudly Made in America American Flags around Ary KY 41712 A nationwide icon that has the nicknames “The Stars and Stripes”, “Old Glory”, and also “The Star-Spangled Banner”, the American flag is among the extremely identifiable icons on the planet today. This is generally as a result of the condition of the United States as one of one of the most influential nations in history. The American Flag is the third oldest of the National Standards of the globe – older than the Union Jack of Britain or the Tricolor of France. It is unique in the deep and noble significance of its message to the entire globe. It stands for a message of national self-reliance, of specific freedom, of optimism, as well as of nationalism. Who created the American Flag? What does the American Flag stand for? Why is the American Flag important to American society? Where can I find American Flags? Who made the American Flag? According to prominent tales, the very first American flag was made by Betsy Ross, a Philadelphia seamstress that was acquainted with George Washington. In May 1776, so the story goes, General Washington as well as two representatives from the Continental Congress went to Ross at her furniture store and also revealed to her a rough design of the flag. Photo via Wikimedia Commons In 1777, the Continental Congress passed an act that gave our nation a main flag. In those days, the flag was not the like we see it today. Instead of the 50 white stars in the field of blue, there was a circle of 13 white stars to represent the 13 colonies. The act stated, “Resolved, that the flag of the United States be thirteen stripes, alternate red as well as white; that the Union be thirteen stars, white in a blue area, representing a brand-new constellation.” What does the American Flag represent? The meaning of the Flag, as quoted from Washington: “We take the stars from Heaven, the red from our mother country, dividing it by white red stripes, hence showing that we have separated from her, and the white red stripes shall drop to posterity standing for Liberty.” Photo via Wikimedia Commons It incarnates for all mankind the spirit of liberty and also the remarkable principle of human freedom; not the freedom of unrestraint or the liberty of license, however a distinct principle of equal opportunity for life, liberty and also the quest of happiness, protected by the stern and also lofty principles of responsibility, of decency and of justice, and also achievable by obedience to self-imposed legislations. It symbolizes the significance of nationalism. Its spirit is the spirit of the American nation. Its history is the history of the American individuals. Laid out upon its folds in letters of living light are the names as well as popularity of our heroic dead, the Fathers of the Republic that committed upon its altars their lives, their fortunes and also their spiritual honor. Twice told tales of nationwide honor as well as magnificence collection heavily regarding it. Ever successful, it has actually arised triumphant from 8 terrific national disputes. It flew at Saratog, at Yorktown, at Palo Alto, at Gettysburg, at Manila bay, at Chateau-Thierry, at Iwo Jima. It bears witness to the enormous growth of our nationwide limits, the growth of our natural deposits, as well as the fantastic structure of our world. It prophesises the victory of preferred federal government, of civic and religious freedom as well as of nationwide righteousness throughout the world. Why is the American Flag important to American society? The American flag is extremely essential because it represents the independent federal government as explained under the United States Constitution. The flag likewise signifies the numerous successes of the country as well as the pride of its people. This national icon advises individuals, not just in the state of Kentucky, but throughout the whole USA about the different important aspects of the Declaration of Independence. It is a complex icon, which represents the liberty and legal rights of Americans. Drifting from the soaring pinnacle of American idealism, it is a beacon of withstanding hope. It is the indicator made visible of the strong spirit that has brought liberty and also prosperity to the people of America. It is the flag of all us alike. Let us accord it recognize and loyalty. Where can I get American Flags? You possibly already observed this, however there are a lot of areas where you can obtain American flags. Nonetheless, it is necessary to note that the flag you are going to acquire need to be “Made in America”. Based upon data, Americans spend over 5.3 million dollars on imported flags each year – the majority of which are made in China. Perhaps a lot more disturbing is that during 2001, in the wave of patriotism that washed over America after 9/11, Americans bought $52 million dollars in imported flags. The flag must represent the blood, sweat, as well as tears of American people that brought this nation into existence, not our indebtedness to China and also the fatality of the American manufacturing field. The flag represents nationwide independence and also popular sovereignty. It is not the flag of a ruling household or imperial house, yet of the millions free people bonded right into a nation, one as well as indivisible, united not only by community of passion, yet by essential unity of belief and also purpose; a country identified for the clear specific conception of its residents alike of their duties and also their opportunities, their obligations and also their civil liberties. So have a little pride, invest a couple more dollars, and get an American flag made by Americans in the USA. Ary ZIP codes we serve: 41712
larvalbug bytes archives / Main Index / previous / next by Larry April, 2014 Ten Tin Facts Everyone has heard about the Tin Man, from "The Wizard of Oz," right? However, did you know that, despite what that story maintains, tin does not rust? Iron does, but the story would somehow have a different quality if they called him "Iron Man." That label needed to wait another one to four thousand years after the smelting of tin for a rather dissimilar type of movie. I wonder how the first wizards of those distant times figured out how to get tin out of the earth, process it, and mix it with copper just the right way, so people could then make pots and weapons of the resulting alloy, bronze, ushering in a new (middle) age of mankind. It would fit neatly between the Stone and Iron Ages. Depending on the peoples, their relative isolation, and the geography, the Bronze Age began roughly 3300 BC (Middle East), 3000 BC (south Asia), 2300 BC (Europe), 2000 BC (China), and 1100 AD (the New World, which had the least cultural mixing). Buddy Ebsen's first make-up screentest as The Tin Man (Wikipedia) Tin whistles, tin cans, Rin Tin Tin, tin soldiers, tin foil, and Tin Pan Alley notwithstanding, many of us are little acquainted with tin. Here are a few interesting bits of trivia about this usually malleable metal: 1. Tin's chemical symbol from the Periodic Table is Sn, based on its Latin name, Stannum. It is no. 50 on that chart, having 50 electrons and protons (and so 50 is its atomic number). It has the largest number of stable isotopes (10) of any element. 2. Cassiterite is the ore from which most tin has been derived. It was often smelted by ancients using coal fires. 3. These days, 35 countries produce tin, though China is by far the most important tin processor. 4. Tin can be alloyed with niobium to create a superconductor, for which it is used to create magnets that have quite high field strength yet require little energy. 5. When alloyed with copper and antimony, it results in a very durable metal useful as bearings. 6. Since it is rather inert, tin is used in a number of coatings of other materials, such as steel, lead, and zinc, and for the metals used in water distillation. 7. Tin is quite rare, occurring in only two parts per million of Earth's crust. 8. Stannous fluoride is a tin compound used in most modern toothpaste to help prevent cavities. 9. A common use for tin now is in solder, replacing lead-based solder which can have adverse health effects. 10. Tin's uses are going up, for instance in the manufacture of window glass (the molten glass being floated on molten tin), as a coating to prevent corrosion, in alloys with copper of bronze, in organ pipes, and in die casting, yet supplies are running out. With rising rates of depletion, we could have exhausted the world's supply in only the next generation or two. Meanwhile, its price is likely to keep rising. Competition for the vital element could again become fierce. In ancient times, Britain was invaded by the Romans partly to secure this as a relatively good source of tin and other metals. Thus, besides its modern practical functions, tin's importance extends to the long-term effects of Roman colonization on the development of Western Civilization. larvalbug bytes archives / Main Index / previous / next
Baha'is see all people as one Yonat Shimron: Baha'is see all people as one Yonat Shimron Logo Question: Hue Huynh of Durham asks, "What is the Baha'i faith?" Answer: The Baha'i religion calls itself a universal faith. It teaches that all the world's people form one race and that the purpose of religion is to overcome divisions of race, gender and class. The faith was founded by a 19th century nobleman from Teheran, Iran, named Mirza Husayn Ali. In 1863, he became convinced he was a messenger following in the tracks of Moses, Buddha, Jesus and Muhammad, and he took the name "Baha'u'llah," or "Glory of God." The Baha'u'llah shunned regionalism and division and declared what he found to be a central truth that, "The earth is but one country and all mankind its citizens." This principle of world unity extended to religion, as well. The Baha'u'llah believed all religions share a Golden Rule, something like the Christian ethos of "Do unto others as you would have others do unto you." Once people recognized the essential oneness of the world's faiths, they would drop their prejudice and work together, the Baha'u'llah said. His ideas, however, did not find favor with leaders in Iran or the Ottoman Empire, which ruled the Middle East. He was exiled to Baghdad, Iraq, and eventually to Palestine, now Israel, where he died in 1892. The world headquarters for the new faith was established in Haifa, a northern city in Israel. In the past century, many have converted to the faith. There are an estimated 5 million Baha'is, or followers of Baha'u'llah, including about 1 million in India. There are an estimated 130,000 followers in the United States, many of whom live in California. During the height of the civil rights movement, many Southern blacks converted to the faith, largely because of its emphasis on racial reconciliation. South Carolina has the second-largest Baha'i community in the United States with about 17,000 followers. North Carolina has some 4,500 Baha'is. "It's one thing to say we're all created equally but when you find yourself in an all black or white congregation, then you're not really dealing with the issue," said Eric Johnson, the chairman of the Raleigh Spiritual Assembly and a composer. "Baha'is are spiritually obligated to deal with the issue of racism. We're not allowed to separate along racial lines." Wake, Durham and Orange counties have seven Baha'i communities. The faith has no clergy. Each community elects nine elders who form a "local spiritual assembly." The religion draws a mixture of liberals and conservatives. Most believers are civil rights champions. But Baha'is believe that abortion is forbidden as a method of controlling conception, though individual decisions are left in the hands of believers. The faith forbids homosexual relations and approves of capital punishment. The nine-member Universal House of Justice, based in Haifa, has developed into a central organization that controls all matters of faith, say academics who have studied the religion. "There's a strong emphasis on obedience to the central administration," said Juan Cole, a professor of history at the University of Michigan at Ann Arbor. "It's my perception that the leadership is moving to the right." Do you have a question of faith? Call me at 829-4891; send faxes to 829-4529; send e-mail to; or write to me at The News & Observer, P.O. Box 191, R a l e i g h, N. C. 27602. ©Copyright 1998, The News & Observer Publishing Co. Original Story Page last revised 051599
Mexico - Guerrero - Cualác Information and facts about the municipality of Cualác Location of Cualác The municipality of Cualác is located in the Mexican state of Guerrero México Population of Cualác The overall population of the municipality named Cualác is 6816 citizens, 3184 males and 3632 females. Age distribution The population of Cualác is divided into 3435 minors and 3381 adults, with 716 of them older than 60 years. Indigenous population of Cualác 3075 people in Cualác live in indigenous households. An indigenous language is spoken by 1652 people who are older than 5 years. The number of people who only speak an indigenous language is 5 and 1537 speak both an indigenous language and Spanish. Social Structure A legal claim on health care and social insurance benefits have 269 citizens of Cualác. Economic situation In Cualác about 1536 households are registered. 1456 of these households are common houses or apartments, 712 are without floor and about 181 consist of one room only. 927 of the normal households have sanitary installations, 966 are connected to the public water supply, 1337 have access to electricity. The economic situation allows 32 households to own a computer, 246 own a washing machine and 904 households are equipped with one ore more televisions. School and education in Cualác Besides the 1243 analphabets aged 15 or older, about 163 minors between 6 and 14 are not visiting a school. 1089 inhabitants of the population of 15 years and older did not visit a school and 1904 persons did not finish the school. 396 visited only the 6 years lasting primary school, 433 visited and finished the college or similar scholar institutions. A total of 315 aged 15 to 24 years visited a school, the medium time school is visited through the whole population is 5 years. Add a reference to Cualác <a href="">Cualác</a> PHP Link Directory
Total Pageviews Wednesday, September 26, 2007 How do we get rubber from trees? Rubber comes from a tropical tree. The juice of the rubber tree, called latex, is extracted through slanting cuts is the bark. The juice drips into a container attached to the tree. It is then collected and made into rubber, which can be used for car tyres, boots etc., Another juice extracted from trees is maple syrup, it comes from the maple tree which is grown in North America. The Juice flows out of holes bored into the wood of the tree. Maple syrup is popular in the USA and is used on pancakes and ice cream Judy March 8, 2011 at 1:08 PM where's the picture?
Primer on how taxes work. OK. So I read someones blog that had this story that explains it all. As I understand it, this is an article that was attributed to David R. Kamerschen, Ph.D. and Professor of Economics at the University of Georgia. It, however, was not and it is still undetermined in it's authorship. It is very poignant nonetheless! The Story of How Taxes Are Paid In America Suppose that every day, ten men go out for drinks and the bill for all ten comes to $100. If they paid their bill the way we pay our taxes, it would go something like this: * The first four men (the poorest) would pay nothing. * The fifth would pay $1. * The sixth would pay $3 * The seventh would pay $7. * The eighth would pay $12. * The ninth would pay $18. * The tenth man (the richest) would pay $59. So, that's what they decided to do. The ten men drank in the bar everyday and seemed quite happy with the arrangement, until one day, the owner threw them a curve. 'Since you are all such good customers, he said, 'I'm going to reduce the cost of your daily drinks by $20. Drinks for the ten now cost just $80.' The group still wanted to pay their bill the way we pay our taxes so the first four men were unaffected. They would still drink for free. But what about the other six men - the paying customers? How could they divide the $20 windfall so that everyone would get his 'fair share?' They realized that $20 divided by six is $3.33. But if they subtracted that from every body's share, then the fifth man and the sixth man would each end up being paid to drink his drink. So, the bar owner suggested that it would be fair to reduce each man's bill by roughly the same amount, and he proceeded to work out the amounts each should pay. And so: * The sixth now paid $2 instead of $3 (33%savings). * The seventh now paid $5 instead of $7 (28%savings). * The eighth now paid $9 instead of $12 (25% savings). * The ninth now paid $14 instead of $18 (22% savings). * The tenth now paid $49 instead of $59 (16% savings). 'I only got a dollar out of the $20', declared the sixth man. He pointed to the tenth man,' but he got $10!' 'Yeah, that's right', exclaimed the fifth man. 'I only saved a dollar,too. It's unfair that he got ten times more than I!' 'That's true!!' shouted the seventh man. 'Why should he get $10 back when I got only two? The wealthy get all the breaks!' 'Wait a minute,' yelled the first four men in unison. 'We didn't get anything at all. The system exploits the poor!' The nine men surrounded the tenth and beat him up. Wow, now if that isn't the best explanation I have ever read! Ryan Anderson said… How poignant! jeana said… that story looks familiar..;) and AMEN! Popular posts from this blog Thanks for the company Let's try this... Summer is Coming
Are older vehicles fitted with LPG as environmentally friendly? Based on the results of the Federal Governments own test programs which indicate that tail pipe C02 emissions produced by older cars (pre 1993) fitted with LPG are still some 14% lower than their petrol powered counterparts. Unless if these are GTO treated.... If you are considering converting your car into LPG... consider the following comparison chart. Yes we can save the world. ;-] LPG for transport By Nicolaj Stenkjaer, February 2010 Many Danish cars drove during the period 1960 - 1990 on LPG gas (Liquified Petroleum Gas) also known as the GPL, LP gas or auto gas. LPG is a liquid that is a by product from the refinery processing oil. The reason for virtually no one is running on this fuel in Denmark today is that tax rules were changed in the 1980s. But there are still a few stations back offering LPG gas and in Norway there are approximately 25,000 cars that have LPG as a propellant. Benefits of LPG cars are that ordinary cars relatively easily are rebuilt to run on LPG gas and there are conversion kits for ordinary gasoline cars. LPG gas is not stored under high pressure, but only need an operating pressure of 10 bar which is very little compared the operating pressure of natural gas at 200 bar. The low pressure makes it easier to build tanks. LPG vehicles have CO2 emissions levels like ordinary petrol cars and higher particulate emissions than natural gas, so there are no environmental benefit. Another problem is the explosion hazard, which is quite big. Denmark has earlier had many buses running on LPG gas, but they are also moving away. No comments: Carbon Footprint Calculator Notes to ponder NASA claims that the government could slow down worldwide global warming by cutting down on soot emissions. Studies by NASA show that cutting down on soot would not only have an immediate cooling effect, but would also put a stop to many of the deaths caused by air pollution. When soot is formed, it typically travels through the air absorbing and releasing solar radiation which in turn begins to warm the atmosphere. Cutting soot emissions would be an immediate help against global warming, as the soot would quickly fall out of the atmosphere and begin to cool it down. Cutting back on soot emissions would buy us time in our fight against global warming. Soot is caused by the partial burning of fossil fuels, wood and vegetation. Soot is known to contain over forty different cancer causing chemicals, and a complete cut would offer untold health benefits worldwide. Environmental conservation has always been a topic for lengthy discussions, but up until recent times, global warming and climate changes were vague subjects, with no hard proof. Not surprisingly, the previous lack of attention to these issues have created a very gloomy outlook on our future. So, considering all this, what could be the biggest contributor to climate changes through global warming? Transportation - the man-made iron horses, flying machines and sea monsters, so to speak. The question we have now is how green is our transportation? The majority of the worlds' vehicles are fueled by oil (petrol, diesel and kerosene). Even if they rely on electricity, the stations used to generate this electricity use fossil fuels for power! Excluding vehicle manufacture, transportation is responsible for 14% of the artificially created greenhouse emissions, mostly carbondioxide. Automobiles, trains and planes are all responsible for this problem, but cars are the highest impact-makers. They release approximately six times more carbondioxide than a plane and seven times more than sea vessels. What is Air Pollution? Air pollution is somewhat difficult to define because many air pollutants, at low concentrations, are essential nutrients for the sustainable development of ecosystems. So, air pollution could be defined as:A state of the atmosphere, which leads to the exposure of human beings and/or ecosystems to such high levels or loads of specific compounds or mixtures thereof, that damage is caused. With very few exceptions, all compounds that are considered air pollutants have both natural as well as human-made origins. Air pollution is not a new phenomenon; in Medieval times, the burning of coal was forbidden in London while Parliament was in session. Air pollution problems have dramatically increased in intensity as well as scale due to the increase in emissions since the Industrial Revolution.
IISA2017 \| Smart Cities: Integrating Power and Information Systems singular,single,single-post,postid-8311,single-format-standard,ajax_fade,page_not_loaded,,qode-child-theme-ver-1.0.0,qode-theme-ver-3.1,wpb-js-composer js-comp-ver-4.11.1,vc_responsive Smart Cities: Integrating Power and Information Systems \| Tutorials \| No comment Miltos Alamaniotis Background and Goals In the megacities of the future, information and computing technologies are expected to play a crucial role to transform current cities into smart cyber-physical systems where information is accessible by everyone. The term Smart Cities refers to integration of city assets with information technologies to improve quality of residents’ lives and public services. Among a city’s assets, power grid is the most preeminent one. Given that residents’ activities and cities assets on way or another include the utilization of electrical power, the power grid will be the cornerstone for making cities green, safe and secure while improving utilization and availability of public services. In addition, computational intelligence and machine learning are expected to be at the forefront of innovation for implementing smart cities. The goal of this tutorial, is to provide an overview of existing tools regarding advanced smart power systems pertained to smart cities. Furthermore, implications for future research activities and challenges will be discussed including, but not limited to, smart homes, intelligent energy management and cybersecurity systems.
Wednesday, September 25, 2013 Thoughts, data and theories on the early Pyburns MD>VA>NC/TN According to scholarly articles, most marriages did not take place at age 13-15 in the 18th century. Among the Quakers marriages were 25-30 and among others 20-25 on average. Women could marry younger but they didn't on the average. Marriage Mary Piborn Dec 10, 1704 to Joseph Jones Marriage Richard Piborn Nov 11 1718 to Sarah Morrice William and Mary Piborne Richard Piborne 13 Dec 1686 John Piborne 5 Aug 1686 John and Sarah No dates Richard and Sarah Mary Nov 4 1716 (first wife) Jacob May 1 1722 Sarah Nov 17, 1724 Ed Pybourn and Mary Mary July 12 1727 Thomas April 12 1729 Will of John Sr Liber 25, folio 168 23 Sept. 1747 PIBORN, JOHN, Sr., Prince George's Co. Extrs: sons Jacob Piborn & Benjamin Piborn. To son John Piborn, my roan mare Blaze. To son Benjamin Piborn, my 2 plough horsees, a bed, my gray mare, & the orphan boy Charles Hyatt till he is 21. To son Jacob Piborn, bay horse Punch, called Benjamin . To dau. Ruth Piborn, either the colt that belongs to the gray mare or the roan called Benjamins mare & a cow & calf & a bed. To dau. Mary Piborn, a bed & a cow & calf. To daus. Rachel Calvin & Sarah Prather, 1 sh. each. What is left to daus. Mary & Ruth to be held by their bros. Jacob & Benjamin till they are married. Witn: Benjamin Chitty, Charles O Neal, Geo. Nichols. 25 Nov. 1747, sworn to by Chitty & Neal So, assuming that he was 25-30 when he married, (avg for the time) John Pyburn married 1711-1716. His eldest son would seem to be John. None of the boys were under 21 in 1747, so they were all born 1711-1726. If this is the case at the time he died, John Pyburn's sons were between 21-36 years old. Capt Jeduthan Harpers Co Miltia 1772 Chatham (NC) Benjamin Pyburn Jacob Pyburn Sept 30 1757 Loudon Co Va lease Joshua Pyburn Benjamin Pyburn estimate born 1713 1749 signs petition in Frederick Co MD 1752 Lunenburg Co, Va Benjamin Pyburn (abt 30-40) Based on his age, it seems doubtful, when 60's was the avg lifespan that he enlisted in the milita at almost 60. The following Benjamin Pyburn would have to be a son of one of the Pyburn's Benjamin Pyburn II This Benjamin would be born 1740-1750's. Most likely a grandson of John 1772 Militia Chatham NC a Benj Pyburn November 18, 1775 Land Grant (Wash Co TN) Benjamin Pyburn, 1777 Payroll James Knox Co, 8th VA Reg Benj Pyburn deserted May 20 1776 1778 Washington Co Benj Pyburn stole a horse from John Steel (he escaped the gaol) 1779 Watauga TN Benj Pyburn sold 480 acres to George Webb John Pyborn 1750's Constable in VA (no county) ? Bedford 1758 Bedford militia 1765 NC Colonial records, taken up for being a rogue And also, the Bill for Encouraging the Culture of Hemp and Flax and other purposes Endorsed 27th February 1764 In the upper House of Assembly read the third time and passed—Ordered to be engrossed. Mr. Gibson acquainted the House that William Crane together with six others, went on a party in the Back Country in order to apprehend several Rogues and vagabonds whoare Confederated together and Infest the Frontier and other Counties, committing several outrages -------------------- page 1187 -------------------- and Murders therein. In consequence whereof the said William Crane with his Party took John Pyburne one of the Confederates, and hath delivered him to the Keeper of His Majesty's Goal in Wilmington, And that several of the said William Cranes Party are now out in Quest of the other Confederated Rogues, All which having been made appear to the House It is therefore Resolved that the said William Crane have and Receive from the Public Treasurers the sum of Fifty Pounds out of the Contingent Fund for the use of himself and his party, And that the said sum be allowed the said Treasurers on Passing their Accounts with the Public, Resolved that the following Message be sent to His Majesty's Council Vizt Gentlemen of His Majesty's Honble Council, This House having received sufficient Testimony that William Crane together with a party of six others have taken John Pyburne—One of the Confederated Rogues and Vagabonds who have for some time past Infested several counties of this Province and Committed Sundry Outrages Robberies and Murders and delivered him to the Keeper of his Majesty's Goal in Wilmington, in Consideration of which Service this House have Resolved that the said William Crane be paid the sum of Fifty pounds for the use of himself and party by the Public Treasurers out of the Contingent Fund, And that the said Treasurers be allowed the same on passing their Accounts with the Public, to which desire your Honors Concurrence. Jacob Pyburn I b ca 1713 1758 Bedford Grants land to ? wife Mary Webb not sure on this source... The same situation applies for this Jacob as Benjamin. It is doubtful it is either the son of Richard or the son of John. It has to be a grandson. Jacob Pyburn II born 1740-1750's 1772 Chatham Co NC milita This is the Jacob over 45 in NC. This could be Jacob 1 or Jacob 2. Assuming Sarah was 18-20 (avg age was 20-25) to marry, she would be born 1766 ish. That places the eldest Jacob born about 1713 at 53, old enough to be her father, as is the younger Jacob IF he was born 1740's. 1786 Jacob Piborn signs permission for dtr Sarah to marry Charles Eades (pension packet) in Bedford County, VA Thomas Pyborn Index to tithables Loudon County Also a Joshua here 1757 1773 Tithable list Bedford county 1780's James Pyburn involved with John Lawrence in Georgia in theft. American Revolution Elias Pyburn Pvt Capt Conway, Maj Rhea's co from Jonesboro Territory James Shelby pension pkt. Document with Benjamin, Elias and Lewis Pyburn, this is an accounting of “board” and something else, all financial papers but hard to read microfilm. Benjamin Pyburn as under him. Green Y Choate deserted same day, so did John Williams, John Marion, Burke Co NC Jacob 3 males over 16 1 under 16 5 females Edgefield Co NC Benjamin 1 male over 16 Richard 1 male over 16 3 Females Not listed in US 1784-1786 Jacob Pyburn and wife. He is at least 30 in 1784. 1792 Buncombe Jacob guardian of Edward Pyburn 1794 Jacob and Edward to Bunscombe (land grant) NC 1799 Tennessee Jacob Pyburn signs petition Buncombe Christopher 26-44 Jacob over 45, male 16-25 (Edward?) Louisiana Territory Lewis Pyburn and family Alabama Territory Jacob Pyburn in his mother's home in Baldwin Co, AL Florida (Spanish) Territory Benjamin Pyburn and siblings in Pensacola Haywood NC, Sarah Pyburn widow 26-44 and family Buncombe NC Christopher over 45 and family Mecklenburg NC Edwin 26-44 and family ? Edward Hardin, KY Richard Pyburn 26-44 and family Louisiana Ouachita Enos Pyburn 26-44 and family Overton, TN Sarah Pyburn 26-44 and family Wayne, TN Christopher over 45 and family William 26-44 and family Baldwin Co AL (state) Jacob Pyburn (III) Over 21 and family Baton Rouge Sims? Pyburn over 45 and family too many to list Eastern Cherokee application of Choate/Pyburn 1841 Mary Choate (Eastern Cherokee App) grandparents Austin Choate and mother Omi Pyburn, her father was Edward Choate and Elizabeth Cole. Born in Jackson Co, TN. Witness said they were cousins and he was half Cherokee and she was full. They died in Putnam County, TN. State Edward Choate born about 1817. Read the other two files and both say Austin Choate married Omi Pyburn. His mother should have been born 1780-1797 Information on the Choates 1840 in Fentriss County, TN find an Edward and an Austin Choate, both 30-39 years old (1800-1809), along with a Thomas 30-39, Jacob and John 30-39 and a Gabriel 20-29. A Christ (Christian?) Choate 70-79 with wife age 50-59 is in this county. If Austin Choate married his cousin, Naomi (Omi) then the wife of Christian should be a Pyburn born 1780-1789 or a sibling of Naomi's mother. If this is in NC then the most obvious choice is Jacob who is living there in 1790 and 1800. In Fentriss 1850 find John Choate b 1805 wife Anna b 1813 Edward Choate's census says wife is Priscilla. He's born 1799 NC. Thomas Choate born 1811 In Jackson in 1850 is the right Edward Choate.. with dtr Mary 10. Says he is 31 born TN (born 1819) wife is Elizabeth 27 born in TN. There is a Naomi Ramsey age 20 on same page. I also find a Medder Shoate and wife Lucinda in Jackson, a Nancy Shoat born 1797 with a son Jacob? Age 20. Edward names a dtr Nancy, and Nancy is the right age to be his mother If Nancy is a Pyburn, then we need to see has a female her age in NC. Jacob Pyburn has one daughter 16-25 in 1800, and 4 females in his home in 1790 besides his wife. 1790 Austin Choate is in Burke over 16 (also there is Christopher Sr and Jr and Moses) In 1790 Jacob has 5 females and Richard has 3 females. I don't find Austin in 1800 or 1810. To be the mother of all of his children, the Pyburn would have to be born prior to 1783 based on the 1850 ages of the folks who are with Austin in 1840. His wife should be born 1780-1790 based on her age in 1840. In 1820 Austin is in Jackson County, Tn. He has a wife 16-25 years old (born 1795-1804) which fits with the age of Nancy in 1850. He has a son 10-15 (couldn't be Nancy's) and 4 sons under 10 and 3 females 10-15. Austin either has siblings or he was married prior to Nancy. Of the 1820 Pyburn's in Tennessee I am perplexed. Sarah is 26-44,there is a 16-25 year old female, a female under 10 a male 16-25, (16-18 also which is same person), and 2 males 10-15. It may be this is her son who is 18 with a wife and an infant and two children. William Pyburn in Wayne is 16-25 with a wife and 2 daughters under 10, Christopher is over 45 with a female over 45, 2 males 16-25, 1 of them 16-18, and 3 females 16-25 and one 10-15. In 1810, we have Edwin (Edward), Richard and Christopher with Sarah. Sarah has a male in her home that is also 26-44, a male 10-15, two female 10-15, and one female and 3 males under 10. I am seriously wondering if Jacob didn't remarry and have a second younger set of children. The only other option would be that Sarah married Benjamin after 1800 and is living with children of Jacob. Between 1775 and 1812 I find no records for a Pyburn (except the petition about the state of TN). The first Tax record is in 1812 for Christopher in Warren. (Mike found a land record in 1802 Smith for Lewis) The earliest land record I can find is 1825 for Christopher In 1830 I find Jacob in Hardin age 20-29 and Susanne age 30-39. Mary Pyburn age 50-59 in marion would seem to be the widow of Christopher. There is a Lone and a Riley both 20-29 in that county. James Pyburn in McNairy is also 20-29 and then a James Pebourne is in Mcminn 30-39. Edward Pyburn age 40-49 is now in Missouri as is Richard Pyburn 50-59. Aman/Amon Pyburn age 20-29 and William Pyburn 20-29 are also in Missouri. Benjamin Pyburn and John Pyburn, 30-39 are both in Arkansas. Benjamin has 2 males 20-29 who are probably brothers or brother in law. I find a William Pyburn with a female 50-59 in Jackson Arkansas (that's it) and another William 20-29 in Lawrence. I also find a Richard and a Richard Jr in Indiana. This Richard is also 50-59. If I were to hazard a guess, I would think that Richard Pyburn would descend from the Richard the son of John, who we know had a son Jacob. It is a good question as to whether or not the second Jacob (age 50 in 1772) is the Jacob II or did the son of John (sr) die without Issue. The William who only shows a wife 50-59 in 1830 would seem to be the family of William Pyburn who was in Wayne County, TN. At least the wife part. Neither Elias or the second Benjamin appear in records after 1777. Lewis shows up in the Louisiana Territory in 1810, and is the father of Enos I am pretty sure. While certainly one of these men could be the father of the Jacob in 1799 (who would be 21 by then), it seems odd that he disappears altogether. I read that someone found land records for Lewis in Smith county. If Lewis and Elias served in the American revolution they could be young boys, but were likely teenagers or young men, so 15-20 years from 1777 is 1757-1762. Benjamin who served with them would probably be a brother, but could be a father. I speculate that these three men are decendents of John and not Richard Pyburn. It is possible that the Benjamin in SC in 1790 is the Benjamin who was a crook. Edward Pyburn who needs a guardian in 1792 but is old enough for a land grant in 1794 (maybe Jacob was still his agent?) was 26-44 in 1810 or born sometime between the years 1766-1784. If he was not 21 in 1792, then he would have to be born 1772-1784. He could not be the father in law of Austin Choate, as his wife was born in the 1790's. This is probably Jacob Pyburn who was living in NC. We already know that in 1790 Jacob had 3 males over 16 in his home, at least one of them was Jacob and he was likely already over 45 in 1790, or born 1740-1750. Based on that information, I would speculate that he is the father of Christopher and Richard. Edward is probably his grandson or a nephew. Jacob is probably the same Jacob who signed consent for his daughter to marry Charles Eades, but there is no way to rule out that the other Jacob didn't have a daughter, except that there only seems to be one Jacob in the records we find from 1747-1757. I can't explain the cousin part. In order for Austin and Namcy/omi to be cousins, either their mother's were siblings, or Austin's mother was a Pyburn. Nancy Omi could not be full Cherokee. The Pyburn's were not indian to start with, it has to come in through the wives. I have no idea who the Pyburn in 1820 is in Baton Rouge. The name looks like Sims or Sens, and they kind of seem to disappear from records after that. As for the 2nd Richard, I have no explanation as he appears out of nowhere. When you look at who Sarah was married to it's another good question. Without a doubt there are members in her household that are too old to be children. It is possible they are siblings of Sarah or her husband. But if they are Pyburn's who is their father? By process of elimination there are only four unaccounted for Pyburn men that could be Sarah's husband, Elias from the Am revolution, Benjamin from SC, Jacob who signed the 1799 petition and James Pyburn who was running around Georgia stealing with John Lawrence. I can find nothing on this James other than the testimony that occurred in the Tensaw area in 1787. By 1789 John Lawrence was murdered by Creek Indians. I see where someone has Jacob Pyburn married to a Mary Webb and having a daughter Elizabeth Naomi who married to a Jesse Beene. If this is true (since he's not in any censuses), then we can scratch him off the list. I can't seem to find him myself in a record. Thus far we have the following list. (theory) Thomas Pyburn likely the father of Joshua who is on a lease in Loudon in 1757. Possible that William in Wayne comes from this line (but unlikely) Richard to Jacob to ;Jacob Jr then Christopher, Richard, Nancy Omi , Sarah and ? (father of Edward?) the First John I am betting his Jacob had only daughters or no kids John arrested 1764 in NC for being a rogue Either of these two are the father of the second Benjamin, Elias, Lewis, Jacob Pyburn (mine) and James Pyburn. Possibly a second Benjamin (the one in SC). These are first cousins most likely if not siblings. Benjamin or Elias should be the father of the Jacob said to be born in TN. I kind of doubt Lewis but we can't rule him out. My Jacob arrived in Spanish Territory in 1784, his son Jacob was already 7 years old. I read some articles and most men married 22-25 back then. So if that's the case my Jacob was at least born 1750, thus I am saying he should be the same age to be the brother of the other two. I can't rule out his name wasn't Benjamin Jacob (mine). :It may be why the second Benjamin (who kept getting in trouble with the law) ran off. That Benjamin could also be the man in SC. As for James in Georgia, we must assume he was a man (sounds like it) when he was robbing in Georgia. John Lawrence swore his oath the same day as Jacob Pyburn in December 1784, so that means that this occurrred prior to 1784. Thus James Pyburn was born anytime 1764 prior. As for William in Wayne.. hmm he's with Christopher so that would seem to be a good match. We don't know what happened to John in 1764, but if he was arrested for murder, I would guess that he may have been hung (it's not in the colonial record book). Thus if John had a family, it was before 1764. I think the average lifespan was early 60's for this time frame. When you got to 40 you were old, but old men had kids, lol. So, I guess the big question is can we find anything on Benjamin, John or Jacob? The reason that I don't think there are two Jacob's in the records is simply that the Jacob in NC seems to descend from Richard, they use completely different names pretty much. There is only one Jacob listed in the records, so.. kind of would seem to have to be. Thomas and Joshua seem to disappear entirely from Loudon after 1773. I still don't know who the heck Edward was who had baptisms. I guess he could be a brother to John and Richard, but with his kids born 1722 he's not a son. Maybe Edward who is Jacob's ward is a son of Thomas? 1 comment: 1. Thank you for investigating this. I wrote to you a long while ago about this. Austin Choate and Elizabeth Naomi "Omi" Pyburn were my mother's ancestors.
Penguins dive after small sea animals to eat. Different types eat small fishes, squid, and shrimplike animals called krill. Penguins breed in large groups called nesting colonies. Some types travel long distances to reach their nesting colonies. They may return to the same nesting place year after year. Click Here to subscribe Translate this page
The Structure of a Leaf How the Leaf Makes Food Why Leaves Change Color and Fall How to Make a Leaf Collection Late spring, when leaves are fresh and green, is the time to start a leaf collection. Keep the leaves fresh and uncrushed as you collect them. Spread them carefully between two or three layers of newspaper on a flat surface. Then place books on the top layer of paper and put something heavy on the books. Change the papers every day for the first four days, then leave the leaves pressed, undisturbed, for another week.… Click Here to subscribe
Tutoring Physics, Dot Products and Cross Products Return We looked at induced currents, loops, magnetic fields. Spent some time on the right hand rule. Also looked at the difference between dot products and cross products. They are important for the current material. The result of a dot product is a scalar, the result of a cross product is a vector. One has the sine function in it and the other has a cosine. So if you took the dot product of two perpendicular vectors, you would get zero. If you took the cross product of two parallel vectors, you would get zero. Good not to mix them up. Neither one of them is simply ‘multiplication’, though sometimes they reduce to that depending on the scenario. The cross product will still have a direction in addition to a simple multiplication even with orthogonal vectors. Speak Your Mind
Share on Facebook What Mysterious Creature Ate This 9-Foot-Long Great White Shark? Experts Search for Answers By Talan Torriero May 18, 2015 In a recent documentary, _The Search for the Ocean’s Super Predator_, produced by the Australian Broadcasting Corporation, researchers set out to gather more in-depth studies of great white shark’s movements along Australia’s coast by tagging it with a tracker. Among many things, these trackers monitor body temperatures which can give them a lot of different conclusive data. The great white shark, also known as “white death,” is not the largest shark in the ocean. That title belongs to the whale shark which has the largest recorded size of 40 feet long, though experts believe they can get even bigger. The whale shark is more of a docile beast which is more subject to filter-feeding on smaller organisms. The great white is quite different. Great whites typically reach a max of 20 feet though there have been larger but questionable recordings of up to 21 feet and more. These sizes are not common. This beast is not a filter-feeder. White death goes for the good stuff and likes to take large bites of its prey and wait for them to bleed to death before devouring them. Why is size so important when discussing what these researchers discovered in this documentary? The answer to that is quite fascinating. When these researchers tagged the 9 foot long great white featured in the video below, a few months later their tracker turned up with some very interesting and puzzling results. Their beauty of a shark seemed to have been eaten by something much larger. The question was “What?” What could have eaten this already monstrous predator? Experts are saying it was a colossal cannibal great white shark. Basically a much larger shark ate the beast that was already considered massive. Why would a shark eat another shark? Apparently, it’s as simple as one being smaller than the other. This must be their own way of evolution that keeps their kind a large threat in the ocean. Kill the smaller and weaker so the great white can remain the GREAT white. It turns out that the shark they thought was so large and glorious was nothing but a tiny little bottom feeder. In other words, Jaws is out their capping all the smaller sharks making a bad name for his kind. Check out the video below and make sure to share.
Saturday, April 5, 2008 Rhodes (3) As we moved on into Stoic physics, I could readily see why it was important first to review the older Greek philosophers. It became obvious that the Stoics blended all these older concepts together to develop their own sense of cosmology. • Ancient Greek physics consisted of air, fire, water, and earth. Consequently, Stoic philosophers forged their cosmology within this context. Also, earlier Greek philosophy held that the cosmos as a whole was a single living being. • Even more specifically, early Stoic philosophers stressed a cosmic-biological character when it came to the universe. For example, the early Stoics believed that the cosmos originated out of the "fire of the conflagration." As Zeno of Citium (the founder of Stoicisim) reportedly put, the fire is "as it were a seed of the future cosmos, possessing the Logoi (Reason) of all things." • Eventually this primeval fire changes into water. Out of this comes the concept that body and soul are as two distinct entities, in that the water is body and fire is soul. • Continuing with biological terms, the Stoics refer to seed in terms of sperm, which was wet, watery. As put by one lecturer, "as the seed is embraced in the seminal fluid, so also this (i.e. god), being a spermatikos logos of the cosmos is left behind--making the matter adapted to himself for the genesis of the next things..." • Eventually Stoic physics moved beyond biological terms when it came to discussing the cosmos. They considered Pneuma (Spirit) as an all-pervasive intelligent force that mixes with "shapeless and passive matter" and imbued it with all its qualities. • The Stoics also referred to heimarmene as an orderly succession of cause and effect. As put from the lectures, "heimarmene is the natural order of the Whole by which from eternity one thing follows another...and embodied in the definition of heimarmene follows its meaning as Logos (Eternal Reason), as the divine order and law, by which the cosmos is administered." • Essentially this idea of Eternal Reason--the Logos--is about an intelligently designed Fire that structures matter in accordance with it's plan. Hence, out of a "shapeless and passive matter" the Stoics endowed the cosmos with Intelligence and Reason via the workings of the Fire of the Spirit, the Pneuma. • In due course the Stoics addressed the existence of human beings in this Living Cosmos. They considered Man as a microcosm to the macrocosm. Referring back to the Pneuma, the Stoic philosopher Chrysippus considered that "the cosmos is permeated and given life by the Pneuma, the same...makes a man a living, organic whole." Hence, the Stoic emphasis on the microcosm vis-a-vis the macrocosm! My reaction to all this was satisfaction, in that all by myself, harkening back to my cousin Marc's agricultural notes, that I had been inclined towards my very own "Seeding" hypothesis. BUT--well and good, whether my own considerations, whether that of those ancient philosophers unto the Stoa, in the end all of this amounted only to philosophic speculation! Perhaps pragmatic, but I would have wished for some tangible proof that stood behind all the speculation. I did know that surely some of these philosophers worked from their own observations of the physical world. One example was Anaximander, who drew his conclusions from his studies in astronomy and by observing natural surroundings. Maybe the study of astronomy might be my next step, though I had little idea how I might begin. So often astronomy has been mixed with astrology, which seemingly indulges more into fortune telling. No, that wouldn't do--not at all. It likely will not be easy finding serious astronomers who might provide some valuable insight into how the heavens and the earth work. No comments:
Science backs hiking for brain wellness Science backs hiking for brain wellness Hiking improves your brain function in the hippocampus thereby generating neurons and inducing brain power and cell division in the circuit of brain. It increases brain function and replenishes brain cells. It makes you focused and creative thereby increasing the levels of your concentration, thought process, problem solving and decision making. Walking on a treadmill helps lose weight but does not really expand cognitive function. As per the Attention Restorative Theory hiking in the company of nature can actually restore those parts of the brain that have been exhausted due to overuse and limitless engagement with technology and gadgets. Hiking helps to disconnect with technology. Hiking reduces levels of stress, worrying patterns, rumination, performance pressure and anxiety. Hiking helps to increase the brains skills by almost 50 percent. Hikers might be the smartest people in the world. Hiking in natural environment is different from taking a walk in an urban setting. Read : 10 Smart packing tricks for traveling Travel Dejavu Connect on Facebook @ThetravelDejavu and on Twitter @Thetraveldejavu Recommended Posts Leave a Reply Yes No
Mythology Research Project Mythology Research Project : In The Yoruba and Madagascar myths of creation, the beginning of the world was a formless Chaos which was neither sea nor land. Orisha Nla, also called the Great God, was sent down from the sky to the Chaos by Olorun, the Supreme Being. His obligatory mission was to create solid land and to aid him in the accomplishment of this task. He was given a snail shell, a pigeon and a five-toed hen. After the earth and land were separated, a chameleon was sent with Orisha Nla to inspect his work and report to the Supreme Being. Olorun was satisfied with the good things reported to him and sent Orisha Nla to finish. He planted trees, Olorun made rain water fall from the sky and grew the seeds into a great forest. The creation of earth took four days and on the fifth Orisha Nla rested from his work. Orisha fashioned the first people from earth for Olorun, but only the Supreme Being was able to give them life. Orisha Nla hid in his workshop trying to watch him, but a spell of deep sleep was cast onto him so that only Olorun knew the secret. He made the first man and woman and their daughter and her husband. The rest of the human beings descended from them. As time passed, the Creator noticed that as humans multiplied and prospered, they gave thanks to Mother Earth but forgot about him. He decided thenceforth to take the souls of half the humans signifying a tribute. In the myth, Why Men Must Die told by the Zulu's of Natal in South Africa, we are told how because of a slow moving tiny animal man-kind suffered and still does of mortality. The first man on earth, also a god, sent the chameleon to give humans the message that they will be like the gods and never die promptly. Because he took too long to travel to mankind and spread the good news, he sent a viper out of annoyance with the message that he changed his mind and they will not live forever. In the Egyptian creation story my group has studied, everything descends from Nu, the sea. His son Ra, becomes the Creator and makes a god for everything in our world: Shu, the wind god, his consort Tefnut, "The Spitter", brought rain, Seb, the earth god, Nut, goddess of the firmament, who were the parents of Osiris and his consort Isis and Set and his consort Nepthys. The story also tells about sins that people had since their earliest existence, such as desire, impatience, deception and lying. Isis, who is greedy for power, goes as far as poisoning the Creator, in order to obtain his secret and sacred name, which is the symbol and holder of the Creator's powers. A short legendary history of some customs (such as those of the New Year's celebration) is given. By reading these stories, one can see some of the similarities present between the myths of Christianity (mainly Roman and Greek) and those of Africa, such as the story of the creation, the deceiving of the God, his anger with the people and the punishment he gave them in order to teach them a lesson and his forgiveness, etc. Death is first introduced in the form of punishment, which Ra is giving the people, with the help of Hathor, who is doing the actual slaying. Ra also divided the world between two of his gods…Osiris who will rule the dead, and Horus who will rule on the island of the fiery flames. Once people die, they enter Osiris' kingdom, where they are divided between those who can stay and those who will be taken by the serpents, "dragging them away, while they utter loud and piercing cries of grief and agony, to be tortured and devoured; lo!" Mythology Research Project More College Admission Essays Mythology Research Project : Essays Index Mythology Research Project To HOME PAGE Related Links : Mythology Research Project
Google tugs at heartstrings with adorable pangolin-themed Valentine's doodle google doodle (Screenshot from Google and the World Wildlife Fund are casting a spotlight on the plight of the pangolins with an incredibly intricate and cute Google Doodle. Lasting for four days, the delightful Doodle is all about pangolins and love. It features a multi-level game starring a small rolling pangolin; using the arrow keys and the space bar, people can send the little pangolin rolling across Ghana, India, China (where it swings from ribbons attached to lanterns) and the Philippines. There are eight pangolin species, which not coincidentally, live in all those regions. The initiative is meant to raise awareness about the endangered pangolins, which are threatened by trafficking. The World Wildlife Fund describes the unique creature as “the world's only truly scaly mammal.” “Pangolins are the most-trafficked mammals in the world, in high demand by consumers for their meat and their unique scales,” the WWF said. “More than one million pangolins have been illegally taken from the wild to be used in fashion products and purported medicinal remedies.” In addition to the game, the Google Doodle also includes facts about pangolins— like about how long their tongues are (which they use to grab food like ants and termites), or how the babies ride on their mother’s tales, or that their scales are made from keratin. Check out the Doodle and the game here.
Friday, January 28, 2011 Five Gallons At A Time: Water Chemistry, Part III The content of this page was updated on 9/7/2012. If you've read Parts I and II, you're up to speed on the importance of mash pH and you know a few simple treatments to get it in the right ballpark with Madison municipal water. Now it's time to learn a little bit more about why calcium is good and alkalinity is bad. Based on my own experiments, mashing Pilsner malt with distilled water will result in pH near 5.65. From there, several things will affect mash pH: -Alkalinity in the water will raise mash pH. -Calcium and magnesium in the water will lower mash pH. -Adding acid to the water will lower mash pH. -In general, darker malts will lower mash pH more than lighter malts. -In mashes with alkaline water, thinner mashes will raise mash pH. -In mashes with acidic water, thinner mashes will lower mash pH. Alkalinity is the amount of strong acid required to lower the pH of a solution to a given value. For us, that value is 4.3. An alkaline solution doesn't necessarily have a high pH, but a lot of acid is needed to lower its pH. It may seem counter-intuitive, but distilled water has a small amount of alkalinity because its pH is higher than 4.3. For brewing water, alkalinity can be thought of as the number of bicarbonate ions (HCO3-) plus twice the number of carbonate ions (CO3--) present in a given volume of water. These two compounds, plus carbonic acid (H2CO3), comprise a buffer system that resists changes in water pH. If you want to treat your water with slaked lime, it'll be important to know the concentrations of the three molecules in your water supply. Otherwise, knowing the overall alkalinity will be sufficient. In a mash, calcium ions (Ca++) react with malt phosphates to release hydrogen ions (H+). In essence, adding calcium is an indirect way of adding acidity. I suspect that magnesium ions (Mg++) behave in a similar manner, but I don't know for sure. Treating water with magnesium isn't very common because the ion is detrimental to beer flavor at fairly low concentrations. In water reports, ion concentrations are commonly quantified in the weight-based unit ppm (parts per million) or mg/L. At the minuscule concentrations we're dealing with, the two units are interchangeable. However, because pH measures the number of hydrogen ions in a solution - i.e. molecules with one unit of ionic charge - the interactions between acidic and alkaline compounds are governed more by electric charge than molecular mass. A convenient unit to use is milliequivalents per liter (mEq/L), i.e. the number of millimoles of ionic charge contributed by a compound in a liter of water. Here's how to convert the values in your water report to mEq/L: mEq/L = mg/L x Ionic Charge / Molecular Mass For example, a calcium ion (Ca++) has an ionic charge of 2 (the number of + or - signs) and a molecular mass of 40.08 mg/mmol. If the calcium concentration of a given water supply is 80 mg/L, its equivalent concentration is 80 x 2 / 40.08 = 3.992 mEq/L. With that sorted out, our water utility throws us for a loop and reports alkalinity as "mg/L as CaCO3". Furthermore, water reports that simply say "mg/L" for alkalinity often mean "mg/L as CaCO3". It's a stupid unit that equals the equivalent weight of a calcium ion plus the equivalent weight of a carbonate ion, but it can (and sometimes is) used to describe the concentrations of compounds that involve neither calcium nor carbonate. Really, it's just [mEq/L x 50]. If a given water supply has an alkalinity of 350 mg/L as CaCO3, its equivalent concentration is 350 / 50 = 7 mEq/L. In the 1950s, a German brewing scientist named Paul Kohlbach found that the pH of 12-Plato kettle wort from a pale malt mash could be estimated by the following equation (adjusted to use mEq/L as the unit for alkalinity, calcium and magnesium): Wort pH = pHdw + 0.084(Alkalinity - Calcium/3.5 - Magnesium/7) In the equation, pHdw is the pH of wort produced by a distilled water mash. I don't think Kohlbach accounted for the fact that distilled water has an alkalinity of about 0.05 mEq/L, so this is probably a better equation: Wort pH = pHdw + 0.084(Alkalinity - Calcium/3.5 - Magnesium/7 - 0.05) The take-home message here is that a unit of alkalinity is 3.5 times more effective at raising pH than a unit of calcium is at lowering it, and 7 times more effective at raising pH than a unit of magnesium is at lowering it. The term [Alkalinity - Calcium/3.5 - Magnesium/7] is known as Residual Alkalinity (RA), and it quantifies the degree to which a given water supply will raise or lower the pH of wort. The same holds true for mashes, but the 0.084 multiplier will be replaced by a series of values that depend on mash thickness. We'll get to that in another post. Returning to our water supply, here are some values from a Madison water report and their conversions to mEq/L: Calcium (Ca++) = 80 mg/L -> 80 x 2 / 40.08 = 3.992 mEq/L Magnesium (Mg++) = 45 mg/L -> 45 x 2 / 24.31 = 3.702 mEq/L Chloride (Cl-) = 36 mg/L -> 36 x 1 / 35.45 = 1.016 mEq/L Sulfate (SO4--) = 17 mg/L -> 17 x 2 / 96.06 = 0.354 mEq/L Alkalinity = 339 mg/L as CaCO3 -> 339 / 50 = 6.78 mEq/L Plugging these values into Kohlbach's equation allows us to calculate the residual alkalinity of the water supply: RA = 6.78 - 3.992/3.5 - 3.702/7 = 5.111 mEq/L Since residual alkalinity is often reported in mg/L as CaCO3, it's often nice to know the value for comparative purposes. In our example, RA = 5.111 x 50 = 256 mg/L as CaCO3. To brew a Pilsner at a water-to-grain ratio of 1.5 qt/lb, mash water with a residual alkalinity around -150 mg/L as CaCO3 would be ideal. For a stout, mash water with a residual alkalinity of 40 mg/L as CaCO3 could be appropriate. Regardless of your intended grainbill, the residual alkalinity of our water supply is astronomical. That's why Madison water is challenging to brew with. The next article in this series is here. No comments: Post a Comment
From MeritBadgeDotOrg Revision as of 22:05, March 18, 2007 by Optimist (Talk \| contribs) Jump to: navigation, search Merit badge requirements 3. Do TWO of the following: b. Interview your parents and grandparents about music. Find out what the most popular music was when they were your age. Find out what their favorite music is now, and listen to three of their favorite tunes with them. How do their favorites sound to you? Had you ever heard any of them? Play three of your favorite songs for them, and explain to them why you like these songs. Ask them what they think of your favorite music. 4. Do ONE of the following: b. Compose and write the score for a piece of music of 12 measures or more. c. Make a traditional instrument and learn to play it. d. Catalog your own or your family's collection of 12 or more compact discs, tapes or records. Show how to handle and store them. Source: 2007 Boy Scout Requirements (33215) Help with these requirements External links Personal tools
3.3. The Special Lojban Characters The apostrophe, period, and comma need special attention. They are all used as indicators of a division between syllables, but each has a different pronunciation, and each is used for different reasons: The apostrophe represents a phoneme similar to a short, breathy English h, (IPA [h]). The letter h is not used to represent this sound for two reasons: primarily in order to simplify explanations of the morphology, but also because the sound is very common, and the apostrophe is a visually lightweight representation of it. The apostrophe sound is a consonant in nature, but is not treated as either a consonant or a vowel for purposes of Lojban morphology (word-formation), which is explained in Chapter 3. In addition, the apostrophe visually parallels the comma and the period, which are also used (in different ways) to separate syllables. As a permitted variant, any unvoiced fricative other than those already used in Lojban may be used to render the apostrophe: IPA [θ] is one possibility. The convenience of the listener should be regarded as paramount in deciding to use a substitute for [h]. The period represents a mandatory pause, with no specified length; a glottal stop (IPA [ʔ]) is considered a pause of shortest length. A pause (or glottal stop) may appear between any two words, and in certain cases – explained in detail in Section 3.1 – must occur. In particular, a word beginning with a vowel is always preceded by a pause, and a word ending in a consonant is always followed by a pause. Technically, the period is an optional reminder to the reader of a mandatory pause that is dictated by the rules of the language; because these rules are unambiguous, a missing period can be inferred from otherwise correct text with all words separated by spaces. Periods are included only as an aid to the reader. A period also may be found apparently embedded in a word. When this occurs, such a written string is not one word but two, written together to indicate that the writer intends a unitary meaning for the compound. It is not really necessary to use a space between words if a period appears. The comma is used to indicate a syllable break within a word, generally one that is not obvious to the reader. Such a comma is written to separate syllables, but indicates that there must be no pause between them, in contrast to the period. Removing a comma has no effect on how a text is pronounced or parsed. Here is a somewhat artificial example of the difference in pronunciation between periods, commas and apostrophes. In the English song about Old MacDonald's Farm, the vowel string which is written as ee-i-ee-i-o in English could be Lojbanized with periods as: Example 3.1. • .i.ai.i.ai.o • [ʔi.ʔaj.ʔi.ʔaj.ʔo] • Ee! Eye! Ee! Eye! Oh! However, this would sound clipped, staccato, and unmusical compared to the English. Furthermore, although Example 3.1 is a string of meaningful Lojban words, as a sentence it makes very little sense. (Note the use of periods embedded within the written word.) If glides were used instead of glottal stops, we could represent the English string as a cmevla, ending in a consonant: Example 3.2. • .i,ia,ii,ia,ion. • [ʔi.ja.ji.ja.jonʔ] If apostrophes were used instead of commas in Example 3.2, it would appear as: Example 3.3. • .i'ai'i'ai'on. • [ʔi.hai.hi.hai.honʔ] which preserves the rhythm and length, if not the exact sounds, of the original English.
Open main menu Wikipedia β UT date and time of equinoxes and solstices on Earth[1] event equinox solstice equinox solstice month March June September December day time day time day time day time 2012 20 05:14 20 23:09 22 14:49 21 11:12 2015 20 22:45 21 16:38 23 08:21 22 04:48 2018 20 16:15 21 10:07 23 01:54 21 22:23 2019 20 21:58 21 15:54 23 07:50 22 04:19 2020 20 03:50 20 21:44 22 13:31 21 10:02 An equinox is the moment in which the plane of Earth's equator passes through the center of the Sun's disk,[2] which occurs twice each year, around 20 March and 23 September. On an equinox, day and night are of approximately equal duration all over the planet. They are not exactly equal, however, due to the angular size of the sun and atmospheric refraction. The word is derived from the Latin aequinoctium, from aequus (equal) and nox (genitive noctis) (night). The sun at the equinox seen from the site of Pizzo Vento, Fondachelli-Fantina, Sicily Equinoxes on EarthEdit The equinoxes are the only times when the solar terminator (the "edge" between night and day) is perpendicular to the equator. As a result, the northern and southern hemispheres are equally illuminated. The word comes from Latin equi or "equal" and nox meaning "night". In other words, the equinoxes are the only times when the subsolar point is on the equator, meaning that the Sun is exactly overhead at a point on the equatorial line. The subsolar point crosses the equator moving northward at the March equinox and southward at the September equinox. The equinoxes, along with solstices, are directly related to the seasons of the year. In the northern hemisphere, the vernal equinox (March) conventionally marks the beginning of spring in most cultures and is considered the New Year in the Persian calendar or Iranian calendars as Nowruz (means new day), while the autumnal equinox (September) marks the beginning of autumn.[3] When Julius Caesar established the Julian calendar in 45 BC, he set 25 March as the date of the spring equinox. Because the Julian year is longer than the tropical year by about 11.3 minutes on average (or 1 day in 128 years), the calendar "drifted" with respect to the two equinoxes — such that in AD 300 the spring equinox occurred on about 21 March, and by AD 1500 it had drifted backwards to 11 March. This drift induced Pope Gregory XIII to create a modern Gregorian calendar. The Pope wanted to continue to conform with the edicts concerning the date of Easter of the Council of Nicaea of AD 325, which means he wanted to move the vernal equinox to the date on which it fell at that time (21 March is the day allocated to it in the Easter table of the Julian calendar). However, the leap year intervals in his calendar were not smooth (400 is not an exact multiple of 97). This causes the equinox to oscillate by about 53 hours around its mean position. This in turn raised the possibility that it could fall on 22 March, and thus Easter Day might theoretically commence before the equinox. The astronomers chose the appropriate number of days to omit so that the equinox would swing from 19 to 21 March but never fall on the 22nd (although it can in a handful of years fall early in the morning of that day in the Far East). • Vernal equinox and autumnal equinox: these classical names are direct derivatives of Latin (ver = spring and autumnus = autumn). These are the historically universal and still most widely-used terms for the equinoxes, but are potentially confusing because in the southern hemisphere the vernal equinox does not occur in spring and the autumnal equinox does not occur in autumn. The equivalent common language English terms spring equinox and autumn (or fall) equinox are even more ambiguous.[4][5][6] It has become increasingly common for people to mistakenly refer to the September equinox in the southern hemisphere as the Vernal equinox.[7][8] • March equinox and September equinox: names referring to the months of the year they occur, with no ambiguity as to which hemisphere is the context. They are still not universal, however, as not all cultures use a solar-based calendar where the equinoxes occur every year in the same month (as they do not in the Islamic calendar and Hebrew calendar, for example).[9] Although the terms have become very common in the 21st century, they were sometimes used at least as long ago as the mid-20th century.[10] • Northward equinox and southward equinox: names referring to the apparent direction of motion of the Sun. The northward equinox occurs in March when the sun crosses the equator from south to north, and the southward equinox occurs in September when the sun crosses the equator from north to south. These terms can be used unambiguously for other planets. They are rarely seen, although were first proposed over 100 years ago.[11] • First Point of Aries and first point of Libra: names referring to the astrological signs the sun is entering. Due to the precession of the equinoxes, however, the constellations where the equinoxes are currently located are Pisces and Virgo, respectively.[12] Length of equinoctial day and nightEdit Contour plot of the hours of daylight as a function of latitude and day of the year, showing approximately 12 hours of daylight at all latitudes during the equinoxes Day is usually defined as the period when sunlight reaches the ground in the absence of local obstacles.[citation needed] On the day of the equinox, the center of the Sun spends a roughly equal amount of time above and below the horizon at every location on the Earth, so night and day are about the same length. Sunrise and sunset can be defined in several ways, but a widespread definition is the time that the top limb of the sun is level with the horizon.[13] With this definition, the day is longer than the night at the equinoxes:[2] 1. From the Earth, the Sun appears as a disc rather than a point of light, so when the centre of the Sun is below the horizon, its upper edge is visible. Sunrise, which begins daytime, occurs when the top of the Sun's disk rises above the eastern horizon. At that instant, the disk's centre is still below the horizon. 2. The Earth's atmosphere refracts sunlight. As a result, an observer sees daylight before the top of the Sun's disk rises above the horizon. In sunrise/sunset tables, the assumed semidiameter (apparent radius) of the Sun is 16 arcminutes and the atmospheric refraction is assumed to be 34 arcminutes. Their combination means that when the upper limb of the Sun is on the visible horizon, its centre is 50 arcminutes below the geometric horizon, which is the intersection with the celestial sphere of a horizontal plane through the eye of the observer.[14] These effects make the day about 14 minutes longer than the night at the equator and longer still towards the poles. The real equality of day and night only happens in places far enough from the equator to have a seasonal difference in day length of at least 7 minutes,[15] actually occurring a few days towards the winter side of each equinox. The times of sunset and sunrise vary with the observer's location (longitude and latitude), so the dates when day and night are equal also depend upon the observer's location. A third correction for the visual observation of a sunrise (or sunset) is the angle between the apparent horizon as seen by an observer and the geometric (or sensible) horizon. This is known as the dip of the horizon and varies from 3 arcminutes for a sunbather stood on the sea shore to 160 arcminutes for a mountaineer on Everest.[16] The light path of such a large dip (over 2½°) accounts for the phenomenon of snow on a mountain peak turning gold in the sunlight long before the lower slopes are illuminated. At the equinoxes, the rate of change for the length of daylight and night-time is the greatest. At the poles, the equinox marks the transition from 24 hours of nighttime to 24 hours of daylight (or vice versa).[citation needed] The word equilux is sometimes (but rarely) used to mean a day in which the durations of light and darkness are equal.[17][note 1] Geocentric view of the astronomical seasonsEdit In the half-year centered on the June solstice, the Sun rises north of east and sets north of west, which means longer days with shorter nights for the northern hemisphere and shorter days with longer nights for the southern hemisphere. In the half-year centered on the December solstice, the Sun rises south of east and sets south of west and the durations of day and night are reversed. Also on the day of an equinox, the Sun rises everywhere on Earth (except at the poles) at about 06:00 and sets at about 18:00 (local solar time). These times are not exact for several reasons: • The Sun is much larger in diameter than the Earth, so that more than half of the Earth could be in sunlight at any one time (due to unparallel rays creating tangent points beyond an equal-day-night line). • Most places on Earth use a time zone which differs from the local solar time by minutes or even hours. For example, if a location uses a time zone with reference meridian 15° to the east, the Sun will rise around 07:00 on the equinox and set 12 hours later around 19:00. • Day length is also affected by the variable orbital speed of the Earth around the sun. This combined effect is described as the equation of time. Thus even locations which lie on their time zone's reference meridian will not see sunrise and sunset at 6:00 and 18:00. At the March equinox they are 7–8 minutes later, and at the September equinox they are about 7–8 minutes earlier. • Sunrise and sunset are commonly defined for the upper limb of the solar disk, rather than its center. The upper limb is already up for at least a minute before the center appears, and the upper limb likewise sets later than the center of the solar disk. Also, when the Sun is near the horizon, atmospheric refraction shifts its apparent position above its true position by a little more than its own diameter. This makes sunrise more than two minutes earlier and sunset an equal amount later. These two effects combine to make the equinox day 12 h 7 min long and the night only 11 h 53 min. Note, however, that these numbers are only true for the tropics. For moderate latitudes, the discrepancy increases (e.g., 12 minutes in London); and closer to the poles it becomes very much larger (in terms of time). Up to about 100 km from either pole, the Sun is up for a full 24 hours on an equinox day. • Height of the horizon changes the day's length. For an observer atop a mountain the day is longer, while standing in a valley will shorten the day. Day arcs of the SunEdit Some of the statements above can be made clearer by picturing the day arc (i.e., the path along which the Sun appears to move across the sky). The pictures show this for every hour on equinox day. In addition, some 'ghost' suns are also indicated below the horizon, up to 18° below it; the Sun in such areas still causes twilight. The depictions presented below can be used for both the northern and the southern hemispheres. The observer is understood to be sitting near the tree on the island depicted in the middle of the ocean; the green arrows give cardinal directions. • In the northern hemisphere, north is to the left, the Sun rises in the east (far arrow), culminates in the south (right arrow), while moving to the right and setting in the west (near arrow). • In the southern hemisphere, south is to the left, the Sun rises in the east (near arrow), culminates in the north (right arrow), while moving to the left and setting in the west (far arrow). The following special cases are depicted: Celestial coordinate systemsEdit The vernal equinox occurs in March, about when the Sun crosses the celestial equator south to north. The term "vernal point" is used for the time of this occurrence and for the direction in space where the Sun is seen at that time, which is the origin of some celestial coordinate systems: Diagram illustrating the difference between the Sun's celestial longitude being zero and the Sun's declination being zero. The Sun's celestial latitude never exceeds 1.2 arcseconds, but is exaggerated in this diagram. Strictly speaking, at the equinox the Sun's ecliptic longitude is zero. Its latitude will not be exactly zero since the Earth is not exactly in the plane of the ecliptic. Its declination will not be exactly zero either. (The ecliptic is defined by the center of mass of the Earth and Moon combined). The modern definition of equinox is the instants when the Sun's apparent geocentric longitude is 0° (northward equinox) or 180° (southward equinox).[18][19][20] See the adjacent diagram. Because of the precession of the Earth's axis, the position of the vernal point on the celestial sphere changes over time, and the equatorial and the ecliptic coordinate systems change accordingly. Thus when specifying celestial coordinates for an object, one has to specify at what time the vernal point and the celestial equator are taken. That reference time is called the equinox of date.[21] The autumnal equinox is at ecliptic longitude 180° and at right ascension 12h. The upper culmination of the vernal point is considered the start of the sidereal day for the observer. The hour angle of the vernal point is, by definition, the observer's sidereal time. Using the current official IAU constellation boundaries – and taking into account the variable precession speed and the rotation of the celestial equator – the equinoxes shift through the constellations as follows[22] (expressed in astronomical year numbering in which the year 0 = 1 BC, −1 = 2 BC, etc.): • The March equinox passed from Taurus into Aries in year −1865, passed into Pisces in year −67, will pass into Aquarius in year 2597, and then into Capricornus in year 4312. In 1489 it came within 10 arcminutes of Cetus without crossing the boundary. • The September equinox passed from Libra into Virgo in year −729, will pass into Leo in year 2439. Cultural aspectsEdit The equinoxes are sometimes regarded as the start of spring and autumn. A number of traditional (harvest) festivals are celebrated on the date of the equinoxes. Effects on satellitesEdit One effect of equinoctial periods is the temporary disruption of communications satellites. For all geostationary satellites, there are a few days around the equinox when the sun goes directly behind the satellite relative to Earth (i.e. within the beam-width of the ground-station antenna) for a short period each day. The Sun's immense power and broad radiation spectrum overload the Earth station's reception circuits with noise and, depending on antenna size and other factors, temporarily disrupt or degrade the circuit. The duration of those effects varies but can range from a few minutes to an hour. (For a given frequency band, a larger antenna has a narrower beam-width and hence experiences shorter duration "Sun outage" windows.)[citation needed] Equinoxes on other planetsEdit When the planet Saturn is at equinox, its rings reflect little sunlight, as seen in this image by Cassini in 2009. Equinoxes occur on any planet with a tilted rotational axis. A dramatic example is Saturn, where the equinox places its ring system edge-on facing the Sun. As a result, they are visible only as a thin line when seen from Earth. When seen from above – a view seen by humans during an equinox for the first time from the Cassini space probe in 2009 – they receive very little sunshine, indeed more planetshine than light from the Sun.[23] This phenomenon occurs once every 14.7 years on average, and can last a few weeks before and after the exact equinox. Saturn's most recent equinox was on 11 August 2009, and its next will take place on 6 May 2025.[24] Mars's most recent equinox was on 5 May 2017 (northern spring), and the next will be on 22 May 2018 (northern autumn). See alsoEdit 1. ^ This meaning of "equilux" is rather modern (c. 1985 to 1986) and unusual. Technical references since the beginning of the 20th century (c. 1910) use the terms "equilux" and "isophot" to mean "of equal illumination" in the context of curves showing how intensely lighting equipment will illuminate a surface. See for instance John William Tudor Walsh, Textbook of Illuminating Engineering (Intermediate Grade), I. Pitman, 1947. The earliest confirmed use of the modern meaning was in a post on the Usenet group net.astro dated 14 March 1986 net.astro - Spring Equilux Approaches, which refers to "discussion last year exploring the reasons why equilux and equinox are not coincident". Use of this particular pseudo-latin protologism can only be traced to a extremely small (less than six) number of predominently US American people in such online media for the next 20 years until its broader adoption as a neologism (c. 2006), and then its subsequent use by more mainstream organisations (c. 2012) The Equinox and Solstice, UK Meteorological Office. 1. ^ United States Naval Observatory (21 September 2015). "Earth's Seasons: Equinoxes, Solstices, Perihelion, and Aphelion, 2000-2025". Retrieved 9 December 2015. 2. ^ a b "Equinoxes". USNO Astronomical Information Center FAQ. Retrieved 4 September 2015. 3. ^ "March Equinox - Equal Day and Night, Nearly". Time and Date. 2017. Retrieved 22 May 2017. 4. ^ Michelle Skye (2007). Goddess Alive!: Inviting Celtic & Norse Goddesses Into Your Life. Llewellyn Worldwide. pp. 69–. ISBN 978-0-7387-1080-8. 5. ^ Howard D Curtis (5 October 2013). Orbital Mechanics for Engineering Students. Butterworth-Heinemann. pp. 188–. ISBN 978-0-08-097748-5. 6. ^ Mohinder S. Grewal; Lawrence R. Weill; Angus P. Andrews (5 March 2007). Global Positioning Systems, Inertial Navigation, and Integration. John Wiley & Sons. pp. 459–. ISBN 978-0-470-09971-1. 7. ^ Nathaniel Bowditch; National Imagery and Mapping Agency (2002). The American practical navigator : an epitome of navigation. Paradise Cay Publications. pp. 229–. ISBN 978-0-939837-54-0. 8. ^ Exploring the Earth. Allied Publishers. pp. 31–. ISBN 978-81-8424-408-3. 9. ^ Paula LaRocque (2007). On Words: Insights Into How Our Words Work - And Don't. Marion Street Press. pp. 89–. ISBN 978-1-933338-20-0. 10. ^ Popular Astronomy. 1945. 11. ^ Notes and Queries. Oxford University Press. 1895. 12. ^ Spherical Astronomy. Krishna Prakashan Media. pp. 233–. GGKEY:RDRHQ35FBX7. 13. ^ Forsythe, William C; Rykiel, Edward J; Stahl, Randal S; Wu, Hsin-i; Schoolfield, Robert M (1995). "A model comparison for daylength as a function of latitude and day of year". Ecological Modelling. 80: 87. doi:10.1016/0304-3800(94)00034-F. 14. ^ Seidelman, P. Kenneth, ed. (1992). Explanatory Supplement to the Astronomical Almanac. Mill Valley, CA: University Science Books. p. 32. ISBN 0-935702-68-7. 15. ^ "Sunrise and Sunset". 21 October 2002. Retrieved 22 September 2017. 16. ^ Biegert, Mark (21 October 2015). "Correcting Sextant Measurements For Dip". Math Encounters (blog). Retrieved 22 September 2017. 17. ^ Owens, Steve (20 March 2010). "Equinox, Equilux, and Twilight Times". Dark Sky Diary (blog). Retrieved 31 December 2010. 18. ^ Meeus, Jean (1997). Mathematical Astronomy Morsels. 19. ^ United States Naval Observatory (2006). Astronomical Almanac 2008. Glossary Chapter. 20. ^ Meeus, Jean (1998). Astronomical Algorithms, Second Edition. 21. ^ Montenbruck, Oliver; Pfleger, Thomas. Astronomy on the Personal Computer. Springer-Verlag. p. 17. ISBN 0-387-57700-9. 22. ^ J. Meeus; Mathematical Astronomical Morsels; ISBN 0-943396-51-4. 23. ^ "PIA11667: The Rite of Spring". Jet Propulsion Laboratory, California Institute of Technology. Retrieved 21 March 2014. 24. ^ Lakdawalla, Emily (7 July 2016). "Oppositions, conjunctions, seasons, and ring plane crossings of the giant planets". The Planetary Society. Retrieved 31 Jan 2017. External linksEdit
Bemidbar: Tribes in Four Directions May 22, 2015 at 10:07 am \| Posted in Bemidbar \| 1 Comment Tags: , , , by Melissa Carpenter, maggidah The Israelites leave Egypt in a rush, in a swarm, in no particular order. At the beginning of the book of Numbers/Bemidbar (“In a wilderness”), they prepare to leave Mount Sinai in orderly formation. One difference is that now they have made the portable sanctuary for God. The tribe of Levi is responsible for the sanctuary, both when the people are camping and the sanctuary is assembled, and when they are marching and the Levites are carrying the disassembled parts. So the Levites camp in the middle of the Israelites, immediately around the sanctuary: the priests (kohanim) and Moses on the east, the clan of Kehat on the south, the clan of Geirshon on the west, and the clan of Merari on the north. (See my post Naso (and Bemidbar): Four Duties, Four Directions for details.) Camping Formation Camping Formation Surrounding the Levites, but at a greater distance from the sanctuary, are the remaining twelve tribes. They camp and march in four blocks: east, south, west, and north. Each block has a leading tribe and two supporting tribes. God spoke to Moses and to Aaron, saying: Each man shall camp next to his banner, with the insignia of their father’s house. They shall camp at a distance around the Tent of Meeting. And those camping keidmah, mizrachah, shall be the banner of the camp of Yehudah… And those camping next to them: the tribe of Yissachar …the tribe of Zevulun … All those counted for the camp of Yehudah were 186,400, by their legions; the first to pull out. (2:1-9) keidmah (קֵדְמָה) = to the east, in front, originally. From the root verb kadam (קָדַם) = came toward, went first, confronted, preceded. mizrachah (מִזְרָחָה) = to the east, toward sunrise. From the root verb zarach (זָרַח) = shone forth. When the Israelites break camp, the tribe of Yehudah (יְהוּדָה), Judah in English, sets off toward the east, then veers in whatever direction the people will actually travel that day. In the Torah, the east represents origins and birth. The front gate of the courtyard around the tent-sanctuary is on the east side. So is the curtain at the entrance into the sanctuary proper, which only priests (and Moses) are allowed to enter. sunriseMoses and the priests (Aaron and his sons) camp just east of the courtyard gate. Farther east is the camp of Yehudah, accompanied by Yissachar and Zevulun. In the book of Genesis, Yehudah gradually becomes the leader of all the brothers who confront Joseph. King David was from the tribe of Yehudah, and after Assyria conquered the northern kingdom of Israel, the kingdom of Yehudah survived for two more centuries. When you face east, the south is on your right. That means Reuven is Yehudah’s right-hand man in this week’s Torah portion: The banner of the camp of Reuven shall be teymanahAnd those camping next to them shall be the tribe of Shimon…and the tribe of Gad… All those counted for the camp of Reuven were 161,450, by their legions; and they shall pull out second. (2:10-16) teymanah (תֵּימָנָה) = to the south. (From the root yamin, יָמִין, = right side, south side, right hand.) In the Torah, south is the direction of the Negev desert, the kingdom of Edom in the hills of Sei-ir, Mount Paran, and Mount Sinai. Moses says in his final speech to the Israelites: God came from Sinai, and shone forth from Sei-ir for them, having radiated from Mount Paran… (Deuteronomy/Devarim 33:2) menorahAll of this divine light dawns in the south. Inside the sanctuary tent, the menorah (lampstand) is by the south wall. The Levite clan of Kehat camps just south of the sanctuary. Beyond them are the camps of Reuven and its two assisting tribes, Shimon and Gad. Reuven is the firstborn of the twelve sons of Jacob, a.k.a. Israel, but he does not inherit the leadership of the extended family. His tribe gets second place, but at least it is close to God’s illumination in the south. Then the Tent of Meeting shall set out, the camp of the Levites, in the middle of the camps; as they camp, so shall they pull out, each man in position next to their banners. (2:17) Next come the tribes in the back, to the west of the sanctuary: The banner of the camp of Efrayim by its legions shall be yammah…And next to them shall be the tribe on Menasheh…and the tribe of Binyamin… All those counted for the camp of Efrayim: 108,100, by their legions; and they shall pull out third. (2:18-24) yammah (יָמָּה) = to the west, toward the (Mediterranean) Sea (yam). sunsetThe other Biblical Hebrew word for west is ma-arav (מַעֲרָב), toward the sunset. In the Bible, the west represents the unknown: the great sea, the future, and death. The western end of the tent sanctuary is the back wall of the Holy of Holies. The Levite clan of Geirshon camps just west of the sanctuary courtyard. Behind them, in the position farthest west, is the tribe of Efrayim and its assistant tribes, Menasheh and Binyamin. In Genesis, Jacob rearranges his hands when he blesses Joseph’s two sons Menasheh and Efrayim, so that even though Menasheh is older, Efrayim receives the blessing of the firstborn. Thus the chief tribe on the east is named after Yehudah, who took the role of the firstborn by his own leadership. The chief tribe on the south is named after Reuven, who was the firstborn but lost his position. And the chief tribe on the west is named after Efrayim, who was born second but promoted to firstborn. The chief tribe on the north, Dan, does not even care about the rights of the firstborn. The banner of the camp of Dan shall be tzafonah, by their legions… And those camping next to them shall be the tribe of Asher…and the tribe of Naftali… All those counted for the camp of Dan: 157,600; as the last they shall pull out, next to their banners. (2:25-31) tzafonah (צָפֹנָה) = to the north. From the same root as the verb tzafan (צָפַן) = hide treasure, hide in ambush. mountainIn the Bible, the north is where the Assyrians came from when they swept down and conquered the kingdom of Israel. It is also the direction of Mount Tzafon, a peak near the Mediterranean coast in present-day northern Syria. In Canaanite mythology, when Baal became the supreme god, he built a palace on top of Mount Tzafon, and the gods assembled there. Inside the sanctuary, the table displaying the twelve loaves of bread stands by the north wall. The loaves stand for the tribes of Israel, on display before God. The Levite clan of Merari camps just north of the sanctuary. Dan is the leader of the three tribes camping farther north. Jacob’s fifth son, Dan, is unimportant in the book of Genesis. But in Judges the tribe of Dan abandons its allotted territory and heads north. As the tribe crosses Efrayim’s territory, it captures a priest and a molten idol. Then Dan seizes the Canaanite city of Laish. Both conquests are surprise attacks; perhaps the whole tribe of Dan is good at hiding in ambush. Laish, renamed Dan, becomes the northernmost city in the kingdom of Israel. The word for northward, tzafonah, is related not only to hiding, but also to the center of Canaanite religion at Mount Tzafon. In the first book of Kings, the city of Dan has its own temple and a golden calf. Maybe when the Israelites break camp the tribe of Dan pulls out last because it is not wholehearted about either the community of Israel or its god. Dan goes its own way, then follows the rest of Israelite and its sanctuary after all. compassWhen the Israelites leave Mount Sinai, they march and camp in a formation that positions each tribe in relation to the four directions and to the sanctuary in the center. Today, we also need to put what is holy to us at the center of our lives. Otherwise we will swarm about aimlessly. In addition to holding a holy center, we need to operate in the world. The four compass points might indicate four ways of operating. If we are fortunate, our primary strategy is represented by the east and Yehudah: taking the lead in our own lives and setting off on new ventures. A second strategy is represented by the south and Reuven: seeking and remembering moments of illumination. Third is the strategy represented by the west and Efrayim: humbly accepting the unknown future, as well as unexpected blessings from those wiser than we. Finally there is the strategy represented by the north and Dan: stepping away when we need to, coming out of hiding, and doing the unexpected. May all these elements be present when we organize our own lives. 1 Comment » RSS feed for comments on this post. TrackBack URI 1. Thank you so much for giving direction for setting direction. Tomorrow, we set out to the south and return home. On Shavuot, traveling to the sacred waters of lago atitlan, I take your teachings with us. Love Elisabeth Leave a Reply You are commenting using your account. Log Out / Change ) Twitter picture Facebook photo Google+ photo Connecting to %s Blog at Entries and comments feeds. %d bloggers like this:
What is random? That which cannot be predicted with any confidence. But there is a weak and a strong sense to ‘unpredictable’. We might say that the motion of a leaf blown about by the wind is ‘random’ ― but then that may simply be because we don’t know the exact speed and direction of the wind or the aerodynamic properties of this particular leaf. In classical mechanics, there is no room for randomness since all physical phenomena are fully determined and so could in principle be predicted if one had sufficient data. Indeed, the French astronomer Laplace claimed that a super-mind, aware of the current positions and momenta of all particles currently in existence could predict the entire future of the universe from Newtonian principles. In practice, of course, one never does know the initial conditions of any physical system perfectly. Whether this is going to make a substantial difference to the outcome hinges on how sensitively dependent on the initial conditions the system happens to be. Whether or not the flap of a butterfly’s wings in the bay of Tokyo could give rise to a hurricane in Barbados as chaos theory claims, systems that are acutely sensitive to initial conditions undoubtedly exist, and this is, of course, what makes accurate weather forecasting so difficult. Gaming houses retire dice after a few hundred throws because of inevitable imperfections creeping in and a certain Jagger made a good deal of money because he noted that certain numbers seemed to come up slightly more often than others on a particular roulette wheel and bet on them. Later on, he guessed that the cause was a slight scratch on this particular wheel and there seems to have been something in this for eventually the management thwarted him by changing the roulette wheels every night (Note 1). All sorts of other seemingly ‘random’ phenomena turn out, on close examination, to exhibit a definite bias or trend: for example, certain digits turn up in miscellaneous lists of data more often than others (Bensford’s Law) and this bias, or rather its absence, has been successfully used to detect tax fraud. There is, however, something very unsatisfactory about the ‘unpredictable because of insufficient data’ definition of randomness: it certainly does not follow that there is an inherent randomness in Nature, nor does chaos theory imply that this is the case either. Curiously, quantum mechanics, that monstrous but hugely successful creation of modern science, does maintain that there is an underlying randomness at the quantum level. The radioactive decay of a particular nucleus is held to be not only unforeseeable but actually ‘random’ in the strong sense of the word ― though the bulk behaviour of a collection of atoms can be predicted with confidence. Likewise, genetic mutation, the pace setter of evolution, is regarded today as not just being unpredictable but, in certain cases at least, truly ‘random’. Randomness seems to have made a strong and unexpected come-back since it is now a key player in the game or business of living ― a bizarre volte-face given that science had previously been completely deterministic. The ‘common sense’ meaning of randomness is the lack of any perceived regularity or repeating pattern in a sequence of events, and this will do for our present purposes (Note 2). Now, it is extremely difficult to generate a random sequence of events in the above sense and in the recent past there was big money involved in inventing a really good random number generator. Strangely, most random number generators are not based on the behaviour of actual physical systems but depend on algorithms deliberately concocted by mathematicians. Why is this? Because, to slightly misquote Moshe, “complete randomness is a kind of perfection”(Note 3). The more one thinks about the idea of randomness, the weirder the concept appears since a truly ‘random’ event does not have a causal precursor (though it usually does have a consequence). So, how on earth can it occur at all and where does it come from? It arrives, as common language puts it very well, ‘out of the blue’. Broadly speaking there are two large-scale tendencies in the observable universe: firstly the dissipation of order and decline towards thermal equilibrium and mediocrity because of the ‘random’ collision of molecules, secondly the spontaneous emergence of complex order from processes that appear to be, at least in part, ‘random’. The first principle is enshrined in the 2nd Law of Thermo-dynamics : the entropy (roughly extent of disorder) of a closed system always increases, or (just possibly) stays the same. Contemporary biologists have a big problem with the emergence of order and complexity in the universe since it smacks of creationism. But at this very moment the molecules of tenuous dispersed gases are clumping together to form stars and the trend of life forms on earth is, and has been for some time, a movement from relative structural simplicity (bacteria, archaea &c.) to the unbelievable complexity of plants and mammals. Textbooks invariably trot out the caveat that any local ‘reversal of entropy’ must always be paid for by increased entropy elsewhere. This is, however, not a claim that has been, or ever could be, comprehensively tested on a large scale, nor is it at all ‘self-evident’ (Note 4). What we do know for sure is that highly organized structures can and do emerge from very unpromising beginnings and this trend seems to be locally on the increase ― though it is conceivable that it might be reversed. For all that, it seems that there really are such things as truly random events and they keep on occurring. What can one conclude from this? That, seemingly, there is a powerful mechanism for spewing forth random, uncaused events, and that this procedure is, as it were, ‘hard-wired’ into the universe at a very deep level. But this makes the continued production of randomness just as mysterious, or perhaps even more so, than the capacity of whatever was out there in the beginning to give rise to complex life! The generation of random micro-events may in fact turn out to be just about the most basic and important physical process there is. For what do we need to actually produce a ‘world’? As far as I am concerned, there must be something going on, in other words we need ‘events’ and these events require a source of some sort. But this source is remote and we don’t need to attribute to it any properties except that of being a permanent store of proto-events. The existence of a source is not enough though. Nothing would happen without a mechanism to translate the potential into actuality, and the simplest and, in the long run, most efficient mechanism is to have streams of proto-events projected outwards from the source at random. Such a mechanism will, however, by itself not produce anything of much interest. To get order emerging from the primeval turmoil we require a second mechanism, contained within the first, which enables ephemeral random events to, at least occasionally, clump together, and eventually build up, simply by spatial proximity and repetition, coherent and quasi-permanent event structures (Note 5). One could argue that this possibility, namely the emergence of ‘order from chaos’, however remote, will eventually come up ― precisely because randomness in principle covers all realizable possibilities. A complex persistent event conglomeration may be termed a ‘universe’, and even though an incoherent or contradictory would-be ‘universe’ will presumably rapidly collapse into disorder, others may persist and maybe even spawn progeny. So, which tendency is going to win out, the tendency towards increasing order or reversion to primeval chaos? It certainly looks as if a recurrent injection of randomness is necessary for the ‘health’ of the universe and especially for ourselves ― this is one of the messages of natural selection and it explains, up to a point, the extraordinarily tortuous process of meiosis (roughly sexual reproduction) as against mitosis when a cell simply duplicates its DNA and splits in two (Note 6). But there is also the “nothing succeeds like success” syndrome. And, interestingly, the evolutionary biologist John Bonner argues that microorganisms “are more affected by randomness than large complex organisms” (Note 7). This and related phenomena might tip the balance in favour of order and complexity ― though specialization also makes the larger organisms more vulnerable to sudden environmental changes. SH Note 1 This anecdote is recounted and carefully analysed in The Drunkard’s Walk by Mlodinow. Note 2 Alternative definitions of randomness abound. There is the frequency definition whereby, “If a procedure is repeated over and over again indefinitely and one particular outcome crops up as many times as any other possible outcome, the sequence is considered to be random” (adapted from Peirce). And Stephen Wolfram writes: “Define randomness so that something is considered random only if no short description whatsoever exists of it” (Stephen Wolfram). Note 3 Moshe actually wrote “Complete chaos is a kind of perfection”. Note 4 “The vast majority of current physics textbooks imply that the Second Law is well established, though with surprising regularity they say that detailed arguments for it are beyond their scope. More specialized articles tend to admit that the origins of the Second Law remain mysterious” (Stephen Wolfram, A New Kind of Science p. 1020 Note 5 This is essentially the principle of ‘morphic resonance’ advanced by Rupert Sheldrake. Very roughly, the idea is that if a certain event, or cluster of events, has occurred once, it is slightly more likely to occur again, and so on and so on. Habit thus eventually becomes physical law, or can do. At bottom the ‘Gambler’s Fallacy’ contains a grain of truth: I suspect that current events are never completely independent of previous similar occurrences despite what statisticians say. Clearly, for the theory to work, there must be a very slow build-up and a tipping point after which a trend really takes off. We require in effect the equivalent of the Schrodinger equation to show how initial randomness evolves inexorably towards regularity and order. Note 6. In meiosis not only does the offspring get genes from two individuals rather than one, but there is a great deal of ‘crossing over’ of segments of chromosomes and this reinforces the mixing process. Note 7 The reason given for this claim is that there are many more developmental steps in the construction of a complex organism and so “if an earlier step fails through a deleterious mutation, the result is simple: the death of the embryo”. On the other hand “being small means very few developmental steps, with little or no internal selection” and hence a far greater number of species, witness radiolaria (50,000) and diatoms (10,000). See article Evolution, by chance? in the New Scientist 20 July 2013 and Randomness in Evolution by John Bonner. “He who examines things in their growth and first origins, obtains the clearest view of them” Aristotle. Calculus was developed mainly in order to deal with two seemingly intractable problems: (1) how to estimate accurately the areas and volumes of irregularly shaped figures and (2) how to predict physical behaviour once you know the initial conditions and the ‘rates of change’. We humans have a strong penchant towards visualizing distances and areas in terms of straight lines, squares and rectangles ― I have sometimes wondered whether there might be an amoeba-type civilization which would do the reverse, visualizing straight lines as consisting of curves, and rectangles as extreme versions of ellipses. ‘Geo-metria’ (lit. ‘land measurement’) was, according to Herodotus, first developed by the Egyptians for taxation purposes. Now, once you have chosen a standard unit of distance for a straight line and a standard square as a unit of area, it becomes a relatively simple matter to evaluate the length of any straight line and any rectangle (provided they are not too large or too distant, of course). Taking things a giant step forward, various Greek mathematicians, notably Archimedes, wondered whether one could in like manner estimate accurately the ‘length’ of arbitrary curves and the areas of arbitrarily shaped expanses. At first sight, this seems impossible. A curve such as the circumference of a circle is not a straight line and never will become one. However, by making your unit of length progressively smaller and smaller, you can ‘measure’ a given curve by seeing how many equal little straight lines are needed to ‘cover’ it as nearly as possible. Lacking power tools, I remember once deciding to reduce a piece of wood of square section to a cylinder using a hand plane and repeatedly running across the edges. This took me a very long time indeed but I did see the piece of wood becoming progressively more and more cylindrical before my eyes. One could view a circle as the ‘limiting case’ of a regular polygon with an absolutely enormous number of sides which is basically how Archimedes went about things with his ‘method of exhaustion’ (Note 1). It is important to stop at this point and ask under what conditions this stratagem is likely to work. The most important requirement is the ability to make your original base unit progressively smaller at each successive trial measurement while keeping them proportionate to each other. Though there is no need to drag in the infinite which the Greeks avoided like the plague, we do need to suppose that we can reduce in a regular manner our original unit of length indefinitely, say by halving it at each trial. In practice, this is never possible and craftsmen and engineers have to call a halt at some stage, though, hopefully, only when an acceptable level of precision has been attained. This is the point historically where mathematics and technology part company since mathematics typically deals with the ‘ideal’ case, not with what is realizable or directly observable. With the Greeks, the gulf between observable physical reality and the mathematical model has started to widen. What about (2), predicting physical behaviour when you know the initial conditions and the ‘rates of change’? This was the great achievement of the age of Leibnitz and Newton. Newton seems to have invented his version of the Calculus in order to show, amongst other things, that planetary orbits had to be ellipses, as Kepler had found was in fact the case for Mars. Knowing the orbit, one could predict where a given planet or comet would be at a given time. Now, a ‘rate of change’ is not an independently ‘real’ entity: it is a ratio of two more fundamental items. Velocity, our best known ‘rate of change’, does not have its own unit in the SI system ― but the metre (the unit of distance) and the second (the unit of time) are internationally agreed basic units. So we define speed in terms of metres per second. Now, the distance covered in a given time by a body is easy enough to estimate if the body’s motion is in a straight line and does not increase or decrease; but what about the case where velocity is changing from one moment to the next? As long as we have a reliable correlation between distance and time, preferably in the form of an algebraic formula y = f(t), Newton and others showed that we can cope with this case in somewhat the same way as the Greeks coped with irregular shapes. The trick is to assume that the supposedly ever-changing velocity is constant (and thus representable by a straight line) over a very brief interval of time. Then we add up the distances covered in all the relevant time intervals. In effect, what the age of Newton did was to transfer the exhaustion procedure of Archimedes from the domain of statics to dynamics. Calculus does the impossible twice over: the Integral Calculus ‘squares the circle’, i.e. gives its area in terms of so many unit squares, while the Differential Calculus allows us to predict the exact whereabouts of something that is perpetually on the move (and thus never has a fixed position). For this procedure to work, it must be possible, at least in principle, to reduce all spatial and temporal intervals indefinitely. Is physical reality actually like this? The post-Renaissance physicists and mathematicians seem to have assumed that it was, though such assumptions were rarely made explicit. Leibnitz got round the problem mathematically by positing ‘infinitesimals’ and ultimate ratios between them : his ‘Infinitesimal Calculus’ gloriously “has its cake and eats it too”. For, in practice, when dealing with an ‘infinitesimal’, we are (or were once) at liberty to regard it as entirely negligible in extent when this suits our purposes, while never permitting it to be strictly zero since division by zero is meaningless. Already in Newton’s own lifetime, Bishop Berkeley pointed out the illogicality of the procedure, as indeed of the very concept of ‘instantaneous velocity’. The justification of the procedure was essentially that it seemed to work magnificently in most cases. Why did it work? Calculus typically deals with cases where there are two levels, a ‘micro’ scale’ and a ‘macro scale’ which is all that is directly observable to humans ― the world of seconds, metres, kilos and so on. If a macro-scale property or entity is believed to increase by micro-scale chunks, we can (sometimes) safely discard all terms involving δt (or δx) which appear on the Right Hand Side but still have a ‘micro/micro’ ratio on the Left Hand Side of the equation (Note 2). This ‘original sin’ of Calculus was only cleaned up in the late 19th century by the key concept of the mathematical limit. But there was a price to pay: the mathematical model had become even further away removed from observable physical reality. The artful concept of a limit does away with the need for infinitesimals as such. An indefinitely extendable sequence or series is said to ‘converge to a limit’ if the gap between the suggested limit and any and every term after a certain point is less than any proposed non-negative quantity. For example, it would seem that the sequence ½; 1/3; ¼……1/n gets closer and closer to zero as n increases, since for any proposed gap, we can do better by making n twice as large and 1/n twice as small. This definition gets round problem of actual division by zero. But what the mathematician does not address is whether in actual fact a given process ever actually attains the mathematical limit (Note 3), or how near it gets to it. In a working machine, for example, the input energy cannot be indefinitely reduced and still give an output, because there comes a point when the input is not capable of overcoming internal friction and the machine stalls. All energy exchange is now known to be ‘quantized’ ― but, oddly, ‘space’ and ‘time’ are to this day still treated as being ‘continuous’ (which I do not believe they are). In practice, there is almost always a gulf between how things ought to behave according to the mathematical treatment and the way things actually do or can behave. Today, because of computers, the trend is towards slogging it out numerically to a given level of precision rather than using fancy analytic techniques. Calculus is still used even in cases where the minimal value of the independent variable is actually known. In population studies and thermo-dynamics, for example, the increase δx or δn cannot be less than a single person, or a single molecule. But if we are dealing with hundreds of millions of people or molecules, Calculus treatment still gives satisfactory results. Over some three hundred years or so Calculus has evolved from being an ingenious but logically flawed branch of applied mathematics to being a logically impeccable branch of pure mathematics that is rarely if ever directly embodied in real world conditions. SH Note 1 It is still a subject of controversy whether Archimedes can really be said to have invented what we now call the Integral Calculus, but certainly he was very close. Note 2 Suppose we have two variables, one of which depends on the other. The dependent variable is usually noted as y while the independent variable is, in the context of dynamics, usually t (for time). We believe, or suppose, that any change in t, no matter how tiny, will result in a corresponding increase (or decrease) in y the dependent variable. We then narrow down the temporal interval δt to get closer and closer to what happens at a particular ‘moment’, and take the ‘final’ ratio which we call dy/dt. The trouble is that we need to completely get rid of δt on the Right Hand Side but keep it non-zero on the Left Hand Side because dy/0 is meaningless ― it would correspond to the ‘velocity’ of a body when it is completely at rest. Note 3 Contrary to what is generally believed, practically all the sequences we are interested in do not actually attain the limit to which they are said to converge. Mathematically, this does no9t matter — but logically and physically it often does. What is time? Time is succession. Succession of what? Of events, occurrences, states. As someone put it, time is Nature’s way of stopping everything happening at once. In a famous thought experiment, Descartes asked himself what it was not possible to disbelieve in. He imagined himself alone in a quiet room cut off from the bustle of the world and decided he could, momentarily at least, disbelieve in the existence of France, the Earth, even other people. But one thing he absolutely could not disbelieve in was that there was a thinking person, cogito ergo sum (‘I think, therefore I am’). Those of us who have practiced meditation, and many who have not, know that it is quite possible to momentarily disbelieve in the existence of a thinking/feeling person. But what one absolutely cannot disbelieve in is that thoughts and bodily sensations of some sort are occurring and, not only that, that these sensations (most of them anyway) occur one after the other. One outbreath follows an inbreath, one thought leads on to another and so on and so on until death or nirvana intervenes. Thus the grand conclusion: There are sensations, and there is succession. Can anyone seriously doubt this? Succession and the Block Universe That we, as humans, have a very vivid, and more often than not acutely painful, sense of the ‘passage of time’ is obvious. A considerable body of the world’s literature is devoted to bewailing the transience of life, while one of the world’s four or five major religions, Buddhism, has been well described as an extended meditation on the subject. Cathedrals, temples, marble statues and so on are attempts to defy the passage of time, aars long vita brevis. However, contemporary scientific doctrine, as manifested in the so-called ‘Block Universe’ theory of General Relativity, tells us that everything that occurs happens in an ‘eternal present’, the universe ‘just is’. In his latter years, Einstein took the idea seriously enough to mention it in a letter of consolation to the son of his lifelong friend, Besso, on the occasion of the latter’s death. “In quitting this strange world he [Michel Besso] has once again preceded me by a little. That doesn’t mean anything. For those of us who believe in physics, this separation between past, present and future is an illusion, however tenacious.” Never mind the mathematics, such a theory does not make sense. For, even supposing that everything that can happen during what is left of my life has in some sense already happened, this is not how I perceive things. I live my life day to day, moment to moment, not ‘all at once’. Just possibly, I am quite mistaken about the real state of affairs but it would seem nonetheless that there is something not covered by the ‘eternal present’ theory, namely my successive perception of, and participation in, these supposedly already existent moments (Note 1). Perhaps, in a universe completely devoid of consciousness, ‘eternalism’ might be true but not otherwise. Barbour, the author of The End of Time, argues that we do not ever actually experience ‘time passing’. Maybe not, but this is only because the intervals between different moments, and the duration of the moments themselves, are so brief that we run everything together like movie stills. According to Barbour, there exists just a huge stack of moments, some of which are interconnected, some not, but this stack has no inherent temporal order. But even if it were true that all that can happen is already ‘out there’ in Barbour’s Platonia (his term), picking a pathway through this dense undergrowth of discrete ‘nows’ would still be a successive procedure. I do not think time can be disposed of so easily. Our impressions of the world, and conclusions drawn by the brain, can be factually incorrect ― we see the sun moving around the Earth for example ― but to deny either that there are sense impressions and that they appear successively, not simultaneously, strikes me as going one step too far. As I see it, succession is an absolutely essential component of lived reality and either there is succession or there is just an eternal now, I see no third possibility. What Einstein’s Special Relativity does, however, demonstrate is that there is seemingly no absolute ‘present moment’ applicable right across the universe (because of the speed of light barrier). But in Special Relativity at least succession and causality still very much exist within any particular local section, i.e. inside a particular event’s light cone. One can only surmise that the universe as a whole must have a complicated mosaic successiveness made up of interlocking pieces (tesserae). In various areas of physics, especially thermo-dynamics, there is much discussion of whether certain sequences of events are reversible or not, i.e. could take place other than in the usual observed order. This is an important issue but is a quite different question from whether time (in the sense of succession) exists. Were it possible for pieces of broken glass to spontaneously reform themselves into a wine glass, this process would still occur successively and that is the point at issue. Time as duration ‘Duration’ is a measure of how long something lasts. If time “is what the clock says” as Einstein is reported to have once said, duration is measured by what the clock says at two successive moments (‘times’). The trick is to have, or rather construct, a set of successive events that we take as our standard set and relate all other sets to this one. The events of the standard set need to be punctual and brief, the briefer the better, and the interval between successive events must be both noticeable and regular. The tick-tock of a pendulum clock provided such a standard set for centuries though today we have the much more regular expansion and contraction of quartz crystals or the changing magnetic moments of electrons around a caesium nucleus. Continuous or discontinuous? A pendulum clock records and measures time in a discontinuous fashion: you can actually see, or hear, the minute or second hand flicking from one position to another. And if we have an oscillating mechanism such as a quartz crystal, we take the extreme positions of the cycle which comes to the same thing. However, this schema is not so evident if we consider ‘natural’ clocks such as sundials which are based on the apparent continuous movement of the sun. Hence the familiar image of time as a river which never stops flowing. Newton viewed time in this way which is why he analysed motion in terms of ‘fluxions’, or ‘flowings’. Because of Calculus, which Newton invented, it is the continuous approach which has overwhelmingly prevailed in the West. But a perpetually moving object, or one perceived as such, is useless for timekeeping: we always have to home in on specific recurring configurations such as the longest or shortest shadow cast. We have to freeze time, as it were, if we wish to measure temporal intervals. Event time The view of time as something flowing and indivisible is at odds with our intuition that our lives consist of a succession of moments with a unique orientation, past to future, actual to hypothetical. Science disapproves of the latter common sense schema but is powerless to erase it from our thoughts and feelings: clearly the past/present/future schema is hard-wired and will not go away. If we dispense with continuity, we can also get rid of ‘infinite divisibility’ and so we arrive at the notion, found in certain early Buddhist thinkers, that there is a minimum temporal interval, the ksana. It is only recently that physicists have even considered the possibility that time is ‘grainy’, that there might be ‘atoms of time’, sometimes called chronons. Now, within a minimal temporal interval, there would be no possible change of state and, on this view, physical reality decomposes into a succession of ‘ultimate events’ occupying minimal locations in space/time with gaps between these locations. In effect, the world becomes a large (but not infinite) collection of interconnected cinema shows proceeding at different rates. Joining forces with time The so-called ‘arrow of time’ is simply the replacement of one localized moment by another and the procedure is one-way because, once a given event has occurred, there is no way that it can be ‘de-occurred’. Awareness of this gives rise to anxiety ― “the moving finger writes, and having writ/ Moves on, nor all thy piety or wit/Can lure it back to cancel half a line….” Most religious, philosophic and even scientific systems attempt to allay this anxiety by proposing a domain that is not subject to succession, is ‘beyond time’. Thus Plato and Christianity, the West’s favoured religion. And even if we leave aside General Relativity, practically all contemporary scientists have a fervent belief in the “laws of physics” which are changeless and in effect wholly transcendent. Eastern systems of thought tend to take a different approach. Instead of trying desperately to hold on to things such as this moment, this person, this self, Buddhism invites us to ‘let go’ and cease to cling to anything. Taoism goes even further, encouraging us to find fulfilment and happiness by identifying completely with the flux of time-bound existence and its inherent aimlessness. The problem with this approach is, however, that it is not clear how to avoid simply becoming a helpless victim of circumstance. The essentially passive approach to life seemingly needs to be combined with close attention and discrimination ― in Taoist terms, Not-Doing must be combined with Doing. Note 1 And if we start playing with the idea that not only the events but my perception of them as successive is already ‘out there’, we soon get involved in infinite regress. Time and place “Absolute, true and mathematical time, of itself, and from its own nature, flows equably without relation to anything external” (Newton, Principia Scholium to Definition VIII) Newton does not say whether there are any absolute units or measures to his absolute time, i.e. whether any exact meaning is to be given to the term ‘moment’. Rather he implies that there are no such units since time ‘flows’, i.e. is continuous. He does, however, contrast ‘absolute time’ with “relative, apparent, and common time” which is “some sensible and external (whether accurate or unequable) measure of duration by the means of motion…. such as an hour, a day, a month, a year”. He also believes that each object has what he calls a ‘place’ which fixes it in absolute space and absolute time. “All things are placed in time as to order of succession; and in space as to order of situation. It is from their essence or nature that they are places; and that the primary places of things should be movable, is absurd. These are therefore the absolute places; and translations out of these places are the only absolute motions” (Ib.) This view is to be contrasted with Leibnitz’s which sees the position and motion of bodies as essentially relative: a body’s ‘place’ merely indicates where it is in relation to other bodies at a given moment. This ‘relational’ approach has been adopted by several modern physicists beginning with Mach. As Lee Smolin puts it, “Space is nothing apart from the things that exist; it is only an aspect of the relationships that hold between things” (Smolin, Three Roads to Quantum Gravity p. 18). Much the same goes for time: “Time also has not absolute meaning…..Time is described only in terms of change in the network of relationships that describes space” (Smolin, Ib.) What about ‘change of place with respect to time’ or motion? To determine a body’s motion we have to establish what a body’s ‘place’ was before motion began and the same body’s ‘place’ when motion has ceased. Newton concedes that the ‘parts of space’ cannot be seen and so we have to assume that there is a body which is immoveable and measure everything with respect to it. “From the positions and distances of things from any body considered as immovable, we define all places” (p. 8). But is there such a thing as an immovable body ? Newton is undecided about this though he would like to answer in the affirmative. He writes, “It may be that there is no body really at rest” but a few lines further on he adds that “in the remote regions of the fixed stars, or perhaps far beyond them, there may be some body absolutely at rest”. However, since such bodies are so far away, they are of little use as reference points practically speaking while “absolute rest cannot be determined from the position of bodies in our region”. Newton concludes that we have to make do with ‘relative places’ though he is clearly bothered by this since it means that motion will also have to be treated as relative. This leads straight on to the Galilean ‘law’ that rest and constant straight line motion cannot be distinguished. Newton’s position is, however, to be contrasted with the modern interpretation of Galileo’s claim. For Newton is not saying that ‘rest’ and ‘constant straight line motion’ are ‘equivalent’. Instinctively, he feels that there must be such a thing as ‘absolute place’ and ‘absolute rest’ and is chagrined that he cannot provide a reliable test to distinguish true rest from motion. When discussing circular motion Newton invokes the backdrop of the ‘fixed stars’ which “ever remain unmoved and do thereby constitute immovable space”. Thus, it is, according to Newton, possible to distinguish between relative and absolute circular motion because in the latter case there is a force at work which makes a body “recede from the axis of circular motion”. He gives the celebrated example of a bucket of water suspended by a chord which is twisted and then released so that the water climbs up the sides of the vessel. Today we would use the example of a merry-go-round which is, according to Newton’s test, a genuine case of absolute circular motion since we feel a definite force pushing us towards the outer edge. Continuous and Discontinuous When analysing the perceived motion of bodies, Newton treats motion as at once continuous and discontinuous: a projectile or a planet is never at rest as it pursues its path (unless interrupted by something in the way). But if a body is accelerating it does not have a constant velocity at that instant, and if it is in motion at any particular instant it cannot have a precise position. At the end of the day, provided we make the time interval small enough, it would appear that everything is at rest. However, the use of ‘infinitesimals’ allows one to decrease the time interval down to ‘almost nothing’ so that we can speak of a body’s ‘instantaneous velocity’ ― despite this being a contradiction in terms. In effect, the Infinitesimal Calculus which Newton co-invented, allows him to have his cake and eat it too as Bishop Berkeley pointed out to Newton and his supporters. This is probably the main reason why Newton avoids calculus methods as such in the Principia employing instead cumbersome geometrical constructions which in effect treat motion as an infinite succession of stills. Newton struggles to defend the logic behind his treatment in the beginning of Book I which treats the Motion of Bodies. But he cannot decide whether the ‘ultimate ratio’ of distance versus time ― what we call dy/dt ― is ever actually attained, a rather important point (Note 1). More precisely, Bishop Berkeley made it clear that Newton was contradicting himself by first assuming that x has an increment and then, “in order to reach the result, allows the increment to be zero, i.e. assumes that there was no increment.” Modern mathematics gets round this problem by defining the ‘limit’ to an ‘infinite series’ in such a way that it is not required that this limiting value is actually attained ― indeed in practically all cases of interest it cannot be. The price we have to pay for this rationalization of the Calculus is loss of contact with physical reality. Even if Newton had been capable of formulating the concept of a ‘limit’ in the precise modern sense I doubt if he would have employed it. Why not? Because Newton, like Leibnitz, and like practically every other ‘natural philosopher’ of the time, was a realist. In Newton’s time mathematics had not yet separated into ‘pure’ and ‘applied’ and the question as to whether infinitesimals ‘existed’ or not was the same sort of question as asking whether atoms existed. Pre-modern mathematics required infinitesimals to get tangible results which could be checked and usually turned out to be correct. But Newton was pragmatist enough to realize that, taken literally, Calculus methods made little sense. Boyer naturally champions the modern view. “His [Berkeley’s] argument is of course absolutely valid as showing that instantaneous velocity has no physical reality, but this is no reason why, if properly defined or taken as an undefined notion, it should not be admitted as a mathematical abstraction” (Boyer, The History of the Calculus p. 227). But why should one allow mathematics to wag the tail of physics to this extent? The real world cannot be handwaved into irrelevance just because it hampers the style of pure mathematicians. It is in fact deeply shocking that contemporary physics, on the face of it the most ’down to earth’ of the sciences, has been transformed into a piece of recondite pure mathematics. For mathematics, as a logico-deductive system, does not and cannot guarantee the existence of anything. Yet, for all that, most of us would like to know what is ‘really real’ and what is imagination: science is not the same thing as science fiction. Boyer claims that mathematics only deals in ‘relations’ not actualities which is all right up to a point ― but one has to ask, ‘relations between what sort of things?’ Since mathematics is a symbolic system, either its symbols ‘represent’ or stand in for realities of some sort or they do not, in which case they are simply decorative in the same sort of way in which embroidery patterns are decorative. It is quite conceivable that a different intelligent species might use embroidery or textile design as a way of communicating truths about the cosmos but our species has not gone down this route and has restricted its scientific pattern-making to geometrical drawings and algebra. Newton’s Approach and UET How does Newton’s idea of ‘absolute time and place’ play out in terms of the basic assumptions of Ultimate Event Theory? In UET ‘ultimate events’ replace Newton’s ‘bodies’ and ‘time’ is the rate at which ultimate events succeed each other. Newton’s assumption of ‘absolute time’ is tantamount to suggesting that there is a fixed, universal and absolute rate at which certain events succeed each other and which is entirely regular. Most sequences of events, of course, probably only approximate to this measure in principle it is always there in the background. There is, then, a sort of metronome according to whose ticks all other sequences can be measured, and towards which all actual rates of actual events tend. Is such an ‘absolute rate’ conceivable? (This is a different question to whether it actually exists.) If we assume, as I do, that all ultimate events have the ‘same extent’, i.e. occupy spatially equivalent ‘places’ on the Locality, and last for exactly the same ‘length of time’, we obtain a basic regular rate if (and only if) the intervals between successive ultimate events are equal. And the simplest case would be when the interval between successive events is a minimum, i.e. just enough to keep the events separate, like a cell membrane that is one molecule thick. As far as I am concerned, I believe that Newton was right in thinking that every object must have a ‘place’: this strikes me as even more necessary when dealing with events, which are by definition transitory, than with semi-permanent objects. I simply cannot conceive of ‘space’, or whatever is out there, as being simply composed of ‘relations’. But the UET conception is not the same as Newton’s concept of absolute space and time since the latter provide a fixed framework whether or not anything exists inside this framework or not. One should conceive of an ‘ultimate’ rate for event chains as a constraint or asymptotic limit to which actual event sequences may tend, rather than something existing independently of all actual events. What it means, however, is that the time variable δt cannot be arbitrarily diminished, so there is always a final ratio of distance versus time for consecutive events. Moreover, one could state as a postulate that a ‘rest’ event sequence, the equivalent of a stationary object, proceeds at the minimal rate, i.e. one ksana at a time (sic) with the distance between any two consecutive events in an event-chain being a minimum ― or, alternatively, a maximum. SH 18/03/15 Note 1 Newton writes, “There is a limit which the velocity at the end of the motion may attain, but not exceed. This is the ultimate velocity”. But, a little further on, he changes tack and writes, “those ultimate ratios with which quantities vanish are not truly the ratios of ultimate quantities, but limits towards which the ratios of quantities decreasing without limit do always converge, and to which they approach nearer than by any given difference, but never go beyond, nor in effect attain to, till the quantities are diminished in infinitum”. Note 2 And again, “Berkeley was unable to appreciate that mathematics was not concerned with a world of “real” sense impressions. In much the same manner today some philosophers criticize the mathematical conceptions of infinity and the continuum, failing to realize that since mathematics deals with relations rather than with physical existence, its criterion of truth is inner consistency rather than plausibility in the light of sense perception or intuition”. Minkowski, Einstein’s old teacher of mathematics, inaugurated the hybrid ‘Space-Time’ which is now on everyone’s lips. In an address delivered not long before his death in 1908 he said the now famous lines, But why should Minkowski, and whole generations of scientists, have ever thought that ‘space’ and ‘time’ could be completely separate in the first place? Certain consequences of a belief in ‘Space-Time’ in General Relativity do turn out to be scarcely credible, but there is nothing weird or paradoxical per se about the idea of ‘time’ being a so-called fourth dimension. To specify an event accurately it is convenient to give three spatial coordinates which tell you how far the occurrence of this event is, or will be, along three different directions relative to an agreed fixed point. If I want to meet someone in a city laid out like a grid as New York is (more or less), I need to specify the street, say Fifth Avenue, the number of the building and the floor (how high above the ground it is). But this by itself will not be enough for a successful meet-up : I also need to give the time of the proposed rendez-vous, say, three o-clock in the afternoon. The wonder is, not that science has been obliged to bring time into the picture, but that it was possible for so long to avoid mentioning it (Note 1) Now, if you start off with ‘events’, which are by definition ‘punctual’ and impermanent, rather than things or ‘matter’ you cannot avoid bringing time into the picture from the start: indeed one might be inclined to say that ‘time’ is a good deal more important than space. Events happen ‘before’ or ‘after’ each other; what happened yesterday preceded what happened this morning, and you read the previous sentence before you started on the current one. The very idea of ‘simultaneous’ events, events that have occurrence ‘at the same time’, is a tricky concept even without bringing Special Relativity into the picture. But the idea of succession is both clearcut and basic and one could, as a first bash, even define ‘simultaneous’ events negatively as bona fide occurrences that are not temporally ordered. So, when I started trying to elaborate an ‘event-orientated’ world-view, I felt I absolutely had to have succession as a primary ingredient : if anything it came higher up the list than ‘space’. Originally I tried to kick off with a small number of basic assumptions (axioms or postulates) which seemed absolutely unavoidable. One such assumption was that most events are ‘ordered temporally’, that they have occurrence successively, ‘one after the other’ ─ with the small exception of so-called ‘simultaneous events’. Causality also seemed to be something I could not possibly do without and causality is very much tied up with succession since it is usually the prior event that is seen as ‘causing’ the other event in a causal pair. Again, one might tentatively defined ‘simultaneous events’ as events which cannot have a direct causal bond, i.e. function as cause and effect (Note 2). And, in an era innocent of Special Relativity and light cones, one might well define space as the totality of all distinct events that are not temporally ordered. From an ‘event-based’ viewpoint, chopping up reality into ‘space’ and ‘time’ is not fundamental : all we require is a ‘place’ where events can and do have occurrence, an Event Locality. Such a Locality starts off empty of events but has the capacity to receive them, indeed I have come to regard ultimate events as in some sense concretisations or condensations of an underlying substratum. Difference between Space and Time There is, however, a problem with having a single indivisible entity whether we call it ‘Space-Time’ or simply ‘the Locality’. The two parts or aspects of this creature are not at all equivalent. Although I believe, as some physicists have suggested, that, at a certain level, ‘space’ is ‘grainy’, it certainly appears to be continuous : we do not notice any dividing line, let alone a gap, between the different spatial ‘dimensions’ or between different spatial regions. We don’t have to ‘add’ the dimension height to pre-existing dimensions of length and width for example : experience always provides us with a three-dimensional physical block of reality (Note 3). And the fact that the choice of directions, up/down, left/right and so on, is more often than not completely arbitrary suggests that physical reality does not have inbuilt directions, is ‘all-of-a-piece’. Another point worth mentioning is that we seem to have a strong sense of being ‘at rest’ spatially : not only are we ‘where we are’, and not where we are not, but we actually feel this to be the case. Indeed we tend to consider ourselves to be at rest even when we know we are moving : when in a train we consider that it is the other things, the countryside, that are in motion, not us. It is indeed this that gives Galileo’s seminal concept of inertia its force and plausibility; in practice all we notice is a flagrant disturbance of the ‘rest’ sensation, i.e. an ‘acceleration’. What about time? Now it is true that time is often said to ‘flow’ and we do not notice any clearcut temporal demarcation lines any more than we notice spatial ones. Nonetheless, I would argue that it is much less natural and plausible to consider ‘time’ as a continuum because we have such a strong sense of sequence. We continually break up time into ‘moments’ which occur ‘one before the other’ even though the extent of the moment varies or is left vague. Sense of sequence is part of our world and since our impressions are themselves bona fide events even if only subjective ones, it would appear that sequence is a real feature of the physical world. There is in practice always an arrow of time, an arrow which points from the non-actual to the actual. Moreover, the process of ‘actualization’ is not reversible : an event that has occurrence cannot be ‘de-occurred’ as it were (Note 4). And it is noteworthy that one very seldom feels oneself to be ‘at rest’ temporally, i.e. completely unaware of succession and variation. The sensation is so rare that it is often classed as ‘mystical’, the feeling of being ‘out of time’ of which T.S. Eliot writes so eloquently in The Four Quartets. Heroin and certain other drugs, by restricting one’s attention to the present moment and the recent past, likewise ‘abolish time’, hence their appeal. In the normal way, even when deprived of all external physical stimuli, one still retains the sensation of there being a momentum and direction to one’s own thoughts and inner processes : one idea or internal sensation follows another and one never has any trouble assigning order (in the sense of sequence) to one’s inner feelings and thoughts. It is now thought that the brain uses parallel processing on a big scale but, if so, we are largely unaware of this incessant multi-tasking. Descartes in his thought experiment of being entirely cut off from the outside world and considering what he simply could not doubt, might well have concluded that sequence, rather than the (intemporal) thinking ego, was the one item that could not be dispensed with. For one can temporarily disbelieve in one’s existence as a particular person but not in the endless succession of thoughts and subjective sensations that stream through one’s mind/brain. All this will be dismissed as belonging to psychology rather than physics. But our sense impressions and thoughts are rooted in our physiology and should not be waved aside for that very reason : in a sense they are the most important and inescapable ‘things’ we have for without them we would be zombies. Physical theories that deny sequence, that consider the laws of physics to be ‘perfectly reversible’, are both implausible and seemingly unliveable, so great is our sense of ‘before and after’. Einstein towards the end of his life decided that it followed from General Relativity that everything happened in an ‘eternal present’. He took this idea seriously enough to mention it in a letter to the son of his college friend, Besso, on receiving news of the latter’s death, writing “For those of us who believe in physics, this separation between past, present and future is only an illusion, however tenacious”. Breaks in Time If, then, we accept succession as an unavoidable feature of lived reality, are we to suppose that one moment shifts seamlessly into the next without any noticeable demarcation lines, let alone gaps? Practically all physicists, even those who toy with the idea that Space-time is in some sense ‘grainy’, seem to be stuck with the concept of a continuum. “There is time, but there is not really any notion of a moment in time. There are only processes that follow one another by causal necessity” as Lee Smolin puts it in Three Roads to Quantum Gravity.. But I cannot see how this can possibly be the case, and this is precisely why the ‘time dimension’ of the Event Locality is so different from the spatial one. If I shift my attention from two items in a landscape, from a rock and its immediate neighbourhood to a tree, there is no sense that the tree displaces the rock : the two items can peaceably co-exist and do not interfere with each other. But if one moment follows another, it displaces it, pushes it out of the way, as it were, since past and present moments, prior and subsequent events, cannot by definition co-exist ─ except perhaps in the inert way they might be seen to co-exist in an Einsteinian perpetual now. And all the attributes and particular features of a given moment must themselves disappear to make way for what follows. We do not usually see this happening, of course, because most of the time the very same objects are recreated and our senses do not register the transition. We only notice change when a completely different physical feature replaces another one, but the same principle must apply even if the same feature is recreated identically. Since a single moment is, in its physical manifestation, three-dimensional, all these three dimensions must go if a new moment comes into being. Whether there is an appreciable gap between moments apart from there being a definite change is an open question. In the first sketch of Ultimate Event Theory I attribute a fixed extent to the minimal temporal interval, the ksana, and I allow for the possibility of flexible gaps between ksanas. The phenomenon of time dilation is interpreted as the widening of the gap between ksanas rather than as an extension of the ‘length’ of a ksana itself. This feature, however, is not absolutely essential to the general theory. What we actually perceive and consider to constitute a ‘moment’ is, of course, a block containing millions of ksanas since the length of a ksana must be extremely small (around the Planck scale). However, it would seem that ksanas do form blocks and that there are transitions between blocks and that sometimes, if only subliminally, we are aware of these gaps. Instead of being a flowing river, ‘time’ is more like beads on a string though the best image would be a three-dimensional shape pricked out in coloured lights that is switched on and off incessantly. Mosaic Time Temporal succession is either a real feature of the world or it is not, I cannot see that there is a possible third position. In Einstein’s universe “everything that can have occurrence already has occurrence” to put things in event terms. “In the ‘block universe’ conception of general relativity….the present moment has no meaning ─ all that exists is the whole history of the universe at once, timelessly. When laws of physics are represented mathematically, causal processes which are the activity of time are represented by timeless logical implications…. Mathematical objects, being timeless, don’t mhave present moments, futures or pasts” (Lee Smolin, It’s Time to Rewrite time in New Scientist 20 April 2014) This means that there is no free will since what has occurrence cannot be changed, cannot be ‘de-occurred’. It also makes causality redundant as Lee Smolin states. One could indeed focus on certain pairs of events and baptise them ‘cause and effect’ but, since they both have occurrence, neither of them has brought the other about, nor has a third ‘previous’ event brought both of them about simultaneously. Causality becomes of no account since it is not needed. Even a little acquaintance with Special Relativity leads one to conclude that it is impossible to establish a universally valid ‘now’. Instead we have the two light cones, one leading back to the past and one to the future (the observer’s future), and a large region classed as ‘elsewhere’. It is notorious that the order of events in ‘elsewhere’, viewed from inside a particular light cone, is not fixed for all observers : for one observer it can be said that event A precedes event B and for another that event B precedes A. This indeterminacy if of little or no practical consequence since there is (within SR) no possibility of interaction between the two regions. However, it does mean that it is on the face of it impossible to speak of a universally valid ‘now’ ─ although physicists do use expressions like the “present state of the universe”. I personally cannot conceive of a ‘universe’ or a life or indeed anything at all without succession being built into it : the timeless world of mathematics is not reality but a ‘take’ on reality. The only way to conceptually save succession while accepting some of the more secure aspects of Relativity would seem to be to have some sort of ‘mosaic time’, physical reality split up into zones. How exactly these zones, which are themselves subjective in that they depend on a real or imagined ‘observer’, fit together is not a question I can answer though certain areas of research into general relativity can presumably be taken over into UET. One could perhaps define the next best thing to a universal ‘now’ by taking a weighted average of all possible time zones : Eddington suggested something along these lines though he neglected to give any details. Note that if physical reality is a mosaic rather than a continuum, it would in principle be possible to shift the arrangement of particular tesserae in a small way, exchange one with another and so on. SH 23/01/15 Note 1 Time was left out of the picture for so long, or at any rate neglected, because the first ‘science’ to be developed to a high degree of precision in the West was geometry. And the truths of (Euclidian) geometry, if they are truths at all, are ‘timeless’ which is why Plato prized geometry above all other branches of knowledge except philosophy. Inscribe a triangle in a circle with the diameter as base line and you will always find that it is right-angled. And if you don’t, this is to be attributed to careless drawing and measurement : in an ‘ideal’ Platonic world such an angle has to be a right angle. How do we know? Because the theorem has been proved. This concentration on space rather than time meant that although the Greeks set out the basic principles of statics, the West had to wait another 1,600 years or so before Galileo more or less invented the science of dynamics from scratch. And the prestige of Euclid and the associated static view of phenomena remained so great that Newton, perversely to our eyes, cast his Principia into a cumbrous geometrical mould using copious geometrical diagrams even though he had already invented a ‘mathematics of motion’, the Calculus. Note 2 Kant did in point of fact defend the idea of ‘simultaneous causation’ where each of two ‘simultaneous’ events affects the other ‘at the same time’. He gave the example of a ball resting on a cushion arguing that the ball presses down on the cushion for the same amount of time as the cushion is deformed by the presence of the ball. And if we take Newton’s Third Law as operating exactly at the same time on or between two different objects, we have to accept the possibility of simultaneous causation. Within Ultimate Event Theory, what would normally be called ‘causality’ is (sometimes) referred to as ‘Dominance’. I chose this term precisely because it signifies an unequal relation between two events, one event, referred to as the ‘cause’, as it were ‘dominating’ the other, the ‘effect’. In most, though perhaps not all, cases of causal relations I believe there really is priority and succession despite Newton’s Third Law. I would conceive of the ball pressing on the cushion as occurring at least a brief moment before its effect ─ though this is admittedly debatable. One could introduce the category of ‘Equal Dominance’ to cover cases of Kant’s ‘simultaneous causality’ between two events. Note 3 I have always found the idea of Flatland, which is routinely trotted out in popular books on Relativity, completely unconvincing. I can more readily conceive of there being more than three spatial dimensions as there being a world with less than three : a line, any line, always has some width and height. Note 4. If it is possible for an event in the future to have an effect ‘now’, this can only be because the ‘future’ event has already somehow already occurred, whereas intermediate events between ‘now’ and ‘then’ have not. I cannot conceive of a ‘non-event’ having any kind of causal repercussion — except, of course, in the trivial sense that current wishes or hopes about the future might affect our behaviour. Such wishes and desires belong to the present or recent past, not to the future. One can trace contemporary physics back to the suggestion, or intuition, of certain ancient Greeks, especially Democritus and Epicurus, that at bottom reality is composed of atoms, minute indestructible ‘bodies’ that combine with each other to form objects. The most important addition to this ultra-reductionist picture of reality was Newton’s idea of particular forces operating between bodies composed of atoms, both short-range contact forces and long-range non-contact forces. And forces could only operate because of ‘mass’. So what exactly is ‘mass’? Newton originally defined it as the “quantity of matter within an object”, an intuitively clear definition but one that physics has largely discarded today. And Newton himself obviously envisaged mass as something much more elusive and more metaphysical than a mere question of numbers of atoms and how densely packed together they were. Inertial mass was a property that objects possessed which could be measured by their capacity to resist forces that attempted to change their state of motion. And gravitational mass measured a body’s capacity to respond to a particular kind of force operating at a distance. Now, the starting point of Ultimate Event Theory is the notion that ‘objects’, which are relatively stable and permanent things, consist, not of smaller relatively stable and long-lasting objects such as atoms, but of what I call ‘ultimate events’. And ‘ultimate events’ are inherently unstable in the sense that they appear and disappear almost as soon as they have appeared; also, while some ultimate events occur again and again at successive instants, i.e. repeat, most do not. Instead of being a collection of solid objects, physical reality, according to this view, is rather a sort of cosmic kaleidoscope or cinema show where the successive stills are run through so fast that we can’t keep up and perceive them as continuous movement. In effect, instead of basing our notion of physical ‘reality’ on our perception of solidity and permanence around and inside us, Ultimate Event Theory appeals rather to our sense of the transience of everything and everyone. Time thus becomes the basic dimension rather than space. This mode of perception seems to be more ‘Eastern’ than ‘Western’ since two of the chief religions/philosophies of the East, Buddhism and Taoism, emphasize transience, indeed make it the cornerstone of the entire conceptual system. Now, it is my contention, or ‘intuition’ if you like, that a system of physical science could have been developed on such premises especially by certain Indian Buddhists during the first few centuries of our era. That it was not can be ascribed on the one hand to the greater difficulty of experimenting usefully with transient items such as ultimate events (the dharmas of Hinayana Buddhism) rather than relatively permanent solid objects. But there was also a cultural reason: Buddhist thinkers did develop a sophisticated kind of psychology (Abhidharma) and a form of logic but this was mainly because both these disciplines were useful in making converts and in making sense of their own meditative experiences. But these people had very little interest in the physical world per se, tending to view it, if not as a complete delusion, as at any rate a barrier to ‘deliverance’ and ‘enlightenment’. There was thus insufficient motivation within this particular intellectual milieu for developing a branch of knowledge devoted exclusively to physical matters as happened in the West during the fifteenth and sixteenth centuries. In any case, all such speculation about what ‘might have happened if…’ is irrelevant. The question I ask myself is, “Can any sort of a coherent physical system be developed from the premise that the basic elements of existence are not ‘things’ but ephemeral ‘ultimate events’?” And one of the very first sub-questions that arises is: “What is the equivalent of ‘mass’ in this system?” Returning to the ‘classical’ Newtonian concept of inertial mass, we see that it tends to ‘keep things as they are’, hence the term ‘inertia’ with its largely negative overtones. In Ultimate Event Theory (UET) there can, of course, be no question of ‘keeping things as they are’ in the usual sense, since the innate tendency of ultimate events, is, by hypothesis, to disappear at once, not to remain. But there must, seemingly, be some similar or equivalent ‘property’ for there to be a ‘physical world’ at all, or indeed anything observable and perceptible whether ‘real’ or ‘delusory’. In UET it is supposed that some ultimate events, by processes at present unknown but probably involving chance repetition, form themselves into event-chains and repeating event clusters. It is the latter, i.e. identically repeating event clusters, that we perceive as objects. The equivalent of ‘mass’ would seem to be persistence since ‘persistence’ is not so strongly associated with continuous existence as mass (Note 1). Note that, in contrast to mass which in the Newtonian system is everywhere, persistence is not a property possessed by all ultimate events but only those of a certain class ─ though these are the ones we are normally interested in. However, once an ultimate event acquires persistence, it seems to retain it, if not indefinitely at least for a considerable length of time, thus giving rise to an impression of solidity and permanence. And repeating event clusters’ (‘objects’) usually remain ‘where and as they are’ unless interfered with in some way, i.e. made subject to an external ‘force’. Following Newton, one is thus tempted to define ‘force’ as something that stops a persistent event or event cluster from carrying on repeating identically in the same manner. Note, however, that in UET, everything is, as it were, pushed one stage further back : it is thus necessary to assume some sort of ‘existence-force’ for event-chains without which there would be nothing but a chaos of momentarily existing ‘ultimate events’. Elementary or ‘Static’ Persistence An ultimate event, then, for reasons unknown ─ but which may have something to do with the pre-occurrence of identical or similar events within a neighbouring region of the Locality ─ repeats identically once and keeps on doing so thus forming an event-chain. Now, since the ‘repeat event’ is not, strictly speaking, the ‘same thing’ as the original ultimate event, there is an extra variable which comes into play in UET and which does not appear in the classical concept of an object, namely the re-appearance rate of an event-chain. Suppose an ultimate event that has occurrence at one ksana and repeats at the very next ksana. It does not necessarily keep repeating at the same rate which in this case is 1/1 or one appearance per ksana. It might shift to a rate of one appearance every three ksanas, one appearance every five ksanas and so forth, or it might have an irregular repeat rate but for all that still keep repeating. Since ksanas, the ‘ultimate’ temporal intervals, are so small compared to ‘macroscopic’ time intervals, a different repeat rate on the ‘ultimate’ level would not be distinguishable to our senses, or perhaps even to our most accurate current instruments. Nonetheless, in order to keep things simple, I shall start by assuming that an event chain has a 1/1 reappearance rate even though there are all sorts of other possibilities. So the basic ‘persistence’ of an event within an event-chain is set at one occurrence per ksana unless stated otherwise. In matter-based physics, an object can ‘move’ relative to some other stable easily recognizable object, or relative to a recognizable spot considered the ‘origin’ if we are dealing with a co-ordinate system. But an object cannot meaningfully be said to move ‘relative to itself’ : it is always where it is when it is. However, since an event-chain is by definition discontinuous, being composed of a succession of discrete ultimate events, perhaps with appreciable gaps between such appearances, the situation is rather different. Can we meaningfully consider that a particular ultimate event’s reappearance is shifted to the right or left of its previous position? One’s first inclination is to say, yes, but this immediately gets one into difficulties. An ultimate event is conceived as ‘appearing on’ a backdrop, the Event Locality, or perhaps is better viewed as a ‘localized concretisation’ of this backdrop. Since, by hypothesis, this backdrop (the Event Locality) is ‘neutral’ with respect to what occurs in or on it and is not itself endowed with directions, it makes little sense to speak of the trajectory of an isolated event-chain being ‘straight’ or ‘crooked’ or ‘curved’ with respect to this backdrop ─ although it does still make sense to speak of an event-chain having a certain re-appearance rate. If each ultimate event in an event-chain were conscious, it would consider itself and the entire chain to be ‘at rest’, to be stationary, just as we conceive of ourselves as being stationary and the countryside drifting by when in a train (if it is smooth running). So, if we are to speak of ‘lateral drift’ to right or left at successive ksanas, i.e. to introduce the notion of ‘speed’ into UET, this ‘’lateral shift’ must be related to some real or hypothetical event-chain which is itself regarded as ‘stationary’, i.e. as composed of ultimate events repeating identically at an equivalent spot at successive ksanas. This issue is by the way not specific to UET since it comes up in classical physics : even in Newton’s own time there was considerable, and often heated, discussion about whether one could meaningfully talk of a body isolated in the middle of space as being ‘at rest’ or ‘in motion’ (Note 2). Now, although there is no such thing as velocity in the continuous sense usually implied in normal physics and everyday speech, there is in UET a perceptible ‘lateral drift’ of successive ultimate events relative to an actual or hypothetical ‘landmark event-chain’ whose constituent ultimate events form a ‘straight line’, or are supposed to do so. If the successive constituents of an event-chain are randomly situated to right and left relative to this landmark event-chain, the event-chain in question does not have a proper displacement rate ─ though nonetheless the ultimate events are somehow bonded together, one bringing into existence the next. But if there is a clearcut displacement pattern, the event-chain can be said to have a ‘velocity’, or the UET equivalent. And if the pattern of successive appearances resembles a straight line, we have an event-chain with a constant lateral displacement rate. In such a case, we can say that not only does the event-chain have ‘persistence’ but that its displacement rate also has persistence. An event-chain can thus have two kinds of ‘persistence’ : ‘existence persistence’ and ‘lateral displacement persistence’, roughly the equivalents of the ‘rest mass’ and ‘kinetic energy’ of a particle in Newtonian mechanics. A single ultimate event cannot, of course, have ‘displacement persistence’ if it does not already have ‘existence persistence’ ─ though it can have the latter without the former, i.e. be the equivalent of stationary. And if we take over Newton’s Laws of Motion and re-state them in ‘event’ rather than ‘object’ terms, we can define ‘force’ as that which affects an event-chain’s persistence, either its ‘displacement persistence’ alone or its ‘existence persistence’. In the latter case, an event-chain is replaced by another event-chain or simply annihilated. The doctrine of the ‘conservation of mass-energy’, if taken over into UET, would forbid complete annihilation without replacement, i.e. the simple disappearance of an event-chain without any sequels. It may, however, turn out not to be the case that event-chains must always be replaced by other ones : at any rate the question is left open. If we do introduce the equivalent of a conservation principle, this would mean that as soon as even a single event-chain formed, there would be an endless succession of events since each time one chain terminated it would give rise to another. Such an ‘event-universe’ would thus be endless, ‘infinite’ if you like. However, my feeling is that nothing physical is endless and that not only can event-chains terminate without giving rise to other ones, but that this must happen eventually for all event-chains, i.e. the ‘event-universe’ will simply disappear and, as it were, return to what gave rise to it in the first place. Indeed, according to the ‘Anti-Infinity Principle’, nothing can continue for ever except the background or origin. There does not seem to be any obvious equivalent of ‘energy’ in UET ─ though one must remember that the notion only really entered classical physics during the middle of the 19th century. ‘Energy’ cannot be perceived directly anyway, only inferred, and is, in the framework of Newtonian physics, simply the “capacity to do work”. One could perhaps view an ultimate event’s capacity to repeat (or give rise to a different event) as the UET equivalent of ‘energy’, and the reality of repetition as the equivalent of mass ─ though I am not sure this is a meaningful distinction. Clearly, if an ultimate event does not possess the capacity to repeat, it cannot give rise to an event-chain, while if it does in point of fact repeat, clearly it had the prior capacity to do so. One might also envisage a more general ‘existence capacity’ which covers the two cases of an ultimate event repeating exactly and alternatively giving rise to a different event (an eventuality we have not treated yet). This would correspond to the generalized notion of ‘energy’ in normal physics where ‘energy’ always exists and passes through different forms. But basically it would seem that there are no obvious exact parallels to the dual concepts of mass and energy in matter-based physics. Had an ‘event-based’ physics ever been developed, or were one to evolve now, it would require its own concepts and categories, not all of which would necessarily correspond to the familiar ones we have and which themselves required centuries to evolve. SH 1/1/15 Note 1 Spinoza apparently believed that the most essential feature of anything real is its ‘striving’ to remain what it is. “Each thing, as far as it can by its own power, strives to persevere in its being….The striving by which each thing strives to persevere in its own being is nothing but the actual essence of the thing” Spinoiza, Ethics Part III quoted by Sheldrake, The Science Delusion. This is interesting because a ‘striving to persevere’ is not the same thing as a capacity to persevere. Note 2 Bishop Berkeley, in criticising Newton, wrote that Up, down, right, left, all directions and places are based on some relation and it is necessary to suppose another body distant from the moving one…..so that motion is relative in its nature, it cannot be understood until the bodies are given in relation to which it exists, or generally there cannot be any relation if there are no terms to be related. Therefore, if we imagine everything is annihilated except one globe, it would be impossible to imagine any movement in this globe” (quoted in Rosser, Introductory Relativity p. 276) Galileo’s Ship It was Galileo who opened up the whole subject of ‘inertial frames’ and ‘relativity’, which has turned out to be of the utmost importance in physics. Nonetheless, he does not actually use the term ‘inertial frame’ or formulate a ‘Principle of Relativity’ as such. Galileo wrote his Dialogue Concerning the Two World Systems, Ptolemaic and Copernican in 1616 to defend the revolutionary Copernican view that the Earth and the planets moved round the Sun. The Dialogue, modelled on Plato’s writings, takes the form of a three day long discussion where Salviati undertakes to explain and justify the heliocentric system to two friends, one of whom, Simplicius, advances various arguments against the heliocentric view. One of his strongest objections is, “If the Earth is moving, why do we not feel this movement?” Salviati’s reply is essentially this, “There are many other circumstances when we do not feel we are moving just so long as our motion is steady and in a straight line”. Salviati asks his friends to conduct a ‘thought experiment’, ancestor of innumerable modern Gedanken Experimenten. They are to imagine themselves in “the main cabin below decks on some large ship” and this, given the construction at the time, meant there would have been no portholes so one would not be able to see out. The cabin serves as a floating laboratory and Galileo’s homespun apparatus includes “a large bowl of water with some fish in it”, “a bottle that empties drop by drop into a narrow-mouthed vessel beneath it”, a stick of incense, some flies and butterflies, a pair of scales and so on. The ship, presumably a galley, is moving steadily on a calm sea in a dead straight line. Galileo (via Salviati) claims that the occupants of the cabin would not be able to tell, without going up on deck to look, whether the ship was at rest or not. Objects will weigh just the same, drops of water from a tap will take the same time to fall to the ground, the flies and butterflies will fly around in much the same way, and so on — “You will discover not the least difference in all the effects named, nor could you tell from any of them whether the ship was moving or standing still” (Note 1). Now, it should be said at once that this is not at all what one would expect, and not what Aristotle’s physics gave one to expect. One might well, for example, expect the flies and butterflies flying about to be impelled towards the back end of the cabin and even for human beings to feel a pull in this direction along with many other noticeable effects if the ship were in motion, effects that one would not perceive if the ship were safely in the dock. What about if one conducted experiments on the open deck? It is here that Galileo most nearly anticipates Newton’s treatment of motion and indeed Einstein himself. Salviati specifies that it is essential to decide whether a ‘body’ such as a fly or butterfly falls, or does not fall, within the confines of the system ‘ship + immediate environment’ ─ what we would call the ship’s ‘inertial frame’. Salviati concedes that flies and butterflies “separated from it [the ship] by a perceptible distance” would indeed be prevented from participating in the ship’s motion but this would simply be because of air resistance. “Keeping themselves near it, they would follow it without effort or hindrance, for the ship, being an unbroken structure, carries with it a part of the nearby air”. This mention of an ‘unbroken structure’ is the closest Galileo comes to the modern concept of an ‘inertial frame’ within which all bodies behave in the same way. As Salviati puts it, “The cause of all these correspondences of effects is the fact that the ship’s motion is common to all the things contained within it, and to the air also” (Dialogue p. 218 ). Now, the claim that all bodies on and in the ship are and remain ‘in the same state of motion’ is, on the face of it, puzzling and counter-intuitive. For one might ask how an object ‘knows’ what ‘frame’ it belongs to and thus how to behave, especially since the limits of the frame are not necessarily, or even usually, physical barriers. Galileo does not seem to have conducted any actual experiments relating to moving ships himself, but other people at the time did conduct experiments on moving ships, dropping cannon balls, for example, from the top of a mast and noting where it hit the deck. According to Galileo’s line of argument, a heavy object should strike the deck very nearly at the foot of the mast if the ship continued moving forward at exactly the same speed in a straight line whereas the Aristotelians, on their side, expected the cannon ball to be shifted backwards from the foot of the mast by an appreciable distance. The issue depended on which ‘structure’, to use Galileo’s term, a given object belonged to. For example, a cannonball dropped by a helicopter that happened to be flying over the ship at a particular moment, belongs to the helicopter ‘system’ and not to the system ‘ship’. In consequence, its trajectory would not be the same as that of a cannonball dropped from the top of a mast ─ unless the helicopter and ship were, by some fluke, travelling at an identical speed and in exactly the same direction. By his observations and reflexions Galileo thus laid the foundations for the modern treatment of bodies in motion though this was not really his intention, or at any rate not at this stage in the argument. Newton was to capitalize on his predecessor’s observations by making a clearcut distinction between the velocity of a body which, other things being equal, a body retains indefinitely and a body’s acceleration which is always due to an outside force. Families of Inertial Frames In the literature, ‘inertial frame’ has come to mean a ‘force-free frame’, that is, a set-up where a body inside some sort of a, usually box-like, container remains at rest unless interfered with or, if considered to be already in straight line constant motion, retains this motion indefinitely. But neither Galileo nor Newton used the term ‘inertial reference frame’ (German: Inertialsystem) which seems to have been coined by Ludwig Lange in 1885. The peculiarity of inertial frames is, then, that they are, physically speaking, interchangeable and cannot be distinguished from one another ‘from the inside’. Mathematically speaking, ‘being an inertial frame’ is a ‘transitive’ relation : if A is an inertial frame and B is at rest or moves at constant speed in a straight line relative to A, then B is also an inertial frame. We have, then, a vast family of ‘frames’ within which objects allegedly behave in exactly the same way and which, when one is inside such a frame, ‘feel’ no different from one another. It is important to be clear that the concept of ‘inertial frame’ implies (1) that it is not possible to tell, from the inside, whether the ‘frame’ (such as Galileo’s cabin or Einstein’s railway coach) is at rest or in straight line constant motion, and (2) that it is not possible to distinguish between two or more frames, neither of which are considered to be stationary, provided their motion remains constant and in a straight line. These two cases are distinct: we might, for example, be able to tell whether we were moving or not but be unable to decide with precision what sort of motion we were in ─ to distinguish, for example, between two different straight-line motions at constant speed. As it happens, Galileo was really only concerned with the distinction between being ‘at rest’ and in constant straight-line motion, or rather with the alleged inability to make such a distinction from inside such a ‘frame’, since it was this inability which was relevant to his argument. But the lumping together of a whole host of different straight-line motions is actually a more important step conceptually though Galileo himself did not perhaps realize this. So. Were Galileo in the cabin of a ship moving at a steady pace of, say, 10 knots, he would, so he claims, not be able to differentiate between what goes on inside such a cabin from what goes on in a similar cabin of a similar ship not moving at all or one moving at a speed of 2 or 20 or 200 or even 2,000 knots supposing this to be possible. Now, this is an extremely surprising fact (if it is indeed a fact) since Ship A and Ship B are not ‘in the same state of motion’ : one is travelling at a certain speed relative to dry land and the second at a quite different speed relative to the same land. One would, on the face of it, expect it to be possible to tell whether a ship were ‘in motion’ as opposed to being at rest, and, secondly, to be able to distinguish between two states of straight line constant motion with different speeds relative to the same fixed mass of land. Newton himself felt that it ought to be possible to distinguish between ‘absolute rest’ and ‘absolute motion’ but conceded that this seemed not to be possible in practice. He was obviously somewhat troubled by this point as well he might be. Galileo’s Ship is not a true Inertial Frame As a matter of fact, it would not only be possible but fairly easy today to tell whether we are at rest or in motion when, say, locked up without radio or TV communication in a windowless cabin of an ocean liner. All I would need to carry out the test successfully would be a heavy pendulum, a means to support it so that it can revolve freely, a good compass, and a certain amount of time. Foucault demonstrated that a heavy pendulum, suspended with the minimum possible friction from the bearings so that it can move freely in any direction, will appear to swing in a circle : the Science Museum in London and countless other places have working Foucault pendulums. The time taken to make a complete circuit depends on one’s latitude — or, more correctly, the time it takes the Earth to revolve around the pendulum depends on what we choose to call latitude. A Foucault pendulum suspended at the North Pole would, so we are assured, take 24 hours to make a full circuit and a similar one at the Equator would not change its direction of swing at all, within the margins of experimental error. By timing the swings carefully one could thus work out whether the ship was changing its latitude, i.e. moving ‘downwards’ in the direction of the South Pole, or ‘upwards’ in the direction of the North (geographical) pole. On the other hand, a ship at rest, whatever its latitude, would show no variation in the time of swing ─ again within the limits of scientific error. However, suppose I noted no change in the period of the Foucault pendulum. I would now have to decide whether my ship, galley or ocean liner, was stationary relative to dry land or was moving at constant speed along a great circle of latitude. This is rather more difficult to determine but could be managed nonetheless even with home-made instruments. One could examine the ‘dip’ of a compass needle which points downwards in regions above the Equator and upwards in regions south of the Equator ─ because the compass needle aligns itself according to the lines of force of the Earth’s magnetic field. Again, any change in the angle of dip would be noticeable and there would be changes as the ship moved nearer the magnetic south or north poles. Nor is this all. The magnetic ‘north pole’ differs appreciably from the geographical north pole and this discrepancy changes as we pursue a great circle path along a latitude : so-called isoclinics, lines drawn through places having the same angle of dip, are different from lines of latitude. There are also variations in g, the acceleration due to gravity at the Earth’s surface, because of the Earth’s slightly irregular shape, its ‘oblateness’ which makes the circumference of the Earth measured along the Equator markedly different from that measured along a great circle of longitude passing through the poles. And so, despite Galileo’s claim to the contrary, there would be slight differences in the weight of objects in the cabin at different moments if the ship were wandering about. Only if the Earth were a perfect sphere with the magnetic poles precisely aligned with the geographical poles, would such tests be inconclusive. But a perfect sphere does not exist in Nature and never will exist unless it is manufactured by humans or some other intelligent species. Galileo’s claim is thus not strictly true : it is a typical case of an ‘ideal situation’ to which actual situations approximate but which they do not, and cannot, attain. Einstein’s Generalizations But, one might go on to argue, the discrepancies mentioned above only arose because Galileo’s ship was constrained to move on a curved surface, that of the ocean : what about a spaceship in ‘empty space’? The full Principle of Relativity, Galileian or early Einsteinian, asserts that there is no way to distinguish from the inside between conditions inside a rocket stationary with respect to the Earth, and conditions inside one travelling at any permissible constant ‘speed’ in a straight line relative to the Earth. It is routinely asserted in textbooks on the Special Theory of Relativity that there would indeed be no way to distinguish the two cases provided one left gravity out of the picture. Newton made Galileo’s idealized ship’s cabin into the arena where his laws of motion held sway. An object left to its own devices inside a recognizable container-like set-up (an inertial system) would either remain stationary or, if already moving relative to the real or imagined frame, would keep moving in a straight line at constant speed indefinitely. This is Newton’s First Law. Any deviation from this scenario would show that there was an outside force at work ─ and Newton, knowing nothing of interior chemical or nuclear forces, always assumed that any supposed force would necessarily come from the outside. Thus, Newton’s Second Law. So, supposing I let go of a piece of wood I hold in my hand in this room, which I take as my inertial frame, what happens to it? Instead of remaining where it was when I had it in my hand, the piece of wood falls to the ground and its speed does not stay the same over the time of its trajectory but increases as it falls, i.e. is not constant. And if I throw a ball straight up into the air, not only does it not continue in a vertical line at constant speed but slows down and reverses direction while a shot fired in the air roughly northwards will be deflected markedly to the right because of the Earth’s rotation (if I am in the northern hemisphere). Neither this room nor the entire Earth are true inertial frames : if they were Newton’s laws would apply without any tinkering about. To make sense of the bizarre trajectories just mentioned it is necessary to introduce mysterious forces such as the gravitational pull of the Earth or the Coriolis ‘force’ produced by its rotation on its own axis. As we know, Einstein’s theory of Special Relativity entirely neglects gravity, and introducing the latter eventually led on to the General Theory which is essentially a theory of Gravitation. Einstein’s aim, even in 1905, was quite different from Galileo’s. Whereas Galileo was principally concerned to establish the heliocentric theory and only introduced his ship thought-experiments to deal with objections, Einstein was concerned with identifying the places (‘frames’) where the ‘laws of physics’ would hold in their entirety, and by ‘laws’ he had in mind not only Newton’s laws of motion but also and above all Maxwell’s laws of electro-magnetism. Einstein’s thinking led him on to a search for a ‘true’ inertial frame as opposed to a merely stationary frame such as this room since the latter is certainly not a ‘force-free’ frame. Einstein, reputedly after speculating about what would happen to a construction worker falling from the scaffolding around a building, decided that a real or imaginary box falling freely under the influence of gravitation was a ‘true’ inertial frame. Inside such a frame, not only would the ‘normal’ Newtonian laws governing mechanics hold good but the effects of gravity would be nullified and so could be legitimately left out of consideration. Such a ‘freely-falling frame’ would thus be the nearest thing to a spaceship marooned in the depths of space far away from the influence of any celestial body. A freely falling frame is not a true inertial frame So, would it in fact be impossible to distinguish from the inside between a box falling freely under the gravitational influence of the Earth and a spaceship marooned in empty space? The answer is, perhaps surprisingly, no. In a ‘freely falling’ lift dropping towards the Earth, or the centre of any other massive body, there would be so-called ‘tidal effects’ because the Earth’s gravitational field is not homogeneous (the same in all localities) and isotropic (the same in all directions). If one released a handful of ball-bearings or a basketful of apples in a freely falling lift, the ball-bearings or apples at the ‘horizontal’ extremities would curve slightly towards each other as they fell since their trajectories would be directed towards the centre of the Earth rather than straight downwards. Likewise, the top and bottom apples would not remain the same distance apart since the forces on them, dependent as they are on the distances of the two apples from the Earth’s centre of mass, would be different and this difference would increase as the falling lift accelerated. It turns out, then, that, at the end of the day, Einstein’s freely falling lift is not a great deal better than Galileo’s ship ─ although both are good enough approximations to inertial frames, or rather are very good imitations of inertial frames. One can, of course, argue in Calculus manner that the strength of the Earth’s gravitational field will be the same over an ‘infinitesimally small region’ ─ though without going into further details about the actual size of such a region. Newton’s Laws in their purity and integrity are thus only strictly applicable to such ‘infinitesimal’ regions in which case there will inevitably be abrupt transitions, i.e. ‘accelerations’, as we move from one infinitesimal region to another. The trajectory of any free falling object will thus not be fluent and continuous but jerky at a small enough scale. For that matter, it is by no means obvious that a spaceship marooned in the middle of ‘empty’ space is a true ‘inertial frame’. According to Einstein’s General Theory of Relativity, Space-time is ‘warped’ or distorted by the presence of massive objects and this space-time curvature apparently extends over the whole of the universe ─ albeit with very different local effects. If the universe is to be considered a single entity, then strictly speaking there is nowhere inside it which is completely free of ‘curvature’, and so there is nowhere to situate a ‘true’ inertial frame. What to Conclude? So where does all this leave us? Or, more specifically, what bearing does all this discussion have on the theory I am attempting to develop ? In Ultimate Event Theory, the basic entities are not bodies but point-like ultimate events which, if they are strongly bonded together and keep repeating more or less identically, constitute what we view as objects. In its most simplistic form, the equivalent of an ‘object’ is a single ultimate event that repeats indefinitely, i.e. an event-chain, while several ‘laterally connected’ event-chains make up an event cluster. There is no such thing as continuous motion in UET and, if this is what we understand by motion, there is no motion. There is, however, succession and also causal linkage between successive ultimate events which belong to the ‘same’ event-chain. Although I did not realize this until quite recently, one could say that the equivalent of an ‘inertial frame’ in UET is the basic ‘event-capsule’, a flexible though always finite region of the event Locality within which every ultimate event has occurrence. There is no question of the basic ‘building block’ in Eventrics ‘moving’ anywhere : it has occurrence at a particular spot, then disappears and, in some cases, re-appears in a similar (but not identical) spot a ksana (moment) later. One can then pass on to imagining a ‘rest event-chain’ made up of successive ultimate events sufficiently far removed from the influence of massive event-clusters for the latter to have no influence on what occurs. This is the equivalent, if you like, of the imaginary spaceship marooned in the midst of empty space. So, where does one go from here? One thing to have come out of the endless discussions about inertial frames and their alleged indistinguishability (at least from the inside), is that the concept of ‘motion’ has little if any meaning if we are speaking of a single object whether this object or body is a boat, a particle, ocean liner or spaceship. We thus need at least two ‘objects’, one of which is traditionally seen as ‘embedded’ in the other more or less like an object in a box. In effect, Galileo’s galley is related to the enclosing dry land of the Mediterranean or, at the limit, to the Earth itself including its atmosphere. The important point is being able to relate an object which ‘moves’ to a larger, distinctive object that remains still, or is perceived to remain so. In effect, then, we need a system composed of at least two very different ‘objects’, and the simplest such system in UET is a ‘dual event-system’ made up of just two event-chains, each of which is composed of a single ultimate event that repeats at every ksana. Now, although any talk of such a system ‘moving’ is only façon de parler , we can quite properly talk of such a system expanding, contracting or doing neither. If our viewpoint is event-chain A , we conceive event-chain B to be, for example, the one that is ‘moving further away’ at each ksana, while if we take the viewpoint of event-chain B, it is the other way round. The important point, however, is that the dual system is expanding if this distance increases, and by distance increasing we mean that there is a specified, finite number of ultimate events that could be ‘fitted into’ the space between the two chains at each ksana. This is the broad schema that will be investigated in subsequent posts. How much of Galileo’s, Newton’s and early Einstein’s assumptions and observations do I propose to carry over as physical/philosophic baggage into UET? To start with, what we can say in advance is that the actual distance (in terms of possible positions for ultimate events) between two event-chains does not seem to matter very much. Although Galileo, or Salviati, does not see fit to mention the point ─ he doubtless thinks it too ’obvious’ ─ it is notable that, whether the ship is in motion or not, the objects inside Galileo’s cabin do not change wherever the ship is, neglecting the effects of sun and wind, i.e. that position as such does not bring about changes in physical behaviour. This is not a trivial matter. It amounts to a ‘law’ or ‘principle’ that carries over into UET, namely that the Event Locality does not by itself seem to affect what goes on there, i.e. we have the equivalent of the principle of the ‘homogeneity’ and ‘isotropy’ of Space-time. As a contemporary author puts it : “The homogeneity of space means that all points in space are physically equivalent, i.e. a transportation of any object in space does not affect in any way the processes taking place in this object. The homogeneity of time must be understood as the physical indistinguishability of all instants of time for free objects. (By a free object we mean an object which is far from all surrounding objects so that their interaction can be neglected.)” Saxena, Principles of Modern Physics 2.2) What about the equivalent of velocity? Everything we know about so-called ‘inertial systems’ in the Galileian sense suggests that, barring rather recondite magnetic and gravitational effects, the velocity of a system does not seem to matter very much, provided it is constant and in a straight line. Now, what this means in UET terms is that if successive members of two event-chains get increasingly separated along one spatial direction, this does not affect what goes on in each chain or cluster so long as this increase remains the same. What does affect what goes on in each chain is when the rate of increase or decrease changes : this not only means the system as a whole has changed, but that this change is reflected in each of the two members of the dual system. When travelling in a car or train we often have little idea of our speed but our bodies register immediately any abrupt substantial change of speed or direction, i.e. an acceleration. This is, then, a feature to be carried over into UET since it is absolutely central to traditional physics. Finally, that there is the question of there being a limit to the possible increase of distance between two event-chains. This principle is built into the basic assumptions of UET since everything in UET, except the extent of the Locality itself, has an upper and lower limit. Although there is apparently nothing to stop two event-chains which were once adjacent from becoming arbitrarily far apart at some subsequent ksana provided they do this by stages, there is a limit to how much a dual system can expand within the ‘space’ of a single ksana. This is the (now) well-known concept of there being an upper limit to the speed of all particles. Newton may have thought there had to be such a limit but if so he does not seem to have said so specifically : in Newtonian mechanics a body’s speed can, in principle, be increased without limit. In UET, although there is no continuous movement, there is a (discontinuous) ‘lateral space/time displacement rate’ and this, like everything else is limited. In contrast to orthodox Relativity theory, I originally attempted to make a distinction between such an unattainable upper limit, calling it c, and the highest attainable rate which would be one space less per ksana. This means one does not have the paradox of light actually attaining the limit and thus being massless (which it is in contemporary physics). However, this finicky separation between c s0/t0 and c* = (c – 1) s0/t0 (where s0 and t0 are ‘absolute’ spatial and temporal units) may well prove to be too much of a nuisance to be worth maintaining. SH 21/11/14 Note 1 This extract and following ones are taken from Drake’s translation of Dialogue concerning two world systems by Galileo Galilei (The Modern Library)
7 5 In 1913 in Russian bookshops appeared a book by the outstanding educationalist Yakov Isidorovich Perelman entitled Physics for Entertainment. It struck the fancy of the young who found in it the answers to many of the questions that interested them. Physics for Entertainment not only had an interesting layout, it was also immensely instructive. In the preface to the 11th Russian edition Perelman wrote: "The main objective of Physics for Entertainment is to arouse the activity of scientific imagination, to teach the reader to think in the spirit of the science of physics and to create in his mind a wide variety of associations of physical knowledge with the widely differing facts of life, with all that he normally comes in contact with." Physics for Entertainment was a best seller. Ya. I. Perelman was born in 1882 in the town of Byelostok (now in Poland). In 1909 he obtained a diploma of forester from the St. Petersburg Forestry Institute. After the success of Physics for Entertainment Perelman set out to produce other books, in which he showed himself to be an imaginative popularizer of science. Especially popular were Arithmetic for Entertainment, Mechanics for Entertainment, Geometry for Entertainment, Astronomy for Entertainment, Lively Mathematics, Physics Everywhere, and Tricks and Amusements. Today these books are known to every educated person in the Soviet Union. He has also written several books on interplanetary travel {Interplanetary Journeys, On a Rocket to Stars, World Expanses, etc.). The great scientist K. E. Tsiolkovsky thought highly of the talent and creative genius of Perelman. He wrote of him in the preface to Interplanetary Journeys: "The author has long been known by his popular, witty and quite scientific works on physics, astronomy and mathematics, which are moreover written in a marvelous language and are very readable." Perelman has also authored a number of textbooks and articles in Soviet popular science magazines. In addition to his educational, scientific and literary activities, he has also devoted much time to editing. So he was the editor of the magazines Nature and People and In the Workshop of Nature. Perelman died on March 16, 1942, in Leningrad. Many generations of readers have enjoyed Perelman's fascinating books, and they will undoubtedly be of interest for generations to come. Fun with Maths and Physics Brain Teasers Tricks Illusions S. I. Lion. Prusakov Translated from Russian by Alexander Repyev Cover: I. Mir Publishers. Keidan. Stulikov. I. 1984 . Kravtsov. R. Sokolov.H. D. First published 1984 Second printing 1988 Ha UMAUUCKOM H3blKe Printed in the Union of Soviet Socialist Republics ISBN 5-03-000025-9 © English translation. Yu. r i e p e j i b M a H 3AHMMATEJlbHbIE 3A/I. V. V. Mukhin. L. Perevezentsev. Saksonov. Varshamov. M. V. MocKBa Compiled by I. A.AMH M O n b l T b l M 3/iarejihc I B O «X(eTCKaH jiHTeparypa». Kravtsov. Kabakov. Vashchenko Yu. Stulikov Artistic Book Design: I. By the Way 33 . 6-7 For Young Physicists 53 . A Sheet of Newspaper 86 . 8-9 Seventy-Five More Questions and Experiments on Physics 100 . Optical Illusions 143 . 10-11 Brain-Twisting Arrangements and Permutations 164 . Skilful Cutting and Connecting 178 . 22-13 n Problems with Squares 1 8 4 . Problems on Manual Work 188 . 14-15 Problems on Purchases and Prices 193 . Weight and Weighing 199 . 16-17 Problems on Clocks and Watches 205 . Problems on Transport 211 . 18-19 Surprising Calculations 215 . Predicaments 221 . 20-21 Problems from Gullivers Travels 229 . Stories about Giant Numbers 237 . 22-23 Tricks with Numbers 250 . Merry Arithmetic 273 . 24-25 20 Count 285 . 72 lo \ ( #5 6o\75 57 105 772 728 ml 7 5 5 6S\ 85 702 77Q 736 1 72i 7 < 77' .Fast Reckoning 289 27 m <+4: J y / po . 26-27 22 Magic Squares 296 . Arithmetic Games and Tricks 25 303 . 28-29 2U- With a Stroke of the Pen 332 - . Geometric Recreations 25 338 . 30-31 Without a Tape-Measure 354 . Tricks and Diversions Drawing Puzzles I C O O .27 -3) \\ Simple. In the corner of a room being repaired I once came across several used postcards and a heap of narrow paper strips that had been trimmed from wall paper." I thought.32-33 By the Way Scissors and Paper Three pieces from one cutm Placing a strip on an edge• Charmed rings • Unexpected results of cutting • Paper chain • Thread yourself through a sheet of paper. and what is useless for business might be suitable for leisure. What is useless for one purpose. Cut it into three with one cut of the scissors. that there are some unnecessary things in this world." "Too bad. he said: "Take a pair of scissors and cut the strip in three. He started with the paper strips.. Figure 1 "You're pulling my leg. My elder brother Alex showed me some things you could do with them. Let me. I tried one way and then another. Perhaps you think. I haven't finished yet. "It's impossible. folded it in two and cut it in the middle to produce three pieces." I said." "I have worked it out that the problem has no solution." "Well. and then began to think my brother had posed a virtually impossible problem." Brother took the strip. "You see?" . "Rubbish for the fire. Eventually it occurred to me that it was absolutely intractable. think again. You're quite mistaken: there is no junk that might not be of help sometime for some purpose. comes in nandy for another.. as I once did. maybe you'll work it out." This was more difficult. But it turned out that even with this junk one can interestingly amuse oneself. Giving me a piece of strip about 30 centimetres long." I was about to cut but Alex stopped me: "Wait a bit. " "So that it stands. "Some delusion! Again." "But I didn't say you couldn't either. You won't catch me out again. on its edge. I found to my surprise I had absent-mindedly drawn the blue line on both sides of the ring. trying very hard not to go over to the other side somehow. not stood on edge." "As you like.. and. I was upset. I even didn't notice how I had drawn the both sides." "So that it stands or falls?" I asked suspecting a trap. both sides appeared blue! There was no room for the red. Simply agree that you didn't see the solution." "All right.m -& Figure 2 38-39 By the Way "Yes. joined up the line. but you've folded the strip. standing on its edge! You didn't say I couldn't bend it!" I said triumphantly. About to weep. Give me another." I muzed. of course. put it on its edge. "Standing.." "And then?" "That's all. "Right. but somehow it didn't quite come off... I started as carefully as possible to draw the line along one side." "Here is another strip." He took a paper ring and swiftly drew a red line all round the outside and a blue one on the inside. You see I've glued the ends of several strips and produced paper rings. "Such a simple thing and you can't do it. please. I did so and put it on the table." "More of your problems." A silly job. too. it will mean that it was laid." Well. and ." But the second was a failure. Take a red-and-blue pencil and draw a blue line all along the outside of this ring and a red along the inside. "I've accidentally spoiled the first one. "Give me another. Dear me! Both sides again. When I had joined up the ends of the blue line and wanted to do the red. "Just look. Give me another problem. If it falls. and it suddenly occurred to me that I could bend the strip." "Why didn't you?" "You didn't say I could." "You are welcome. what do you think? Again." smiled brother. I in bewilderment glanced at my brother. Having received a fresh ring." I was embarrassed. "There. The key thing is that before you glue the ends of the paper strip twist one of them like this (Figure 3). can you cut this ring to get two thinner ones?" "Nothing special. It'll be even more interesting. that I had in my hands only one long ring. I used an ordinary ring.. I was about to demonstrate two thin rings I had got when I noticed." Having cut the ring. For example.." Alex enquired. you would cut three of the rings?" . the ring was enchanted all right! "The trick is very simple. Brother was right. I'll try again. much to my surprise." I did. "and see what happens. This time I had two rings.. if the end is twisted twice." "What magic? Just rings." "Try to make something else with these rings.34-35 By the Way Figure 3 only then I guessed from his grin that something was wrong." my brother explained. not just once. "What would you do.. You've just fixed up something." "Is it all because of that?" "Yes! Sure. "The rings are magic. this is simple: cut one ring in each pair. it turned out that it was impossible to disentangle them for they were linked together. "So. Is it a trick?" I asked. "Okay. not two smaller ones. I prepared three more rings for myself and obtained three more pairs of inseparable rings. "Another ring. "Well." "Why? Just cut the one you've got. "You can make such unusual rings for yourself. no kidding." my brother asked again. where are your two rings?" Alex asked mockingly. you just." Before my very eyes Alex prepared a ring in this way and handed it to me. "Cutting along the middle." he said. it was impossible to take them apart. "if you had to connect all four pairs of rings to form one long open-ended chain?" "Oh. So funny. and glue them together again. But when I wanted to separate them." I did and got two rings but one now went through the other. " said Alex and set out to cut. how can you possibly connect them by only breaking two rings? Impossible!" Figure 4 I was dead sure." I punched the card with my scissors and carefully cut a rectangular hole in it.. Of course. For instance. You've got some old postcards over there. So that you could thread all yourself through it. Just enough for a hand to go through." "But what if you cut less than three?" "We have four pairs of rings. Let's have some fun with them." "No trick will help you here.38-39 By the Way "Of course. he had another opinion. my brother took the scissors. Next he cut the bent edge from point A to point . "Enough of these paper rings. I watched him curiously. That would be some hole. Ridiculously simple! N o trick in this and I could only be surprised why such a simple idea hadn't occurred to me. Confident that he was joking. He bent the card in two. leaving only a narrow edge. In answer.. What is impossible is impossible. try and cut in a card the largest hole you can. "This is a hole among holes! A larger one is impossible!" I contentedly showed the result of my job to Alex. "The hole is too small. "The head and the body. nevertheless." "And what is possible is possible. Many times larger." "Ha-ha! Do you really want to get a hole larger than the paper itself?" "Exactly. it seems. Lo and behold! a chain of eight rings. too." "You'd like it to be large enough for a head?" I retorted acidly. cut both rings in one pair and with them connected the remaining three pairs. then drew two lines with a pencil near the long edges of the bent postcard and made two incisions near the other two edges. " I reminded my brother at breakfast." Alex pushed the bowl a bit farther away from me until I couldn't see the coin any more since it was shielded by the side of the bowl.38-39 By the Way B and began to make a lot of cuts next to each other as shown in Figure 5." proclaimed my brother. as if it's been lifted up together with the bottom. Then empty the washing bowl. zigzagging about me. Why?" My brother sketched the bowl with the coin in it on a sheet of paper. this time only with coins. "Look into the bowl without moving from your place and without leaning over. What has happened to the coin?" "It's visible again. "Finished. all right. "How can you get through such a hole? What do you say to that?" "Big enough for two!" I said with admiration. don't move. "Sit still. Tricks with Coins A visible and invisible coin • A bottomless glass • Where has the coin goneArranging coins0 Which hand holds the two-pence piece?• Shi/ting coins • An Indian legend • Problem solutions. "Tricks? First thing in the morning? Hm. I pour water into the bowl. and then everything became clear to . "Yesterday you promised to show me a trick with coins. Just imagine: it developed into a long-long chain that he easily threw over my head. At that Alex finished his tricks." And Alex expanded the paper. promising to treat me next time to a whole heap of new ones. "Why? I see no hole!" Figure 5 "Take another look." Alex put a silver coin on the bottom of the empty bowl. See the coin?" "Yes. It fell to my feet. we are used to seeing things only at a place where straight rays come from and this is why I mentally placed the coin somewhat higher than where it really was. the deepest place appears to us to lie just beneath the boat even if the bottom were perfectly flat. the situation changed since light rays coming from water into air get bent (physicists say "refracted") and now can slid over the bowl edge and come into my eyes. When the water was added. Bathing children often get into a trouble for this reason: relying on the deceptive appearance. it appears that the greatest depth is just under the boat and it's much shallower everywhere else. But shift to another place and again everywhere is shallow and beneath the boat is deep. The point is that the rays coming straight up out of the water change direction least of all. Naturally. they usually underestimate depth. "What do you think will happen if now I drop a two-pence piece into the glass?" "The water will overflow. "Now let's put in another coin. thus the bottom there appears to be less elevated than the places which send oblique rays to our eyes." "Let's try. "I advise you to remember this experiment. of course. It seems as if the deepest place travels with the boat. "Now it's sure to overflow. But now let's do quite another experiment." Carefully. the apparent depth is only 75 centimetres." my brother added. Why?" "Now you can understand that easily. While the coin was at the bottom of the dry bowl." "I noticed that when you float slowly in a boat over a place where the bottom is visible. that is along a continuation of the refracted ray. However. "It will be useful when bathing. And substantially so. my brother lowered the coin into the brimful glass.38-39 By the Way Figure 6 me." Alex filled a glass with water right up to the brim." . So it seemed to me that the bottom had risen with the coin. In a shallow place where you can see the bottom never forget that you see it higher than really is." he said. I warned him. for water appears to be shallower by about a quarter of its real depth. no ray of light could come from the coin because light travels in straight lines and the opaque sides of the bowl were just in the way. Where the actual depth is 1 metre. say. without jerking. N o t a drop overflowed. "The answer lies in the bulging. three times wider-nine times the area. So. sloping down at the edges as if it were in a transparent bag. sixth." I went on to conclude. and so on. the water has bulged up at the glass's edge. Alex silently and cooly kept on lowering one coin after another into the glass. he was still carefully dropping coins and only stopped at the 15 th two-pence piece.t h e glass was about four times wider than a two-pence. the water had bulged above the edge by about the thickness of a match." "Fifteen coins have displaced so little water?" I was astounded. "Take a look. I never!" "You should have known it. But my brother took his time to explain. the . The glass could only receive four coins. "Well." "Well." he said at last. it seems. "Four times wider and the same thickness. With rings the same rule holds: if a ring is two times wider than another. it has four times the surface area. The layer may be not thicker than a two-pence piece. but you've already put in 15 and plan." "Take its area into consideration.n o overflowing. 100 times 100 which is 10. too. A third and a fourth coin followed each other into the glass. "What a bottomless glass!" I exclaimed. Alex went on to say. The stack of 15 two-pence pieces is rather high but here is only a thin layer. If a ring is four times larger across than another.000. but how many times larger is it across?" I gave some thought to i t . its surface area will be 16 times larger. A fifth. "The layer is only four times larger than a two-pence. Where's the room?" "Your calculation is wrong. How many square centimetres are there in a square metre? One hundred?" "No.38-39 By the Way And I was mistaken: in the full glass there was room for the second coin. just thicker than a penny. to add some more. not four. four times wider-16 times the area. This is where the water is that was expelled by the coins." "You see. that'll do. I couldn't believe my eyes and was impatient to find out the explanation. not only the thickness. seventh time coins fell onto the b o t t o m ." Indeed. . "Now that's where we'll place the 11th coin that we put tentatively into the first saucer." "Could you really put 20 coins into the glass?" "Even more. as you please." And ignoring my pleads he gave me a fresh problem. do it just with six. "Another physics experiment?" "No." I gave up at once. the third coin goes into the second saucer." I did as he said." He took the extra coin from the first saucer and placed it into the 10th saucer.." "Eleven coins in 10 saucers." "I wouldn't ever have believed that a brimful glass could have enough room for so many coins. On with the job." "Everyone can do it with nine." "That takes nine coins. "Go ahead. without shaking. one in each. just for a time. the fifth into the fourth. Arrange them in three rows so that there are three coins in each. "Saucers with water?" "With or without water. Now 11 coins were lying in 10 saucers. I can't.. We'll place the first coin in the first saucer and the 11th as well. "Here are six coins. The fourth into the third saucer. No. That'll be both more interesting and more useful than getting ready-made solutions." he laughed. Fantastic! Brother swiftly collected the coins not caring to explain the trick to me. psychological. if only you dip them carefully. "Now. and so forth. You see now where all the room is in the glass. "Just think. No. can you place 11 coins into 10 saucers so that there is only one coin in each saucer?" the brother asked. I'll help you. What is going to follow? "Two coins? Well. It has even more room because the water can rise up about two two-pence pieces thickness." When I had placed the 10th coin into the ninth saucer I was surprised to see that the 10th saucer was vacant. waiting in bewilderment.." I had to believe it though when I saw the heap of coins inside the glass with my own eyes.38-39 By the Way volume of the buldge above the brim is 16 times larger than that of a two-pence piece." . Alex said. and one in each. setting 10 saucers in a row. I've just remembered one more trick with coins." he explained. and then add the results. Here are three more problems in the same vein." Alex proclaimed at once and was right on target. "and finally. the next biggest 4 centimetres. But not now. The first one: arrange nine coins in ten rows with three coins in each. I'll show you a fascinating game with counters. Look. and so on down to the smallest which is 1 centimetre in diameter. The biggest counter is 5 centimetres in diameter.. We repeated it once more. Take into one hand a 5 pence. I'd have guessed for myself. odd or even?" "Odd. but don't tell me which coin is in which hand." "You're too quick to give up. I draw a square divided into 36 smaller squares. Only do the following mental arithmetic: double what's in the right hand and treble what's in the left. it's simple." . The result was even and my brother said without mistake that the 10 was in my left hand. I'll figure it out. The second: arrange ten coins in five rows with four coins in each. "But the rows criss-cross." "Well. with three coins in each. but did I say that they mustn't?" "If I'd known that this was allowed. Aha." "Perhaps." "What's the final result. Ready?" "Yes.40—41 Figure 7 By the Way Figure 8 "Now again that's something impossible. I've just made some counters by cutting out differently sized disks from a sheet of cardboard." he said. guess how to solve the problem in another way. The third problem is as follows. into the other a 10 pence." "There are three rows here. "About this problem also think at leisure.. sleep on it. Now try to arrange 18 coins with one in each small square so that in each row and column there are three coins." "The 10 is in the right and the 5 in the left hand. then. . then the third saucer will be vacant for the 3. Add one more counter. how many moves would be required?" "Three: the 1 onto the middle saucer." "Right. I did so. We'll proceed as follows: first we transfer the two smaller coins onto the middle saucer one after the other. After all. "Place the 1 onto the middle saucer. and count how many moves you need to transfer the stack. and so on down to the 1 counter on top of the stack. it's interesting to find the least number of moves that could lead to the goal. "The whole stack of five counters is to be transferred onto the third saucer but you have to observe the following rules. the 2 and the 1. "How many transfer did you make in all?" asked my brother okaying my job. Now a further predicament. "Well. Where was I to place the 4? Accidentally. Finally. This takes. then.. after a long series of move I succeeded in transferring the 5 from the first saucer and ended up with the whole stack on the third saucer. as we already know. We then transfer the 3 onto the vacant third saucer-one more ." my brother prompted. the 2 onto the third one and then the 1 onto the third. "Didn't count. First I placed the 1 counter onto the third saucer. The rules are simple as you can see. and stopped. the 2 counter onto the middle one. go ahead. Rule number 1: each time move 1 counter only. If our stack included only two counters. the 2 onto the third. three moves. and next put the 1 onto the third as well. Rule number 3: counters may be placed temporarily onto the middle saucer but still observing the first two rules and the counters must end up on the third saucer in the initial order. Rule number 2: never put a larger Figure 9 C5D CcS^CcT) counter onto a smaller one. Now.38-39 By the Way He put three saucers side by side. the 3. I hit upon an idea: first 1 transferred the 1 onto the first saucer." "Well let's count then." I started. and put a stack of counters onto the first saucer: so that the 5 counter went on the bottom on top of that was the 4 counter. Where should the 3 counter go? It was larger than both the 1 and 2 counters. not five. if its's even. It says that in the town of Benares is a sanctuary into which the Indian god Brahma. then the 4 goes onto the third s a u c e r . Look!" And Alex wrote out the following table. you got it right." "You say it's an ancient game.t h r e e more moves. 3 1 . The total is 3 + 1 + 3 = 7. "You've thus mastered this ancient game.42^3 38-39 By the Way move. Now." "Well. didn't you invent it yourself?" "No. But the game as such has a very ancient origin and apparently came from India where there is a marvellous legend associated with it. But I'll show you a way to simplify the procedure." "For the four counters. The priests of the sanctuary were obliged ceaselessly to transfer these rings from one stick to another using the third as an auxiliary and observing the rules of our game that is to move one ring at a time . let me count for myself. Next we transfer both counters from the middle saucer. the number of the counters to be transferred equals the number of twos in the product. I only applied it to counters. Thus I get 7 + 1 + 7 = 15. For instance. 15. installed three diamond sticks and put on one of them 64 golden rings with the largest at the bottom and each of the rest being smaller than the one beneath it. I could calculate the number of moves for any stack of counters. Note that the numbers involved-3.o n e move. it goes onto the middle saucer. for seven counters: it's 2 x 2 x 2 x 2 x 2 x 2 x 2 . as he was creating the world. 3= 7= 15 = 31 = 2x2-1 2x2x2-1 2x2x2x2-1 2x2x2x2x2-1 "I see. You need only know one practical rule which is if the stack contains an odd number of counters the first counter is transferred onto the third saucer. and now the three smaller coins go onto the third saucer-seven more moves. And for the five counters?" "15 + 1 + 15 = 31.1 = 1 2 8 .1 = 127. onto the third o n e . too." "Splendid.a l l represent the product of several twos minus one. At first I transfer the three smaller counters onto the middle saucer-seven moves. 7. In 10 days.000. a million moves.709.000. why? After all. I think. and so forth.38-39 By the Way and not to place it onto a smaller one. the number of moves is only equal to the product of 64 twos.000. next we put the third coin into the second saucer. "And about 100.000 in 24 hours.616.." "You are mistaken.446.000 years!" "But. but I was patient and worked it out to the end. you can make 3600 transferrings in an hour. But what about the second coin? It was ignored and that was the trick. A million would be enough. I first found the product of 16 twos. The legend has it that when all the 64 rings have been transferred the end of the world will come. I obtained the number 18. To handle the 64 rings would take as much as 500.000." "Splendid.000. it means the world should've perished long ago!" "Perhaps. I'll have time to go to tend to my business. the fourth coin into the third saucer. Thus my elder brother was right.. They didn't turn out to be all that difficult. While you do your multiplying.000. The business of 11 coins in 10 saucers appeared ridiculously simple: we put the first and eleventh coins into the first saucer. I mustered up courage and set about the problems he had set to me to solve on my own." said brother and left." "Oh.. you think transferring 64 rings won't take much time?" "Of course.073.000.744." Well.000. I'll now multiply and check. Doubling 5 gives an even number but trebling it gives an odd one Figure 10 . Allowing a second per move. then multiplied the result by itself. to transfer even a thousand. some were even rather easy." "'Only' upwards of 18." "Wait a bit. not 64 rings. The idea behind guessing which hand had the 10 pence coin was also simple.551. which amounts to.. A tedious job. 10). the problem with coins in the small squares works out as shown in Fig.and left-hand rule • Mazes in ancient times • Tournefort in a cave • Solution of the maze problem. i. it is clear that the 5 must have been trebled. e. been in the left hand. 11. if the total was even. "Yes. please." "An interesting story." "I remember it had me in stitches! Where are you?" "Where the crowd of people is wandering about in a garden maze. i. looking for a way out. Finally. The solutions to the problems on the coin arrangements are clear from the accompanying drawings (Fig.44-45 Figure 11 By the Way ©© © ©© © © © © ©© © whereas multiplying 10 always gives an even number. it must have been in the right hand. it's Three Men in a Boat by Jerome. He said he went in once to show . Wandering in a Maze Wandering in a maze • People and rats 0 Right." So I read the story aloud from the very beginning: "Harris asked me if I'd ever been in the maze at Hampton Court. and if the total was odd.e. Therefore. ©©© © ©© "What are you laughing at in your book? A funny story?" Alex asked me. The 18 coins are arranged in the square with 36 small squares and giving three coins in each row. then the 5 had been doubled. Read it again for me. 'Oh. but he held on until.' "Harris began to think it rather strange himself. It was a country cousin that Harris took in. and expressed an opinion that he was an impostor. they passed the half of a penny bun on the ground that Harris's cousin swore he had noticed there seven minutes ago. until they had absorbed all the persons in the maze. and followed. and joined the procession. but it's very simple. People who had given up all hopes of ever getting either in or out. one of the largest in Europe. Harris said he should judge there must have been twenty people following him. blessing him. We'll just walk round for ten minutes.' "They met some people soon after they had got inside. Harris said he thought that map must have been got up as a practical joke because it wasn't a bit like the real thing. and then go and get some lunch. Harris told them they could follow him. at the sight of Harris and his party. or of ever seeing their home and friends again. who said they had been there for three-quarters of an hour. so that you can say you've been. if they liked. insisted on taking his arm. It's absurd to call it a maze. said one of the . He had studied it up in a map. 'Not at all. "'Yes. and it was so simple that it seemed foolish-hardly worth the twopence charged for admission.38-39 By the Way somebody else the way. They said it was very kind of him. as they went along. it must be. "They picked up various other people who wanted to get it over. "'The map may be all right enough. That made Harris mad. in all. for fear of losing him. He said: 'We'll just go in here. plucked up courage. and only misleading. and then should turn round and come out again.' as she herself had taken it from the child. but it seemed a long way. because we've walked a good two miles already. replied the cousin. who had been there all the morning.' said Harris. and he produced his map. he was just going in. and thrown it down there. and had had about enough of it. just before she met Harris. impossible!' But the woman with the baby said. and explained his theory. and fell behind. Harris said. and his cousin said he supposed it was a very big maze. She also added that she wished she never had met Harris. You keep on taking the first turning to the right. " ' O h . and one woman with a baby. at last. "Harris kept on turning to the right. It became so regular at length. and came in. and so they turned. Whatever way they turned brought them back to the middle. and they told him to go and curl his hair with it. and he climbed down.38-39 By the Way party. and ask them where they had been. But all their heads were by this time. and he would see them. They huddled together. They did know where they were. Harris drew out his map again. "They had to wait until one of the old keepers came back from his dinner before they got out. he had become unpopular. and he would come to them. and so the man told them to stop where they were. but the crowd looked dangerous. and then he would reappear again in exactly the same spot. and shouted out directions to them. but with regard to the advisability of going back to the entrance there was complete unanimity. after a while. and come back to them. and off. "Harris thought at first of pretending that that was what he had been aiming at. and the thing seemed simpler than ever. and waited." I said. Harris said that he couldn't help feeling that. in such a confused whirl that they were incapable of grasping anything. and rush to get to them. "And three minutes later they were back in the centre again. every now and then. "He was a young keeper." "They were a bit dense. but the sight of it only infuriated the mob. and then they found themselves in the centre. if you know whereabouts in it we are now. and suggested that the best thing to do would be to go back to the entrance. and the man came and climbed up the ladder outside. and they would wait there for about five minutes. he couldn't get to them. and sang out for the keeper. and waited for the others to take a walk round. that some of the people stopped there.they started for the third time. and begin again. For the beginning again part of it there was not much enthusiasm. and trailed after Harris again. "To have a plan and . About ten minutes more passed. "After that they simply couldn't get anywhere else. and new to the business. they has got something to start from then.' "Harris didn't know. and when he got in. as luck would have it. and he decided to treat it as an accident. They caught sight of him. in the opposite direction. "Anyhow. and then he got lost. rushing about the other side of the hedge. and the map was once more consulted. "They all got crazy at last. to a certain extent. the ones I'd just made fun of! "You see. Having wandered a little round about the plan I came. this maze." "Rats? What rats?" "The ones described in this book.000 square metres. scientists make a small plaster model of a maze and put the animals to be tested into it. Found at last." I pointed the match at the centre of the maze and bravely drew it along the winding paths of the maze. the plan is no use. this book is about the mental abilities of animals. only 1." My brother opened the book at a page showing a small plan. The book says that rats can find their way about a plaster maze of Hampton Court in only half an hour and that is faster than the people in Jerome's book. It seems to me I've got the plan of that maze. Do you think this is a treatise on garden design? No. To test the intelligence of animals. Just as Figure K I said Plan of the Maze at Hampton Court." Alex said and began to delve in his bookcase." "Do you think you'd find at once?" "With a plan? Certainly!" "Just wait.." . just as Jerome's characters had.. "Imagine you're here in the central area of the maze and want to get out.. back to the central area. Been in existence for two centuries. but the whole affair appeared to be more involved than I had expected. It seems rather small.Bay the Way not to find the way out. which way would you go to get to the exit? Sharpen a match and use it to show the way.. "Does this maze really exist?" "Hampton Court? Of course. But rats solve the task without any plan. it's near London. Had you marked with a dash line the way you went. mentally wandering about the plan. you can safely enter any maze without any fear of getting lost. the maze doesn't seem to be very difficult. or left for that m a t t e r ." "Just this?" "Yes. but it's no good if you want to walk along all of its paths without exception. "A beautiful rule.. "The rule is good so long as you simply don't want to be lost in a maze.i t makes no difference." "Not really. You would never think that it's so treacherous. You haven't been down this alley. Now try and use the rule in reality. Truly." "But I've just been in all the alleys on the plan." I ran my match along the paths..38-39 By the Way "Judging from the plan. but in ancient times they used to put mazes inside large houses or dungeons. you'd have found that one alley wasn't covered. If you know it." "Are there many different kinds of maze?" "A lot. 13). you wouldn't see much of it." "Which rule?" "You should follow the paths touching its wall with your right hand. But with one hand." "There's a simple rule." "You are mistaken." Alex objected. being guided by the rule. I didn't miss one." "Which one?" Figure 13 "I've marked it with a star on this plan (Fig. to the exit. Nowadays they are only in garden and parks and you wander around in the open air between high green walls of hedge. That was 4 —97J . In other mazes the rule would guide you past large sections of it so that even though you'd find your way out safely. I soon came from the entrance to the centre and back again. all the time. a man called Daedalus. passages and halls. Its paths were so tangled that its own creator. apparently. What did the French botanist do in order not to be lost? This is what his fellow-countryman. One such." "Why didn't they use the rule for walking round mazes you've just told me about?" "For one thing." My brother took down from the bookcase an old book entitled Mathematical Amusements and read aloud the following passage (I copied it later): "Having wandered for a time with our companions . A maze can be contrived in such a way that the user of the rule will miss the place where the treasure is kept." "But is it possible to make a maze from which there is no escaping? Of course. to protect them from robbers. I've already told you that it doesn't always let you visit every part of the maze. You only need to follow a strict system and take certain precautions. the mathematician Lucas.t h e grave of the king would become his grave. he wouldn't be able to find his way o u t . Two centuries ago the French botanist Tournefort dared to visit a cave in Crete which was said to be an inescapable maze because of its innumerable paths. Not only that but every maze has an escape and it is possible to visit every corner without missing one and still escape to safety." brother continued. "The aim of other ancient mazes was to guard the tombs of kings. for instance. allegedly couldn't find his way out of it. There are several such caves in Crete and it may be possible that they gave rise to the ancient legend about the maze of King Minos. This isn't true because it can be proved mathematically that inescapable mazes cannot be built. in ancient times nobody knew about the rule. said about it. someone who enters it using your rule will get out eventually. it would be absolutely impossible to get out of it. was the proverbial maze on the island of Crete and the legend has it that an ancient king called Minos had it built. For another. eventually leading them to starve to death. too.38-39 By the Way Figure 14 done with the cruel aim of dooming the unhappy people thrown into them to wander hopelessly about the intricate tangle of corridors. A tomb was located at the centre of a maze so that if a greedy seeker after buried treasure even succeeded in reaching it. but suppose a man is put inside and left there to wander?" "The ancients thought that when the paths of a maze are sufficiently tangled. however.. These days the rules for walking around mazes have been worked out that are less burdensome but no less reliable than his precautions. that is there and back. "First. deviating neither right nor left. go further down any corridor but mark each time you go down it with a stone the way you have just passed and the way you are going to follow. mark the way with a second stone and go along one of new corridors. a third rule requires that having come to a visited crossing along a corridor that has already been walked. We had counted 1460 steps in half an hour along this gallery. Third. there was no other way since the problem of mazes had not yet been solved. it seemed. Here I've .. might be difficult to find later we attached numbered papers to the wall. "All these laborious precautions might not seem all that necessary to you. Finally. go back at once and place two stones at the end of the corridor. A first rule is that when you walk into a maze." Alex finished reading and said. and the other side of the path he sprinkled with chopped straw. we saw to it to provide for our return. having instructed him to call for the people from a neighbouring village to rescue us should we not return by night fall. each of us had a torch. But as we had a strong desire to be out of the maze. Second. At a crossing. we left one of our guides at the entrance to the cave. we came to a long wide gallery that led us into a spacious hall deep in the maze. at every turn which. every corridor of the maze without missing any corner and return back to safety. which he carried in a bag. take one whose entrance has only one stone (that is a corridor that has only been passed once). On either side there were so many corridors that one would be bound to get lost there unless some necessary precautions were taken. If it is a dead end." "Do you know these rules?" "They aren't complicated. In the times of Tournefort. one of our guides put on the left side bunches of blackthorn he had prepared beforehand. Finally. A second rule states that having arrived along a fresh corridor at a crossing that has earlier been visited (as seen by the stones). return and place two stones at the exit which will indicate that the corridor has been passed twice. Abiding by these rules you can pass twice. follow any path till you reach a dead end or a crossing.50-51 By the Way Figure 15 Figure 16 about a network of underground corridors. If there doesn't happen to be such a corridor. and 16). you could actually make a maze like. If you've enough patience. I hope that now that you know so much you shouldn't be in any danger of getting lost in them. say." . the Hampton Court one that Jerome mentioned . If you wish. 14. 15.you could construct it with your friends out of snow in the yard.38-39 By the Way got several plans of mazes I've cut out at different times from illustrated magazines (Figs. you can try and travel about them. sort of damps the speed down. on the top of a corked bottle and another cork with two forks stuck into it is placed on the top as shown in Fig. The liquid contents of a raw egg is not carried along by the spinning as fast as the shell and. This. Do you know how Columbus stood an egg upright? He simply pressed it down onto a table crushing the bottom of the shell. is used to distinguish a hard-boiled egg from a raw one without breaking the shell. On the contrary. He had. If an egg is placed. If you then stand the egg on its blunt end and keep it this way for a while. The egg will remain upright as long as it spins. the navigator didn't know. which is heavier than the white." The other feat the great navigator had performed is not really all that marvellous. But how can one possibly. This won't work if you try to stand a raw egg upright. You have to shake an egg intensely several times. the whole . the American humorist Mark Twain saw nothing special about Columbus discovering America: "It would have been strange if he hadn't found it there. you may have noticed that raw eggs spin poorly. We have to look for another way of standing eggs and one does exist. A boiled egg can be stood upright simply by spinning it with your fingers or between your palms like a top. there is a third way of putting an egg upright. therefore. Meanwhile it is easier by far than discovering America or even one tiny island. say. After two or three trials the experiment should come out well. I'll show you three methods: one for boiled eggs. stand an egg on end without changing its shape. then the yolk. by the way." This young scholar had thought both deeds equally amazing. and one for both. one for raw eggs.52-53 2 % For Young Physicists More Skilled Than Columbus Figure 17 A schoolboy once wrote in a composition: "Christopher Columbus was a great man because he discovered America and stood an egg upright. of course. changed the shape of the egg. 17. This will bring the centre of mass of the egg down making it more stable than before. Finally. This breaks down the soft envelope containing the yolk with the result that the yolk spreads out inside the egg. will pour down to the bottom of the egg and concentrate there. " This means that the point at which the weight of the system is applied lies below the place at which it is supported. owes its existence to the force.For Young Physicists Figure 18 system (as a physicist would put it) is fairly stable and remains in equilibrium even if the bottle is slightly inclined. In the so-called centrifugal separators it churns cream. the passengers feel directly the centrifugal force that pushes them in the direction of the outer wall of the carriage. But why don't the egg and cork fall down? For the same reason that a pencil placed upright on a finger doesn't fall off when a bent penknife is stuck into it as shown. this force will help you to perform a trick with a glass from which the water doesn't escape. the sling. Centrifugal force helps a circus bicyclist to do a "devil's loop". If you whirl a stone tied to a piece of string. In order to do this you'll only have to swing the glass quickly above your head in a circle. It is put to work. it extracts honey from honey-comb. Centrifugal Force Figure 19 Figure 20 Open an umbrella. spin it and drop a ball into it. The force that threw the ball out in this experiment is generally called the "centrifugal force". We come across centrifugal force more often than you might suspect. Centrifugal force bursts a millstone. if it is spun too fast and is not sufficiently strong. although it would be more appropriate to dub it "inertia". The ancient weapon for hurling stones. you can feel the string become taut and seem to be about to break under the action of the centrifugal force. The ball could be a balled piece of paper or handkerchief. put its end on the floor. The umbrella does not.g. as it were. even though it is upside down. If the speed is sufficiently . as it turns at a crossing. When a tram travels in a circular path.. Centrifugal force manifests itself when a body travels in a circle but this is nothing but an example of inertia which is the desire of a moving body to maintain its speed and direction. A scientist would explain: "The centre of mass of the system lies below the support. etc. e. it dries washing by extracting water in centrifugal driers. etc. desire to accept the present and the thing itself crawls up the edge and then flies off in a straight line. If you are adroit enough. Something will happen you probably wouldn't expect. or any other light and unbreakable thing. For Young large, the carriage could be overturned by the force if the outer rail wasn't laid a bit higher than the inner one: which is why a tram is slightly inclined inwards when it turns. It sounds rather unusual but an inclined tram is more stable than an upright one! But this is quite the case, though. A small experiment will help explain this to you. Bend a cardboard sheet to form a wide funnel, or better still take a conical bowl if available. The conical shield (glass or metallic) of an electrical lamp would be suitable for our purposes. Roll a coin (small metal disk, or ring) around the edge of any of these objects. It will travel in a circle bending in noticeably on its way. As the coin slows down, it will travel in ever decreasing circles approaching the centre of the funnel. But by slightly shaking the funnel the coin can easily be make roll faster and then it will move away from the centre describing increasingly larger circles. If you overdo it a bit, the coin will roll out. For cycling races in a velodrome special circular tracks are made and you can see that these tracks, especially where they turn abruptly have a noticeable slope into the centre. A cyclist rides along them in an inclined position (like the coin in the funnel) and not only does he not turn over but he acquires special stability. Circus cyclists used to amaze the public by racing along a steep deck. Now you can understand that there is nothing special about it. On the contrary, it would be a hard job for a cyclist to travel along a horizontal track. For the same reason a rider and his horse lean inwards on a sharp turn. Let's pass on from small to large-scale phenomena. The Earth, on which we live, rotates and so centrifugal force should manifest itself. But where and how? By making all the things on its surface lighter. The closer something is to the Equator, the larger the circle in which it moves and hence it rotates faster, thereby losing more of its weight. If a 1-kg mass were to be brought from one of the poles to the Equator and reweighed using a spring balance, the loss in weight would amount to 5 grammes. That, of course, is not very much of a difference, but the heavier a thing, the larger the difference. A locomotive that has come from Stockholm to Rome loses 60 kg, the weight of an adult. A battle ship of 20,000-tonne displacement that has come from the White Sea to the Black Sea will have lost as much as 80 tonnes, the weight of a locomotive! Why does it happen? Because as the globe rotates, it For Young tries to throw everything off its surface just like the umbrella in our earlier experiment. It would succeed were it not for the terrestrial attraction that pulls everything back to the Earth's surface. We call this attraction "gravity". The rotation cannot throw things off the Earth's surface, but it can make them lighter. The faster the rotation, the more noticeable the reduction in weight. Scientists have calculated that if the Earth rotated 17 times faster, things at the Equator would lose their weight completely to become weightless. And if it rotated yet quicker, making, say, one turn every hour, then the weight lessness would extend to the lands and seas farther away from the Equator. Just imagine things losing their weight. It would mean there would be nothing you could not lift, you would be able to lift locomotives, boulders, cannons and warships as easily as you could a feather. And should you drop t h e m - n o danger, they could hurt nobody since they wouldn't fall down at all, but would float about in mid-air just where you'd let go of them. If, sitting in the cabin of an airship, you wanted to throw something overboard, it wouldn't drop, but would stay in the air. What a wonder world it would be. So you could jump as high as you've never dreamed, higher than sky-scrapers or the mountains. But remember, it would be easy to jump up but difficult to return back to ground. Weightless, you'd never come back on your own. There would also be other inconveniences in such a world. You've probably realized yourself that everything, whatever its size, would, if not fixed, rise up due to the slightest motion of air and float about. People, animals, cars, carts, ships-everything would move about in the air disorderly, breaking, maiming and destroying. That is what would occur if the Earth rotated significantly faster. Ten Tops The accompanying figures show 10 types of tops. These will enable you to do a number of exciting and instructive experiments. You don't need any special skill to construct them so you can make them yourself without any help or expense. This is how the tops are made: Figure 21 For Young Figure 22 Figure 23 Figure 24 Figure 25 Figure 26 1. If a button with five holes comes your way, like the one shown in the figure, then you can easily make it into a top. Push a match with a sharpened end through the central hole, which is the only one needed, wedge it in and then... the top is ready. It will rotate on both the blunt and pointed end, you only need to spin it as usual by twisting the axle between your fingers and dropping the top swiftly on its blunt end. It will spin rocking eccentrically. 2. You could do without a button, a cork is nearly always at hand. Cut a disk out of it, pierce the disk with a match, and you have top No. 2 (Fig. 22). 3. Figure 23 depicts a rather unusual t o p - a walnut that spins on the pointed end. To turn a suitable nut into a top just drive a match into the other end, the match being used for spinning the top. 4. A better idea is to use a flat wide plug (or the plastic cover of a small can). Heat an iron wire or knitting-needle and burn through the plug along the axis to form a channel for the match. A top like this will spin long and steadily. 5. Figure 24 shows another top: a flat round box pierced by a sharpened match. For the box to fit tightly without sliding along the match, seal the hole with wax. 6. A fancy top you see in Figure 25. Globular buttons with an eye are tied to the edge of a cardboard disk with pieces of string. As the top rotates the buttons are thrown off radially, stretching the strings out taut and graphically demonstrating the action of our old friend, the centrifugal force. 7. The same principle is demonstrated in another way by the top in Figure 26. Some pins are driven into the cork ring of the top with coloured beads threaded onto them so that beads can slide along the pin. As the top spins the beads are pushed away to the pin heads. If the spinning top is illuminated, the pins merge into a solid silvery belt with a coloured fringe of the merged beads. In order to enjoy the illusion spin the top on a smooth plate. 8. A coloured top (Fig. 27). It is fairly laborious to make but the top will reward your efforts by demonstrating an astounding behaviour. Cut a piece of cardboard into a disk, make a hole at the centre to receive a pointed match. Clamp the match on either side of the disk with two cork disks. Now divide the cardboard disk into equal sectors by straight radial lines in the same way a round cake is shared out. Figure 27 For Young Figure 28 Figure 29 Figure 30 Colour the sectors alternately in yellow and blue. What will you see as the top rotates? The disk will appear neither blue nor yellow, but green. The blue and yellow colours merge in your eye to give a new colour, green. You can continue your experiments on colour blending. Prepare a disk with sectors alternately coloured in blue and orange. Now, when the disk is spun it will be white, not yellow (actually it will be light grey, the lighter the purer the paints). In physics two colours that, when blended, give white are called "complementary". Consequently, our top has shown that blue and orange are complementary. If you have a good set of paints you can try an experiment that was first done 200 years ago by the great English scientist Isaac Newton. Paint the sectors of a disk with the seven colours of the rainbow which are: violet, indigo, blue, green, yellow, orange, and red. When all the seven colours are rotated together they will produce a greyish-white. The experiment will help you to understand that the sunlight is composed of many colours. These experiments can be modified as follows: as the top spins throw a paper ring onto it and the disk will change its colour at once (Fig. 28). 9. The writing top (Fig. 29). Make the top as just described, the only difference being that its axle will now be a soft pencil, not match. Make the top spin on a cardboard sheet placed somewhat at an angle. The top will, as it spins, descend gradually down the inclined cardboard sheet, with the pencil drawing flourishes. These are easy to count and, since each one corresponds to,one turn of the top, by watching the top with a clock in hand* you can readily determine the number of revolutions the top makes each second. Clearly, this would be impossible in any other way. A further form of the writing top is depicted in Fig. 30. Find a small lead disk and drill a hole at the centre (lead is soft and drilling it is easy), and a hole on either side of it. Through the centre hole a sharpened stick is passed, and through one of the side holes a piece of fishing-line * By the way, seconds can also be reckoned without a clock just by counting. To do so, you should at first drill yourself a bit to pronounce "one", "two", "three", etc., so that each number takes exactly one second to pronounce. Don't think that it's difficult, the practice shouldn't take more than 10 minutes. For Young (or bristle) is threaded so that it protrudes a bit lower than the end of the top axle. The fishing-line is fixed in with a piece of match. The third hole is left as it is, its only purpose is to balance the disk since otherwise the top won't spin smoothly. Our writing top is ready, but to experiment with it we need a sooty plate. Hold a plate over a smoky flame until it is covered with a uniform layer of dense soot. Then send the top spinning over the sooty surface. It will slide over the surface and the end of the fishing-line will draw, white on black, an intricate and rather attractive ornament. 10. Our crowning effort is the last rig, the merry-goround top. However, it is much easier to make that it might seem. The disk and stick here are just as in the Figure 31 earlier coloured top. Into the disk, pins with small flags are stuck symmetrically about the axis, and tiny paper riders are glued in-between the pins. Thus, you have a toy merry-go-round to amuze your younger brothers and sisters. Impact When two boats, trams or croquet balls collide (an incident or move in a game) a physicist would call such an event just "impact". The impact lasts a split second, but if the objects involved are elastic, which is normally the case, then a lot happens in this instant. In each elastic impact physicists distinguish three phases. In the first phase both colliding objects compress each other at the place of contact. Then comes the second phase when the mutual compression reaches a maximum, the internal counteraction begins in response to the compression and prevents the bodies from compressing further, so balancing the thrusting force. In the third phase the counteraction, seeking to restore the body's shape deformed during the first phase, pushes the objects apart in opposite directions. The receding For Young object, as it were, receives its impact back. In fact, when we observe, say, one croquet ball striking another, stationary, ball of the same mass, then the recoil makes the oncoming ball stop and the other ball roll forward with the velocity of the first. It is very interesting to observe a ball striking a number of other balls arranged in a file touching each other. The impact received by the first ball is, as it were, transferred through the file, but all the balls remain at rest and only the outermost one jumps away as it has no adjacent ball to impart the impact to and receive it back. Figure 32 This experiment can be carried out with croquet balls, but it is also a success with draughts or coins. Arrange the draughts in a straight line, it can be a very long one, but the essential condition is that they touch one another. Holding the first draught with a finger strike it on its edge with a wooden ruler, as shown. You will see the last draught jump away, with the rest of the draughts remaining in their places. An Egg in a Glass Circus conjurers sometimes surprise the public by jerking the cloth from a laid table so that everythingplates, glasses, and bottles - remain safely in place. This is no wonder or deceit, it is simply a matter of dexterity acquired by prolonged practice. Such a sleight-of-hand is too difficult for you to attain but on a smaller scale a similar trick is no problem. Place a glass half-filled with water on a table and cover it with a postcard (or half of it). Further, borrow a man's wide ring and a hard-boiled egg. Put the ring on the top of the card, and stand the egg on the ring. It possible to jerk the card away so that the egg doesn't roll down onto the table? At first sight, it may seem as difficult as jerking the Figure 33 For Young table-cloth from under the table things. But a good snap with a finger on the edge of the card should do the trick. The card flies away and the egg... plunges with the ring safely into the water. The water cushions the blow and the shell remains intact. With some experience, you could try the trick with a raw egg. This small wonder is explained by the fact that during the fleeting moment of the impact the egg doesn't receive any observable speed but the postcard that was struck has time to slip out. Having lost its support, the egg drops into the glass. If the experiment is not at first a success, first practice an easier experiment in the same vein. Place half a postcard on the palm of your hand and a heavy coin on top of it. Now snap the card from under the coin. The card will fly away but the coin will stay. Unusual Breakage Figure 34 Conjurers sometimes perform an elegant trick that seems amazing and unusual, though it can be easily explained. A longish stick is suspended on two paper rings. One of the rings is suspended from a razor blade, the other, from a clay pipe. The conjurer takes another stick and strikes the first one with all his strength. What happens? The suspended stick breaks but the paper rings and the pipe remain absolutely intact! The trick can be accounted for in much the same way as the previous one. The impact was so fast that it allowed no time for the suspended stick's ends and the paper rings to move. Only the part of the stick that is directly subjected to the impact moves with the result that the stick breaks. The secret is thus that the impact was very fast and sharp. A slow, sluggish impact will not break the stick but will break the rings instead. The most adroit conjurers even contrive to break a stick supported by the edges of two thin glasses leaving the glasses intact. I do not tell you this, of course, to encourage you to do such tricks. You'll have to content yourself with a more modest form of them. Put two pencils on the edge of a low table or bench so that part of them overhang and place a thin, long stick on the overhanging ends. A strong, sharp stroke with the edge of a ruler at the middle of the stick would break it in two, but the pencils would remain in their places. For Young Figure 35 Now it should be clear to you why it is difficult to crack a nut by the strong pressure of a palm, but the stroke of a fist does the j o b easily. When you hit it, the impact has no time to propagate along the flesh of your fist so that your soft muscles do not yield under the upthrust of the nut and act as a solid. For the same reason a bullet makes a small round hole in the window-pane, but a small stone traveling at a far slower speed breaks the pane. A slower push makes the window frame turn on its hinges, something neither the bullet nor the stone can make it do. Finally, one more example of the phenomenon is being able to cut a stem of grass by a stroke of a cane. By slowly moving the cane you can't cut a stem, you only bend it. By striking it with all your strength you will cut it, if, of course, the stem is not too thick. Here, as in our earlier cases, the cane moves too fast for the impact to be transferred to the whole of the stem. It will only concentrate in a small section that will bear all the consequences. Just Like a Submarine A fresh egg will sink in water, a fact known to every experienced housewife. If she wants to find out whether an egg is fresh, she tests it in exactly this way. If an egg sinks, it is fresh; and if it floats, it is not suitable for eating. A physicist infers from this observation that a fresh egg is heavier than the same volume of fresh water. I say "fresh water" because impure (e.g. salt) water weighs more. It is possible to prepare such a strong solution of salt that an egg will be lighter than the amount of brine displaced by it. Then, following the principle of floating discovered in olden days by Archimedes, even the freshest of eggs will float in the solution. For Young 54-55 Figure 36 Use your knowledge in the following instructive experiment. Try to make an egg neither sink nor float, but hang in the bulk of a liquid. A physicist would say that the egg is "suspended". You'll need a water solution of salt that is so strong that an egg submerged in it displaces exactly its own weight in the brine. The brine is prepared by the trial-and-error method: by pouring in some water if the egg surfaces and adding some stronger brine if it sinks. If you've got patience, you'll eventually end up with a brine in which the submerged egg neither surfaces nor sinks, but is at rest within the liquid. This state is characteristic of a submarine. It can stay under water without touching the ground only when it weighs exactly as much as the water it displaces. For this weight to be reached, submarines let water from the outside into a special container; when the submarine surfaces the water is pushed out. A dirigible-not an aeroplane but just a dirigible - floats in the air for the very same reason: just like the egg in the brine it diplaces precisely as many tonnes of air as it weighs. Floating Needle Is it possible to make a needle float on the surface of water like a straw? It would seem impossible: a solid piece of steel, although it's small, would be bound to sink. Many people think this way and if you are among the many, the following experiment will make you change your mind. Get a conventional (but not too thick) sewing needle, smear it slightly with oil or fat and place it carefully on the surface of the water in a bowl, pail, or glass. To your surprise, the needle will not go down, but will stay on the surface. Why doesn't it sink, however? After all, steel is heavier than water? Certainly, it is seven to eight times as heavy as water, if it were under the water it wouldn't be able to surface like a match. But our needle doesn't submerge. To find a clue, look closely at the surface of the water near the floating needle. You'll see that near the needle the surface forms sort of a valley at the bottom of which lies our needle. The surface curvature is caused by the oil-smeared needle being not wetted by the water. You may have For Young Figure 37 noticed that when your hands are oily, water doesn't wet the skin. The feathers of water birds are always covered with oil exuded by a gland, which is why water doesn't wet feathers ("like water off a duck's back"). And again this is the reason why without soap, which dissolves the oil film and removes it from the skin, you cannot wash your oily hands even by hot water. The needle with oil on it is not wetted by water either and lies at the bottom of a concavity supported by the water "film" created by surface tension. The film seeks to straighten and so pushes the needle out of the water, preventing it from sinking. As our hands are always somewhat oily, if you handle a needle it will be covered by a thin layer of oil. Therefore, it is possible to make the needle float without specially covering it with oil-you'll only have to place it extremely carefully on some water. This can be made as follows: place the needle on a piece of tissue-paper, then gradually, by bending down the edges of the paper with another needle, submerge the paper. The paper will descend to the bottom and the needle will stay on the surface. Now if you came across a pondskater scuttling about the water surface, you won't be puzzled by it. You'll guess that the insect's legs are covered with oil and are not wetted by the water and that surface tension supports the insect on the surface. Diving bell This simple experiment will require a basin, but a deep, wide can would be more convenient. Besides, we'll need a tall glass (or a big goblet). This'll be our diving bell, and the basin with water will be our "sea" or "lake". There is hardly a simpler experiment. You just hold the glass upside down, push it down to the bottom of the basin holding it in your hand (for the water not to push it out). As you do so you'll see that the water doesn't find its way into the glass-the air doesn't let it in. To make the performance more dramatic, put something easily soaked, e.g. a lump of sugar, under your "bell". For this purpose, place a cork disk with a lump of sugar on it on the water and cover it by the glass. Now push the glass into the water. The sugar will appear to be below the water surface, but will remain dry, as the water doesn't get under the glass. You can perform the experiment with a glass funnel, Figure 38 For Young if you push it into the water, its wider end down and its narrow end covered tightly with a finger. The water again doesn't get inside the funnel, but once you remove your finger from the hole, thereby letting the air out of the funnel, the water will promptly rise into the funnel to reach the level of the surrounding water. You see that air is not "nothing", as some think, it occupies space and doesn't let in other things if it has nowhere to go. Besides, these experiments should graphically illustrate the way in which people can stay and work under water in a diving bell or inside wide tubes that are known as "caissons". Water won't get into the bell, or caisson, for the same reason as it can't get into the glass in our experiment. Why Doesn't It Pour Out? The following experiment is one of the easiest to carry out, it was one of the first experiments I performed when I was a boy. Fill a glass with water, cover it with a postcard or a sheet of paper and, holding the card slightly with your fingers, turn the glass upside down. You can now take away your hand, the card won't drop and the water won't pour out if only the card is strictly horizontal. You can safely carry the glass about in this position, perhaps even more comfortably than usually since as the water won't spill over. As the occasion serves, you can astound your friends (if asked to bring some water to drink) by bringing water in a glass upside down. What then keeps the card from falling, i.e. what overcomes the weight of the water column? The pressure of air! It exerts a force on the outside of the card that can be calculated to be much greater than the weight of the water, i.e. 200 grammes. The person who showed me the trick for the first time also drew my attention to the fact that the water must fill the glass completely for the trick to be a success. If it only occupies a part of the glass, the rest of the glass being filled by air, the trial may fail because the air inside the glass would press on the card balancing off the pressure of the outside air with the result that it might fall down. When I was told this, I set out at once to try it with a glass that wasn't fully filled in order to see for myself of the card would drop. Just imagine my astonishment Figure 39 For Young when I saw that in that case too, it didn't fall! Having repeated the experiment several times, I made sure that the card held in place as securely as with the full glass. This has taught me a good lesson about how the facts of nature should be perceived. The highest authority in natural science must be experiment. Every theory, however plausible it might seem, must be tested by experiment. "Test and retest" was the motto of the early naturalists (Florentine academicians) in the 17th century, it is still true for 20th century physicists. And should a test of a theory indicate that experiment doesn't bear it out, one should dig for the clues to the failure of the theory. In our case we can easily find a weak point in the reasoning that once had seemed convincing. If we carefully turn back a corner of the card covering the overturned, partially filled glass, we'll see an air bubble come up through the water. What is it indicative of? Obviously the air in the glass was slightly rarefied, otherwise the outside air wouldn't rush into the space above the water. This explains the trick: although some air remained in the glass, it was slightly rarefied, and hence exerted less pressure. Clearly, when we turn the glass over, the water, as it goes down, forces some of the air out of the glass. The remaining air, which now fills up the same space, becomes rarefied and its pressure becomes weaker. You see that even simplest physical experiments, when treated attentively, can suggest fundamental ideas. These are those small things that teach us great ideas. Dry Out of Water You'll now see that the air surrounding us on all sides exerts a significant pressure on all the things exposed to it. The experiment I'm going to describe will show you more vividly the existence of what physicists call "atmospheric pressure". Place a coin (or metal button) on a flat plate and pour some water over it. The coin will be under water. It's impossible, you are sure to think, to get it out from under the water with your bare hands without getting your fingers wet or removing the water from the plate. You're mistaken, it is possible. Proceed as follows. Set fire to piece of paper inside a glass and when the air has heated, upend the glass and put it on the plate near the coin. Now watch, you Figure 40 For Young won't have to wait long. Of course, the paper under the glass will burn out soon and the air inside the glass will begin to cool down. As it does so, the water will, as it were, be sucked in by the glass and before long it will be all there, exposing the plate's bottom. Wait a minute for the coin to dry and take it without wetting your fingers. The reason behind these phenomena is not difficult to understand. On heating, the air in the glass expanded, just as all bodies would do, and the extra amount of air came out of the glass. But when the remaining air began to cool down, its amount was no longer enough to exert its previous pressure, i.e. to balance out the external pressure of the atmosphere. Therefore, each square centimetre of the water under the glass was now subject to less pressure than the water in the exposed part of the plate and so no wonder it was forced under the glass by the extra pressure. In consequence, the water was not really "sucked in" by the glass, as it might seem, but pushed under the glass from the outside. Now that you know the explanation of the phenomenon in question, you will also understand that it is by no means necessary to use in the experiment a burning piece of paper or cotton wool soaked in alcohol (as is sometimes advised), or any flame in general. It suffices to rinse the glass with boiling water and the experiment will be as much of a success. The key thing here is to heat the air in the glass, no matter how that is done. The experiment can be performed simply in the following form. When you have finished your tea, pour a little tea into your saucer, turn your glass upside down while it is still hot, and stand it in the saucer and tea. In a minute or so the tea from the saucer will have gathered under the glass. Parachute Make a circle about a metre across out of a sheet of tissue-paper and then cut a circle a few centimetres wide in the middle. Tie strings to the edges of the large circle, passing them through small holes; tie the ends of the strings, which should be equally long, to a light weight. This completes the manufacture of a parachute, a scaled-down model of the huge umbrella that saves lives of airmen who, for some reason or other, are For Young Figure 41 compelled to escape from their aircraft. To test your miniature parachute in action drop it from a window in a high building, the weight down. The weight will pull on the strings, the paper circle will blossom out, and the parachute will fly down smoothly and land softly. This will occur in windless weather but on a windy day your parachute will be carried away however weak the wind and it will descend to the ground somewhere far from the starting point. The larger the "umbrella" of the parachute, the heavier the weight the parachute will carry (the weight is necessary for the parachute not to be overturned), the slower it will descend without a wind and the farther it will travel with a wind. But why should the parachute keep up in the air so long? Surely, you've guessed that the air stops the parachute from falling at once. If it were not for the paper sheet, the weight would hit the ground quickly. The paper sheet increases the surface of the falling object, yet adding almost nothing to its total weight. The larger the surface of an object, the more drag there is on it. If you've got it right, you'll understand why particles of dust are carried about by the air. It is widely believed that dust floats in air because it is lighter. Nonsense! What are particles of dust? Tiny pieces of stone, clay, metal, wood, coal, etc., etc. But all of these materials are hundreds and thousands of times heavier than air; stone, is 1,500 times heavier; iron, 6,000 times; wood, 300 times, and so on. A speck of solid or liquid should infailingly fall down through the air, it "sinks" in it. It does fall, only falling it behaves like a parachute does. The point is that for small specks the surface-to-weight ratio is larger than for large bodies. Stated another way, the particles' surfaces are relatively large for their weight. If you were to compare a round piece of lead shot with a round bullet that is 1,000 times as heavy as the shot, the shot's surface is only 100 times smaller than the bullet's. This implies that the shot's surface per unit weight is 10 times larger than the bullet's. Imagine that the shot shrinks until it becomes one million times lighter than the bullet, that is, turns into a speck of lead. Its "specific" surface would be 10,000 times larger than the bullet's. Accordingly, the air would hinder its motion 10,000 times more strongly than it does the bullet's. Instead of a shake you can use a piece of paper in another shape. Hang the butterfly above a lamp and it will rotate like a live one. the butterfly will cast its shadow on the ceiling and the shadow will repeat the motions of the rotating paper butterfly magnified up. So. But the fresh portion of air heats at once and. In other words. Also. e. This flow occurs because air. N o w that the snake is ready. as shown in Fig. making it rise.68-69 54-55 For Young Physicists That's why it would hover in the air hardly falling and being carried by the slightest wind away and even upwards. The surrounding air. etc. jyst as wind makes the arms of a windmill rotate. Near every heated object. Make a small recess in the tail to receive a knitting-pin fixed upright. bind in the middle and suspend from a piece of a very thin string or hair. the snake will spin very fast if suspended above a kerosene lamp from a piece of string. A Snake and a Butterfly Figure 42 Figure 43 Cut a circle about the size of a glass hole from a postcard or a sheet of strong paper. lighter. which is colder and thus denser and heavier. i. You can also make as follows: strick a needle into . just like the first one is ousted by a yet fresher amount of colder air.) the snake will rotate while the object remains hot. It strikes the coils of our paper snake making it rotate. Cut a spiral in it in the form of a coiled-up snake. Cut it out of tissue-paper. In this way. and occupies its place. What makes the snake rotate? The same thing that makes the arms of a windmill r o t a t e . The coils of the snake will hang down forming sort of a spiral stairs. a barely noticeable warm wind blows upwards from every heated object. 42. displaces the hotter air. we can set out to experiment with it.t h e flow of air. there is an air flow moving upwards. for example a butterfly. Near any hot object (a lamp or tea kettle. expands on heating and becomes thinner. the hotter the stove. Place it near a hot kitchen stove: the snake will spin and the faster. just like any other material. each heated object gives rise to an ascending flow of air around it. which is maintained all the time the object is warmer than the surrounding air. It'll seem to an uninitiated person that a large black butterfly has flown into the room and is hectically hovers under the ceiling. This occurs because water. trade winds. as it were. If you want to keep the warmth in a heated room you should see to it that no cold air comes in from under the door. You will obtain ice but the bottle will be destroyed in the process. the water frozen in the neck becomes. you'll see that it is not that easy. Ice in a Bottle Is it easy to get a bottle full of ice during the winter? It would seem that nothing could be easier when it is frosty outdoors. cold air will flow into the warm one along the floor and warm air will flow out along the ceiling. That's way it seems sometimes that there is a draught near our feet when the room hasn't properly heated up. The butterfly will rotate quickly if placed above a warm thing. N o wonder that Figure 44 . water can break the 5-cm walls of a steel bomb. But if you actually try to do the experiment. You need only to cover the gap by a rug or just a newspaper. The expansion is so powerful that it bursts both a corked bottle and the bottleneck of an open bottle. We come across the expansion of air as it heats and ascending warm currents everywhere. The flame of candle placed near the door will indicate the direction of these flows. monsoons. by about a tenth of its volume. So. expands markedly. It is well known that the air in a heated room is the warmest near the ceiling and the coldest near the floor. breezes and the like but it would lead us too far astray. it'll burst under the pressure of the freezing water. If you leave the door from a warm room to a colder one ajar.54-55 For Young Physicists a cork and place the paper butterfly on the needle's tip at the point of equilibrium which can be found by trial and error. Just put a bottle of water outside the window and let the frost do the job. an ice cork. The frost will cool the water and you will have a bottleful of ice. on freezing. in fact putting your palm under it will be enough for the butterfly to rotate. And what is the draught in a furnace or a chimney stack but an ascending flow of warm air? We could also discuss the warm and cold flows in the atmosphere. Then the warm air won't be ousted from below by the colder one and won't leave the room through holes higher up in the room. The expansion of freezing water can even break metal walls if they are not too thick. Finally.. This doesn't mean that pieces of ice freeze up more strongly when exposed to pressure. When we compress pieces of ice. You can test this by an elegant experiment. When a skater presses all his weight on his skates. the beam will still remain one piece.. the wire should be 0.. while the wire cut the lower layers.. yielding water at a temperature below zero. the upper layers were freezing again. On the contrary. just like all other liquids do. Ice is the only material in nature with which you can do this experiment.5 millimetre or a little less thick. the ice melts under the Figure 45 . it refreezes (as its temperature is below 0°C). If water contracted on cooling. Under the thrust of the wire the ice melted but the water flowed over the wire and free of the pressure refroze at once. but once the cold water produced in the process is free of the pressure. Get a beam of ice. suspend something heavy (about 10 kilogrammes) from the ends of the wire. You may safely take it in your hands as it will be intact as if it had not been cut! After you've learned about the freezing up of ice. It's for this reason that we can skate and toboggan over ice. The ends of the parts that contact each other and are subject to high pressure melt. Under the pressure of the heavy object the wire will bite into the ice and cut slowly through the whole of the beam but. Leave It One Piece You may have heard that pieces of ice "freeze up" under pressure. And those of us in northern countries wouldn't enjoy skating and travelling on the ice of our rivers and lakes. and support its ends by the edges of two stools.70-71 For Young Physicists water pipes burst so often in winter. then ice wouldn't float on the water's surface but would go down to the bottom. In plain English. The expansion of water on freezing also accounts for the fact that ice floats on water and doesn't sink. thus soldering the pieces of ice into a solid block. To Cut Ice and. This water fills in tiny interstices between the parts that are sticking out and when it is not subjected to the high pressure any more it freezes at once. under strong pressure ice melts. the following occurs. chairs or the like. you'll see why it works. Make a loop of a thin steel wire 80 centimetres long and put it round the beam. After trying several times you'll find a place where the sound of a stroke comes just at the moment of a visible stroke. Sound Transmission You may have observed from a distance a man using an axe or a carpenter driving in nails. you do not hear the stroke when the axe touches the tree or when the hammer hits a nail. although the temperature might be below freezing point. move a little forward or backward. So sound covers one kilometre in 3 seconds. Now it should be easy for you to guess the reason behind this enigmatic phenomenon. Therefore. Then return to where you started and you'll again notice the lack of coincidence between the sound and the visible stroke. but approximately it is about 1/3 of a kilometre. Then your eyes will see what your ears hear and it'll seem to you that the sound comes when the tool is up and not when the tool is down. light does it nearly instantaneously. only it'll be different strokes since you'll hear an earlier stroke. of course. but you hear it later when the axe (or hammer) is ready for the next stroke. Next time you happen to observe something similar. Sound takes some time to cover the distance from the place where it originated to your ear. and if the wood-cutter swings his axe twice a second. covered by the sound during a swing of the axe. you'll see and hear a stroke simultaneously. That's why it's so slippery. What is the distance covered by sound in one second? It has been measured exactly. Now. You may then have noticed an unusual thing. But light travels each second in air almost . you'll have to be 160 metres away for the sound to coincide with the axe as he raises it. then by the time the sound reaches your ear the axe will strike again. And it may happen that while the sound is travelling through the air to your ear. But if you move in either direction just a distance. the axe (or hammer) will have been raised for a new stroke.74-75 For Young Physicists pressure (if the frost is not too severe) and the skate slides along where it again melts some ice and the process occurs continuously. Wherever the skate goes a thin layer of ice turns into water that when free of the pressure refreezes. perhaps the last but one or even earlier. the ice is always "lubricated" with water under skates. on the other hand. leaning forward Figure 46 . e. soft tissues and loose. A further fascinating experiment testifying to the good transmission of sound through your skull. Press these ends with your fingers to your closed ears and. cast iron. Elastic solids are better still as sound transmitters. Do you want to make sure that the bones of your skull have this property? Hold the ring of a pocket watch with your teeth and close your ears with your hands. Put your ear to the end face of a long wood beam or a block and ask somebody to tap it slightly at the other end. This sound comes to your ears through the bones of your skull. If it's rather quiet and spurious noises don't interfere. Carpets. wood. If you put your ear to the ground you can hear the clatter of horses' hoofs long before the sound comes through the air and in this way you can hear thunder that is so far away that no sound comes to you by air at all. and they'll be louder than the ticking perceived through the ear. g. you can even hear a clock ticking at the opposite end of your beam. You'll hear the dull sound of the stroke transmitted through the entire length of the beam. and even soil. Sound is transmitted equally well along iron rails or beams. A Bell Among the materials distinguished for their perfect sound transmission I've mentioned bones. sound travels four times faster than in air. liquids and solids. inelastic materials are very poor sound transmitters since these "absorb" it. That's why they hang thick curtains near doors if they don't want any sound to reach an adjacent room. So you can understand that for any distances on earth we can safely take the speed of light to be infinite. Only elastic solids transmit sound so well. and under water sound can be heard distinctly. So in water. and bone. You'll still quite distinctly "hear" the measured strokes of the balance.72-73 74-75 For Young Physicists a million times as far as sound. Tie a soup spoon in the middle of a piece of string so that the string has two loose ends. People working in underwater caissons can hear sounds from the shore perfectly and anglers will tell you how fish scatter at the slightest suspicious noise from the shore. cast iron tubes. soft furniture and clothes have the same effect on sound. Sound is transmitted not only through the air but also through other gases. make it strike something solid. There was Figure 47 a mirror on the wall covered with a sheet of paper that had eyes. The experiment comes out better if you use something heavier instead of the spoon. I might have taken to my heels had it not been for my brother's laughter behind me. a nose. .74-75 For Young Physicists for the spoon to swing freely. After I'd learned the rule it was no problem to work out where to locate the candle with respect to the mirror for the light spots to be cast at the required place on the shadow. it turned out that arranging the mirror properly is not that easy. It took a lot of practice to master the art. Flat as a shadow. it stared at me. I was scared by my own shadow. when I attempted to play this joke on my friends." The room was dark. and a mouth cut in it. But suddenly I was stunned: an incongruous monster eyed me from the wall. Light rays are reflected in a mirror according to the following rule: the angle at which light rays strike the mirror equals the angle at which they are reflected. "Want to see something unusual? Come into this room. But later. I led the way and so was the first to enter the room. To tell the truth. I turned round and saw the reason. Alex had so directed the candle's light that these parts of the mirror reflected directly onto my shadow. Thus. You'll hear a low-pitched drone as if a bell is ringing near your ears. Alex took a candle and we walked in. I got a little frightened. A Frightening Shadow One evening my brother Alex asked. clearly. i.e. . In order to obtain the earlier illumination at double the distance you'd have to put two times two. For this purpose place the lamp and a burning candle at one end of a table and at the other you stand a sheet of white cardboard clamped between books as Figure 48 * This explains why a whisper from your neighbour drowns the loud voice of an actor on the stage in a theatre. If the actor is only 10 times farther away from you than your neighbour. nine candles. you want to find out how many candles you need to replace the lamp to obtain the same illumination. It follows that at twice the distance illumination is four times weaker. and so on. For example. you wish to compare the brightness of your lamp with that of a conventional candle. Knowing this law we can make use of it to compare the brightness of two lamps. But how many times weaker? Two? No. This is the law of weakening illumination with distance. not three. four candles. a candle illuminates much weaker. At triple the distance you'd need three times three. or any two light sources in general. not by 6 times. in other words. It's not surprising then that for you the actor's voice is weaker than the whisper. and at five times the distance. Note in passing that this is also the law of sound attenuation with distance. you won't obtain the previous illumination. 16 times. For instance. sound attenuates on six times the original distance by 36 times. and so forth. at four times the distance. if you place two candles at double the distance.74-75 For Young Physicists To Measure Light Brightness At twice the distance. at three times the distance. i.e. then the actor's voice is attenuated 100 times more than what you'd hear if the same sound came to you from the lips of your neighbour. The teacher's words reaching students (especially those far away) are so attenuated that even a soft whisper from a neighbour will muffle them completely. not two. 5 x 5 or 25 times weaker. nine times weaker. For exactly the same reason it's important for students to keep quiet when the teacher speaks. So the sources to be compared can be placed at such distances that the spot will seem equally illuminated on either side. say. It will cast two shadows onto the cardboard. generally speaking. You'll have to close the window with a shield. e. You'll immediately see on it a reduced image of what can be Figure 49 . one from the lamp and the other from the candle. The density of the two shadows is. This will be your "screen". and dark if lit from the front. a pencil. also upright. Remember the law? Another way of comparing the luminous intensity of two sources relies on the use of an oil spot on a sheet of paper. made of a plywood or cardboard glued with dark paper with a small hole made in it. This will mean that the illumination due to the lamp just equals that due to the candle. But the lamp is farther away from the cardboard than the candle. different because both are lit. the lamp is three times farther away from the cardboard than the candle. Then it only remains to measure the respective distances and repeat the previous process. nine times the brightness of the candle.g. Just in front of the sheet fix up a stick. By bringing the candle nearer you can achieve a situation in which both shadows will have the same "blackness". If. Measuring how many times farther away will tell you how many times the lamp is brighter than the candle.74-75 For Young Physicists shown. Upside Down If your home has a room facing south. one by the bright lamp.e. you could easily make it into a physical device that has an old Latin name camera obscura. And in order that both sides of the spot might be compared it is a good idea to place the paper near a mirror. The spot will seem light if illuminated from behind. you should know how. the other by the dimmer candle. On a fine sunny day close the doors and windows to darken the room and place a large sheet of paper or a sheet opposite the hole. i. then its brightness is 3 x 3. You might drill a round hole. trees. You can make a simple model of this sort of camera. Houses. too. The back wall is a frosted glass on which the image is produced. Remove the wall opposite the hole and stretch over the gap an oiled piece of paper instead-a substitute for the frosted glass. you'd have got something different. The rays from the upper and lower parts of an object cross in the hole and travel on so that now the top rays appear below and the bottom rays above.. upside down of course. Bring the box into our dark room and place it so that its hole is just opposite the hole in the darkened window. or make a square. the small spots under trees turn into small crescents as well.. The old photographer's camera. Put a sheet of paper at right angles to the solar rays and you'll obtain round spots on it. but. You'll only need to cover your head and the camera with a dark cloth for the spurious light not to interfere. everything will appear on the screen in its natural colours. . If the rays were not straight but curved or broken. hexagonal. The photographer can only view it if he covers himself and the camera by a dark cloth to keep out any spurious light. again upside down of course. the shape of the hole has no effect whatsoever on the image. Find a closed elongated box and drill a hole through one wall. or other h o l e . upside down. What does this experiment prove? That light propagates in straight lines. the only difference being that at the hole an objective lens is fitted for the image to be brighter and clearer. On the back side you'll see a distinct image of the outside. animals. and elongated because the rays are obliquely incident on the ground. is nothing but a camera obscura.t h e image on the screen would be the same.76-77 For Young Physicists seen from the room through the hole. Your camera is convenient in that you no longer need a dark room and you can bring it out into the open and put it where it suits you. Significantly. and people. triangular. During solar eclipses when the dark sphere of the moon blots out the sun leaving only a bright crescent. Did you happen to observe oval light circles under a dense tree? These are nothing but images of the Sun painted by the rays that pass through various gaps between the leaves. The images are roundish because the sun is round. at the back of the eye. distinct images. That this is really true. This unusual situation is presented in Fig. your eye is just like the box that you were shown how to make above. Despite all these distinctions the eye is still a camera obscura. Just fancy. and what is of the more importance here. we'll in this case too see an inverted image. With this arrangement you'll see the pin as if it were behind the hole. Accordingly. 50. So. Move the pin to the right and your eyes will tell you it's moved to the left. Next to the pupil behind it is the crystalline lens having the form of a convexo-convex glass. The hole is covered with a transparent envelope on the outside and with a jelly-like and transparent substance underneath. on which the image is produced.For Young Physicists Overturned Pin We have just discussed the camera obscura and a way of manufacturing it but we omitted one interesting thing: every human being always has a pair of small cameras like that about him or her. We'll attempt to contrive it so that we get at the back of the eye not an inverted. This turning over is due to long habit. These are our eyes. only an improved one. is filled with a transparent substance. We are used to seeing with our eyes so that each visual image obtained is converted into its natural position. but direct image of an object. What we call the pupil of the eye is not a black circle on the eye but a hole leading into the inside of your organ of sight. an 8-m high lamp-post seen 20 metres away from the eye is only a tiny line. and the inner cavity of the eye between the crystalline lens and the back wall. In actual fact that is exactly what happens and the following experiment will demonstrate it in a fairly graphic manner. about 5 millimetres long. as the eye produces high-quality. But the most interesting thing here is that although all the images are upside down. The images at the back of the eye are minute. we perceive them as they are. upside down. you could test by an experiment. we'll invert this one as well. What will we see then? Since we are used to inverting every visual image. 51. Make a pinhole in a postcard and hold it against a window or a lamp about 10 centimetres away from your right eye. Figure 50 Figure 51 . Hold the pin between you and the postcard so that its head is opposite the hole. A cross section through the eye is given in Fig. not a direct one. Ice only collects solar rays. The shadow falls on the pupil and its image is not inverted as it's too close to the pupil." "What's a lens?" "We'll shape a piece of ice like this glass and it will be a lens: round and convex which means thick in the middle and thin at the edges. just like this glass. it's possible to light a cigarette with ice. the sun does.t h e image of the hole in the card. my brother told me to fetch a washing basin. but we could make a burning lens from ice. On it the dark silhouette of the pin is seen which is its shadow." . I liked watching my brother lighting a cigarette with a magnifying glass. Alex poured some clean water into it and put it outside. nobody can. Igniting with Ice When a boy. the right way up. But it seems to us that through the hole in the card we see the pin behind the card (as only the part of the pin that gets in the hole is seen) and inverted at that because our eyes are in the habit of turning images upside down." "And will it ignite things?" "Yes." "With ice?" "Ice doesn't ignite it. We need a curved bottom. On the back wall of the eye a light spot is p r o d u c e d . The hole in the card plays the role of a light source producing the shadow of the pin. the bottom is flat. of course. He would put the glass in the sunlight and train the spot of light on the cigarette end. too." "But it's cold!" "What of it? Let's try. We'll then have an ice lens with one side flat and the other convex. After a while it would begin to give off a bluish smoke and smolder." When I brought a suitable basin. When I did he rejected it: "Nothing doing." "So you want to make a magnifying glass out of ice?" "I can't make glass of ice. You see. "Let it freeze down to the bottom.74-75 For Young Physicists The explanation is that the pin at the back of your eye is here depicted not upside down but directly. "You know. the temperature outdoors being below freezing point." To begin with. One winter day Alex said. the needle will obediently approach the appropriate edge of the saucer. He took aim painstakingly but eventually succeeded in training the lightspot directly on the end of the cigarette. namely north-south. "Good weather. therefore it'll even approach a nonmagnetized iron object." Magnetic Needle You can already make a needle float on the surface of water. Indeed. if only a small horse-shoe one. Here you'll have to use your skill in a new and more impressive experiment. "Let's take it out of the basin. If you bring it near the saucer with a needle floating in it.74-75 For Young Physicists Figure 52 Figure 53 "So big?" "The bigger. Bring one end (pole) of the . just like the needle of a compass. The water had frozen right through to the bottom. Leave it alone without attracting it by a piece of iron or the magnet and it'll orient itself in the water in one direction. it'll catch more sunlight. if only you had firewood. Alex put the icy basin into another one containing hot water and the ice at the walls melted quickly." First thing in the morning I ran to inspect our basin. when the spot got onto the end of the cigarette and had stayed there for about a minute. When the spot rested on my hand. We got the ice basin out into the yard and placed the lens on a board. ins't it!" Alex screwed up his eyes in the sunlight. This turns the needle itself into a magnet. taking hold of the lens with both hands turned it towards the sun but so that he wasn't in the way of the rays himself. "Ideal for igniting. the better. we've lit it with ice. I felt it was hot and already I had no doubt that the ice would light the cigarette. The effect will be more noticeable. Find a magnet." This turned out to be no problem. My brother took a puff at the cigarette. Just hold the cigarette. In this way you could make a fire without matches even at the pole. Turn the saucer and the needle will still point to the north with one end and to the south with the other. the tobacco smoldered and discharged some bluish smoke." I did so and my brother. You can make many curious observations with the magnetic needle. if before placing the needle on the water you pass the magnet several times along it (but only use one end of the magnet in one direction only)." Alex said tapping the ice with finger. "Here you are. "What a good lens we'll have. as starring in it are rope dancers cut out of paper (of course). make a toy paper boat and hide your needle in its folds. At the bottom of it you'll stretch a wire and fix above the stage a horse-shoe magnet. First of all. their stance being chosen to suit the purpose. They'll swing and jump all the while keeping their balance. 6 — 975 . but will stay upright pulled by the magnet. The only condition is that their height be equal to the length of a needle glued on from behind along the length of the Figure 55 figure. as shown. This is a case of an interaction between two magnets. The law of this interaction states that unlike ends (the north pole of one magnet and the south pole of another) are attracted and like ones (both north or south) are repelled. They are cut out of paper. Magnetic Theatre Or rather circus. Having investigated the behaviour of the magnetized needle. If a figure like this is installed onto the "rope". you have to make the circus building out of cardboard. Of course. It may turn away from the magnet in order that the opposite end might approach. By slightly jerking the wire you'll animate your rope dancers. Now to the artists. You might astonish your uninitiated friends by controlling the motion of the boat without so much as touching it: it would obey every motion of your hand. you would be holding the magnet so that the spectators wouldn't suspect it.74-75 For Young Physicists Figure 54 magnet to an end of the needle and you'll find that it won't be attracted to the magnet at that end. You could use two or three drops of sealing-wax for the glue. it not only won't fall. Bring a rubbed comb close to some pieces of paper. chaff. etc. Now. if it's woollen. to our experiments. Your comb had been electrified by friction with the hair. You could stage the experiment in a more impressive way. But the experiment with silk is only a success in exceedingly dry air and only then if both the silk and the glass are well dried by heating. As the electrified comb approaches one of its ends the ruler will turn fairly quickly.74-75 For Young Physicists Electrified Comb Figure 56 Even if you're ignorant of electricity and not even acquainted with its ABC. Here is a further funny experiment on electrical attraction. is electrified if rubbed by silk. These experiments are especially successful in dry air. The best place for these electrical experiments is a warm room in a frosty winter. You can make it follow the comb obediently moving it in any direction and making it rotate. say) it also acquires electrical properties and to quite a larger degree. The comb can also be electrified by material other than hair. If you rub it against a dry woollen fabric (a piece of flannel. A rod of sealing-wax rubbed against a piece of flannel or the sleeve of your coat. If you did so in a warm room in full silence. you can still do a number of electrical experiments that would be fascinating and will. . These properties manifest themselves in a wide variety of ways. You'll be able to control the movements of your paper fleet using an electrified comb like a magic wand. You may have passed a conventional comb over dry ( completely dry) hair. Empty a chicken egg through a small hole. A glass rod or tube. An Obedient Egg Electrical behaviour is inherent not only in the comb but in other things as well. Place an egg in a dry egg-support and balance a rather long ruler on it. and in winter warm air is far drier than air at the same temperature during summer. you may have heard some slight crackling on the comb. in any case. be useful when you meet this amazing force of nature in future. behaves in the same way. too. Make tiny ships of light paper and launch them on water. a ball of elder core. notably by attracting light objects. and these small things will all stick to the comb. It would be of interest to test the way in which another. board or large plate and. using the electrified rod. in fact. Any action is. You've thus obtained an empty shell (the holes are sealed with wax). It shows up always and everywhere-any action is an interaction of two bodies affecting each other in opposite directions. then it itself is attracted to them. or rod. Nature doesn't know of an action that is one-sided and doesn't involve the interaction of another body. say-attracts the comb making it turn. If you bring an electrified glass rod to the electrified comb. thing affects it. doesn't exist. To repeat. An experiment will convince you that two electrified bodies can interact in different ways. like charges repel.g. Like charges 6 . in general. But if you bring an electrified sealing-wax rod or another comb to the comb. and so forth. an interaction. In consequence. We've seen that it is attracted by any electrified body. e. or any one-sided action. Interaction Mechanics teaches that one-sided attraction. make the empty egg roll obediently after it. To bear this out you have only to make the comb. Put it on a smooth table. easily movable. not aware that the egg is empty. this is a general law of nature. also electrified. too. if the electrified rod attracts various things. The physical law describing this fact of nature states: unlike charges attract. you will quickly find that any electrified thingyour hand. A paper ring or a light ball. would Figure 57 O be bewildered by experiment (invented by the English scientist Faraday). the two things will attract each other. Then. Electrical Repulsion Figure 58 Let's return to the experiment with the suspended electrified comb.82-83 For Young Physicists which is best done by blowing the contents out through another hole at the opposite end. by suspending it from a loop made of a piece of thread (the thread should preferably be a silk one). the interaction will be repulsive. follow an electrified rod. An outsider. Finally. too. it enters words like "telescope". folded in two. To the end of the rod two strips of foil or tissue-paper are attached using wax. O n touching a ball with a thing being tested you'll notice that the other ball deflects if the thing is charged. but will still work. Next the neck is plugged with the cork or cardboard circle. then make another such support. is suspended from a pin stuck into a cork. therefore. and on protruding parts at that. the two strips will become electrified. sealing the edges with sealing wax. . A foil strip. a rod is passed.74-75 For Young Physicists Figure 59 Figure 60 will be those on plastics and sealing-wax (the so-called amber or negative. "microscope". The repulsion of like-charged things lies at the basis of a simple device to detect electricity-the so-called electroscope. It won't be as convenient and sensitive. and so forth. If now you bring an electrified thing to the protruding end of the rod. being completely replaced by the names "negative" and "positive" charges. You can make this simple device on your own. separate due to electrostatic repulsion. The electroscope is ready to use. The word "scope" comes from Greek and means to "indicate". The separation of the strips is the indication that the thing that touched the electroscope rod is electrified. If you are no good at handiwork. That's all. part of it protruding from the top. Suspend two elder-core balls on a stick from pieces of string so that they hang in contact with each other. Through the middle of a cardboard circle or a cork that fits the neck of a jar or bottle. in the accompanying figure you can see yet another form of a primitive electroscope. you could make a simpler version of the device. One Characteristic of Electricity With the help of an easily manufactured makeshift device you can observe the interesting and very important feature of electricity .to accumulate on the surface of an object only. The ancient names "amber" and "glass" charges have now gone out to use. They charge up simultaneously and. charge) and unlike charges are those on amber and glass which is positive. Touching the pin with an electrified thing makes the strips separate. Cement a match vertically to a match box using a sealing-wax drop. 84-85 Figure 61 74-75 For Young Physicists Now cut out a paper strip about a match-length wide and three match-lengths long. you'll see that the electric charge is only present on the convex parts of the paper. Glue three or four narrow ribbons of thin paper-tissue to the either side of the strip (Fig. If you make the strip into an S-shape. . This can be judged by the ribbons sticking out on either side. O u r device is ready for experiments. What does this indicate? That the electric charge has only accumulated on the convex side. Touch the straight strip with an electrified sealing-wax rod and the paper and all the ribbons on it will charge up simultaneously. and charge it up. Now arrange the supports so that the strip curves into an arc. 61) and fix the assembly on the matches. those on the concave one will dangle as before. The strips will now stick out on the convex side only. Turn the ends of the paper strip into a tube so that you could fix it to the supports. with your eyes. "Experiments? New experiments! When? Right now? I'd like to now!" "Patience. Now I must be off. carelessly leaving the bag with the machine in on a small table in the hall.. my friend." my brother proclaimed tapping the tiles of the warm stove. "You'll find nothing. It's not enough just to look. and will only make a mess. "In the bag. The experiments will be this evening. You didn't use your brains. It was absolutely impossible to think about something different or divert my eyes from the b a g It's so strange that an electric machine can go inside a bag. This evening we are performing electrical experiments. putting his coat on. attracting all my feelings and thoughts. don't worry. The bag was pulling me. with my eyes?" "That's just it. What did you look with?" "With what? Why." . That is called looking with your mind. Books? Only books. The bag wasn't locked and I carefully peaped inside. books. Something wrapped in newspaper." "The machine that we'll need is already available." "But the machine is there?" "There. We'll need a machine for our experiments. I was delighted.. nothing more in the bag? I should have understood at once Alex was joking: how can you possibly hide an electric machine in a bag! Alex came back with empty hands and guessed at once the reason for my sorrowful looks. He went on to say. "Where is the machine?" I answered with a question. I did not imagine it to be that flat." "To get the machine?" "What machine?" "Electric." Alex had read my thoughts.A Sheet of Newspaper What is to "Look with Your Mind"? • Heavy Newspaper "Agreed. you have to understand what you see. If iron could feel.." My brother went out. "We seem to have visited the bag don't we?" he said. it's in my bag." "And the machine! You didn't look very far. And don't you dare delve in there while I'm away. A small box? No.. didn't you see?" "There are only books in there. it would feel near a magnet exactly what I was feeling left alone with my brother's bag. This implies that all the points of this dash line are equidistant from 2 and 3. Imagine that a straight line is drawn from J at a right angle to the lower highway 2-5. yes. See the difference?" "I see. but now you're using your head. of course.highways. But now look at the figure with the whole of your head. you'll think that you can always lift it even with a single finger. What will you say now about point 1 ? Is it closer to 2 or J ?" "Now I see that it's the same distance from 2 and 3." "It's got serrated and isn't good for anything. "How will my line separate the highways? Into what parts?" "In two. But where's the machine?" "What machine? Oh." "But how? I can't. the single ones . "The double lines here are railways." "All the better." "You see it with your eyes. But someone who can use his brains will perceive a physical device in this paper. "According to your eyes. "Do you think it's only paper and nothing more?" My brother went on to say. the one from 7 to 2 or from 1 to 3?" "From 1 to 3.86-87 Figure 62 A Sheet of Newspaper "How do you look with your mind?" "Do you want me to show to you the difference between looking with your eyes and looking with the whole of your head?" My brother produced a pencil and drew a figure (Fig. It's still there." "Exactly. yes. isn't it? And." "Physical device? To make experiments?" "Yes. In the bag. You didn't notice because you didn't look with your mind. But earlier it seemed that the right-hand railway was longer than the left. of course." "Like this." My brother took a bundle of books out of the bag. Hold the newspaper in your hands." "Earlier you only looked with your eyes. Take a look and say which of the railways is longer. the electric machine." . it doesn't matter if it gets broken. carefully unwrapped it from a large newspaper sheet and gave it to me. "Here's our electric machine. Give me that ruler." my brother drew a dash line in his drawing. It's light. But now you'll see that this very newspaper can at times be very heavy." I looked at the newspaper in bewilderment. 62) on a sheet of paper. "I'll strike it so hard that the ruler will break through the paper and hit the ceiling!" " G o ahead. I shifted the eyes from the fragment of the ruler to the newspaper." "But why didn't it let the ruler go? Look. and said. "Touch the protruding end. "Now take a stick and strike the protruding part of the ruler very hard. isn't it? Well. try to press it down after I've covered the other end with the newspaper." He spread the newspaper on the table over the ruler. But your stroke was so fast that air had no time to get under the paper." That is the kernel of the experiment. and so the newspaper should rise. "Is it an experiment? Electric?" "It's an experiment but not electric one. don't spare your strength. carefully smoothing tne folds. I just wanted to show you that a newspaper can actually be a device to do physical experiments with." The result was astonishing: there was a crack. the ruler broke. Therefore. The electric ones will follow. It's easy to press it down. Air presses down on the ruler with a powerful force: a good solid kilogramme on each centimetre of the newspaper. I can easily lift it from the table. "The newspaper appears to be heavier than you've been thinking?" Bewildered. When you strike the protruding end of the ruler. Thus the edges of the paper were still sticking to the table when its middle was already being forced upwards. you had to lift not only the paper but also . Figure 63 Alex asked archly. still covering the other piece of the ruler. its other end pushes up against the newspaper from below. Strike with all you strength!" I swung the stick back. If it's done slowly some air gets under the rising paper and compensates for the pressure from above.86-87 A Sheet of Newspaper Alex put the ruler on a table so that a part of it overhung the edge. but the newspaper remained on the table. and accordingly. moved his spread fingers of the other hand to it. "Now watch my hand. And t h e n . Want to try for yourself?" ." I guessed. the paper stuck to the smooth tiles as if glued. He then began to rub the newspaper with the brush like a decorator smoothing wall-paper on the wall for the paper stick perfectly." "So. The friction electrified it. you had to lift with the ruler as many kilogrammes as there were square centimetres in the newspaper." In the dark the black figure of my brother and the greyish spot of the stove looked blurred. But the area you lifted was notably larger. In a nutshell. however. He took the paper down from the stove and. "Look!" Alex said and took both hands away from the paper. you had to lift a substantial weight.86-87 A Sheet of Newspaper the paper with the air pressing down on it. before your eyes. it's a real electric experiment?" "Yes. The ruler couldn't bare this load and broke. by rubbing it with the brush." Sparks from Fingers• Obedient Electricity in Mountains Sticks My brother took a clothes-brush in one hand and held the newspaper against the warm stove with the other. then the air pressure would be 16 kilogrammes. bluish-white sparks! "The sparks were electricity. I did it right now. perhaps something near 50 kilogrammes. didn't happen: strange as it was. holding it with one hand. rather than saw what he did. I had expected that the paper would slide down onto the floor.." "Why didn't you tell me that the newspaper in the bag was electrified?" "It wasn't. "How does it keep on? It's not smeared with glue. If it were an area of only 16 square centimetres (a square with a side of 4 centimetres). but we're just beginning. This. Turn off the lights please. It's now electrified and attracted to the stove." "The paper is held by electricity.. I asked.I could hardly believe my eyes-sparks flew out from his fingers. Now do you believe that a newspaper can be used for physical experiments? After dark. we'll make the experiments. brushed it and again produced an avalanche of long sparks from his fingers. Now. Elm's fires. Simultaneously with the sparks I felt a slight prick but the pain was trifling. Indeed. there's no newspaper there. Now I am going to show you a flow of electricity.." "Where do they come from?" "You mean who holds an electrified newspaper above the masts? True. After I had the sparks to my heart's content my brother proclaimed: "That'll do.. I managed to notice that he didn't touch the newspaper at all. N o t for the world! My brother again applied the paper to the stove." And it was true. Give me your hand. Pass me the scissors. only far larger ones." "It's possible without the brush too if only your hands are dry. the lower part being still "glued". In their light I saw that my brother had only partially detached the newspaper from the stove. Alex applied the newspaper to the stove and began to rub. the points of the scissors were crowned by glowing bundles of short bluish and reddish threads although the scissors were still far away from the paper. just try. "What are you doing? Have you forgotten the brush?" "It's all the same. "Spread your fingers!.86-87 A Sheet of Newspaper Figure 64 Figure 65 I promptly hid my hands behind the back. "Don't be scared. are you ready?" "Nothing doing! You've rubbed it with bare hands without using the brush. this time also sparks rained from my fingers. at the mastheads and yardarms. but held his fingers about 10 centimetres away from it. which was halfseparated from the stove." he took hold of my hand and led me to the stove. They called them St. I expected to see sparks but saw something new. it doesn't hurt. "Again!" I asked. Well! Does it hurt?" In a twinkling of an eye a bundle of bluish sparks shot out from my fingers. You just have to rub. just like the one Columbus and Magellan saw at the tops of the masts of their ships.. this time only with his palms. "Sailors often see the same sort of fire brushes. but a low . This was accompanied by faint prolonged hissing." In the dark Alex brought the points of the spread scissors near to the newspaper. nothing to be scared of. like the one produced by our scissors. Of course." "But I think it is burning because flames are coming out straight from the head. After all. "Any progress?" "None.." "Turn on the light and inspect the match.o n the contrary they view them as a good omen. to business. It's a substitute for the newspaper." "Now." "Does this fire burn strongly?" "Not at all. however. it must touch nothing. And you see: the head is surrounded by the electric glow.. It was thus indeed surrounded by a cold light. A short one wouldn't. Look: instead of the scissors I use a match. but it doesn't go off. that this sort of electric glow on pointed structures only occurs at sea. "A pencil. "I didn't know that a stick could be supported in this way. however.t h a t is." "It works for exactly that reason." Alex shifted a chair to the middle of the room and put a stick across its back. no means. "Leave the light on. on all the protruding parts. In the process. Sailors and soldiers are not afraid of these electric l i g h t s . especially in the mountains. and not fire. insight!" I put my face close to the stick and began sucking air into my mouth to attract the stick to me.90-91 86-87 A Sheet of Newspaper Figure 66 electrified cloud. on their hair. but a glow. just a cold glow. they often hear a buzz. After several tries he managed to balance the stick at one point. Julius Caesar wrote that on a night in a cloudy weather the spear heads of his legionnaires glowed this way. it's also observed on land. So cold and harmless that it cannot even ignite a match. for example." I said. "If we loop a rope onto its end. We'll carry out the next experiment in the light. So. this isn't a fire." I agreed. It's impossible!" . caps. "it's so long." I began. It didn't stir. You shouldn't think. e a r s . without any reasonable grounds. A pencil. Can you make the stick turn towards you without touching it?" I thought about it. In the mountains electric glows even occur on people at times." I made sure that the match not only hadn't charred but it hadn't even blacken. Can you?" "Aha. " N o ropes. on the contrary... a newspaper can be dried with a kitchen stove when it's not too hot for the paper not to ignite on it. which is more than 3 kilometres high. And here's what they experienced there." "It's a pity that these experiments cannot be performed in the s u m m e r . Dryness is crucial for these experiments. Thinking some pins had got into my canvas cape. In summer. attracts the stick so strongly that it follows and will follow the paper until all the electricity has flowed from the newspaper into the air. You may have noticed that newspapers absorb moisture from the air and therefore are always somewhat damp.t h e stove will be cold. you see. but not as with a tile stove. You shouldn't think. The paper electrifies. By moving the newspaper Alex made the stick follow it rotating at the back of the chair. let's call it a day. first in one direction. it's brought onto a dry table and rubbed hard with a brush. thumbed through it and gave me the following passage to read: "The climbers leaned their alpenstocks against a cliff and were preparing for their dinner when Saussure felt a pain in his shoulders and back as if a needle were being driven slowly into his body. "The electrified newspaper. Well. down from the stove." "Also electric?" "Yes. that in summer our experiments are impossible. and began slowly to move it sidewards towards the stick. At about half a metre away the stick "felt" the attraction of the electrified newspaper and obediently turned in its direction. They can be done but not so well as in winter when the air in a heated-up room drier than in summer . however. and with the same electric machine. that's why it has to be dried. Tomorrow we'll do some new experiments. the .that's the reason.' recounted Saussure." "The stove is only necessary to dry up the paper since these experiments are only a success with an absolutely dry newspaper. our newspaper." He took the newspaper.86-87 A Sheet of Newspaper Figure 67 "Impossible? Let's see. Alex took down the book The Atmosphere by Flammarion from the bookcase. 'I threw it off but there was no relief. In 1867 he with several companions climbed the Sarley Mountain. where that had been sticking to the tiles. then in the other. Meanwhile I'll give you an interesting account of Elm's fires by the famous French naturalist Saussure. After the paper has been dried adequately. "On June 10. It was a fine morning but the travellers got into a strong hail storm in the pass. The pain continued and came to feel like a burn.'" In the same book I read about other cases of Elm's fires. Watson and several tourists climbed up the Jungfrau pass in Switzerland. In short. The noise continued for five minutes or so. It was as if a wasp was walking all over my skin stinging it everywhere. As we were climbing down. A terrible clap of thunder came and soon Watson heard a hissing sound coming from his stick that resembled the sound of a kettle about to boil. In the broad daylight I didn't see any glow on the alpenstocks. hair. our alpenstocks were producing ever lower noise and finally. It came from the alpenstocks we had leaned against the cliff and resembled the rumbling of heated water about to boil. or horizontally. ears. "The liberation of electricity by protruding rocks is often observed when the sky is covered by low clouds gliding just over summits. electricity was being liberated from sticks. No sound came from the soil. and didn't stop making the sound even when stuck with one end into the . 'In several minutes I felt that the hair on my head and beard were rising as if a dry razor was being passed over a stiff beard. The people stopped and found that their sticks and axes produced the same sound. My young companion cried out that the hair of his moustache was rising and the tops of his ears were giving off strong currents. I hastily threw off another coat but I could find nothing that could hurt so badly.86-87 A Sheet of Newspaper pain became more accute and embraced the whole of my back from shoulder to shoulder. 'I then understood that the painful sensation was caused by an electrical flux released by the mountain. They produced the same sharp noise whether they were held vertically with the tip pointed up and down. Having raised my hands. clothing. 'We left the summit hastily and descended about a hundred metres. the sound became so soft that we could only hear it by bringing them close to our ears. It seemed to me that my woollen sweater had caught fire and I was about to undress when my attention was attracted by a noise. I felt currents emanating from my fingers. a sort of hum. in fact everything that was protruding. 1863. When he got to about the sixth strip. But he didn't allow them to rest long: by alternately moving the newspaper to and from them he made the buffoons stand up and lie down again. Alex brushed along the strips several times . holding it horizontally with both hands. "This is for the buffoons not to be scattered and blown away by the newspaper. Then he asked me to get him paper denser than newspaper. out of which he cut out some funny figures. "The performance starts!" He "unglued" the newspaper from the stove and. Holding the upper part with one hand. First of all he "glued" the newspaper to the stove. as I had expected. but stayed put. One of the guides took his hat off and cried that his head was burning. Where are the scissors?" I passed them to him and. He had thus produced a sort of paper beard that didn't slide down from the stove. Alex commanded. Watson's hair straightened out completely. small dolls in various stances. "Stand up!" And just imagine: the figures obeyed.A Sheet of Newspaper ground. "You see." Dance of Paper Buffoons • Snakes Hair on End • Figure 68 Figure 69 Alex kept his word. writing paper for example. he cut all the way to the edge. This is electric attraction. "These paper buffoons will now dance. Fetch me a few pins. brought it down to the tray with the figures." My brother took the pins out of some of the figures. they would have jumped up and stuck to the newspaper. Alex began to cut a long. And now we'll experiment with electric repulsion. too. third and other strip. They stood up and stayed that way until he removed the newspaper when they lay down again." Alex proclaimed arranging the figures on a tray. they've stuck to the newspaper and won't separate from it." Soon each buffoon's foot was pinned up. The stirring of fingers in the air produced electric hiss from their tips. thin strip from its lower edge almost up to the upper one. His hair stood on end as if electrified and everybody had tickling feelings on the face and other parts of the body. Similarly. "If I hadn't burdened them with pins. he made a second. having "glued" the newspaper to the stove. Next day after dark he resumed the experiments. That is. we repeated yesterday's experiments and then my brother discontinued the "session". "No. "Is it another experiment?" "The same experiment we've just done. "They repel one another because they are charged up identically. although the mirror clearly showed to me that my hair under the newspaper stood on end. My brother explained. as he called it. ." "Does it hurt?" "Not a bit. how scared. However they are attracted to the things that are not charged. Look in the mirror and I'll show you your own hair standing on end in the same fashion. The newspaper electrified my hair and it is now attracted to the newspaper while each piece of hair repels the others like the strips of our paper beard. not so much as Figure 71 tickling. Look. Poke your hand into the bell from below and the strips will be attracted to it. only another form of it." "But I'm scared." Really. I felt not the slightest pain." Alex raised the newspaper above his head and I saw his long hair literally stand on end. they are only paper. In addition. "Aren't you frightened by these snakes?" asked Alex. I wanted to poke my hand there but couldn't because the paper strips wound themselves round my hand like snakes. promising to do some new experiments tomorrow. Instead of freely dangling the strips spread out into a bell shape noticeably repelling one another." I sat down and put my hand into the space between the strips.94-95 86-87 A Sheet of Newspaper Figure 70 and then took the "beard" down from the stove holding it at the top. t h a t is. "What is it going to be?" I inquired. rather like the crack and spark in our experiment.." "You will when we repeat it in the dark." "But I won't touch that tray any more. "How did you like it? You were struck by a lightning. We always hear thunder later.. but I didn't see any lightning. and promptly jerked it back: something had cracked and pricked my finger painfully. and it travels so fast as to . "Silence now. lightning is light. Keep your eyes open!" a voice said in the dark. Is it cold?" Suspecting nothing. "That's not necessary." "True. Next he "unglued" it from the stove tiles and swiftly put on the tray. Alex laughed. "Shouldn't the glasses be placed on the tray and not vice versa?" "Just wait. say. Crack! and a bright bluish-white spark about 20 centimetres long darted between the edge of the tray and the key. with a key or a tea-spoon. warmed them at the stove.. It's going to be an experiment with miniature lightning.." "I felt a strong prick." "Why then is the thunder later?" "You see. I light-heartedly stretched out my hand." He turned off the light. put them on the table and covered with a tray that he had also preheated. "See the lightning? Hear the thunder?" "But they were at the same time. "Feel the tray. but the sparks will be as long as they were earlier. He took three glasses. he simply rubbed the newspaper on the stove." I proclaimed decisively. take your time. they occur simultaneously. Heard the crack? That was miniature thunder. The first sparks I'll extract myself while your eyes adapt to the dark. A real thunder always comes after you see the lightning. You'll feel nothing. He then folded the newspaper in two and resumed the rubbing." Alex used the "electric machine" a g a i n .86-87 A Sheet of Newspaper Miniature Lightning 0 Experiment Herculean Breath with a Water Stream • Figure 72 On the next night my brother Alex made some unusual preparations. Still. we can produce sparks. "Now. or forward?" I replied at random. Meanwhile it only remains for you to look with your eyes not head. Don't touch the tap while I fetch the newspaper. he drew it forward so much that the water poured over the basin edge. but sound travels in air not so fast and markedly lags behind the light. "Without the newspaper. will there be any spark?" "Just try. By the way. left. thus coming to us later. this experiment can also be easily performed without a stove or oven. We'll make it in the kitchen at the water tap.96-97 86-87 A Sheet of Newspaper Figure 73 cover terrestrial distances in almost no time. Thunder is an explosion. without touching the stream. long and bright. He did so dozens of times (without rubbing the newspaper again on the stove). which was getting ever weaker. . instead of the charged newspaper you take a conventional plastic comb like this one. removed the newspaper a n d . I'll make it fall somewhere else. Let the newspaper stay on the stove. That's why we see a lightning flash before we hear the accompanying thunder." my brother produced a comb and passed it through his thick hair." Alex passed me the key. "To the left. Having transferred the newspaper on the other side." I had hardly put the key near the tray edge when I saw a spark." We make a thin stream of water from the tap so that it hits the basin bottom loudly. though it was weaker this time. he made the stream deflect to the right. sound. e." "All right. with a water stream." Alex was back with the newspaper. right.suggested extract a "lightning" from the tray. Which way do you want it to be deflected. i. Finally. "The sparks would continue for a longer time if I held the newspaper silk strings or ribbons rather than with my bare hands.m y eyes had now adapted . If. My brother again put the newspaper on the tray and again I extracted a spark. He brought the newspaper close to the stream from the left and I clearly saw it bend to the left. trying to hold it with his arms outstretched so as not to lose too much electricity. "You see how strongly the attractive force of electricity manifests itself. and each time I made a spark. When you study physics you'll understand what occurred. Now one more experiment. " "Perhaps you want to blow those books away?" I asked laughing. nearly without effort. the last one. ." When the comb was brought to the water stream. "Can you inflate this bag with your mouth?" "Of course. "Exactly. it's just like yours or anybody else's. "While it dries. You need to have neither an elephant's lungs nor the muscles of an athlet-everything comes about on its own accord. Look. This time he loaded the bag with all three tomes. I'll inflate the bag. "Just watch. I managed to overturn the books as easily as Alex did. My brother asked. Alex prepared to repeat the trick." We returned to the sitting room and Alex began to cut and glue a long bag out of a newspaper. rather like the experiment with the ruler. get several books. it made it deflect noticeably." "But your hair is not electrical. He b l e w . large and heavy. It gets far less than the 'electric machine' that can be made from a simple newspaper. I'd like to make one more experiment with the newspaper." "No.a Herculian breath!-and the three tomes overturned." "A simple business. Just imagine: as the bag swelled the lower book sloped up and overturned the top one." On the bookshelf I found three massive volumes of some medical atlas and placed them on the table. But the two books weighed about five kilograms! Without allowing me to recover from my surprise." Alex started to blow into the bag. This time it's not an electric experiment. "The comb is unsuitable for other our experiments since it accumulates too little electricity.A Sheet of Newspaper Figure 74 Figure 75 "I have charged it up this way. but again one with air pressure." Alex silently put the bag at the edge of the table. isn't it? But what if I put a couple of these volumes on the bag?" "Oh. When I dared to repeat it for myself. then the bag won't inflate no matter how hard you try. covered it with one of the volumes and stood another one upright on it. But if you rub plastic on your hair. it gets charged in the same way the newspaper does by the brush. The amazing thing is that this experiment had nothing miraculous in it. a hundred grammes per square centimetre.e.000 grammes on each square centimetre. If you express the area under the books in square centimetres. Clearly this force is sufficient to overturn the books.86-87 A Sheet of Newspaper My brother later explained the reason to me. we forced some air into it that is more compressed than the air around us. you can readily work out that even if the excess pressure in the bag is only a tenth of that outside of it. i. Thus ended our physics tests with the newspaper. When we inflated the paper bag. otherwise the bag wouldn't expand. . The air outside presses down with about 1. then the total force from the air pressure inside the part of the bag under the books may be as high as 10 kilogrammes. What load will he be able to lift using this rig? Such a pulley could help him lift no more than what . since it's impossible to weigh anything accurately with inaccurate weights. Weight on Pulley Suppose a man is able to lift a mass of 100 kilogrammes from the floor. It should be clear why. Then on the other pan put as many weights as will be required to make the beam balance. This excellent way of weighing accurately using inaccurate scales was discovered by the great Russian chemist Dmitri Mendeleyev. Which way will the platform move. suppose you have beam scales with pans. Why? Because as he is squatting the muscles pulling the man's body down also pull the legs up. In order to balance the beam again you will need to remove some of the weights and the weights removed will show the correct weight of your object. For example. then you can still weigh quite accurately with inaccurate scales. Place a weight that is heavier than your object on one pan. this pan will sink. Next put your object onto the pan with the weights and. Wanting to lift more he passed a rope tied tc the load through a pulley fixed in the ceiling (Fig. of course.t h e weights. Hence your object and the total of the weights you took off weigh the same.Seventy-Five More Questions and Experiments on Physics How to Weigh Accurately An Inaccurate Balance with Which is the more important possession. thus reducing the force with which the body presses on the platform with the result that it goes up. up or down? The platform will move upwards. but in f a c t . On the Platform of a Weighing Machine Figure 76 A man stands on the platform of a weighing machine and suddenly he squats down. a precise pair of weighing scales or a precise set of weights? Many people believe that the scales are more important. 76). If the set of weights is true. your object now pulls down its pan with the same force with which the weights you took off did before. In the first case the 10 kilogrammes are distributed over an area * of 3. the second 120 kilogrammes. the first one weighing 60 kilogrammes. the pressure will be higher in the barrel where the load per square centimetre is larger. though in general the second harrow is heavier. he could not lift a mass exceeding his own. he would be unable to handle a 100-kilogramme load with the pulley. The following example will clarify the difference between weight and pressure and at the same time give you an idea of how to work out the pressure a body exerts on its support. one with 20 teeth. perhaps even less. Consequently. With the first harrow the total load of 60 kilogrammes is evenly distributed among the 20 teeth. hence 3 kilogrammes per tooth. An object may have a marked weight but still exert a negligible pressure on its support.e. In which is the pressure larger? Clearly. the other with 60.14 times the circle's radius (half the diameter) times the circle's radius. its teeth penetrate less deeply than the first harrow's. 120/60.100-101 Seventy-Five More Questions and Experiments on Physics he could do with his own hands.14 x 12 x 12 = 452 square centimetres. If his mass is less than 100 kilogrammes. Two Harrows People often confuse weight and pressure. By contrast something else may have a small weight but exert a large pressure on its support. Which one penetrates more deeply into the soil? It's easy to figure out that the greater the force acting on a harrow's teeth. The pressure per tooth with the first harrow is larger than with the second. One disk is 24 centimetres across and the stones on it weigh 10 kilogrammes while the other is 32 centimetres across and its stones weigh 16 kilogrammes. With the second harrow. However. Two barrels of pickled cabbage are each covered with a wooden disk held down by stones. i. the deeper they penetrate the soil. 2 kilogrammes per tooth. * The area of a circle is about 3. Let two harrows of the same type work in field. Pickled Cabbage Consider another simple calculation of the pressure. If he pulled the rope passed through a fixed pulley. . they are by no means the same. Seventy-Five More Questions and Experiments on Physics Hence the pressure is 10. The slight force of hand creates a pressure of hundreds of kilogrammes per square centimetre on the thin edge of the razor that can cut through hair. For instance.000/452. Why then do the horse's legs are mired in loose ground. about 22 grammes per square centimetre. then the material under the chisel blade is subjected to a pressure of 1 kilogramme per square centimetre. and the tractor doesn't? To grasp this. let the awl's surface area at the point be 1 square millimetre and the chisel's be 1 square centimetre. You'll now understand that when you are pressing with your finger on a needle when you are sewing you produce a very great pressure. you'll have to remember once again the difference between weight and pressure. The pickled cabbage is thus more compressed in the first barrel. This is also the principle behind the cutting action of the razor. This is inconceivable to many people since the tractor is far heavier than the horse and very much heavier than man. i. The enormous weight of a crawler tractor is distributed over the larger . Awl and Chisel Why does an awl penetrates deeper than a chisel does if both are acted upon by an equal force? The point is that when thrusting the awl all the force is concentrated at an extremely small area at its point.e.01 square centimetre). Now it is clear why the awl penetrates deeper than the chisel. 000/804. In the second barrel the pressure will be 16. If the force on each tool is one kilogramme. The pressure of the awl is one hundred times larger than of the chisel. less than 20 grammes per square centimetre. Horse and Tractor A heavy crawler tractor is well supported by loose ground into which the legs of horses and people are mired. i. not smaller than the steam pressure in a boiler. and under the awl 1/0. An object does not penetrate deeper because it is heavier but because it exerts a higher pressure (or force per square centimetre) on its support. With the chisel the force is distributed over a much larger surface.01 = 100 or 100 kilogrammes per square centimetre (since 1 square millimetre = 0.e. What load can ice support without breaking? The answer is dependent on the thickness of the ice. If now you pull a ruler tied to the bottom of the string. In other words. For this purpose 10-12 centimetres would be sufficient. the upper part of the string will break.this decreases the pressure on the ice. but the supporting area increases. but if you jerk it. doesn't change. Some people also use a wide board and lie on it as they move about thin ice. Figure 77 Where Will the String Break? You'll need an arrangement shown in Fig. according as you pull. Crawling Over Ice If ice on a river or lake is insecure. than walk over it. tie a string to the stick and tie a heavy book in the middle.102-101 Seventy-Five More Questions and Experiments on Physics surface area of its tracks. his weight. which increase the supporting area of horses' hooves with the result that they are mired much less. where will the string break: above or below the book? The string can break both above and below. thus giving more than 1. the horse's weight is distributed over the small area under its hooves. each square centimetre of the tractor's support carries a load as low as several grammes. each square centimetre of it thus carries less load. It is of interest to know the thickness of ice required for a skating rink on a river or lake. you can break it either way. Some of you may have seen that to ride over marshes and bogs horses are shod with wide "shoes". 77. Put a stick on top of the open doors. It's now clear why it's safer to move over thin ice by crawling . the lower part breaks. Why does this happen? Careful pulling breaks the upper part of the string because the string is being pulled down both by the force of your hand and by the . the man's pressure on his support is reduced. If you pull carefully. Therefore. It's up to you. experienced people crawl rather. Ice 4 cm thick can support a walking man.000 grammes per square centimetre or ten times more than the tractor. Why? When a man lies down. N o wonder then that a horse's feet sink more deeply into mud than does a heavy crawler tractor. On the other hand. of course. Partly cut or tear the strip in two places (Fig. 78) and ask your friend what will happen to it if it's pulled by the ends in the opposite directions. which breaks even if it's thicker than the upper part. You can repeat the experiment many times taking strips of various length and making little tears of various depth and you'll never get more than two pieces." If you receive this answer. You might perhaps be very pleased to know that in making this trifling experiment you've visited a serious branch of science of importance for engineering that is called "strength of materials". Much to his surprise he will see that he was mistaken. A Strong Match Box What will happen to an empty match box if you strike it with all your might? I'm sure that nine out of ten readers will say that the box won't survive such handling. And once begun the breaking would continue to the end because the strip would become ever weaker at this place. one will still be deeper. for the strip will only separate into two parts.Seventy-Five More Questions and Experiments on Physics weight of the book. ask your friend to test his hunch by an experiment. Generally the answer is: "Into three parts.the person . whilst the lower part of the string is only acted upon by the force of your hand. of course. "Into how many parts?" you ask then. He will answer that it'll break in the places where it's been torn. Torn Strip Figure 78 A strip of paper that is about 30 cm long and one centimetre wide can be material for a funny trick. The entire force is thus "consumed" by the lower part. however hard you strive to make them identical. The tenth . one is bound to be deeper than the other. The strip breaks where it's weaker which goes to prove the proverb: "The chain is only as strong as its weakest link". The weakest place of the strip will be first to begin to break. The reason is that of the two tears or cuts. Even if it's imperceptible to your eyes. Whereas during the short instant of the jerk the book doesn't acquire very much motion and therefore the upper part of the string doesn't stretch. you'll find that each one is intact. Clearly this is no problem. 80). but that won't work of course. There'll hardly be many who'll twig. 79. Grandfather's Clock Suppose a grandfather's clock that uses weights to wind it up is fast or slow. Bringing Something Closer by Blowing Place an empty match on a table and ask somebody to move it away by blowing.104-105 Figure 79 Seventy-Five More Questions and Experiments on Physics who has actually performed the experiment or heard about it from somebody-will maintain that the box will survive. is very simple. as shown in Fig. "failsafe".e. Some will try to move the box nearer by sucking in air. however. make the box approach without leaning forward to blow the box from behind. You . The box behaves like a spring and this saves it because it bends but doesn't break. Strike this assembly sharply with your fist. having collected them. Begin to blow and the air that reflects from the hand will strike the box and shift it towards you (Fig. The answer. Put the parts of an empty box one on top of the other. What should be done with the pendulum to correct it? The shorter a pendulum the quicker it swings. The experiment should be staged as follows. Figure 80 The experiment is. What will occur will surprise you: both parts will fly apart but. Then ask him or her to do the opposite. i. What is it? Ask somebody to put the hand vertically behind the box. You'll only have to make sure it's on a sufficiently smooth table (even unpolished) which is not of course covered with a table-cloth. so to speak. it's impossible to predict the final position of the rod. 81)-horizontal. How Will Rod Settle Down? Figure 81 Two balls of equal mass are fixed to the ends of a rod (Fig. Right in the middle of the rod a hole is drilled through which a spoke is passed. 81). Could you predict in what position the rod will come to rest? Those who think that the rod will invariably settle down in a horizontal position are mistaken. You shouldn't think that while you've been in the air the floor (together with the carriage) has shifted forward.Seventy-Five More Questions and Experiments on Physics can easily prove this by an experiment with a weight suspended from a piece of rope. so making the pendulum swing faster. Aboard a Ship Two people are playing ball on the deck of a steaming vessel (Fig. vertical. 82). Jumping in Railway Carriage Imagine you are travelling in a train at a speed of 36 kilometres an hour and you jump up. where will you land. One stands nearer the aft and the other . Any body supported or suspended at the centre of mass be in equilibrium at any position. or at an angle-since it's supported at the centre of mass. It can remain balanced in any position (see Fig. it'll rotate several times and settle down. Supposing that you manage to spend a whole second in the air (a brave assumption because you'll need to jump up more than a metre). If the rod is spun about the spoke. Therefore. All the time you were directly above the place from which you jumped up. where then-closer to the beginning or end of the train? You'll land at the same place. at the same place from where you started or somewhere else? If somewhere else. This suggests the solution of our problem: when the clock is slow you shorten the pendulum a little by lifting a ring on the pendulum rod. the carriage was tearing along but you also were travelling in the same direction and at the same speed carried by inertia. and when the clock is fast you lengthen the pendulum. To be sure. just as if they were on a stationary ship. the motion of the ship (uniform and rectilinear) gives neither player an advantage. Walking and Running What is the difference between running and walking? Before answering remember that running can be . Which way will the balloon move in the process. since the man pushes the cable (and the balloon) in the opposite direction as he is climbing. By inertia the ball has the ship's speed which is equally possessed by both partners and the ball. The situation is similar to what happens if someone walks forward over the bottom of a small rowing boat: the boat shifts backwards. Therefore. You should not suppose that the man standing nearer the bows recedes from the ball after it's been thrown or that the other man moves to meet it. In which direction will flags on its car fly? The balloon carried by an air flow is at rest with respect to the surrounding air. therefore the flags won't be blown by the wind. Flags A balloon is being carried away due north. Which one can throw the ball easier to his partner? If the ship is travelling with a steady speed and in a straight line neither has any advantage. A man gets out of the car and begins to climb up the cable.106-101 Figure 82 Seventy-Five More Questions and Experiments on Physics nearer the bows. but will dangle limply like they do in still weather. On a Balloon A balloon floats motionlessly in the air. upwards or downwards? The balloon will shift downwards. Now move your fingers together to meet each other half-way. When your fingers are spread apart. and you'll notice the same behaviour. the larger load is on the finger that is closer to the stick's centre of mass. Replace the stick by a ruler.Seventy-Five More Questions and Experiments on Physics slower than walking and that you can even run on the spot. the result will invariably be the same: the stick will be balanced each time. or a broom. in the final position the stick doesn't fall off but keeps its balance. Since only one finger is moving at each instant of time. 83. Once the moving finger is closer to the centre of mass than the other. a billiards cue. on the other hand. Make the experiment several times varying the initial position of your fingers. the fingers change their roles. When we walk our body is in contact with the ground all the time at some point in our feet. Strangely. The difference between running and walking is not the speed. the finger that is closer to the centre of mass doesn't slide under the stick and at all times the only finger that moves is the one farther away from this point. as shown in Fig. there are moments when the body is completely separated from the ground and does not touch it at any point. the change taking place several times until the fingers come together. A Self-Balancing Stick Put a smooth stick on the index fingers of both of your hands. When we run. namely the one that is . this suggests that your fingers have closed up under the centre of mass (a body is in equilibrium if the centre of mass is over an area confined by the support's boundaries). Figure 83 What is the secret? The following is clear: if the stick is balanced on your fingers brought together. Therefore. Friction increases as the load grows and the finger closer to the centre of mass is subject to larger friction than the other one. accordingly. if we take into account that when the broom was balanced on your fingers the gravity forces of both parts were applied to unequal arms of the lever. But if the point you are going to reach is floating alongside. Before we leave this experiment. to reach a point rowing upstream is more difficult than rowing downstream. It's more difficult. No doubt. to pass the chip is easier than to lag behind it. we'll repeat it with a broom (the top of Fig. On the pans of the scales. by contrast. to row upstream than downstream. in both cases the rower needs exactly the same effort whether he wishes to pass or lag behind the boat. 84) and ask ourselves what would happen if we cut the broom at where it's supported by the fingers and place the parts on different pans. the part with the brush will outweigh. Rowing in the River A rowing boat and wooden chip alongside it are floating in a river. . What is it easier for the rower: to get ahead of the chip by 10 metres or to lag behind it by 10 metres? Even those practising water sports often give the wrong answer. Actually. One should take into account that the boat carried by the current is at rest with respect to the water. The clue is not difficult to find. it's only natural that eventually both fingers end up under the centre of mass of the stick. which pan would sink? Figure 84 — It would seem that if both parts of the broom balance each other on your fingers these should also do so on the pans of the scales. Thus. they argue. The situation is the same as what it would be on the still water of a lake. just like our chip. the same forces are applied to the ends of an equal-arm lever.108-101 Seventy-Five More Questions and Experiments on Physics farther away from the centre of mass. the situation is quite different. n o matter with what velocity. But if we attentively observe the waves produced by a stone thrown into the river. A force imparts to a body with a small mass a larger velocity than to a body with a larger mass. Deflection of Candle Flame If you carry a candle about a room you will have noticed that initially the flame deflects backwards. Which way will it deflect if the candle is carried about in a closed casing? Which way will the flame in the casing deflect if it's uniformly rotated. What form will the waves have if the stone is thrown into the flowing water of a river? If you fail. What will happen to the circular waves? They'll undergo a translation without any distortion.t h e motion has only to be translational. Simple reasoning will lead to the conclusion that the waves should be circular both in still and in flowing water. Let's treat the motion of particles of the waves as a combination of two movements: radial (from the centre of oscillations) and translational (downstream). you'll be easily lost in the argument and come to the conclusion that in the flowing water the waves should assume the form of an ellipse or an oblong somewhat wider in the upstream direction. Therefore. we'll find no deviation from the circular shape.Seventy-Five More Questions and Experiments on Physics Circles on Water A stone thrown into still water produces concentric waves. i. There is nothing extraordinary in that. Now suppose that the water is m o v i n g . uniformly or n o t . to follow the right track. horizontally in an outstretched hand? If you think that in the casing there'll be no deflection. the flame will deflect.e. In that case. A body participating in several motions eventually comes to the same point it would come to. you are mistaken. Experiment with a burning match and you'll see that if it's protected by the hand as it's moved. from the very beginning. . We'll therefore assume that the stone is thrown into still water. This is because the flame is thinner than the surrounding air. will remain circular. but forwards-quite unexpectedly!-not backwards. if it performed all the component motions in succession. the waves will clearly be circular. however fast the stream is. The mercury tries to be farther away from the rotation axis than the water. the lighter-than-air flame "floats up" within the casing. it would appear that the bottle would not hit the ground so strongly if you throw it forwards. the flame deflects inwards. in the direction to the rotation axis. their resultant force cannot be zero. it is bound to sag. whose ropes are not so taut.e. Gravity that causes the sagging acts normally. to stretch a hammock so that its ropes are horizontal.110-101 Seventy-Five More Questions and Experiments on Physics the flame moving faster than the air in the casing deflects forwards. whereas the stretching force on the rope has no vertical component.e. This is not so: objects should be thrown backwards. And the hammock. The latter. i. the one in which bodies are displaced by the centrifugal effect). floats up in the mercury. Consequently. by the way. you can reduce it to a desired degree but cannot make it zero. i. as it were. And this resultant force is responsible for the sagging. The taut net of a bed sags under the weight of a man. No force. any nonvertically stretched rope or driving belt will sag. if we consider the "bottom" to be the direction away from the rotational axis (i. How to Drop a Bottle? In which direction with respect to a moving railway carriage should you throw a bottle so that the danger that it gets broken when hitting the ground is the least? As it is safer to jump forwards from a moving carriage. The same reason (the smaller density of the flame than that of the surrounding air) also accounts for the unexpected behaviour of the flame when we move the casing in a circle. In that . In our circular rotation.e. not outwards as might be expected. For the same reason it is impossible. A Sagging Rope With what force must one pull at a rope for the latter not to sag? However taut the rope is. This would be clear if we remember how mercury and water are arranged in a ball rotated in a centrifuge. Two such forces can never balance each other out. can stretch a rope strictly horizontally (except when the rope is upright). however strong. turns into a dangling bag when a man lies on it. The sagging is unavoidable. The cork is small enough to pass freely through the neck. In midsummer. the river surface becomes concave . Cork A piece of cork has got into a bottle with water.lower in the middle than near the banks. In this case logs will accumulate in the middle (the bottom of Fig. shaking or upending the bottle. The cork can only come to the opening when almost all of the water has come out. the velocities would add up and the collision would be stronger.Seventy-Five More Questions and Experiments on Physics case the velocity imparted to the bottle by throwing it will be subtracted from the one due to inertia with the result that the bottle will strike the ground with a smaller velocity. That's why it is the last to leave the bottle. Floods During a spring flood the surface of a river becomes convex . If loose logs float along such a swollen river. they will slide down to the banks leaving the mainstream free (the top of Fig. It's only when the bottle is completely empty that the cork leaves the bottle with the last bit of the water.higher in the middle than near the banks. the outpouring water will not for some reason bring the cork out. That it is safer for a man to jump forward is accounted for by quite a different reason: he is hurt less by jumping this way. when the water is low. but try as you can. Throwing the bottle forwards will cause the reverse. 85). 85). What's the reason? This is explained by the fact that in the middle water flows quicker than near the banks because the friction Figure 85 . Why? The water doesn't bring the cork out for the simple reason that cork is lighter than water and therefore is always on its surface. its size being sufficient to cover the hole of the tube. you will notice that the disk holds securely on its own without being pressed on with the finger or held with the string. on the bottom of a vessel. its height being equal to the depth of the disk in the water. When the tube has sunk to a certain depth. Liquids. if more water comes to the middle. The situation changes in midsummer when water subsides. is known even to those who have never studied physics. By the way. Carefully pour some water into the tube.112-101 Seventy-Five More Questions and Experiments on Physics of the water along the bank slows the current down. A glass tube will help you to make sure such a pressure does exist. it can be held by a piece of string passed through its centre or pressed on with a finger. Cut out a disk of a strong cardboard. You can even measure the amount of this upward pressure. But many people don't suspect that liquids press upwards as well. Press Upwards! That liquids exert a pressure downwards. water comes from the upper reaches faster along the middle than near the banks because the current's speed is faster in the middle. During a flood. This is a law about the pressure of liquids on a submerged body. Now. For the disk not to drop off when you are dipping it. on its walls. Understandably. The water pressure on the disk from below is thus balanced out by the pressure of the water column within the tube. Put it over the hole and dip both into some water. this also causes the weight "loss" in liquids and was formulated as the famous Archimedes principle. Figure 86 . being supported by the water that presses it up.. and sidewards. then the river should swell here. owing to the swifter current the water run-off in the middle is higher than near the banks with the result that the river becomes concave. Once the water level approaches the level outside the tube.. the disk will fall off. not the length. the pressure due to water columns of various shapes is the same if only their base areas and heights are the same. Some answered that the pail with the wood would be heavier because "the pail has the water and the wood. 87). On the other pan.g. there is less water in the second pail than in the first because the floating piece of wood displaces some water. Suppose I place on the scales . The immersed part of every floating body displaces exactly the same weight of water as the whole of the body weighs. That's why the scales will be in equilibrium. In consequence. but with a piece of wood floating in it (Fig. exactly the same sized pail is placed. 86) you can also test another law relating to liquids. Dip them into the water to the same depth (for which purpose you'll have to glue paper strips onto them at the same height) and you'll notice that the disk will always fall off at the same level of the water within the tube (Fig. on the contrary.Seventy-Five More Questions and Experiments on Physics If you have several glass tubes of various shapes but with the same opening (e." Others held that. 86). as shown in Fig. Which is Heavier? On one pan of scales is placed a pail that is filled to the brim with water. Notice that it's the height. An experiment with the various glass tubes is described below. the first pail would be heavier "since water is heavier than wood. True. also brimful. Which pail will be heavier? Figure 87 I asked various people this question and got conflicting answers. namely the pressure of a liquid on the bottom of a vessel is only dependent on the bottom area and the level and is independent of the vessel shape. that matters because a long inclined column exerts exactly the same pressure on the bottom as a short upright column of the same height (the base areas being equal)." Both views are a mistake for both pails have the same weight. Another problem. You'll need a wire screen about 15 centimetres across with a mesh size of about 1 millimetre. Immerse the network into melted wax and when it is taken out of the wax the wire will be covered with a thin layer of wax hardly noticeable for the naked eye. What will happen with the balance? According to the Archimedes principle the weight in the water becomes lighter than before. I drop a weight into the glass.114-101 Seventy-Five More Questions and Experiments on Physics a glass of water and put a weight near it.a pin will freely pass through its m e s h . which has risen above the initial level. When the system is balanced by the weights on the other pan. 88). Such a waxed screen may be placed on water and it will remain on the surface. in general. It is thus possible not only to carry water on a screen but to float on it too. It might be expected that the pan with the glass would rise but in actual fact the scales will remain in equilibrium. Tarring barrels and boats. these are all nothing but the making of "screens" like the one just described. The screen will still remain a screen . with the result that the pressure on the bottom of the vessel has increased so that the bottom is acted upon by an added force equal to the weight lost by the weight. The weight in the glass has displaced some water. and the rubberizing of fabrics.b u t now you will be able literally to carry water on it. You need only to pour the water carefully and see to it that the screen is not jerked. coating things we want to render water-tight with oily materials. This paradoxical experiment accounts for a number of the everyday phenomena we take for granted because we get used to them so. The screen will hold a fairly high level of water without any seepage through the mesh. Water on a Screen It turns out that water can be carried on a screen in real life and not only in fairy tales. A knowledge of physics will help to make this proverbially impossible thing possible. The idea behind each phenomenon is the Figure 88 . Why then doesn't the water seep? Because it doesn't wet wax and thus forms thin films between the meshes and it is the films' downward convexity that holds the water (Fig. painting with oil paints and. Explain. it may take a lifetime to investigate it." Indeed. and the study of the tension in these frail films gives an insight into the laws governing the interaction between particles. but we'll only describe the simplest of the experiments here. remove foam and bubbles from the surface and insert into it a long clay tube whose end on the outside and inside has already been smeared with soap. . A piece of soap is carefully dissolved in pure cold water until a fairly thick solution is obtained.Seventy-Five More Questions and Experiments on Physics same. For bubbles to have a long life it is recommended to add one third of the volume of glycerin. incessantly deriving lessons of physics from it. These can be performed using a solution of a conventional soap. "Blow a soap bubble and observe it. but for best results olive. Rain or thaw water is the best but if it's unavailable cooled boiled water will do. But is it worthwhile to occupy yourself with such a trifling business as blowing soap bubbles? Used as a figure of speech the notion of soap bubbles is not complimentary. The great English scientist Lord Kelvin wrote. those cohesion forces without which there would be nothing in the world but fine dust. Those interested are referred to this fascinating book. they are just amusements that will only acquaint you with the art of blowing soap bubbles.or almond-oil soaps are recommended. Only in the case of the screen it appears in a somewhat unusual disguise. Good results are also achieved with straws about 10 Toilet soaps are unsuitable. In his book Soap Bubbles the English physicist Charles Boys gave a detailed account of a number of experiments involving them. Using a spoon. the fabulous play of colours on the surface of thin soap films enables physicists to measure the wavelengths of light. Soap Bubbles Can you make soap bubbles? This is not as simple as it might seem. But the physicist has another view of them. The several experiments that follow do not pursue such serious objectives. I also once thought that it didn't take much dexterity until I found out practically that blowing large and beautiful bubbles is an art that requires much exercise. Then. First you need to drop some solution onto the head of the statue and then. By carefully drawing the straw back. A Bubble Around a Flower. after blowing the large bubble. and quietly. and so on. The following are a number of entertaining experiments with soap bubbles. blow into the narrow tube to form a soap bubble. otherwise the bubbles will not show their iridescent play. dip a finger into the soap solution and try to punch the bubble. add some more soap. otherwise some more soap will have to be added to the liquid until bubbles of the above-mentioned size are obtained. The bubbles are blown thus: dip the tube into the solution holding it upright so that a liquid film be formed at the end and carefully blow into it. If it doesn't burst you may proceed to the experiments. But this test is not sufficient. Once the bubble has reached a largish size. Pour some soap solution onto a plate or a tray so that the bottom is covered with a layer 2-3 mm thick. If from the very beginning you can produce a bubble 10 centimetres in diameter. slowly lifting the funnel. When a bubble is produced. 90) can be blown between two wire rings. slowly. Instead of a flower you can take a small statue and crown its head with a soap bubble. and liberate the bubble from under it. If possible. Bubbles Inside One Another. which is lighter than the surrounding air in the room. Since the bubble is filled with warm air from your lungs. Blow a large bubble using the funnel. then immerse a straw into the soap solution so that only the end you will put into your mouth is dry and poke it carefully through the wall of the first bubble to the centre. Experiments should be carried out carefully. tip the funnel over as shown in Fig. In order to do this lower . fourth. The flower will then be under a transparent hemispherical hood of soap film which will show all the colours of the rainbow. the solution is good. but if the bubble doesn't survive the test. Place a flower or small vase in the middle and cover it with a glass funnel. then a third. A Cylinder of Soap Film (Fig. a second bubble can be blown inside the first one. pierce it and blow a smaller one inside it. the illumination should be bright. the bubble just blown will rise into the air. 89.116-117 Seventy-Five More Questions and Experiments on Physics Figure 89 centimetres long that are split across the end. thus again enabling some more liquid to go in. An Improved Funnel Those who have poured water through a funnel into a bottle know that it is necessary to raise the funnel from time to time. 90). Furthermore. Understandably. if you raise the upper ring higher than the length of the ring's circumference. otherwise the liquid will not pour out of it. If. and conversely it will expand when brought from the cold room into the warm one. it should be noted that the common idea that soap bubbles are short-lived is wrong since with adequate handling a soap bubble can survive for weeks. the reason is that the air in the bubble expands and contracts. The English physicist Dewar (famous for his works on air liquefaction) kept soap bubbles in special bottles that were protected from dust. Under these conditions he managed to keep some bubbles for a month or so. Curiously enough. for example. by raising the funnel we let the compressed air out. It is interesting just to observe a bubble when it is taken from a warm room into a cold one. stops more liquid from coming in from the funnel. Then put a wetted second ring over the top of the bubble and by raising it the bubble will extend until it becomes cylindrical. It's the air inside the bottle that. Lawrence. Clearly.000 cubic centimetres and the bubble is brought into a room at + 1 5 ° C . its volume will increase by about 1. It would perhaps be quite practical to design a funnel so that it has longitudinal crests on its outer surface . the volume of a bubble at — 15 °C is 1. The film of a soap bubble is always in tension and exerts a pressure on the air inside it. and then it will disintegrate into two bubbles. when compressed by the incoming liquid and unable to escape. It will shrink appreciably. By directing the funnel at the flame of a candle you can make sure that the force of the thin film is not all that negligible since the flame will be deflected quite a bit (Fig. the cylinder will become narrower at one end and wider at the other.Seventy-Five More Questions and Experiments on Physics Figure 90 a conventional ball-shaped bubble onto the bottom ring. succeeded in keeping soap bubbles in a glass cup for years. drying and jerks.000x 30 x 1/273 or about 110 cubic centimetres. An American. t o the atmospheric pressure minus the weight of the water contained in the goblet. Which side will go down? That to which the upturned goblet with water is tied. of course. Remember that a litre jar of the warm summer air near the ground (not in the mountains) weighs 1. To do so. say. then it Figure 91 . On the other side of the balance tie an empty goblet. we'll only need to know how many cubic metres there are in it. 91.2 kilogrammes. i. How Much Does Water Weigh in a Glass Held Upside-Down? You'd say. exactly the same sort. the water in the upturned glass weighs in these circumstances as much as it would in a normally held glass. Perhaps these days there is no one who believes air is weightless as was widely held in ancient times.118-101 Seventy-Five More Questions and Experiments on Physics that would keep the funnel from sticking to the bottleneck.e. what then?" Actually. An upturned goblet tied at the bottom on one side of a balance is filled with water so that it doesn't pour out because the goblet's edges are immersed in water. Now we can easily work out the weight of the air in a room. The method is shown in Fig. This goblet is exposed to atmospheric pressure from above. But even today many wouldn't estimate its weight. A cubic metre holds 1. "Nothing. only in laboratories they use a filter designed after this fashion. If. Accordingly.000 litres and therefore weighs 1. "And if it does stay. Water won't stay in the glass. How Much Does the Air in a Room Weigh? Can you say. But I haven't ever seen such a funnel in everyday life. how much the air in a small room weighs? Several grammes or several kilogrammes? Would you be able to lift such a load with a finger or would it be difficult to hold it on your back.000 times as much. and from b e l o w ." I'd ask. however inaccurately. the area of the room is 15 square metres. 1.2 grammes. For the system to be in balance you'd have to fill the other goblet with water. it is possible to keep water in a glass held upside-down so that it doesn't pour out. the height is 3 metres. . the air inside the bottle becomes thinner and the cork is pushed inside by the pressure of the air outside. But it does not always reach its ceiling. you'll be amazed at the result.e.e. For the experiment we'll only need a common bottle and a cork that's somewhat smaller than the bottleneck. Hold the bottle horizontally. No problem. But try it. 9 kilogrammes. An Unruly Cork This experiment will vividly demonstrate that compressed air has a force and an appreciable one at that. will fly into your face! The harder you blow the faster it'll shoot out.. it would seem. . The Fate of a Balloon Balloons sometimes go astray. but only to its "ceiling". You could not move this load with a finger or carry it about on your back with ease. If you want the cork to slide inside you'll have to do quite the opposite-not to blow at the cork but to suck the air from the hole. i. Since it swells (due to the reduction in the external pressure) it may burst before it reaches the ceiling. The cork won't be driven inside the bottle but. blow hard at the cork. This increases the pressure inside the bottle and throws the cork out. These strange phenomena can be explained as follows. i.Seventy-Five More Questions and Experiments on Physics contains 15 x 3 = 45 cubic metres. The air thus weighs 45 kilogrammes plus 1/5 of 45. which makes 54 kilogrammes in all. But where? How high can they fly? A balloon that escapes is carried always not to the boundaries of the atmosphere. If then you suck the air out. to a height where the air is thin and the weight of the balloon equals that of the air displaced by it. insert the cork into the neck and ask somebody to blow the cork inside the bottle. The trick works out well only when the neck is absolutely dry as a wet cork sticks. When you blow into the bottleneck you drive some air through the gap betwen the cork and the wall of the neck. A steel rail. The flame won't so much as stir. Now by blowing into the funnel you'll easily extinguish the candle. If no space were allowed for the rails to expand.120-121 Seventy-Five More Questions and Experiments on Physics How to Blow Out a Candle? It's child's play. The reason is that all things expand on heating. you might think. these would push against Figure 92 . The question is: in what direction does the air inside the tyre move-against the direction of rotation or in the same direction? The air moves away from the place of compression in both directions . its rim rotating clockwise. But the air along the funnel axis is rarefied with the result that a return air flow sets in near it. Try and blow a candle out through a funnel and you'll see that this requires especial dexterity. You might be shocked by the result: the flame deflects not away from you but towards you. Perhaps you now think the funnel is too far away from the flame. Why Are There Gaps Between the Rails? Railway builders always leave gaps between the butts of adjacent rails on purpose. Tyre A car wheel with a tyre is rolling to the right. Place the funnel against the flame of a candle and blow at it through the thin end. This is explained by the fact that the air stream leaving the narrow part of the funnel does not propagate along its axis but spreads along the walls of the cone. against the stream of the air coming from the funnel. to blow out a candle. It is now clear why a flame located on the axis of the funnel leans towards the funnel. and so you bring it nearer and again begin to blow hard. too. Without the gaps the railway would soon fall into disrepair. heated by the sun. although the stream of air from the funnel would seem to be striking the flame directly. thus forming a sort of an air vortex.forwards and backwards. But occasionally an attempt is a failure. What is to be done then to kill the candle flame? It is necessary to locate the funnel so that the flame is not on the axis of the funnel but in the line of its cone part. and when the flame is on the periphery of the cone. it bends the other way and goes out. elongates in summer. What happens to the hole in the process? Does it become narrower or wider? It becomes wider. When the shoe is allowed to cool down. Thick-bottomed tumblers are not used for hot drinks because the walls of such tumblers would be heated by the hot liquid and expand more than the thick bottom. But the cap expands on heating in all directions. A heated iron shoe is slided onto the rim of a cart wheel. they are calculated very carefully considering the local climate. Why then don't we use tumblers for hot drinks? After all it would be better for glasses to be more stable in that case too.Seventy-Five More Questions and Experiments on Physics adjacent rails with an enormous force and bend sideways wrenching out the spikes and destroying the track. not decreases as is widely believed. thereby additionally increasing the gaps. The Hole in the Cap of a Tea-Kettle The cap of a metallic tea-kettle has a hole. The reason is obvious: such a tumbler is more stable. For that reason. An example of the use of the property of a body to shrink on cooling is the old procedure of shoeing cart wheels. Therefore. the more uniform will be the heating and the less the risk of cracking. the capacity of vessels increases on heating. Smoke Why does smoke go up in still weather? The smoke from a chimney ascends because it's . by the way. The thinner the glassware and the less difference there is between the thickness of the wall and the bottom. A Glass and Tumbler You may have noticed that tumblers for cold drinks are often made with a thick bottom. In general the volume of holes and cavities becomes larger on heating in exactly the same way as an equal piece of surrounding material does. In winter the rails shrink from cold. What for? To let some vapour out. The gaps are designed with due account of winter temperatures. it shrinks and squeezes tightly onto the rim. otherwise it will pop the cap off. just like any metal. How to Seal Window Frames for Winter An adequately sealed window frame keeps out cold. Well sealed or glued windows cut down your heating expenses. it leads away the heat obtained by the paper from the flames. Some people wrongly think that when a frame is sealed for the winter the upper gap in the external frame should be left unsealed. That is not so. On the contrary. Replace the metal rod by a wooden stick and the paper will burn because wood is a poor heat conductor. . If now you introduce the rod with the wound strip into the flame of a candle. Instead of the paper strip you could also use a piece of string wound tightly around a key. Incombustible Paper We can perform an experiment in which a paper strip doesn't burn in the flame of a candle. both frames should be treated painstakingly and not even the tiniest chink should be left. But for best results the air must be sealed tightly inside. Should you do so the air within the cavity would be displaced by outside cold air. Wind a narrow paper strip tightly around an iron rod. the latter will char but not burn down until the rod becomes hot. Alternatively. thus chilling the room. But to seal it properly you should get it right why the frame "heats" a room.122-123 Seventy-Five More Questions and Experiments on Physics carried by hot air that expands on heating. some air adequately confined for it not to carry any heat away prevents the room from cooling. Therefore. the smoke descends and spreads out over the ground. With a copper rod the experiment is even more successful. Why? Because iron. is a good heat conductor. the paper won't catch fire. When the air supporting the smoke particles cools down. thus becoming lighter than the air around the chimney. It's not the second window that matters here but the air confined between the windows. you can with good results glue frames over with strips of strong paper. Air is a very poor heat conductor. Many believe that a second frame is used in winter because two windows are better than one. The fire will lick the paper. where should you place it. but chilling. You know that colder substances are denser than warm ones. the lowest portion cools first. Heating should be done from below. But if the bottle is placed over the ice. flows down to the floor. That's why in winter we feel a draught from a window. There are invisible flows caused by the heating and cooling of the air. These currents in a room are readily discovered using a balloon with a small weight attached to it for it not to strike the ceiling and float freely in the air. Explain why. Let the balloon go near a warm stove and it'll travel about the room pulled around by the invisible air currents: from the stove to the window under the ceiling. That's not the way to do it. The light. and hence lighter. Thus a chilled beverage is denser than a warm one. No mixing occurs here and the chilling is extremely poor. is better from the top. The air inside a room is almost never at rest. the upper portions of the drink (adjacent to the ice) sink on cooling being replaced by another amount of the liquid that in turn cools down and descends as well. carefully sealed and does not have the smallest hole. then down to the floor and back to the stove for a new cycle. on the contrary. Conversely. . especially at the bottom. When you place the ice over the top of the bottle. even though the frame is securely sealed and keeps the outside air out. In a short while all the drink in the bottle will have been in contact with the ice and chilled. on or under the ice? Many put a bottle on the ice without a moment's hesitation. cooling makes it denser and heavier. How to Chill with Ice If you want to chill a bottle of drink. heated air over a lamp or stove is displaced by cold air up to the ceiling because the heavy air that has cooled near the windows or cold walls. its density increases and it stays at the bottom making no room for the rest of the liquid that is warmer. Heating makes air thinner. There is nothing surprising about that.Seventy-Five More Questions and Experiments on Physics Draught from a Closed Window It might seem unusual that in a cold weather there is often a draught from a window that is tightly closed. just like they put a tea kettle on a fire. Being much lighter these are expelled upwards by the surrounding water and as they go up the bubbles pass through water that has a temperature of less than 100 °C. A slightest flow of air will make it . once the water starts to cool down. Thus. If you need to cool a room with ice don't place it on the floor but put it up high on a shelf or suspend from the ceiling. more and more bubbles go up but fail to reach the surface collapsing on the way to produce a cracking sound. The water adjacent to the heater vaporizes to form small bubbles. the bubbles cease to collapse on their way up and the "singing" discontinues. vegetables and fish should be placed under ice as well. Now place the paper on the point of an upright needle so that the latter supports it at the middle. just like air. The Colour of Water Vapour Have you ever seen water vapour? Could you say what colour it is? Strictly speaking. A Miraculous Top Cut a small square out of thin tissue-paper.124-125 Seventy-Five More Questions and Experiments on Physics It pays to chill everything from the top and not just drinks-meat. The white fog that is popularly known as "vapour" is really a multitude of water droplets. They are chilled not so much by the ice itself as by the surrounding air because the cold air comes down. You'll thus know where the centre of mass of the square is. It is invisible. However. The vapour in the bubbles cools. contracts and the bubbles collapse under pressure. Why Does a Boiler "Sing"? A boiler or a kettle produces a singing sound when the water is about to boil. not vapour. When the water eventually heats to boiling temperature. it is a suspension of fine water particles. again the earlier conditions occur and the "singing" resumes. Fold it diagonally twice and smooth it out again. The paper will balance since it's supported at the centre of mass. It is these numerous cracking that produce the sound we hear at the outset of boiling. water vapour is absolutely transparent and colourless. just before boiling sets in. Figure 93 . walls. But a fur coat is not. How to Air Rooms in Winter The best way to air a room is to open a window when a fire is burning. . Fresh. A lamp heats. apart from the outside air some air must come from other rooms where it might be neither pure nor fresh. because all of these bodies are sources of heat. A loose powder substance. some of it will really get into the room but not enough to sustain the fire. That's why a warm-blooded animal whose body itself is a source of heat will be warmer with a fur coat than without it. cold outside air will then force out the warm. In fact. do not think that the same thing will occur when the window is closed. The ice in the coat retains its low temperature longer because the fur c o a t . unfold the fur coat and you'll see that the ice is nearly intact. but only stops the heat of our body from going astray. What objections could be raised here? How could you refute the arguments? There is no objecting or refuting. But the thermometer generates no heat of its own and its temperature won't change in the coat. fur coats don't heat things up if by "heat up" we mean to impart heat. thus hampering 4he melting!. lighter air from the room into the fire-place and out through the chimney into the atmosphere. Or rather we heat the fur coat. snow is a poor heat conductor and helps to keep cold out. When the ice in the uncovered bottle has melted. Farmers are well aware of this heating effect of a snow cover. the answer to the question of whether a fur coat heats or not is that it only helps us to heat ourselves. too.. Snow "heats" the earth in the same way a fur coat does. for the outside air will leak into the room through gaps in the window. Thus.126-127 Seventy-Five More Questions and Experiments on Physics in the coat and allow the other to stand in the room uncovered. cooled it. Not infrequently a thermometer in snow-covered soil indicates it is as much as ten degrees hotter than is exposed soil. not vice versa. True. It generates no heat. etc. a stove heats. However. as it were. In consequence.a fairly poor heat conductor-hinders the passage of heat from the outside. Therefore.. the fur coat not only didn't heat the ice. a human body heats. but. Where to Arrange a Ventilation Pane Where? At the top or bottom of a window? In some homes ventilation panes are at the bottom. but they are inefficient. Let's consider the physics of the air exchange through the ventilation pane. absorbs excess heat from the paper and so does not allow it to heat up more above 100° to a point when it might ignite. but disastrous. these are convenient to open and close.) So the paper does not catch fire although flames touch it. (Perhaps it would be more convenient to make use of a small paper box as shown in the figure. An egg is being boiled in a paper vessel! You'd say. Outside air is colder than that inside and displaces the latter.e. the water. which has a large thermal capacity. Therefore.Seventy-Five More Questions and Experiments on Physics Figure 94 Figure 95 The two accompanying figures demonstrate the difference between the two cases. The air above the pane doesn't contribute to the exchange. i. Paper Saucepan Figure 96 Look at Fig. Admittedly. it occupies the part of the room below the ventilation pane. is not ventilated. 100°C. Make the "saucepan" from parchment paper and attach it to a wire holder. The paper won't be destroyed by the fire. The arrows indicate the flow of air. 96. "Oh.e. "experiment" is at . i. but the paper'll now catch fire and the water will pour out!" Try the experiment on your own. However. The reason is that water in an open vessel can only be heated to boiling temperature. A similar kind. the metal will quickly take away heat from the paper. You see thus that the lamp glass is an invention developed by scores of generations. After it has heated and thereby become lighter. The column of air inside the glass is heated by the flames much faster than the air surrounding the lamp. you could melt a piece of lead in a small box made of a playing card. For millennia people had used flames for lighting without resorting to the services of glass. It took the genius of Leonardo da Vinci (1452-1519) to introduce this important improvement of the lamp. rising dangerously.128-129 Seventy-Five More Questions and Experiments on Physics times performed by absent-minded people who put an empty kettle onto a fire with the pitiful result that the latter gets unsoldered. This results in a steady flow of air upwards. to surround the flame. Further. improves the "draught". You'll only need to expose to flames the place that is in direct contact with the lead. But Leonardo used a metal tube. What's its purpose? Not all of you will come up with the right answer to this natural question. What is the Lamp Glass for? Few people know what a long history the lamp glass went through before it appeared in its present-day form. the more difference there is between the heated and unheated air columns and the more 1 — 975 . To protect the flames from wind is only a secondary role of the glass. Let's take a closer look at this.e. which is insufficient to ignite the paper. This applies to all sorts of soldered things. it intensifies the inflow of air to the flames. The reason is clear now: solder is relatively low-melting and it is only its close contact with water that saves it from its temperature. Its main effect is to increase the brightness of the flames. the air is displaced upwards by the heavier cold air arriving from below through holes in the burner. i. The role of the glass here is like that of a chimney or stack. rather than a glass one. The higher the glass. The temperature of the paper will thus be maintained at about 335 °C (melting point for lead). a flow that continually takes the combustion products out and brings fresh air in. to boost the combustion process. Three more centuries passed before the metal tube was replaced by the transparent cylinder. Being a good heat conductor. in the immediate neighbourhood of the flames. so taking heat away from the burning body.e. once started a flame must be surrounded by noncombustibles that hinder the inflow of air. even Leonardo had understood these phenomena. do not let the combustion products out. The situation is like that in industrial chimney stacks which is why they are made so high.e. After all. i. First. on touching a hot body water turns into vapour. noncombustible substances incapable of supporting the process. At times you make use of this unawares to extinguish the fire in a lamp.. In his manuscripts he says. Why Does Water Kill Fire? A seemingly simple question. any flame would go out after a while on its own.Seventy-Five More Questions and Experiments on Physics intensive is the inflow of fresh air. Accordingly. the resulting vapour occupies hundreds of times more space than the source water. How do you blow out a kerosene lamp? Blow into it from above. an air flow forms around it. Second.. Combustion cannot occur without air and the flame would be bound to die out. "Where fire appears. and hence the burning. Let's briefly explain the phenomenon. The vapour . i. Interestingly. The flames go out deprived of the supply of fresh air. Why then this is not the case? Why does the process of combustion carry on as long as there is a supply of combustibles? For the only reason that gases expand on heating and become lighter. You can easily verify that combustion products kill a flame. the combustion products are carbon dioxide and water vapour. the flow supports and intensifies it. To convert boiling water into vapour takes more than five times as much heat as is required to heat the same amount of cold water to 100 °C. that is not always correctly answered. but are at once forced upwards by fresh air." Why Doesn't a Flame Go Out by Itself? A closer examination of the process of combustion inevitably leads to the above question. If the principle of Archimedes didn't apply to gases (or there were no gravity). It's owing to this that heated combustion products don't stay where they've been formed. the measure is quite reasonable because the powder burns down quickly evolving a great amount of noncombustible gases that cover the burning material to hinder combustion. is .. But one body of boiling water cannot heat another body of boiling water (at the same pressure). but let's analyse it more closely. very hot. and the second will cool down. for at a given pressure boiling water is always at the same temperature. Only you will never see this. too. it is quite possible to cool or heat ice with ice. and under standard conditions its temperature never exceeds this. Put the saucepan on a fire. To bring water to the boil it is not sufficient only to heat it to 100°C-it also needs a substantial supply of so-called latent heat. The water in the bottle will get hot.. then the first piece of ice will heat up (become less cold). Strange as it might seem. Heating with Ice and Boiling Water Is it possible to use a piece of ice to heat another? Or. Quite an unexpected result. In our case the source of heat used to heat the water in the bottle has a temperature of 100 °C. is brought into contact with a piece of ice at a higher temperature. Of course. but boil will it not. To improve the fire-extinguishing power of water they sometimes add . it would seem that the water in the bottle should also boil shortly. The boiling water appears to be too cool to bring another body of water to the boil. Pure water boils at 100 °C. It. When the water in the saucepan boils. to cool? Is it possible to heat one quantity of boiling water with another? If some ice at a low temperature. — 5 °C say. — 20 °C say. gunpowder to it.130-131 Seventy-Five More Questions and Experiments on Physics envelopes the body. it seems. however long you wait. you'll have to suspend the bottle from a piece of wire. cutting off the air that is indispensable for its burning. Therefore. Can You Bring Some Water to the Boil Using Other Boiling Water? Pour some water into a small bottle (jar or phial) and place it in a saucepan with pure water so that it doesn't touch the bottom. however long you heat it. Figure 97 . 132-133 Figure 98 . Even plains or the sea. To see beyond that he'll have to climb up higher. Trees. Take then two coins and tap one on the other at various places in the room but at about the same distance from your friend's ears. so enabling him to determine the location of the source. from 10 kilometres one can see within 380 kilometres. the widest panoramas open up before airmen. How far then does an average-sized man see over a plain? He can only see up to 5 kilometres. material absorbing the fat should placed at the side opposite to the iron. Ask your friend to guess the place whence the sound comes. How Far Can You See From High Places? be From a flat place we only see the group up to a certain boundary. of course. From an altitude of 1 kilometre they can see almost for 120 kilometres in all directions. The experiment makes it clear why it's impossible to spot a grass hopper chirring in the grass. with his eyes blindfolded.Seventy-Five More Questions and Experiments on Physics Accordingly. houses and other high structures lying beyond the horizon line are seen not in full. If you step aside. It will be difficult to do and your friend will point in some other direction. Where Does a Chirring Grass Hopper Sit? Sit somebody in the middle of a room. and astronauts orbiting the Earth see the whole of one side of the globe. because their lower parts are blotted by the convexity of the earth. the errors won't be as bad because now the sound in the nearest ear of your friend will be heard somewhat louder. although apparently flat. But. From the top of a lighthouse towering above water at 60 metres the sea is seen for nearly 30 kilometres. for they are parts of the curved surface of the globe. The sharp . and ask him to sit still and not turn his head. are in fact convex. Further. At twice the height an airman will see for 160 kilometres using a perfect optical device. if not hindered by clouds or fog. A man on horseback on a plainland would see up to 6 kilometres and a sailor on a mast 20 metres high would see the sea around him up to 16 kilometres away. This boundary of view is called the "horizon line". In consequence.) is pronounced in about 1/5 second and we can hear such words echoed at a distance of only 33 metres from an obstacle. But in reality the insect is sitting placidly in place and his "hops" are just an illusion. Clap your hands. Echo When a sound we have produced is reflected from a wall or another obstacle and returns to our ears. the sound will then reverberate. reflect from the walls and come back. "no". If the chirring comes from ahead of you. we don't hear it separately. Which is exactly what we do when we. before the echo arrived. turn it away. but no sooner have you done that than the sound already comes from some other direction. A monosyllabic word ("yes". in large empty halls. but conversely.134-135 Seventy-Five More Questions and Experiments on Physics sound is heard two paces away from you. etc. Imagine that you are standing in an open place and there is a house in front of you 33 metres away. This condition (as you should know it from the experiment just described) is conducive to an error. Our sharp sound was so short that it terminated in less than 1/5 second. but now the sound is distinctly heard from the left. Your problem is that when you turn your head you put it exactly so that the grass hopper becomes equally separated from both of your ears. "prick up our ears".g. if you want to determine where a sound comes from. The sound will travel through the 33 metres. erroneously. At what distance must the obstacle be then so that . e. you should not turn your head towards the sound. How long will that take? Since the sound covered 33 metres there and the same distance back. you place it. The two sounds didn't merge and were heard separately. But for bisyllabic words the echo merges with the initial sound intensifying it but rendering it obscure. You look there and see nothing. i. as it were. Otherwise the reflected sound would melt with the initial one and amplify it. The speed of the grass hopper stuns you and the quicker you turn to the direction of the singing insect the quicker the invisible musician hops about. It is only heard distinctly if the time-lag between the sound generation and its return is not too short. You turn your head in that direction. it'll return in 66/330 or 1/5 of a second.e. we hear an echo. in the opposite direction. Figure 99 . The net result is that it seems to you that the distant object is seen through the shielding palm. sees the palm unclearly.sight with the result that the near palm appeared blurred to it. How many times will the speed be increased with which the boat is approaching the shore? Assume that the boat is sighted 600 metres away and is approaching the observer with a speed of 5 metres per second. whereas in actual fact it has actually covered 300 metres. Now bring your right palm near to your right eye so that it nearly touches the tube. the right one. Through binoculars with triple magnification the boat at 600 metres appears to be at 200 metres. A minute later it will be 5 x 60 = 300 metres closer and will then be 300 metres away from the observer. the left eye clearly sees the distant object. It follows that the speed at which the boat approaches when observed through the binoculars has decreased not increased by three times. adapted to distant. In short. You'll then make sure that your right eye sees perfectly through your palm as if there were a round hole in it. bring it up to your left eye with your left hand and look through it at some distant object. . In the binoculars its apparent size would indicate it were 100 metres away. The speed with which the boat approaches has thus reduced by as many times as the binocular magnifies. by taking the initial distance. The reader can arrive at the same result by another argument.136-137 Seventy-Five More Questions and Experiments on Physics To See Through a Palm Fold a sheet of paper into a tube. Your left eye prepared to view a distant object through the tube and the crystalline lens adapted accordingly. i. an observer looking through the binoculars would think the boat has travelled 200 — 100 = 100 metres. too. Why? The reason of this unexpected phenomenon was as follows. Both hands should be about 15-20 centimetres away from the eyes. The eyes function in such a way that they always adapt in sympathy. Through Binoculars At a seaside you are watching a boat approaching the shore through a pair of binoculars that magnifies three times. Consequently. In the experiment described the right eye. speed and period.e. The impressions left on carbon paper are inverted 'ettering. if they want to see themselves better in the mirror they turn the light on behind themselves in order to "illuminate the reflection". Drawing Before the Mirror That a mirror reflection is not identical with the original may be demonstrated by the following experiment. but follow the movements of its reflection in the mirror. These age-old metaphors of white and black appear. surpasses black velvet in blackness or white snow in whiteness. Just try to read the text on it. it seems. The mirror gives the reflection of what is itself an inverted image of normal writing. Over the years our visual perceptions and motions have been correlated but the mirror violates this and represents our motions to our eyes in an inverted form. however. Quite a challenge! But bring it to a mirror and the text will appear in its habitual form. You'll find that this seemingly simple problem is almost intractable. a rectangle with diagonals. It appears that some people cannot use a conventional mirror either. The result will be a funny confusion. too. and so on. place a sheet of paper on it and try to draw something. instead of illuminating themselves from the front. say. Black Velvet and White Snow Which is the lighter .black velvet on a sunny day or pure snow on a moonlit night? Nothing. Long-term habits rebel against each our motion: you want to draw a line to the right. for example. quite different when viewed by a physical instrument-a photometer. It then . But in doing so don't look directly at your hand. Quite frequently. I've already mentioned that some people cannot use ice properly to chill drinks-they place them on the ice instead of under it. but the hand draws to the left.Seventy-Five More Questions and Experiments on Physics From the Front or the Back? There are many things in each household that are used inefficiently. Stand or hang an upright mirror in front of you on the table. Stranger things will occur if instead of a simple figure you attempt to draw more intricate designs or write something whilst looking in the mirror. For exactly the same reason that ground glass and all ground transparent substances in general are white.scatters 91 per cent of light). however dark it might be. snow is white because it consists of tiny particles. transparent. It is known that the illumination provided by the sun is 400. can beam out more light than strikes it. indeed? It consists of transparent ice crystals. and before your very eyes the snow will become colourless. the snow becomes transparent. when penetrating into tiny pieces of transparent ice. Such an experiment is easy. sunlit black velvet is many times lighter than moonlit snow. Therefore. Since no surface. Thus.000 times that of the moon.138-139 Seventy-Five More Questions and Experiments on Physics turns out that the blackest velvet in sunlight is lighter than the purest snow in moonlight. In other words. and the sun sends out 400. doesn't pass through them but reflects inside them at the boundaries between the ice and the air (total internal reflection). This is because a black surface. doesn't completely absorb all the visible incident light. Why is Snow White? Why. Grind some ice up in a mortar or chip it with a knife and you'll get white powder. But a randomly scattering surface is perceived by the eye as white. this is true not only of snow but also of the best white pigments (the whitest of them all . .lithopone . If the gaps between the snow flakes are filled with water. the 1 per cent of sunlight scattered by the black velvet is thousands of times more intense than the 100 per cent of moonlight scattered by snow. Even soot and platinum black-the blackest substances known-scatter about 1-2 per cent of the incident light. We take 1 per cent for argument's sake and suppose that snow scatters 100 per cent of the incident light (which is undoubtedly an overstatement). The colour is due to the fact that light. Put some snow into a jar and pour some water into it. unless it's hot.000 times as much light as the moon. it's impossible to have a white pigment that would in moonlight be lighter than the blackest pigment on a sunny day. To be sure. Fresh snow only scatters about 80 per cent of light. at the angle of incidence. too. . Such a surface gives mirror reflections.e. Examined uncier the microscope polished surfaces would be like razor blades and for a man reduced 10. If they are smaller than the wavelength of the incident light. Therefore. This suggests. For visible light with a mean wavelength of about half a micrometre (0. It's widely believed that the polished surface is smooth and the dull one is irregular. reducing the irregularities down to a size at which the peaks become smaller than the wavelengths of visible rays and the surface turns into a glossy one. and the surface is called dull. both dull and polished. There are no absolutely smooth surfaces. If. nor the brush seem to have anything to impart the gloss to shoes. But back to the pedestrian subject of our problem. the surface scatters the ray randomly and does not follow the reflection law. on the other hand.0005 mm) a surface with irregularities of about that size will be polished. it's a mystery for many. by the way.000. i. depressions and scratches on any surface. We'll first clear up the difference between the glossy polished surface and the dull one. What matters is the size of these irregularities. There are irregularities. which has shorter wavelength. it's dull. But for ultraviolet light. after all? The unblackened surface of leather has a highly irregular microstructure with "peaks" larger than the mean wavelength of visible light. Such scattered light gives no mirror reflections and highlights. which has longer wavelength it's polished. Brushing removes any excess polish at projections and fills the troughs. This is not so: both are irregular. the irregularities are larger than the wavelength of the incident light. then the rays are reflected correctly. Why do polished shoes shine.000 times the surface of a smoothly polished blade would appear to be a hilly terrain. for infrared light. it shines and we call it polished. it's dull.Seventy-Five More Questions and Experiments on Physics The Shine on a Blackened Shoe Why does a blackened shoe shine? Neither the sticky black shoe polish. that a surface may be polished for some rays and dull for others. By blackening it we smooth out the surface and lay the hairs that stick out down. pink.) are so black as to be next to impossible to make them out against the black background of the leaves and yellow. Professor M. Why? Red light has the longest wavelength in the visible spectrum and is thus less scattered by any particles suspended in the air than are other colours. "Observing flowerbeds through a red glass we see that purely red flowers. yellow flowers emit about an equal amount of red and green. geranium. green foliage appears as absolutely black with a metallic lustre. red flowers are jet black. Red flowers send out mostly red light. for example. "Through a green glass we see the unusually bright green of the foliage and white flowers come out still more distinctly against it. Now you should easily see that the blue flower viewed through green glass will be black as well. made a number of interesting observations in his book Physics on Summer Outings. "It's easily seen from this that red flowers really do emit much more red light than any other colour. Yu. It is of paramount importance to obtain the greatest visibility possible for . the light-pink petals of a wild rose are darker than its richly coloured leaves. a physicist. red light penetrates farther. blue flowers (aconite. artist and acute observer of nature. but very little blue. and blue and dark-blue-almost as bright as the white ones. whilst pink and purple flowers emit a lot of red and blue. Therefore.140-141 Seventy-Five More Questions and Experiments on Physics Through Stained Glass What colour are red or blue flowers viewed through green glass? Green glass will only transmit green light and catch all the rest. and lilac flowers appear more or less dull." A Red Signal On the railways the stop signal is a red colour. lilac and light-pink colours appear as dull and grey so that. Piotrovsky. somewhat more pale are yellow and blue ones. white flowers will look bright. yellow-absolutely black. If we look through green glass at a red flower we'll receive no light from its petals as the only rays it emits are retained by the glass. appear to us as bright as purely white one. say. but very little green light. "Finally a blue glass will again make red flowers look black. etc. The red flower will therefore appear to be black through such glass. . Fine details blurred in a conventional picture come out distinctly on a photograph taken through a glass that only transmits infrared light. by the way.Seventy-Five More Questions and Experiments on Physics a transport signal since to be able to stop his train the engine-driver should begin breaking long before reaching an obstacle. while a conventional picture only shows its atmospheric envelope. In the case of Mars it's possible to photograph the surface of the planet. A further reason for selecting the red light for the stop signal is that our eyes are more sensitive to this colour than to blue or green. explains why astronomers use infrared filters to photograph planets (especially Mars). The greater transparency of the atmosphere to longer waves. and so on. under certain conditions. If we were used to judge about things as these are in reality then this art would be impossible. to see what really is not is a blessing enriching enormously the potentialities of the fine arts. illusions to which this section is devoted are not accidental companions of our vision-they occur in definite circumstances. For him our ability. . many books and articles have been published in this country and elsewhere. No matter what were painted in the picture. The artist would rebel against such an "infallible" vision. psychologist. Brain. here a black and there. i. The whole of the art of painting is based on this. try to make out the signification of all the coloured spots.142-143 Optical Illusions Tricks of Vision The optical. Grey. or visual. physicist. physiologist. being devoid of the pleasure we derive every day from such pleasant and useful arts!" Since the subject is of such lively interest for the artist. whose removal would benefit us in many respects.e. The Neurophysiological Aspects of Hallucinations and Illusory Experience (1960) by W. it would be as if we were all blind. only a relatively small number have well established. punched cards. It would thus be impossible to represent anything. In vain the artist would exhaust his skill in colour blending. Optical Illusions (1964) by S. The 18th century mathematician Euler wrote: "Artists are especially skilled at using this common illusory experience. here a blue one. for we would merely say: there is a red spot on this board. and perhaps we would. weren't we to be pitied greatly. That human beings are subject to visual illusions and can be mistaken as to the source of their visual perceptions. * We'll here consider several types of tricks played by our unaided eye. physician. and for any inquisitive mind. should by no means be considered an undesirable disadvantage or an unqualified flaw in our constitution. * See. As to the causes of one or another visual illusion. e. For all the perfection. several whitish lines. are governed by physical laws and affect any normal human eye. philosopher. Tolansky. Everything is in the same plane and there is no difference in distance. without any appliances such as stereoscopes. in addition. it could seem to be like writing on a paper. The Nature of Experience (1959) by R.g. Most of attempts to explain individual illusions (except for the few mentioned above) are as unreliable and uncertain. As an instructive example we'll consider the optical illusion of Fig. astigmatism illusions. It seems to be well established that this kind of illusion is totally caused by so-called irradiation. so enabling their forms to be distinguished. However. By contrast. it pushes adjacent ones on expanding and appears to be confined by a hexagon". whereas the black fringes around them have already assumed hexagonal forms. It's only at larger distances that the hexagonal configuration is transferred from the fringe to the white spots. is only a plausible assumption and. there are several other possible explanations. This interpretation also covers the paradoxical fact that at some distances white circles continue to appear to be round. clear physical explanation). When viewing from a certain distance. this explanation. "White circles expand due to irradiation and reduce the black gaps between them". 141: white circles arranged in a certain way on a black background are perceived as hexahedrons.e. too. Some tricks of vision still await their explanation. the angle of vision of the gaps between the circles becomes smaller than a limit. He goes on to say that. . These include those due to the structure of our eyes. the apparent expansion of light areas (which can be given a simple. It is necessary to prove that the possible cause is here the actual one. For the two cases to be covered by the same principle the following interpretation might be suggested.Optical Illusions unquestionable explanations. "as each circle is surrounded by six other. Professor Paul Bert writes in his Lectures on Zoology. others have too many explanations each of which would perhaps be sufficient in itself were there not so many additional ones that make it less convincing. Mariotte's illusion (blind spot). Remember the famous illusion discussed since the time of Ptolemy-that of the increasing of the size of celestial bodies near horizon. i. 141) where the same effect is observed for black circles against a white background for this explanation to be rejected: here irradiation only could reduce the size of black spots but could not change them into hexagons. Suffice it to glance at the neighbouring figure (Fig. irradiation. Each of the six neighbouring gaps then appears to be a straight line of a uniform thickness and the circles are thus bounded by hexagons. perhaps. and so forth. the retention of light impressions. however. all those published illusions that have effect not on anybody's eye or are not perceptible enough.. the entire domain of visual illusions is still in the pre-scientific stage of treatment and in need of establishing the basic methodology of its investigation. I also wanted to do away with some of superstitious notions that developed around this unique optical illusion. 10 — 9 7 5 . These are illusions due to the blind spot..". These "physiological" tricks of vision are followed by a much larger class of illusions that are due to psychological reasons. which have not yet been sufficiently * The selection of illusions here is the result of many years of collecting. The effect perhaps is even more striking. So Mariotte writes: "Against a dark background approximately at the level of my eyes I attached a small circle of white paper and at the same time asked someone to hold another circle beside the first one about 2 feet to its right but somewhat lower so that the image would strike the optica] nerve of my right eye when I closed my left one.. For want of any solid foundation in the form of relevant theories I have confined our discussion to the demonstration of unquestionable facts providing no explanations of what caused them and seeking only to present all the major types of visual illusion. The series of illustrations opens with samples of illusions caused by clearly anatomical and physiological peculiarities of the eye. Obviously. astigmatism. irradiation.. and retina fatigue (see Figs. 100-107). "I couldn't ascribe it to its lateral position. each of which has the only drawback that there are five more equally adequate explanations.144-145 Optical Illusions N o less than six possible theories.. the second circle. which was about 4 inches across. In the blind spot experiment some of your field of vision may disappear in another way as well as Mariotte did for the first time in the 18th century. completely disappeared from my field of vision. When I was about 9 feet away. I'd have thought it removed had I not been able to find it again with the slightest movement of my eye. I've excluded. I stood next to the first circle and stepped back gradually without taking my right eye off it. have been suggested. it seems.. as I could discern other things further to the side than it. * Only those involving portraits are explained at the end of the section since these are quite clear and incontestable. not the sensor. Figure 101 Figure 102 The phenomenon is caused by the fact that with this arrangement of the eye with respect to the figure the image of the circle falls on the so-called blind spot . The larger the distance the more pronounced is the illusion. Kant aptly remarked. although they are equal in size. Irradiation. owing to irradiation. Therefore a light surface on the retina is fringed by a light band that increases the place occupied by the surface. The phenomenon is called irradiation (see below). Close the right eye and look with the left one at the upper cross from a distance of 20-25 centimetres. Irradiation is due to the fact that each light point of an object produces on the retina of an eye not a point but a small circle because of so-called spherical aberration. When viewed from a distance the figure with the black cross seems. the circle only disappears in part. but because they do not judge at all". You'll notice that the middle. When viewed from a distance the figures below-the circle and square-seem to be larger than those above. black surfaces produce reduced images because of the light band.Optical Illusions Figure 100 clarified. If. The source of the misperception here is the mind. you look at the lower cross. large white circle disappears completely. On the other hand. It may perhaps be established that illusions of this kind are only the consequence of some preconceived erroneous judgement that is involuntary and subconscious in nature. Irradiation.t h e place insensitive to photic stimulation where the optic nerve is connected. with the same arrangement. to be distorted as shown in the accompanying figure on the right. The Mariotte Experiment. although the two smaller circles on either side are seen distinctly. . "Our senses deceive us not because they do not judge correctly. If you look at the cross at the right of the figure with your left eye at a certain distance you won't see the black circle at all. Astigmatism. etc. This experiment is a modification of the previous one. Figure 105 . horizontal. Look at the lettering with one eye. i. although the two circumferences will be seen.e. different curvatures of the retina in different directions (vertical.146-147 Figure 103 Optical Illusions Figure 104 The Blind Spot. It's only rarely that an eye is free of this imperfection. You need only to turn the page by 45° or 90° and some other letter will seem to be blacker.). Do all of the letters appear equally black? Normally one of the letters appears blacker than the rest of them. The phenomenon is explained by so-called astigmatism. move it to the right and left and it'll seem to you that the eyes in the figure swing horizontally. The segment be seems to be longer than ab. the previous illusion) of identifying astigmatism in an eye. although they are in fact equal. actually both are the same length. If you bring the figure to the eye under examination (the other one being closed) you'll notice at a certain. Figure 105 furnishes another way (cf. 109 and here segment A seems to be shorter than B. . which will appear grey. distance that two opposite sectors will seem blacker than the other two. Figure 108 Figure 109 •< Figure 110 > < Another form of the previous illusion is Fig. rather close. Figure 107 When viewing this figure.Optical Illusions Figure 106 Astigmatism. The Miiller-Lyer Illusion. The deck of the right ship seems to be shorter than that of the left. Having concentrated on the white square at the top you'll notice about half a minute later that the lower white line will have disappeared (owing to retina fatigue). The illusion is accounted for by the eye's property to retain visual perceptions for a short time after the stimulus has disappeared (cinema is based on this). although these are equal (the influence of the arrangement). ^ > < The distance AB seems to be larger than CD. which is equal to it. CD and EF seem to be unequal (the influence of the arrangement). 115). . The equal distances AB. Figure 112 c > — o Figure 113 • e e The lower oblong seems to be larger than the internal one.148-149 Figure i l l Optical Illusions The distance AB seems to be much smaller than BC. Figure 114 The rectangle crossed longitudinally seems to be longer and narrower than the equal rectangle crossed transversely (Fig. which is equal to it. Figure 117 The height of this figure seems to be larger than its width. although the first seems to be longer.Optical Illusions Figure 1 15 Figure 116 Figures A and B are equal squares. to be higher and narrower than the second. Figure 120 . The distances AB and AC are equal. Figure 119 The distances BA and BC are equal. Figure 118 The height of the top hat seems to be longer than its width. although both are equal. although the first seems. although these are equal. although the first seems to be longer. in fact these are all equal. Figure 124 Figure 125 c Figure 126 The "Smoking Pipe" Illusion. The empty gap between the lower circle and each of the upper ones seems to be larger than the distance between the outer edges of the upper circles. This illusion becomes more pronounced with distance (Fig. In actual fact they are equal (Fig. 125). The distance MN seems to be smaller than the distance AB.150-151 Figure 121 Optical Illusions The upright plank seems to be longer than those below. The distance AB seems to be smaller than the equal distance CD. . Figure 122 Figure 123 The right circle in this figure seems to be smaller than the equal-sized circle on the left. 124). which is really equal to it. The dashes on the right in this figure seem to be shorter than those on the left. seems to lie below it.Optical Illusions The "Print Type" Illusion. The Poggendorf Illusion. they will meet the ends of those on the left. The upper and lower parts of each of these characters seem to be equal to each other. Figure 129 X38S Figure I 31 If we continue both arches on the right. But turn the page over and you'll immediately see that the upper parts are smaller. but it seems that the part near the vertex is shorter. Figure 127 Figure 128 The heights of the triangles are divided in two. The oblique straight line intersecting the black and white strips seems to be broken from a distance. . Figure 130 Point c lying on the continuation of line ab. although it seems that they should pass lower. The middle parts of those lines do not seem to be parallel. The two double parallel lines are parallel. The illusion disappears if (1) you hold the figure level to your eyes and view it so that you are glancing along the lines. Figure 133 The Zollner Illusion. . or (2) you point the end of a pencil at some point and concentrate at this point. although they seem to be arches with the crown facing each other (Fig. although these seem to be diverging. Figure 134 The Hering Illusion. although the upper one seems to be the shorter and wider. 135).152-153 Figure 132 Optical Illusions Both figures are identical. The long oblique lines of this figure are parallel. although they are so. in reality they are straight. The letters are upright type. . which is readily found by following anyone of them with a pencil. though. although they are circles. Figure 136 Figure 137 The sides of the triangle seem to be concave. 139 seem to be a spiral.Optical Illusions Figure 135 The lower arch seems to be more convex and shorter than the upper one. Figure 138 The curves in Fig. The arches are similar. 154-155 Figure 139 Optical Illusions Figure 140 . Will the circle on the right of the figure get between lines AB and CDl It seems at first sight that it will. but they are circular. and you will perceive an eye and part of the nose of a female face. 140 seem to be oval.Optical Illusions The curves in Fig. Consider the pattern from a distance. although they are both the same size. At a certain distance the circles in these figures (both white and black) seem to be hexagons. which can be tested with a pair of compasses. But really the circle is wider than the separation between the lines. Figure 141 Autotype Illusion. Figure 142 The upper silhouette seems to be longer than the lower one. . The figure is a part of an autotype (conventional illustration in a book) multiplied tenfold. You'll see a row of pins as if stuck into the . Figure 145 A 0 B Holding Fig. you'll see the picture given on the right. 146 at eye level so that you glance along it.156-157 Figure 143 Optical Illusions Figure 144 Distance AB seems to be wider than distance AC. Close one eye and place the other approximately at the point where the continuations of these lines intersect. which is equal to the former. The figure may represent. call forth one or the other image. as you like it. by exerting your imagination. Also. either a block with a recess (the back side of the recess is the plane AB). you can intentionally. The Schroder Stairs. Shift the figure slightly sidewards and the pins will swing. it'll seem to you that the two cubes at the top and at the bottom stand out alternately. (2) as a step-wise niche. The perceptions may interchange intentionally or unintentionally.Optical Illusions Figure 146 paper. This figure might be perceived in three ways: (1) as stairs. or (3) as a pleated paper strip stretched out. or a part of an empty box with a block . Figure 147 Figure 148 Figure 149 If you view this figure for a long time. as if flashing. darker strip. 151. In actuality.158-159 Figure 150 Optica! Illusions touching the walls from the inside. But by masking neighbouring strips to exclude the influence . the lines are absolutely white throughout. in which white spots appear at the intersections. Figure 151 A modification of the illusion of Fig. Its four strips each seem to be a concave stripe that is lighter at the edge and adjacent to a neighbouring. the box being open at the bottom. The intersections of the white lines in this figure seem to have yellowish square spots that appear and disappear. which can be seen if you cover adjacent rows of black squares with paper. Figure 152 Look at this figure from a distance. The effect is because of the contrast. each about its own centre. and vice versa. Figure 153 Look attentively for a minute at some point on this "negative" portrait of Newton without moving your eyes. but the black spots will become white. For a moment you'll see the same portrait.Optical Illusions of contrast you can see that each strip is uniformly darkened. Figure 154 The Silvanus Thompson Illusion. greyish wall or ceiling. . in the same direction and with the same speed. then quickly shift your glance to a piece of white paper. If you rotate this figure (by turning the book) all the rings and the white toothed wheel will seem to be rotating. only they're shown at different angles. on the r i g h t . Look at the photograph in Fig.a concave one. 157 with one eye 14-16 centimetres away from the centre of the picture.160-161 Optical Illusions Figure 155 Figure 156 On the left you see a convex cross. With this arrangement your eye will see the picture from the same point the objective of the camera "saw" . But turn the book upside down and the figures will change their places. Actually the figures are identical. In exactly the same way if the person being photographed looks into the objective. the water glimmer. too. wherever he or she shifts. It's this that accounts for the liveliness of the impression. in photographing. The Portrait by Gogol). Above all. . the muzzle of the gun is directed at the objective. the explanation of this interesting illusion is very simple. then his eyes in the picture will be directed at the onlooker. However. This feature scares nervous people and is regarded by many as something supernatural. at whatever angle he views the picture. All of these phenomena have one common and * Such a photograph is obtained if. there is no evading a cart riding directly at the onlooker. The landscape acquires depth.Optical Illusions Figure 157 Figure 158 the scene. The eyes and the finger seem to point directly at you and follow you when you shift to the right or left. the illusion is peculiar not only to portraits. but to other pictures. Also. It has long been known that some portraits have the fascinating feature that they sort of follow the onlooker with their eyes and even turn their faces in his or her direction.g. It has given rise to a number of superstitions and fantastic stories (e. A gun drawn or photographed so that it is directed at the onlooker* turns its muzzle in his direction when he moves to the right or left of the picture. When a portrait is perfectly executed the effect is striking. Clearly. there is nothing surprising in this property of portraits. we see another part of it. we would see the side of the face. but in a portrait we always see the same view. and it seems to us that the thing has changed its position. If we view the picture we imagine the things shown in it.162-163 Optical Illusions exceptionally simple cause. The same applies to the portraits. this. But. in essence. it would be more unusual if. When we observe a real face from the side. We can only see the same part as before if the person turns his face to us. is what is expected by those who regard the apparent turn of the face in a portrait as something supernatural! . as we shift sidewards. Conversely. 160 and denote each of the small squares by a letter in the top left corner as shown. and 20 kopeck coins into the three squares of the lower row. Place a match on one coin. Now ask your friends to change the arrangement without moving the coin with the match so that the rows and columns each still contain 6 kopecks.Brain-Twisting Arrangements and Permutations In Six Rows You may have heard the funny story that nine horses have been put into 10 boxes. 15 kopeck. and 3 kopeck coins into the three squares of the upper row. a small trick will help you to perform this "impossible" task. Which moves? * In what follows the answers to problems are given at the end of each section. one in each. Using matches make a square with nine small square cells and place a coin in each so that each row and column contain 6 kopecks (Fig. The rest of the squares are empty. but it has a real solution . By shifting the coins on vacant squares you make the coins exchange their places so that the 1 kopeck changes with the 10 kopecks. the 2 kopecks changes with the 15 kopecks. Put 1 kopeck. Also. Which one? Coin Exchange Figure 160 Make a large drawing of the arrangement in Fig. and the 3 kopecks with the 20 kopecks. They'll say it's impossible. The figure shows the arrangement of the coins. The problem is solved by a long series of moves. . it isn't allowed to skip an occupied square or go beyond the figure. You must arrange 24 people in six rows with five in each. Now put 10 kopeck. You may occupy any vacant place of the figure but you are not permitted to place two coins into one square. The problem that is now posed is formally similar to this famous joke. However. half a trick. In Nine Squares Figure 159 This is a trick question-half a problem. 159). 2 kopeck. Which zeros are to be crossed? Two Draughtsmen Put two different draughtsmen on a draughts board. To simplify the solution I will add that the nine zeros are to be crossed without the pencil leaving the paper. You must cross out 12 zeros so that each row and column retain an equal number of uncrossed zeros. Thirty Six Zeros 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 You see that 36 zeros are arranged in the cells of this network.164-165 Brain-Twisting Arrangements and Permutations Nine Zeros Nine zeros are arranged as shown below: 0 0 0 0 0 0 0 0 0 You must cross all the zeros with four lines only. They happened to have arranged themselves so that no two flies are in the same row. Figure 161 . How many different arrangements are possible? Flies on a Curtain Nine flies are sitting on a chequered window curtain. column. or diagonal (Fig. 161). Brain-Twisting Arrangements and Permutations After a while three flies shifted into neighbouring. as in the two previous problems. They can only make it by leaping from a stump to the other along the lines indicated in the figure. On stumps 1 and 3 sit two rabbits. Which three flies shifted and which cells did they choose? Eight Figure 162 Letters The eight letters arranged in the cells of the square shown in Fig. the squirrels want to take the places of the rabbits. Curiously enough. and on stumps 6 and 8. Figure 163 . the nine flies still continued to be arranged so that not a single pair appeared in the same direct or oblique line. but you are required to achieve the result using a minimum number of moves. Squirrels and Rabbits Figure 163 shows eight numbered stumps. 162 are to be arranged in alphabetical order by shifting them into a vacant cell. and the rabbits the places of the squirrels. This is not difficult if the number of moves is not limited. But both the squirrels and the rabbits are not happy with their seats and want to exchange them. two squirrels. You must find out for yourself what the minimum number is. unoccupied cells and the other six stayed in the same place. and J a c o b . What is the least number of changes required to achieve the goal? Three Paths Three brothers . although it's impossible to make less than 16 leaps.g o t three vegetable gardens located near their houses. Could you indicate these paths? One requirement is that no path should go round Peter's house. a piano. By shifting the things from one room to another the desired arrangement was eventually achieved. Paul.166-165 Brain-Twisting Arrangements and Permutations How could they make it? Observe the following rules: (1) each animal may make several leaps at once. You can see that the gardens are not very conveniently arranged but the brothers failed to agree about exchanging them.Peter. Only room 2 is free of furniture. you should take into account that the animals want to reach their goal using the least possible number of leaps. a sideboard. as shown in the figure. a bed. . The tenant wanted to change around the piano and the bookcase. and a bookcase. The free room 2 was of help. therefore they must only leap on a vacant stump. Cottage Figure 164 Problem The accompanying figure shows the plan of a small cottage whose poky rooms house the following furniture: a desk. Wishing to avoid future conflict the brothers decided to find nonintersecting paths to their respective gardens. (2) two animals may not seat on the same stump. After a lot of searching they succeeded in finding such paths and now they come to their gardens without meeting each other. This appeared to be a difficult problem because the rooms are so small that no two of the above pieces could be in the same room. The shortest paths leading to the gardens crossed and the brothers began to quarrel. Further. Brain-Twisting Arrangements and Permutations Figure 165 Jacob's garden Peter's garden Paul s garden Pranks of Guards The following is an ancient problem having many modifications. Figure 166 . We'll discuss one of them. 166). But the prince wasn't satisfied with the plan because the arrangement made all the castles vulnerable to outside attack. a full dozen guests. They should be connected by walls arranged on five straight lines with four castles on each. And all of these pranks passed unnoticed as the chief always found nine soldiers in the three tents of each row. Later the sentries were allowed to visit each other and their chief didn't punish them when.168-165 Brain-Twisting Arrangements and Permutations The commander's tent is guarded by sentries housed in eight other tents (Fig. the chief thought that all of the guards were present. at another eight. thus if the total number of soldiers in the three tents of each row was nine. and at yet another. he found more than three soldiers in it and less than three in the others. How did they manage to do so? Ten Castles In olden days a prince desired to have 10 castles built. Initially in each of the tents there were three sentries. He only checked the total number of soldiers in each row of tents. having come to a tent. The architect submitted the plan given in Fig. 167. but he wished there to be at least one or Figure 167 . Having noticed this the soldiers found a way to outwit their chief. On later night the guards began to invite guests: at one time four. On the next night six left and got away with that. One night four guards left and this passed unnoticed. Cut down the rest and take them home for firewood as your payment for the work". When the tree felling had finished the gardener came Figure ! 68 . After a lot of head-scratching the architect in the long run came up with an answer. The gardener decided that the orchard was too crowded. The architect objected that it was impossible to satisfy the condition whilst the 10 castles had to be arranged four in each of the five walls.Brain-Twisting Arrangements and Permutations two castles protected within the walls. with four trees in each row. 168. arranged as shown in Fig. to arrange the 10 castles and the frve interconnecting walls so as to meet the above conditions? An Orchard There were 49 trees in an orchard. He called in a workman and ordered: "Leave only five rows of trees. too. Maybe you'll be happy enough. so he wanted to clear the garden of excess trees to make flowerbeds. But the prince insisted. Much to his dismay he found the orchard almost devastated: instead of the 20 trees the workman had left only 10 and cut 39. You only told me to leave five rows with four trees in each. How had the workman managed it? The White Mouse All of the 13 mice in the figure are doomed to be eaten by the cat. But the cat wants to consume them in a certain order.. Which mouse must it start from for the white mouse to be eaten last? Figure 169 . When it gets to 13 it eats the mouse and starts counting again. Just look. 39 trees had been cut down instead of 29. His order had been fulfilled literally. The cat eats one mouse and then counts around the circle in the direction in which the mice are looking. "No.. and still. I did so. missing out the eaten mice. "Why have you cut so many ? You were told to leave 20 trees!" the gardener was enraged.170-165 Brain-Twisting Arrangements and Permutations to see the result." The gardener was amazed to find that the 10 remaining trees formed five rows with four trees in each. Figure 171 Coin Exchange The following is the series of moves required (the number is the coin. the letter is the cell to which the coin is shifted): 2-e 15—i 2-d 10-a 15—b 3-g 1 -h 3-e 10-d 20-c 10-e 15-b 2-h 1-e 2-j 2-d 20-e 3-a 15-i 3-j 10-j 15-b 3-g 2-i It's impossible to solve the problem in less than 24 moves. The arrangement has changed but the requirement of the problem is satisfied: the coin with the match hasn't been shifted.Answers In Six Rows The requirement of the problem is easily met if the people are arranged in the form of a hexagon as shown in the figure. Figure 170 In Nine Squares You don't touch the forbidden coin but shift the whole of the lower row upwards (Fig. . 171). i. 24 zeros with four zeros in each row. the total number of the various permutations of the two draughtsmen is: 64 x 63 = 4.032. 173 indicate which flies must be shifted and in which direction. The remaining zeros will be arranged as follows: 0 0 0 0 0 0 0 0 Two 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Draughtsmen One draughtsman may be placed at any of the 64 squares of the board. we'll have 36—12. Figure 172 Thirty Six Zeros As it's required to cross out 12 of the 36 zeros.e. . Flies on a Curtain The arrows in Fig. then the second one can occupy any of the 63 remaining squares. i. 172. Consequently. in 64 ways. Hence for each of the 64 positions of the first draughtsman you can find 63 positions for the second one.e.172-173 Answers Nine Zeros The problem is solved as shown in Fig. Table 16. The total number of leaps required is 16. Piano 7. 4-3. Piano 6. Piano 13. 7-1. 3-7. Bookcase 15. 1-5. 5-6. 2-8. 5-6. 3-7. Table 17. Bed 2. 174. namely: 1-5. Sideboard 3.Answers Figure 173 I w w I If T ' / i l i i i i M Eight Letters The least number of moves is 23. 8-4. Bookcase 11. Piano 10. Table 4. Cottage Problem The exchange can be achieved in no less than 17 moves. 6 . 4-3. 6-2. The pieces of furniture are moved in the following sequence: 1. 1-5 means that a squirrel has leapt from the first stump to the fifth). 2-8.2 . 7-1. Sideboard 14. Bookcase 8. Sideboard 5. . These are as follows: A B F E C A B F E C A B D H G A B D H G D E F Squirrels and Rabbits Shown below is the shortest way of the rearrangement The first number in each pair indicates from which stump an animal should leap and the second number the destination stump (for example. Bed 12. 8-4. Sideboard 9. Piano Three Paths The three nonintersecting paths are shown in Fig. Ten Castles Figure 176 (on the left) shows the arrangement with two castles protected from the external attack. 175e. In the same way we find that there must be one soldier in the upper tent of row V and one in the lower. Accordingly. the required arrangement for four soldiers to be absent is as shown in Fig. A similar argument yields the desired arrangement for six soldiers to be absent (Fig.174-175 Figure 174 Answers Peter's house Jacob's garden Peter's garden Paul's garden Pranks of Guards The problem is easily solved by the following reasoning. Fig. As the total number is 24 — 4 = 20. 175c). 175b.18 = 2. 175«) there are nine soldiers in each. i. 175/ shows the arrangement for 12 guests. For eight guests in Fig. For four guests the arrangement is shown in Fig.e. For four guards to be able to be absent unnoticed by the chief it's necessary that in rows / and III (Fig. It is now clear that the corner tents must house four guards. 175d. one soldier in the left tent of this row and one in the right. then in row II there will Figure 175 "••• a ' • • • IV V VI 0 0 0 000 b c 0 B0 • • • • • • 0 • 0 0 • 0 d 0 0 0 0 * 0 • Q • 0 « 0 000 000 e O00 f be 20 . You see that the 10 castles are disposed as required in the problem: . It is easy to see that under these conditions no more than six soldiers can be absent with impunity and no more than 12 guests can visit the guards. And finally. On the right of Fig.Answers Figure 176 four on each of the five lines. 177. These form five straight rows with four trees in each. Figure ill . An Orchard The uncut trees were disposed as given in Fig. four more solutions to the problem are given. 176. . e. the sixth one from the white. Try it by beginning with this mouse and cross out every 13th mouse. You'll see that the white mouse will be the last to be crossed out. i.176-177 Answers The White Mouse The cat should first eat the mouse at which it is looking. and eventually hit upon an idea as to how to execute his order. too? Cut out two paper figures. 178 into seven sections with three straight lines so that there is one animal in each section. 180 (only larger) and use them to arrive at the solution. Figure 179 Into Four Parts This ground area (Fig. Draw the area on a sheet of paper. A Clock Dial The clock dial in Fig. tried one way and then another. 179) consists of five equal squares. not five? To Make a Circle A joiner was given two pieces of rare wood with holes in them (as shown) and was asked to make them into a perfectly circular solid board for a table so that no scraps of the expensive wood would be left over.Skilful Cutting and Connecting 7 Figure 178 With Three Straight Lines Cut Fig. The joiner was a master craftsman but the order was not easy. exactly like the ones in Fig. Perhaps you'll twig it. Can you cut it into four identical areas. All the wood must be used. He scratched his head for a long time. 181 must be cut into six parts of any shape so that the sum of numbers in each section Figure 180 . Crescent The crescent (Fig. but how many different figures can be obtained in this way? In other words. 185a? If you've already found the solution. To Make Up a Square Can you make up a square from five pieces of paper like the ones shown in Fig. 182) must be divided into six parts by only two straight lines. Figure 184 Figure 183 It's curious. the other on the left. in how many ways can a cube be developed? I warn the impatient reader that there are no less than 10 different ways. The aim of the problem is not so much to test your resourcefulness but the quickness of your thought. then two semicircles are drawn around the middles of the segments AC and CB. try and make up . Figure 182 To Divide a Comma In the accompanying figure you will see a wide comma. you'll get a figure like one of those shown in Fig. How? To Develop a Cube If you cut a cardboard cube along edges so that it could be unfolded and placed with all six squares on a table. You must cut the figure into two identical parts by a single curved line. 184. The figure is also interesting in that two such figures make up a circle. one on the right.178-179 Figure 181 Skilful Cutting and Connecting would be the same. It's constructed very simply: a semicircle is drawn on the straight line AB around point C. 185b). You may cut one of the triangles into two parts but the other four must be used as they are (Fig.Skilful Cutting and Connecting a square from five identical triangles like the ones you have just used (the base is twice as long as the height). Figure 185 . 187). 188.180-181 Answers With Three Straight Lines The problem is solved as follows: Figure 186 Into Four Parts The dash lines show the way in which the ground must be divided (Fig. From the four smaller parts he makes up a smaller inner circle to which he glues the other four parts. Figure 188 . He thus got an excellent board for a round table. Figure 187 To Make a Circle The joiner has cut each of the boards into four parts as shown on the left of Fig. The first and fifth figures can be turned upside down and this will add two more involutes. Figure 189 J ^ T j Z ^ K . Crescent The answer is shown in the accompanying figure. one white and one black. Figure 190 To Divide a Comma The solution is seen in the accompanying drawing. the sum of each of the six sections mast be 78-f-6 = 13. Both parts of the comma are equal. 192. increasing the total to 12. The figure shows how the circle is made of two commas. This facilitates finding the solution that is shown in Fig. as they are made up of equal parts. The resultant six parts are numbered. . Figure 191 To Develop a Cube All the 10 possible solutions are shown in Fig.Answers A Clock Dial As the sum of all the numbers on the face of the dial is 78. 189. 193b. The case of triangles is given in Fig.182-183 Figure 192 Answers To Make Up a Square The solution of the first problem is shown in Fig. 193a. One triangle is first cut up as shown. Figure 193 . 194) with four old oaks growing at its corners. If both diagonals were equal. In his opinion it proved that the rectangle cut was square. A Parquet Maker When cutting wooden squares a parquet maker tested them thus: he compared the lengths of sides and if all four sides were equal he considered the square to be cut correctly. Are you of the same opinion? Yet Another Parquet Maker Yet another worker checked his squares by seeing if all the four sections into which the diagonals divide each other (Fig.Problems with Squares A Pond There is a square pond (Fig. 195) are equal to each other. What do you make of that? . Is this test reliable? Another Parquet Maker Figure 195 Another parquet maker checked his work otherwise: he measured diagonals not the sides. he considered the square to be true. the square shape being retained and the old oaks not destroyed or swamped. It is required to expand the Figure 194 pond so that its surface area be doubled. of course. using two lines. Is it possible. What would you say about this test? Figure 196 A Joiner's Problem A young joiner has the five-sided board shown in Fig. O u r young joiner is just going to do so.184-185 Problems with Squares A Seamstress A seamstress wants to cut out a piece of linen in the form of a square. but he wants to cut the board along no more than two straight lines. Having cut several pieces she checks her work by bending each piece along its diagonal to see if the edges coincide. 196. She bent her piece first along one diagonal and then after smoothing the linen she bent it along the other. each piece is perfectly square. You see that it seems to be composed of a square glued to a triangle that is four times smaller than the square. The joiner is asked to make the board into a square. If they do. involves cutting it into sections. to cut the figure into parts from which the joiner could make a square? And if the answer is "yes" how does he go about it? . This. It was only if the edges of the piece coincided in both cases that she thought the square was correct. taking nothing away from the board and adding nothing to it. Is she right? Another Seamstress Another seamstress wasn't satisfied with the check her companion used. she thinks. Figure 198 gives examples of quadrilaterals whose sides are equal but whose angles are not right (rhombs). just draw in the diagonals of the earlier pond and count the resultant triangles. You can easily see that the new area is twice the earlier. 199. Figure 198 Another Parquet Maker This test is as unreliable as the first one. . Figure 199 The parquet makers should apply both tests to each quadrilateral produced.n Figure 197 Answers A Pond It is possible to double the surface area of the pond with the square shape retained and the oaks intact. Some quadrilaterals that are by no means squares will pass. The accompanying figure shows how this can be done. One could then be sure that the work has been done correctly. A Parquet Maker The test is not sufficient. To be sure. It is clearly seen from the examples in Fig. a square's diagonals are equal but not every quadrilateral with equal diagonals is a square. Any rhomb with equal diagonals is bound to be a square. You could cut any number of quadrilaterals out of paper that would pass this test. Figure 200 A Seamstress The test is far from adequate. as is seen in Fig. from the last point to vertex a. Another Seamstress This test is no better than the previous one. 200.186-187 Answers Yet Another Parquet Maker The test might only show that the quadrilateral in question has right angles. You see how far Figure 201 a quadrilateral may differ from a square and still satisfy this test. e. i. that it is a rectangle. Figure 201 presents several quadrilaterals whose edges coincide when bent along the diagonals. the other. c Figure 203 . the seamstress should additionally check if the diagonals (or angles) were equal. no more. 202 all have equal sides (these are rhombs) but the Figure 202 angles are not right-hence these are not squares. yet they are not squares. A Joiner's Problem One line should go from the vertex c to the middle of side de. The test only shows that the figure is symmetrical. The examples in Fig. A square can be made up from the three pieces 1. 2. But it fails to verify that all its sides are equal. although they are by no means squares. In order to make really sure that the pieces cut out are squares. and 3 as shown in Figure 203. The total number of wheels on the vehicles was 100. links. the other two. If the job . The second worked 25 minutes longer than the first. One completed three pieces a minute. fewer A shop repaired 40 vehicles (cars and motocycles) in a month. but the joiner got 3 roubles more than the average earnings of all the seven team members. How much did the joiner earn? Five Pieces of Chain Figure 204 A blacksmith was given five pieces of chain with links in each (Fig.Problems on Manual Work Navvies Five navvies excavate a 5-metre ditch in 5 hours. 204) and asked to connect The blacksmith opened and reclosed four But is it not possible to do the same job with links tampered with? How Many Vehicles? three them.5 minutes. how long will it take to cut the log? Joiner and Carpenters A team of six carpenters and a joiner did a job. How long did each work? Two Workers Two workers can perform a job in seven days provided the second starts two days later than the first. Each carpenter earned 20 roubles. If each cut takes 1. How many cars and motocycles were repaired? Potato Peeling Two people peeled 400 potatoes. How many navvies are required to dig 100 metres of ditch in 100 hours? Lumberjacks A lumberjack cuts a 5-metre log into 1-metre lengths. 188-189 Problems on Manual Work were done by each of them separately. 115 kg. 112 kg. 113 kg. But the bags weighed 50-60 kilogrammes each. Thus in our problem they would find the share of the work done by each typist. How much did each bag weigh? . 117 kg. How long will it take them to do the job if they divide it so as to spend the least time possible? Problems of this kind are normally solved according to the procedure of the famous problem on reservoirs. Typing a Report Two typists type a report. add up the fractions and divide unity by the resultant sum. Of the five bags it is possible to make 10 different pairs. 121kg. so he had to make 10 weighings. Could you think of some other procedure? Weighing Flour A salesman has to weigh five bags of flour. the other in 3 hours. His problem was that the shop had a balance but some weights were missing so that it was impossible to weigh from 50 to 100 kilogrammes. then the first would take four days more than the second. 116 kg. The more experienced one could finish the work in 2 hours. 118 kg. How many days would each of them take to perform the job individually? The problem permits of a purely arithmetic solution without any need to manipulate fractions. 114 kg. The man began to weigh the bags in pairs. 120 kg. He produced the series of numbers given below in the ascending order: 110 kg. we should add 50 koppecks * to the 20 roubles earned by each carpenter to arrive at the average earnings of each of the seven workers. We'll thus obtain that the joiner earned 20 roubles 50 kopecks plus 3 roubles. Replacing a single motocycle by a car increases the total number of wheels by two and the difference decreases by two. then by dividing 350 by 5 we find that each would have worked for 70 minutes. i. How Many Vehicles? If all the 40 vehicles were motocycles.e. i. there were 10 cars and 30 motocycles. In fact.5 x 4 = 6 minutes. 10 such replacements are required for the difference to be reduced to zero. then it would take 100 people to dig 100 metres in 100 hours. So. * 1 rouble = 100 kopecks. and this will take 1.5 x 5. i. . 7. Lumberjacks The common answer would be 1. Joiner and Carpenters We can easily find the average earnings of a member of the team by dividing the extra 3 roubles between the six carpenters. five navvies dig 5 metres in 5 hours.5 minutes. not five. Accordingly. the total number of wheels would be 80. Potato Peeling During the 25 extra minutes the second peeler put out 2 x 25 = 50 pieces. e. Thus.e. so they can do 1 metre in 1 hour. no more. Five Pieces of Chain It's only necessary to open the three links of one of the pieces and to use the links obtained to connect the other four pieces. since the same five navvies would be required.Answers vJ' Navvies It's easy to swallow the bait and think that if five navvies dug 5 metres of the ditch in 5 hours. it's only necessary to cut the log four times. 23 roubles 50 kopecks. As their production per minute was 2 + 3 = 5 pieces. We subtract 50 from 400 to find that if the two had worked an equal time they would have yielded 350 potatoes. and in 100 hours-100 metres. by 20 less than in reality. In fact: 1 0 x 4 + 3 0 x 2 = 100. But that argument is absolutely wrong. That is because many people often forget that the last cut will give two 1-metre lengths. Clearly. 116 kg. 115 kg. Thus.5 times larger than that of the other if both are to stop simultaneously. e. The last quantity (121) is the sum of the two heaviest bags. As the more experienced typist types 1. i. No. 2. the salesman summed up the 10 numbers. it is then obvious that during the seven-day period the first worker performs half the job. If we divide . No. without any time wasted. 120 kg. 1 and No. 5. 4 and No. Thus. and the penultimate. of No. No. of No. the first worker would be able to do the whole job himself in 14 days and the second in 10 days. First. No. 112 kg. the second quantity. 1 1 3 4 and and and and No.. how should they divide it? (Clearly.156 kilogrammes) is nothing but the fourfold weight of the bags: the weight of each bag enters the sum four times. 118 kg. No. No. 5. 1 and No. It only remains to find the time taken by the first typist to do her share of the job. hence the three fifths of the job will be carried out in 2 x 3/5 = 11/5 hours. As a matter of fact the problem is nearly solved. It will be seen that in the series of quantities: 110 kg. Weighing Flour To begin with. We know she can do the whole job in 2 hours. The resultant sum (1. Thus: No. In fact: 3 x 70 + 2 x 95 = 400. 1. etc. the second one worked for 70 + 25 = 95 minutes. No.by four. As in our case the difference is just two days when the two work together. whereas the second does his half in five days. and accordingly the second two fifths. the first quantity is the sum of the weights of the two lightest bags. 2. 5. the shortest time required for both typists to type the report is 1 hour and 12 minutes. 113 kg. Typing a Report A nonstereotyped approach is as follows. the first would need two days more than the second (because the difference in duration for the whole job is four days). 117 kg. 2 give 110 kg 3 » 112 kg 5 » 120 kg 5 » 121 kg . 3. We'll now for convenience assign numbers to the bags in ascending order of their weights. we'll ask the question: if the typists are to finish the work simultaneously. 114 kg. and 121 kg. Two Workers If each worker performs half the job individually. 3 and No. it's only under this condition. the second No. that the work will be done in the shortest time possible). we'll find that the total weight of the five bags is 289 kilogrammes.5 times faster it's obvious that her share should be 1. It follows that the first typist should take over three fifths of the report. No. The lightest bag will be No. and the heaviest. No. During exactly this time the second typist will finish her share of the job.190-187 This is the actual duration of work of the first peeler. The weight of No. We have solved the problem without any resort to equations. The weights of the bags are thus 54 kg.58 = 62 kg. 3 (58 kg) to get the weight of No. knowing the sum of No. namely-58 kg. Further. 58 kg. from the sum of No. i. and No. 3 to arrive at the weight of No. 2 by subtracting 54 kg from 110 kg. 1. 5) we subtract the weight of No. . No. 5 (121 kg). 2 will thus be 110 — . we subtract the now-known weight of No. It remains to determine the weight of No. 59 kg.e. from the sum of No. 3. 1 and No. 1 and No.e. from 112 kg. Subtracting this number from the total weight of the bags (289 kg) gives the weight of No. 62 kg. 2. 4 weighs 59 kg. No. Now from 120 kg (No. Subtracting 62 from 121 gives that No. i. 1: 112 — 58 = 54 kg. 56 kg. 3. 3 + No. 4.Answers We can thus easily find the sum of the weights of No. 2. 4 and No. 5: 110 kg + 121 kg = 231 kg. 5: 120 . In exactly the same way we find the weight of No.54 = 56 kg. 4. How much does a dozen lemons cost? Raincoat. When back home I had as many 1 rouble pieces as there had been 20 kopeck coins initially. Purchases When I went out shopping I had in my purse 15 roubles in 1 rouble pieces and 20 kopeck coins. 175 . The numbers in Fig. When was the price lower. The raincoat costs 90 roubles more than the hat. and plums. and the hat and the raincoat together cost 120 roubles more than the overshoes. and as many 20 kopeck coins as I had had 1 rouble pieces initially. The prices are: water-melons. Two customers bought five of the six barrels. 10 kopecks a piece. apples. 205 show the numbers of litres in each barrel. Hat and Overshoes A raincoat.192-193 Problems on Purchases and Prices How Much are the Lemons? Three dozen lemons cost as many roubles as one can have lemons for 16 roubles. my purse only containing a third of the initial sum How much had I spent? Buying Fruit One hundred pieces of various fruit can be bought for five roubles. How many fruit of each kind are bought? Prices Up and Down The price of a product first went up 10%. initially or finally? Barrels Six barrels of beer were shipped to a shop. 50 kopecks a piece. no equations. How much does each thing cost separately? Use mental arithmetic only. and then down 10%. 10 kopecks a ten. hat and overshoes are bought for 140 roubles. A third only bought one egg. "An egg seller sent her three daughters to the market with ninety eggs.Problems on Purchases and Prices Figure 205 one bought two and the other bought three. the year it was compiled. The collection wasn't printed and remained in a manuscript form to be found only in 1924. Given that the second bought twice as much beer as the first. it's quite solvable. A second buyer bought half the remaining eggs plus another 1/2 of an egg. this ancient problem might seem incongruous as it involves selling half an egg. A first buyer took half her eggs plus 1/2 of an egg. Nevertheless. A peasant woman came to a market to sell some eggs. namely 1869 (the manuscript wasn't dated). She gave ten to the eldest and . which was the last. How many eggs were there initially? Benediktov's Problem Many experts in Russian literature don't suspect that the poet V. Benediktov (1807-1873) was also the author of the first collection of mathematical brain-twisters in the language. based on one of the problems. which barrel wasn't sold? Selling Eggs At first sight. I had the opportunity to get acquainted with the manuscript and even established. The problem given below has been treated by the poet and named "An Ingeneous Solution of a Difficult Problem". G. Furthermore. . All of you should adhere to this price but I hope that the eldest daughter who is so bright will nevertheless be able to get as much for her ten eggs as the second daughter will receive for her thirty and she will teach the second sister how to get as much for her thirty as the youngest sister will get for her fifty eggs. and no less than 90 kopecks for the ninety!'" Here I interrupt Benediktov's story so that the readers could figure it out for themselves how the girls went about their business.194-187 Problems on Purchases and Prices cleverest daughter. I'd like you to sell the eggs so that on average you will receive no less than 10 kopecks for ten. thirty to the second. and fifty to the third. saying: 'You should agree beforehand on the price at which you'll sell the eggs and stick to it. Let the takings and prices be the same for the three of you. Answers 1Q ^ How Much are the Lemons? We know that the 36 lemons cost as many roubles as they sell lemons for 16 roubles. Raincoat. For 16 roubles one can have 16/(price of one lemon). one lemon costs 4/6 = 2/3 rouble and a dozen lemons cost 2/3 x 12 = 8 roubles. Now we find that the raincoat and the hat together cost 140 — 10 = 130 roubles. Hence one hat costs 20 roubles. Purchases Denote the initial number of 1 rouble pieces by x. i. but 120 roubles less. hat. Back from my shopping expedition I had (lOOy + 20x) kopecks. We argue as earlier: instead of the raincoat and hat we could buy two hats. Then when I went out shopping I had in my purse (lOOx + 20y) kopecks. Thus. and we would pay not 130 roubles but 90 roubles less. hence Rearranging the expression gives . Hence. After some algebra we have (price of one lemon) x (price of one lemon) = 16/36. and overshoes only two pairs of overshoes were bought. the h a t . the prices of the things were as follows: the overshoes-10 roubles. 36 x (price of one lemon) = 16/(price of one lemon).2 0 roubles. and the number of 20 kopeck coins by y. Under this assumption I initially had 7 roubles 20 kopecks the former. x = ly. Clearly. But 36 lemons cost 36 x (price of one lemon). 130 — 90 = 40 roubles. the price would be not 140 roubles. the raincoat costing 90 roubles more than the hat. Hat and Overshoes If instead of the raincoat. As stated. If y = 1. e. the latter sum is three times smaller than 3 (100y + 20x) = lOOx 4. then x = 7. and the raincoat-110 roubles.20y. Thus. hence one pair cost 10 roubles. the two pairs of overshoes cost 140— 120 = 20 roubles. When I returned back from my shopping excursion I only had two 1 rouble pieces and fourteen 20 kopeck coin. my purchases had cost 9 roubles 60 kopecks. After the second buyer bought half the remaining eggs plus 1/2 of an egg.99. Selling Eggs The problem is worked out backwards from the end. 15 + 18 = 33 1 6 + 19 + 31 = 66. i. 1 1/2 eggs was half of what remained after the first . The assumption of y = 3 leads to an overestimation: 21 roubles 60 kopecks. The 20 litre barrel remained unsold. Barrels The first customer bought the 15 litre and 18 litre barrels and the second -the 16 litre. This is the only possible solution as no other combination gives the relationship required. the second customer bought twice as much beer as the first one. this gives x = 14. Really.440 — 480 = 960 kopecks. i. 200 + 280 = 480 kopecks. After the price went up the article cost 110%.e. or 1.1 of the initial price. 99% of the initial price.1 x 0. there was only one egg that remained with the peasant woman. e. Consequently. the only fitting answer is 14 roubles 40 kopecks. the final price was 1% lower than the initial one. As I spent 1. But after the price went down it amounted to 1. which actually amounts to a third of the initial sum (1. e. Let's try y = 2.196-187 Answers which is at variance with the statement of the problem ("about 15 roubles").9 = 0. 19 litre and 31 litre barrels.440/3 = 480). It's easily shown that this is not the case. The initial sum is thus 14 roubles 40 kopecks which checks well with the problem statement. Buying Fruit Despite the seeming uncertainty the problem has the only solution: Water melons Apples Plums Total Number 1 39 60 100 Cost 50 kopecks 3 roubles 90 kopecks 60 kopecks 5 roubles 00 kopecks Prices Up and Down It would be erroneous to consider that the two prices are equal. Accordingly. i. In consequence. The youngest sister got 9 kopecks for her single egg and when she added the money to the 21 kopecks for her 7 sevens her total was 30 kopecks.4 = 3 3/2 = 1 1/2. the second sister said. "The last six eggs were sold for nine kopecks each. 'And what will we charge for the remaining eggs?5 the youngest sister asked. the two younger sisters seeking advice of the eldest. the woman had brought seven eggs for sale. We add 1/2 of an egg to obtain half of what the woman had initially. 'the first eggs will have been sold cheaply by the seven. She received 21 kopecks for 7 sevens and one egg remained in her basket. 'What of i t ? the eldest said. Cash down! Those who need eggs badly will pay'. 'we'll raise the price for those eggs that'll remain after we have sold the full sevens. 'Rather dear. the first to go were the fifty eggs of the youngest sister. agreed? 'Dirt-cheap'. The second one sold 4 sevens for 12 kopecks and two eggs remained in her basket. too. One will compensate for the other!' "Understandably.Answers 10 © sale and so the full number is three eggs. So the eldest got 27 kopecks for her three eggs which brought her takings to 30 kopecks. The latter gave some thought to the matter and said: 'Sisters. the eldest sister continued. I've checked beforehand that there'll be no other egg sellers in the market. 1 1/2 + 1/2 = 2. The second sister got 18 kopecks for her last pair of eggs which when added to the 12 kopecks received earlier for her 4 sevens. 3 . we'll sell the eggs not by the ten. And we'll set a price for the seven we'll stick to as Mother said. The eldest sister sold a seven for 3 kopecks and three eggs remained in her basket. 3 1/2 + 1/2 = 4. gave her 30 kopecks as well. The sisters put their heads together on their way to the market. which complies with the conditions of the problem. 'But'. But when there is demand and the supply is dwindling the price rises. "Thus. So we'll make up for our loss with the remaining eggs'. No one to beat down the price.' the second sister noted again. but by the seven." . Benediktov's Problem We continue the interrupted story: "The problem was a very difficult one. Let's check: 7/2 = 3 1/2. as is the custom here. 7 . 'Nine kopecks for each egg. the money they got for ten appeared to be equal to the money they got for fifty. Thus.2 = 1. Not a kopeck down from the set price! The first seven goes for three kopecks. Will the pans be in equilibrium? A Decimal Balance A decimal balance weighs 100 kilogrammes of iron nails that are balanced by iron weights. onto the other 3/4 of a same sized piece plus 3/4 kilogramme. will the balance be in equilibrium? Figure 206 A Piece of Soap Onto one pan of a balance a piece of soap was put. When submerged. What is the weight of a whole piece? Try and solve the problem mentally. How much would it weigh if it were twice as thick. Cats and Kittens The accompanying figure shows that the four cats and three kittens together weigh 15 kilogrammes and that . without a pencil and paper. Honey and Kerosene A jar of honey weighs 500 grammes. I carefully immerse the balance in water. What is the weight of the empty jar? A Log A round log weighs 30 kilogrammes. The same jar filled with kerosene weighs 350 grammes.198-199 Weight and Weighing One Million Times the Same Product A product weighs 89. The balance is in equilibrium. an iron weight of 2 kilogrammes.4 grammes. but twice as short? Under Water Consider a balance on the one pan of which there is a boulder that weighs exactly 2 kilogrammes and on the other. Honey is twice as heavy as kerosene. Figure out how many tonnes a million of them weigh. too. however. but six peaches and one apple weigh as much as one pear. and two jugs are balanced by three saucers. 210 that a bottle and a glass are balanced by a jug. There is. How much does one cat weigh? And a kitten? This problem. the bottle is balanced by a glass and a saucer. How many beads should be placed on the vacant pan for the shell on the other pan to be balanced? Fruit A further problem of the same kind. All the cats have the same weight. so do the kittens. 209 that three apples and one pear weigh as much as 10 peaches. Shell and Beads Figure 208 shows that three children's blocks and one shell are balanced by 12 beads and further that one shell is balanced by one block and eight beads.Weight and Weighing Figure 207 Figure 208 three cats and four kittens weigh 13 kilogrammes. How many peaches are required to balance one pear? How Many Glasses? Figure 209 You see in Fig. It is seen in Fig. should be solved mentally. only one . How many glasses should be placed on the vacant pan for the bottle to be balanced? With a Weight and a Hammer It's required to weigh out 2 kilogrammes of sugar into 200-gramme packets. How should one go about it using the weight and the hammer? Archimedes's Problem The most ancient of brain-twisters pertaining to weighing is undoubtedly the one the tyrant of Syracuse Hieron gave to the famous mathematician Archimedes. If you want to try your hand at the problem suppose that the craftsman was given 8 kilogrammes of gold and 2 kilogrammes of silver and when Archimedes weighed the crown under water the result was 9 1/4 kilogrammes. not 10 kilogrammes. Hieron called in Archimedes and asked him to determine how much gold and silver respectively the. The legend has it that Hieron entrusted a craftsman to manufacture a crown for a statue and ordered to give him the required amount of gold and silver. Archimedes solved the problem proceeding from the fact that in water pure gold loses one twentieth of its weight. the crown weighed as much as the initial amounts of gold and silver had originally weighed together. but the craftsman was alleged to have stolen some of the gold having replaced it by silver. Given that the crown was made of solid metal.200-201 Figure 210 Weight and Weighing Figure 211 500-gramme weight and hammer that weighs 900 grammes. how much gold had the craftsman stolen? . crown contained. When it was ready. and silver one tenth. without any voids. i. by one thousand thousands. and length decreased twice. the honey is two times heavier than the same amount of kerosene. an iron object loses one eighth of its weight. however.4 tonnes.150 = 200 grammes. * The figure wasn't given in the statement of the problem as the exact share of the weight lost is immaterial here.200 = 300 grammes. because the tonne is 1. The weight will thus outweigh the boulder under water.000 = 89. should be the same weight. Under Water Each immersed body becomes lighter by the weight of the water displaced by it.4 kilogrammes because the kilogramme is 1. the equilibrium will not be disturbed. A Log A common answer is that a log. but halving its length halves its volume. the boulder will displace a larger volume of water than the weight and. 89. i. will help us to answer the problem. The weight we seek is thus 89. The net result is that the final log is twice as heavy as the initial one. The 2-kg boulder has a larger volume than the 2-kg iron weight because the material of the boulder (granite) is lighter than iron.e.000 times larger than the kilogramme. whose thickness has increased twice. Honey and Kerosene Since honey is twice as heavy as kerosene.e. Really: 500 . i. Since the weights were 10 times lighter than the nails before immersion and they continue to be 10 times lighter after immersion. according to Archimedes's principle.000 times larger than the gramme. the difference in weight (500 — 3 5 0 = 150 grammes) is the weight of the kerosene in the volume of the jar (the jar of honey weighs as much as a jar containing a double aijiount of kerosene). Accordingly. discovered by Archimedes. We must multiply 89. We can do the multiplication in two steps: 89.000 = 89.4 kilogrammes x x 1. Hence we determine the weight of the jar: 3 5 0 . Decimal Balance When immersed in water. loses more than the weight.4 grammes by one million. it weighs 60 kilogrammes. Then. e.* Thus both the nails and the weights will when immersed have only 7/8 of their former weight.4 x 1. This is not so. This law. .Answers One Million Times the Same Product The mental arithmetic here is as follows. Doubling the diameter increases the volume of a round log fourfold.4 tonnes. Removing the six peaches from each pan gives that the four apples weigh as much as four peaches. i. But a whole piece is 3/4 plus 1/4. With this in mind we in the first weighing replace all the four cats by kittens to obtain 4 + 3 = 7 kittens that will together weigh not 15 kilogrammes but 2 x 4 = 8 kilogrammes less. You'll thus obtain 3 + 9 = 12. replace the cubes and shell on the left pan by an appropriate number of beads. We thus find that two bottles and two glasses are balanced by three saucers. We can now work out the weight of the shell: replacing (second weighing) the cube on the right pan by a bead gives that the weight of the shell is equal to that of nine beads. Cats and Kittens A comparison of both weighings shows that replacing a cat by a kitten reduces the weight by 2 kilogrammes. Hence a kitten weighs 1 kilogramme. Hence one bottle is balanced (compare with the second weighing) by five glasses. If we now remove eight beads from each pan. One cube thus weighs the same as one bead. . The following is just one of them. How Many Glasses? The problem has several different solutions. The result can be checked easily.202-203 Answers A Piece of Soap Three quarters of a piece of soap plus 3/4 kilogrammes weigh as much as the whole piece. Fruit In the first weighing we replace one pear by six peaches and an apple. Now it's easy to figure out that a pear weighs the same as seven peaches. Removing two saucers from each pan shows that four glasses are balanced by one saucer. as required. the seven kittens weigh 15 — 8 = 7 kilogrammes. We then obtain four apples and six peaches on the left pan and 10 peaches on the right. In the first weighing. Accordingly one peach weighs the same as one apple. 3 kilogrammes. hence 1/4 of a piece weighs 3/4 kilogrammes and the whole piece weighs four times as much as 3/4 kilogrammes. Shell and Beads Compare the first and second weighings. We may do so because the pear weighs as much as the six peaches and apple. It follows that a cat is 2 kilogrammes heavier than a kitten. We'll then have four cubes and eight beads on the left pan balanced by 12 beads. we won't upset the balance. It thus appears that four glasses and two saucers are balanced by three saucers. and a cat weighs 1 + 2 = 3 kilogrammes. Consequently.e. In the third weighing we replace each jug by a bottle and a glass (we know from the first weighing that the balance should remain in equilibrium). and four beads on the right. There'll four cubes now remain on the left pan. You'll see that in the first weighing the shell can be replaced by one cube and eight beads. 1/2 kilogramme. It's clear that the sugar weighs 900 — 500 = 400 grammes. The operation is performed three more times. This was because it contained silver-a metal that in water loses 1/10 part of its weight. Thus. i. it would have weighed 10 kilogrammes in air losing when immersed 1/20 part of its weight.9 1/4 = 3/4 kilogramme. . So. the crown contained 5 kilogrammes of silver and 5 kilogrammes of gold instead of the 2 kilogrammes of silver and the 8 kilogrammes of gold the craftsman was given. rather than 1/2 kilogramme. It's a straightforward exercise: the contents of a 400-gramme packet are divided between two packets put on different pans until the balance balances. not 1/2 kilogramme. Suppose in the purely golden crown one kilogramme of gold were replaced by silver. First put the hammer on one pan and the weight on the other. 1 /4 kilogramme more. the crown would when immersed lose another 1/10-1/20 = 1/20 kilogramme. The crown thus contained an amount of silver sufficient for it to lose in water 3/4 kilogramme. But we know that in fact the crown lost in water 1 0 . Then add just enough sugar for the pans to be in equilibrium. Archimedes's Problem If the crown ordered had been made purely of gold. e. in order to decrease the crown's weight by 1/4 kilogramme it was necessary to replace with silver as many kilogrammes of gold as there were 1/20ths in 1/4: 1/4 -4 -1/20 = 5. It is only remains now to halve each of the five 400-gramme packets obtained. The remaining sugar weighs 2.000 — (4 x 400) = 400 grammes. 3 kilogrammes of gold had been stolen and replaced by silver.e.9 Answers *** With a Weight and a Hammer The procedure to be followed is like this. not 1/20 part. i. Consequently. At what time yesterday did I set the clocks? What Time Is It? Figure 212 "Where are you hurrying to?" "To catch the 6 o'clock train." What does this strange answer mean? What time was it? When Do the Hands Meet? Figure 213 At 12 o'clock one hand is above the other But you may have noticed that it is not the only moment when the hands meet: they do so several times a day. the alarm clock gains 1 minute an hour. the second was a minute slow a day. and the third was gaining a minute a day.204-205 72 Problems on Clocks and Watches Three Clocks In my home there are three clocks. On the 1st of January they all showed true time. how long would it take for them all to show true time again? Two Clocks Yesterday I checked my wall clock and alarm clock and set them correctly. Today both clocks stopped simultaneously since they had run down. Should the clocks continue like this. But only the first clock kept perfect time. at 6 o'clock both hands point in opposite directions. How long have I got left?" "50 minutes ago there were four times more minutes after three. But is it only at 6 o'clock that this is the case or there are some other such moments during the next 12 hours? . The wall clock is 2 minutes slow an hour. Can you say when all those moments are? When are the Hands Pointing in Opposite Directions? By contrast. The wall clock shows 7 o'clock and the alarm clock 8 o'clock. make a small experiment. i. move a few steps aside and listen to the ticking. in intervals: ticks for a while. you may have noticed the reverse arrangement of the hands as compared with that just described: viz. it's not a trick question. Put your watch on a table.Problems on Clocks and Watches On Either Side of Six Figure 214 O'Clock I glanced at a clock and noticed that both hands were equally separated from 6. What time was it? The Minute Hand Ahead of the Hour Hand When is the minute hand as far ahead of the hour hand as the hour hand in turn is ahead of the figure 12 on the face? And maybe there are several such moments during the day or none at all? Vice Versa If you observe a clock attentively. then is silent several seconds. e. just in case. When does this happen? Three and Seven A clock strikes three. as it were. How long does it take the clock to strike seven? I warn you. Explain! . that this isn't a joke. you'll hear that your watch sounds. and then starts ticking again. And while it does so 3 seconds elapse. and so on. If it's sufficiently quiet in the room. the hour hand is as far ahead of the minute one as the minute hand is ahead of the figure 12. Ticking Lastly. which is four times longer than the time to go to 6 o'clock. at 11. i. 1/12 part of the circle behind the hour hand.e. and the hour hand 1/12 part of the circle.e. meet during the next hour. the minute hand would have travelled 11/12 part of the circle more. You may have already guessed that. The next meeting occurs another 1 hour 5 5/11 minutes later.e. i. i.e. What Time Is It? Between 3 and 6 o'clock there are 180 minutes. and the third clock will have gained exactly the same time. and so forth. Thus.e. The hands will thus meet 5 5/11 minutes after the first hour has elapsed. 50 minutes before it was 26 + 50 = 76 minutes to go to 6 o'clock. in 60/11 = 5 5/11 minutes. The 11th comes 1 1/11 x 11 = 12 . But after the hour has passed and the hour hand come to the 1 o'clock mark (having completed 1/12th of the full circle). Accordingly. the hands will meet in 1/11 hour. the hands cannot.e.e.206-207 Answers Three Clocks 720 days. and the minute one 1 hour). If the race lasted an hour. When Do the Hands Meet? We start our observation at 12 o'clock. Since the hour hand moves 12 times slower than the minute one (it takes 12 hours to make a complete circle.40. In fact. This requires a period of time that is the same fraction of an hour as 1 /12th is a fraction of 11/12 i. The condition of the race is now different since the hour hand moves slower than the minute one. i. at 10 10/11 minutes past 2 o'clock. every 20 hours. there'll be 11 such meetings. i. at 5 5/11 minutes past one. 60 minutes.e. It was thus 26 minutes to 6 o'clock. This implies that both clocks were set correctly 19 hours 20 minutes before. Thus it gains an hour. i. the minute hand would have gone round a complete circle. i.e. but is ahead of the minute hand which has to overtake it. What about the next meeting? You should be able to see that it'll occur 1 hour 5 5/11 minutes later. of course. Then all the three clocks will show as they did on the 1st of January.e. During this time the second clock will lose 720 minutes. the minute hand has made a complete turn and is again at 12. But during these 20 hours the alarm clock gains 20 minutes compared with true time. true time. But to overtake the hour hand. when both hands meet. all in all. 180 — 76 = 104 minutes had passed since 3 o'clock. Hence. i. Two Clocks The alarm clock is gaining 3 minutes an hour compared with the wall clock. The number of minutes to go to 6 o'clock is easily found by dividing 180 — 50 = 130 minutes into two parts. one of which being four times larger than the other. one eleventh.e. exactly 12 hours. the minute hand must only cover 1/12 of the circle which is the distance separating them. i. at 16 4/11 minutes past 3 o'clock. we'll have to find 1/5 part of 130. i. Hence 1 = 13x and x = 1/13 part of a circle. or 32 8/11 minutes. We'll again begin at 12 o'clock when both hands meet. i. Is this the only moment when we have such an arrangement? Of course. We already know (see the previous problem) that during an hour the minute hand gets ahead of the hour hand by 11/12 part of the circle. it coincides with the first meeting. and so on. 6/11 part of an hour.5 5/11 minutes past 1 o'clock 2nd-10 10/11 minutes past 2 o'clock 3 r d l 6 4/11 minutes past 3 o'clock 4th-21 9/11 minutes past 4 o'clock 5th-27 3/11 minutes past 5 o'clock 6th—32 8/11 minutes past 6 o'clock 7th 38 2/11 minutes past 7 o'clock 8th—43 7/11 minutes past 8 o'clock 9th^49 1/11 minutes past 9 o'clock 10th-54 6/11 minutes past 10 o'clock 11th12 o'clock When Are the Hands Pointing in Opposite Directions? The approach here is very much like that in the previous problem. If the time that has passed is less than one hour. We already know that during a 12 hour's time there are 11 such meetings. The hour hand covers this fraction of .9 Answers hours after the first one. at 12 o'clock.12x = x. with future meetings occurring at the previous times. For it to get ahead by only 1/2 a circle takes less than an hour by so rtiany times as 1/2 is less than 11/12.e. then to meet the conditions of our problem the minute hand must travel a full circle less the angle covered by the hour hand since 12. Imagine that both hands are at 12 and that the hour hand has shifted by a certain part of a circle to be denoted by x. after 12 o'clock the first time the hands point in opposite directions is in 6/11 hours. On Either Side of Six 0'Clock The problem is solved like the previous one. In other words. The hands are so arranged 32 8/11 minutes after each meeting. These moments are easily found: 12 o'clock + 32 8/11 minutes = 32 8/11 minutes past 12 o'clock 1 o'clock 5 5/11 minutes + 32 8/11 minutes = 38 2/11 minutes past 1 o'clock 2 o'clock 10 10/11 minutes + 32 8/11 minutes = 43 7/11 minutes past 2 o'clock 3 o'clock 16 4/11 minutes + 32 8/11 minutes = 49 1/11 minutes past 3 o'clock.e. Hence the hands point opposite ways 11 times every 12 hours. 1 . Look at a watch at this time and you'll see that the hands are really pointing in opposite directions. i. not. it is then that the hands are pointing in opposite directions. We want to find the time required for the minute hand to get ahead of the hour hand by exactly half a circle. In other words. Let's list the times of all the meetings: 1st . Accordingly. I leave it for you to find the remaining moments. Meanwhile the minute hand has turned by 12x. Why? Because the hour hand covers 1/12 part of what the minute hand does.x. But suppose an hour has elapsed and the minute hand is at 12 and the hour hand at 1. whence it follows that a complete turn equals lOx (because 12x — lOx = 2x). and hence lags behind the minute hand far more than is required for the arrangement we seek. To find the next time we'd have to wait till 2 o'clock and now the minute hand is at 12 and the hour hand at 2.e.e. i.12 7. We'll try to find the other solutions. too. The minute hand will then be two times farther away from 12. Reasoning along the same lines as before we arrive at 12x — 2 = 2x. You'll find that the hands arrange themselves in the right way at the following 10 instants in time: 1. I leave it to you to work out further moments. AH told.12 2. 12x. the difference 12x — 1 must be twice as large as x. The hands will meet our requirement next time when the hour hand has shifted 3/13 of a circle away from 12. namely one that comes about in the first hour.e. Hence 2 = 13x and x = 2/13 of a circle. But there are other ones and during a period of 12 hours the hands come to be arranged in the right way several times. 1/12 part of a complete turn ahead of the minute hand. then lx = 1/10 part of a turn. We've thus arrived at the solution: the hour hand must have moved by 1/10 part of a turn past 12 o'clock. Meanwhile the minute hand has covered 12 times more. then during the first hour we won't see the position desired. and so on. Thus 12x . If now we subtract from this a complete turn. Let's see if such an arrangement of the hands may come about during the second hour. So the hands will be in the right position at (1 11/13) x 60 minutes or at 50 10/13 minutes past 1 o'clock. when it is (12/13) x 60 minutes or 55 5/13 minutes past 12 o'clock. as required. from the relation 1 — (12x — 1) = x or 2 — 12x . there are 11 such positions. at 1/5 of a turn away.208-209 a circle in 12/13 part of an hour. the hands changing sides after 6 o'clock. Suppose that the moment has come when the hour hand has turned by a fraction of a circle that we'll denote by x. e. During the same period of time. i. You see that both hands are equally separated from 12. i. i. not a half as is desired. During the second hour this occurs once more and you can find it arguing along the same lines as before. We've found one solution to the problem. the hour hand will only be at 1/12 part of that angle. and hence equally separated from 6. i. e. at 2 10/13 o'clock. We've found one location of the hands.1 = 2x. which corresponds to 60/5 = 12 minutes.e. and hence x = 1/5 part of a complete turn. But if lOx equals a complete turn. The Minute Hand Ahead of the Hour Hand If we start looking at a clock at 12 o'clock exactly. This takes 12/10 hours or 1 hour 12 minutes. the minute hand covers 12 times more.24 14 .24 8. 12/13 part of a circle.e. This corresponds to the moment 12/5 = 2 hours 24 minutes. whence two complete turns are equal to lOx. i.<>75 . 2x. i. Whichever the angle through which the minute hand turns about 12. Then another fatigue period comes on. But when the clock strikes seven.e. The hands will be arranged in the required manner for the second time at a time which can be found from the relation 12x — 2 = x/2. meets the restrictions of our problem.00" and "12. Therefore 1 = 11 1/2 x. the time we seek is 5 5/23 minutes past 2 o'clock. i.e. at 12.00" might appear wrong. and so forth.00 10. (2/23) x 12 hours or 1 1/23 hours after 12 o'clock. if you wish. this problem is an easy exercise. This aural fatigue passes off after a short while and previous ability to perceive the sound returns with the result that you again hear the ticking. there are six such gaps. or x = 2/23 of a turn. Using the same arguments as above we can determine that for the first time the required arrangement will occur at the time given by 12x — 1 = x/2. which is exactly 1/23 part of a turn (the hour hand will be at 2/23 part of a turn). exactly twice as far. that is wrong. Vice Versa After the treatment we have just given.9 Answers 4. Three and Seven The commonest answer is "7 seconds". So. When the clock strikes three we have two gaps: (1) between the first and second strokes. In fact. The third moment is 7 19/23 minutes past 3 o'clock. and so forth. at 12/23 hours mark. It follows that 2 = 11 1/2 x and x = 4/23. e. Ticking The enigmatic interruptions in the ticking are only due to fatigue in your ears. Hence at 2 14/23 minutes past 1 o'clock the hands will be arranged correctly.00 The answers "6. as we'll now see. i. The minute hand will then be midway between 12 o'clock mark and 1 1/23 hours mark.48 6. .48 12. At 12 o'clock the hour hand is separated from 12 by "zero" and the minute one. but only at first sight. by "double zero" (because double zero is just zero). (2) between the second and third strokes. Each gap thus lasts 1 1 / 2 seconds. at 6 o'clock the hour hand is at 6 and the minute one. i. this case. which gives 9 seconds. too. But. From time to time your perception of sound becomes blunted for a second or two so that in these intervals you won't hear the ticking. which makes the coupling become slack. The second reached its destination 2 hours 15 minutes after the same event. in which case the buffers do not press against each other and so the rear locomotive cannot be pushing. one at the front and the other at the back. the buffers press hard against each other. But have you ever given any thought as to what happens to the couplings between the carriages and to their buffers? The front locomotive only pulls the carriages when the coupling is taut. How could you explain it? Two Locomotives You may have seen a train driven by two locomotives. could you work it out from the clatter of the wheels? Two Trains Two trains once left their respective stations for the other's station simultaneously. On the other hand. How many times faster was the first train? The problem can be done using mental arithmetic. Explain why. when the rear locomotive pushes the train. thus rendering the front locomotive useless. It turns out that the locomotives cannot be moving the train at the same time since only one of them is working at a time. . it takes it 80 minutes to get back. The first arrived at its destination an hour after the two trains had met each other. Why then do they employ two locomotives? The Speed of a Train You are travelling in a train and want to find its speed.210-211 Problems on Transport A Plane's Flight An aircraft covers the distance from town A to town B in 1 hour 20 minutes. However. How Does a Train Start From Rest? You may have noticed that before making a train move forward the engine-driver sometimes makes it push back. The first boat covered the whole route with a uniform speed of 20 kilometres an hour whilst the second boat sailed the outward leg at 16 kilometres an hour and sailed back at 24 kilometres an hour.Problems on Transport A Race Two sailing boats are competing against each other. though it would seem that the second one should have gained during the return trip exactly what it lost out during the first section of the route. It should thus have come in at the same time as the first boat. What is the distance between the towns? . A trip between two towns takes it 5 hours less than the return trip. Why did it lag behind? Steaming Up and Down the River A steamer makes 20 kilometres an hour downstream and 15 kilometres an hour upstream. The first boat won. They must sail 24 kilometres there and back in the shortest time possible. We are apt to treat "1 hour 20 minutes" and "80 minutes" just like "1 pound 20 pence" and "80 pence". 215) and are transferred throughout the carriage. however good. divide the result by 1. You only need to count the number of jerks you feel in one minute to find how many rails you've passed. multiply the number of jerks a minute by 15 and then by 60. Strange as it might seem. cannot suppress. about half the carriages. the aircraft takes the same time to travel in both directions. The couplings between the first group of carriages are taut whilst they are slack between the rear ones which are being pushed buffer to buffer. The Speed of a Train You must have noticed that when travelling in a train you feel regular jerks all the time which the springs. and people used to adding up are more likely to make it than those who aren't The explanation lies in the habit of dealing with metric system of measures and money. but only part of it. The front locomotive does not take care of the whole of the train.000 and you'll obtain the * You may work out the length of a rail by pacing it out. So. The rest of them are pushed by the rear locomotive. . Figure 215 This nuisance. Now you only have to multiply this number by the length of a rail to arrive at the distance covered by the train during that minute.212-213 \| Answers A Plane's Flight There is actually nothing to explain here. which is also bad both for the carriages and the tracks. say. many people swallow this bait. seven paces amounting to about 5 metres. So it's really a psychological problem. The regulation length of a rail is about 15 metres. or "1 dollar 20 cents" and "80 cents". The problem has a catch for the inattentive reader who might think that 1 hour 20 minutes and 80 minutes are different times. These jerks come from the wheels being slightly jarred at rail junctions (Fig. lends itself for measuring the speed of the train. Two Locomotives The way it works out is as follows. So. Hence x 2 = 2 1/4 and x = 1 1/2. it travelled at 24 km/h for 24/24 hours. he starts the coach and only then jumps on it.e. i. the faster train covered a distance after the meeting that was as many times shorter than the distance covered by the slower train as its speed was higher. or 300 minutes. i. After the meeting each train has to pass the distance that had been covered by the other one.e. if the locomotive first pushes the train backwards the couplings are no longer taut and the train is started from rest carriage by carriage in succession and that is much easier. In other words.9 Answers number of kilometres covered by the train per hour. In fact. In the first case. If we denote the ratio of the two speeds by x. A Race The second boat lagged behind because it travelled at 24 kilometres an hour for a shorter time than it travelled at 16 kilometres an hour. If the locomotive is to begin to pull the train like this. 300 300 ^ _ 20-15=5. i. (number of jerks) x 15 x 60 = kilometres per hour. the distance between the towns is 300 kilometres. i. the steamer gains 1 minute every kilometre. then the faster train took x 2 times less time than the other to cover the distance from the meeting point to the respective station. otherwise the horse would have to push more load from rest. In other words. Steaming Up and Down the River Travelling downstream the steamer covers 1 kilometre in 3 minutes whilst travelling upstream it covers 1 kilometre in 4 minutes. 1 1/2 hours. . and as the total gain is 5 hours. Really.5 faster than the second train. it lost more time on the journey "there" than gained on the way "back". How Does a Train Start From Rest? When a train arrives at a station and comes to rest. Therefore. On the other hand. 1 hour. which might be too difficult a task for it. the engine-driver does what a coachman does sometimes when the coach is heavily loaded. it would have to start the whole of the train from rest at once.e.e. the couplings between the carriages are taut. Hooo Two Trains The faster train arrives at the meeting point having covered a distance that is larger than the distance covered by the slower train by as many times as the speed of the faster train is higher than that of the slower train. and at 16 km/h for 24/16 hours. the first train is 1. Figure 217 depicts the front view of the Yale lock. Despite its long history. But we need only to look at the construction of the lock to see that it provides for an almost unlimited number of variations. Jr. Thread all the peas on a piece of string like beads. and has come to be almost universally used ever since. You see a small circle around the key hole which is the end face of the cylinder passing through the depth of the lock. The cylinder is secured by five short . i. Linus Yale. Imagine a glass filled to the brim with dry peas. in 1865.Surprising Calculations A Glass of Peas Of course. another a litre of water.e. you've seen peas many times and held a glass in your hand.. and then a spoonful of the mixture thus obtained is transferred from the second bottle into the first one. more water in the first bottle or more wine in the second? A Die Figure 216 shows a die. If the string is stretched. so that you must know the sizes of these things. a cube with from 1 to 6 points on its six faces. but this is the crunch. The lock opens when the cylmder turns. then it is bound to show 1 at least once. Peter bets that if the cube is thrown four times in succession. But Vladimir argues that the 1 will either not appear at all with the four throws or it will show more than once. how long would it be approximately? Water and Wine One bottle contains a litre of wine. What do we now have. Who stands the better chance of winning? The Yale Lock The Yale lock was invented by an American. some people question the possibility of having a large number of versions of the lock. A spoonful of wine is transferred from the first bottle into the second. If you prepare. You just insert the key into the keyhole and the pins are lifted to the height required for the lock to open. 217. four stripes for each part of the face. It depends on the number of ways in which each pin may be severed. Try and work out the number of combinations possible for the Yale lock. right). and the cylinder can only be turned when the double pins are so arranged that the cut lie at the boundary of the cylinder. Each pin actually consists of two pins. Next draw other stripes showing various parts of the face so that any two neighbouring stripes belonging to different portraits might be fitted into another portrait without interrupting the lines. say. Figure 218 . Suppose that each pin may be divided into two parts in 10 ways only. you'll have 36 stripes all in all.Surprising Calculations steel pins (Fig. Figure 217 The pins are arranged this way using a key with serrated edge. You can easily see now that the number of the various combinations of heights in the lock can be exceedingly large. How Many Portraits? Draw a portrait on a sheet of cardboard and cut it into several-say nine-stripes. * These could be conveniently glued onto four faces of a square block. to encircle a large house with it? A Million Steps You must know what a million is and can estimate the length of your step. Whose count was higher? . say. nobody is going to do so in practice. Shops once used to sell ready-made sets of these stripes (or blocks) to make up portraits (Fig. but 25 beads.216-217 Surprising Calculations You'll now be able to make up a variety of faces by taking nine stripes each time. for example. as usual. on top of each other. "Even higher than Mont Blanc (5 kilometres)!" another answered. It was claimed that of 36 stripes one could produce a thousand various faces. Which was closer to the truth? Whose Count Was Higher? Two people kept count of the passers-by on a pavement over a period of an hour. on it. so that you should easily be able to say how far would a million steps take you? More than 10 kilometres away? O r less? Cubic Metre A teacher asked his class if they were to put all the millimetre cubes contained in cubic metre. But the problem becomes more difficult if you must shift not seven beads. how high would the column be? "It'd be higher than the Eiffel Tower (300 metres)!" one student exclaimed. say a lime-tree. how long approximately would the line be? Would it be possible. To be sure. One of them stood near the gate of a house whilst the other strolled to and fro along the pavement. and place them side by side without any breaks. Just try. 218). 25 pounds. Is it so? Abacus Perhaps you can use the abacus and can set. but the problem is not intractable and the answer is rather curious. Leaves of a Tree If we were to take all the leaves from an old tree. i.000 centimetres long. after both transferrals. III. So. the wine in the end contains as much water as there is wine in the water. II.e. i. Then for the three remaining throws the number of all the possible events. Thus. We then argue as follows. A calculation.000 versions of the lock and key as the lock picker has only one chance in 100. V. Suppose that the die has already been thrown once and a 1 appeared. is in order. This shows the advantage of the Yale lock. 10 metres. and hence (1. the second bottle contain n cubic centimetres of wine. 125 outcomes favourable for Peter are possible if the 1 appears only in the second. A centimetre cube contains no less than 2 x 2 x 2 = 8 peas (if tightly packed.e. these are to be found in the first bottle. VI. Clearly it could actually be done in a larger number of ways. there are 1. will be 5 x 5 x 5 = 125. there are 125 + 25 + + 125 + 125 = 500 various possibilities for the 1 to appear once.000 peas.000= 1. in the four throws. When strung these would give a line 1/2 x 2. As to the unfavourable outcomes. Where have the missing n cubic centimetres of water gone? Clearly.296 — 500 = 796 since all the remaining events are unfavourable. Water and Wine In solving the problem we mustn't overlook the fact that the final volume of liquid in the bottles was equal to the initial one. Our calculation is very rough since it assumes that each pin can only be divided in 10 different ways. favourable for Peter. however crude. VII. only in the third or only in the fourth throw. For . Accordingly. In a glass of capacity 250 cubic centimetres there are no less than 8 x 250 = 2. VIII and IX. To show this is true make each of the nine sections of a portrait with one of the Roman numerals I. and only once. IV.n) cubic centimetres of water. we see that Vladimir stands better chance to win than Peter: 797 against 500. the occurrence of any face save for the 1. Each of these locks can only be opened by their own key. How Many Portraits? Far more than a thousand. Let. A Die The number of all the possible events after four throws of the die is 6 x 6 x 6 x 6 = = 1.Answers w A Glass of Peas Any guess here will lead you to an error.296. thus notably increasing the number of different locks possible.000 . In exactly the same way. It is very comforting for the owner of the lock that there are 100.000 to hit upon the right key. The Yale Lock It's easily seen that the number of different locks possible is 10 x 10 x 10 x 10 x 10 = = 100. even more). 1 litre. A dry pea is about 1/2 centimetre across.000. II.3. then it would be more than 260. i. In fact. Not one thousand but more than a quarter of a million different portraits! The problem is a very instructive one and it goes to explain why it's only exceptionally rarely that we may come across two similar faces.000 various faces in existence. this is many times greater than the world's population. or III. then the two upper sections I and II may be joined in 4 x 4 = 16 various ways. We've just seen that if the human face were characterized by as few as nine features with only four versions possible. the foilage of mature tree includes no less than 200-300 thousand leaves.000. could be encircled with the leaves from a tree if we arranged them in a line because the line would be about 12 kilometres long! Really.500 metres. 1. IV. all the nine sections may be fitted together in 4 x x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 = 262.000.218-219 each section there are four stripes. IV.096 ways. so we'll mark these by 1. II.144 ways. II. In actuality. The number of beads is 2 + 4 + 9 + 10 = 25. we may have four combinations.2.250. we would have 1020. if there were 20 features varying in 10 ways each. Consequently. let alone a house.024 ways: I.000.5 kilometres.2. and IV may be arranged in 64 x 4 = 256 various ways: I.000. III.000. But since section I may be represented by four stripes (1. 1. or 100.1.000. Abacus You can set 25 pounds using 25 beads in the following way: Fiaure 219 Actually. III. It may go to II. and VI. II. III. in 4. 2. III.3. V. ways. or 1. this gives 20 pounds + 4 pounds + 90 pence + 10 pence = 25 pounds. If for definiteness we stick to 250 thousand and take a leaf to be 5 centimetres wide. 3 and 4. and so forth.4).l. in 1.1. Lastly. we'll have a line 1.000 centimetres long.3. Reasoning along the same lines. . there are more than nine features and they may vary in more than four ways.2. 1. To each of these 16 arrangements we may attach section III in four ways (III.4. or II. III. or 12. II. Incidentally. Take stripe 1. the first three sections may be combined in 16 x x 4 = 64 various ways. which is 12.e. we find that I. Leaves of a Tree A small town.4) each of which may be connected to II in four ways. and V. 000 metres.9 Answers A Million Paces A million paces is much more than 10 or even 100 kilometres. If you put one on top of another they would form a column 1.000. then 1.000 paces = 750 kilometres. Since the distance from Moscow to Leningrad is about 640 kilometres.000.000. A Cubic Metre Both answers are far from the true figure because the column would be 100 times higher than the highest mountain on Earth. Whose Count Was The counts were equal.000 = 1 milliard cubic millimetres. then a million paces would take farther than Leningrad. in a cubic metre there are 1. If an average pace is about 3/4 metre long. or 1. Indeed.000.000 kilometres.000 x x 1. Higher? .000 x 1.000 millimetres high or 1. without violating the terms of the deal. after he had won his first trial. the money would again be paid according to their deal. e. the money would be recovered by the court. What was to be done? To get his fee the teacher sued his student. whereas if he lost the case. The student. the mother got double the share of the daughter.220-221 Predicaments Instructor and Student The story related below is said to have occurred in Ancient Greece. But it so happened that twins were born. The judge was embarrased but after a great deal of thought he hit upon an idea and passed a decision that. The two sides made a deal that the student pay the fee just after he had made some achievement.) undertook to teach a young man the art of being a barrister. if the child were a boy. How was the legacy to be shared so that the law was completely satisfied? Pouring Consider of jug containing 4 litres of milk. a boy an a girl. The teacher and thinker Protagoras (485-410 B.500 sestertii with her child who was about to be born. The milk must be divided equally between two friends. The student passed the course and Protagoras was waiting for his reward. What was the decision? The Legacy Here is another ancient problem that was a favourite with lawyers in Ancient Rome. but the student wouldn't appear in a court of justice. but the . again he wouldn't have to pay since that would be the decision of the court. however.C. i. A widow has to share a legacy of 3. he wouldn't pay according to the terms of the deal since he would have lost his first case. He argued thus: if he won the case. his mother got a half of the son's share but if it were a girl. According to Roman law. gave the teacher an opportunity to recover his fee. regarded Protagoras's case as absolutely hopeless (he seems to have learned something from his teacher) and reasoned as follows: if the judge decided against him. and hence his student won it. whereas if the judge decided in his favour. How can the milk be divided using the three jugs? Of course. How would you handle the problem? Three Soldiers Three soldiers were having a problem. "They weren't the same. But I didn't find the ends of the candles: somebody had thrown them away. one of which holds 2 1/2 litres and the other holds 1 1/2 litres. The next day they wanted to know how long the electricity was off. "But couldn't you remember their lengths?" I asked. One was four times longer than the other". I was told that the stubs were so small that it wouldn't have paid to keep them. But how? Two Candles The electricity failed in my flat because the fuse had blown. too. I had to be content with the above information and try to work out how long the candles had been burning. It would seem that under these conditions only one soldier could cross the river. They had to cross a river without a bridge. and that the thicker one took 5 hours to burn down completely whilst the thinner one took 4 hours. and I didn't know the initial length of the candles. All my attempts to squeeze out something more failed. However. None of the soldiers could swim.Predicaments only containers available are two empty jugs. all three soldiers were soon on the other bank and returned the boat to the boys. I only knew that the candles were the same length but different thicknesses. it'll be necessary to pour the milk from one jug into another. I lighted two candles that had been specially prepared on my desk. and worked on in their light until the failure was set right. Both were new before I had lighted them up. Two boys with a boat agreed to help the soldiers but the boat was so small it could only support one soldier and even then a soldier and a boy couldn't be in the boat for fear of sinking it. How did they do it? . I had not noticed the time when the electricity failed and was restored. When the porridge was ready. to the fourth eldest. And are there million millimetre squares here? I don't believe it!" "Count them then. The boy decided to do so and count all the squares. "Why so many?" he was surprised. four cows and 1/7 of the remaining cows. Each mark took him a second so the going was rather fast. still do you think he managed to make sure that a square metre has a million square millimetres on the same day? A Hundred Nuts A hundred nuts are to be divided between 25 people so that nobody gets an even number of nuts. To his eldest he gave one cow plus 1/7 of the remaining cows.222-223 Predicaments A Herd of Cows Here is one of the versions of a curious ancient problem. to the third eldest. two cows plus 1/7 of the remaining cows. "Here I've got a sheet of graph paper that is exactly one metre long and one metre wide. three cows plus 1/7 of the remaining cows. The herd was distributed among his sons without remainder. and so forth. he wouldn't believe it. they were joined by a passer-by who partook of their meal and paid them 50 pence. How many sons and how many cows were there? Square Metre When a boy was told for the first time that a square metre contains a million square millimetres. to his second eldest. He worked like blazes. the other 300 grammes. A father distributed his herd amongst his sons. He got up early in the morning and set about counting them neatly marking each square he had counted with a point. Could you do it? Dividing Money Two people were making porridge on a camp-fire. How should they divide the money? . One contributed 200 grammes of cereals." somebody advised. " Since the brothers couldn't persuade each other. The apples. and the youngest walked back down the route. the second went on. Once you have solved that one it should be easy to handle another problem in the same vein: to divide seven apples among 12 boys so that none of the apples is divided into more than four parts. "we'd better go on. When the tram catches up with us. the problem was to divide the five apples equally among the six boys so that none of the apples was cut into more than three pieces. of course. Which of the three got home sooner? Who was the most reasonable? . So. each went his own way. we can jump onto it. A Further Apple Problem Five friends came to see Peter. Peter's father wanted to treat all six boys to apples but there were only five apples. had to be cut but not into small pieces since Peter's father wouldn't cut them into more than three." the youngest brother objected. but by then we'd have got part of the way home and thus we'll get there sooner. Each of them has his own key but he can still unlock the boat without waiting for his friends and their keys. "then we'd better go backwards not forwards: since then we'll meet an oncoming tram sooner and so get home sooner. "Why wait?" the second brother asked.Predicaments Sharing Apples Nine apples must be shared out amongst 12 children so that no apple is divided into more than four parts. What was to be done? Everyone had to have his fair share. There was no tram in sight and the eldest brother suggested they wait. How was Peter's father to get out of his predicament? One Boat for Three Three sports enthusiasts possess one boat. On the face of it the problem is insolvable. How did they arrange it? Waiting for a Tram Three brothers came to a tram stop. They keep it on a chain with three locks so that each of them could use it but a stranger couldn't." "If we decide to go. The eldest stayed to wait. but those who knows about fractions can solve it easily. Solving the equation gives that x = 3 3/4 hours. was equal to the length of the thin stub (1 . Each hour 1/5 part of the original length of the thick candle and 1/4 part of the original length of the thin candle burns away.224-225 Answers Instructor and Student The decision was to decide against Protagoras but give him the right to bring the case before the court a second time. This fulfils Roman law since the widow gets a half of the son's share and double the daughter's. the candles had burned for 3 hours 45 minutes. We'll denote the time (in hours) that the candles burned by x. Thus. i.e. 4(1 . Both boys go to the opposite bank and one of them brings the boat back to the soldiers (the other stays on the opposite bank). e.000 sestertii.x/4 of the original length. 15--975 . i. and the daughter 500 sestertii.000 sestertii. the thick candle's stub will be 1 . the son 2.x/4). the second one should undoubtedly be decided in favour of the instructor.x/5).x/5 of its original length and the thin candle's stub 1 . After the student had won his first trial. Pouring Seven pourings will be required as is shown in the table: Pouring 41 11/21 21/21 1 2 3 4 5 7 11/2 11/2 3 3 2 — 1 1/2 — 1 1 — 2 1/2 1 6 1/2 1/2 1 1/2 2 2 1 — 2 1/2 Two Candles We'll construct a simple equation. Three Soldiers The following six crossings were made: 1st crossing. Accordingly. We know that the candles were originally equally long and that the four times the length of the thick stub. The Legacy The widow gets 1. Further. Other multiples of six would be unreasonable since there couldn't be 24 or more sons. the two youngest sons got 6 + + 6 = 1 2 cows. Therefore. and for a month if he worked 8 hours a day. without resorting to equations). The number 18 won't do either. The third son got 3 + 21/7 = 6 cows. not six. Both boys cross the river and one of them returns with the boat. We'll now work out the residue after the third son got his share: 6 + 6 + 6 = 18 cows is 6/7 part of the residue. Let's assume that the youngest son received six cows and see if this assumption is good. you'll understand the futility of all their efforts since the problem is insolvable. hence the fourth son got 4 + 14/7 = 6 cows.400 squares since there are only 86. Like the third one. 6th crossing. the share of the youngest son amounts to 6/7 of the share of the remainder. six cows all in all. If you give some thought to the problem. The fifth son got five cows plus 1/7 of seven. The youngest son got as many cows as there were sons for he could not get an additional 1/7 of the remaining herd as there were no cows left. the boy would not be able to verify the fact in one day. It turns out that this assumption is unsuitable. plus 1/7 of the remaining cows. Square Metre No. Thus. which accounts for 6/7 part of the herd left after the fourth son has received his share.400 seconds in 24 hours. It thus follows that the number of cows the youngest son got must be divisible by six.e. The boys continue on their journey and the three soldiers are on the opposite bank. Even if he counted for 24 hours without interruption. the next son got one cow less than there were sons.e. The total residue was 12^-6/7 = 14 cows. the total residue was 18—:—6/7 = 21 cows. But are there other solutions? Assume that there were 12 sons. The boat returns with the other boy. he would have counted only 86. A Hundred Nuts Many people would immediately set about tiying a variety of combinations. The second soldier crosses and the boat returns with the boy. 5th crossing. .9 Answers CO 2nd crossing. 3d crossing. The third soldier crosses and the boat returns with the boy. A Herd of Cows Arithmetically (i. Our assumption that there were six sons and 36 cows appears to be plausible. The boy that brought the boat back stays on the bank with the soldiers and a soldier crosses the river in the boat. In exactly the same way we'll find that the second and first sons also got six cows each. 4th crossing. i. the problem should be approached from the end. Accordingly. It follows from the assumption that there were six sons. To count to one million he would have to work for almost 12 days without stopping. but their efforts would all be to no avail. The contributor of the 300 grammes (i. The person who contributed the 200 grammes gave 60 pence worth o f food in terms of money (since a hundred grammes costs 150 :.5 = 30 pence). Reasoning along the same lines. In consequence. A Further Apple Problem The apples were divided thus: three apples were each cut in half to yield six halves that were distributed among the children and the remaining two apples were each cut into three to obtain six thirds that were also given to the children. you would have been able to make an odd number of odd numbers add up to 100 which is an even number. In this case each child should get 7/12 of an apple. and none of the apples was cut into more than three equal parts. we would have to obtain 12 pairs of odd numbers and one more odd number. Since there were three eaters. Therefore three apples are divided into four parts and the four remaining apples into three parts each. The remaining three apples should each be divided into four equal parts to yield 12 quarters. or 7/12. Sharing Apples It's possible to share nine apples equally between 12 children without cutting any apple into more than four parts. Consequently. and that is clearly impossible. Each pair of odd numbers yields an even number. We'll argue as follows: 50 pence was paid for one portion of food. the cost of the porridge (500 grammes) should be 1 pound 50 pence. We thus obtain 12 quarters and 12 thirds. e. However. Six apples should be divided in two each to yield 12 halves. all the boys got their equal share. each child can be given a quarter and a third. out of the 50 pence one person should have 10 pence and the other person 40 pence.50 = 40 pence.it's possible to divide seven apples among 12 children so that each child gets an equal share and no apple needs to be cut into more than four parts. i. Now each child receives a half and a quarter.226-227 Answers If you could break 100 into 25 odd summands. we'll end up with an odd result.e. If then we add an odd number to the total. each boy got a half and a third of an apple. 15' . In fact. because 9-4-12 = 3/4. hence he must get back 60 — — 50 = 10 pence. Dividing Money Most people answer that the one who contributed the 200 grammes should get 20 pence and the other 30 pence. Thus 100 can never be composed of such summands. Thus. but notice that 7/12 = 3/12 + 4/12 = 1 / 4 + 1/3. This division is not fair. 90 pence in terms of money) must get 90 . he also consumed 50 pence worth of porridge. so 12 pairs of even numbers must add up to an even number. So each will get 3/4 of an apple as required. who went backwards. 220. saw an oncoming tram and jumped into it. Figure 220 Waiting for a Tram The youngest brother. The most reasonable brother was the eldest one since he waited quietly at the stop. All the three brothers found themselves in the same tram and. When the tram came to the stop where the eldest brother was waiting. . of course. You can see quite easily that each of the boat's owners can open the chain of the three locks using his key. A short while later the tram caught up the third brother who was walking homewards and collected him. arrived home at the same time.9 Answers '5 Q0 One Boat for Three The locks should be connected as shown in Fig. he got in too. Is it all possible? Hard Bed Lilliputians made the following bed for their giant guest: "Six hundred beds of the common measure were brought in carriages. The boat seemed monstrous to the . which however kept me but very indifferently from the hardness of the floor. Animals of Lilliput Gulliver relates: "Fifteen hundred of the Emperor's largest horses. Why was Gulliver so incomfortable on the bed? And is this computation correct? Gulliver's Boat Gulliver left Lilliput in a boat washed up on the shore by chance.500 horses are a bit too many taking into account the relative dimensions of Gulliver and Lilliputian horses? Also. Every now and then the differences are so amazing that can serve as a material for interesting problems. thickness-of people. A 12-fold increase or decrease doesn't seem to be very much of a change but the nature and way of life in this fantastic countries was strikingly different from those we are used to.. for when he left he just "put them into his pocket". plants and other things were 1/12 of those here.228-229 Problems from Gulliver's Travels Beyond doubt the most fascinating pages in Gulliver's Travels are those describing his unusual adventures in the country of tiny Lilliputians and in the country of giant Brobdingnagians. were employed to draw me towards the metropolis. and worked u p in my house. a hundred and fifty of their beds sewn together made up the breadth and length. In Lilliput the dimensionsheight. that was of smooth stone". width.. We can easily understand why the author of the Travels choose the number 12. animals. if we remember that in the British system of units there are 12 inches in a foot. Gulliver tells us a no less amazing thing about the cows. and sheep." Doesn't it seem to you that 1. bulls. By contrast. in Brobdingnag they were 12 times larger. and these were four double. in little convenient huts built about my house. for it hardly held half a pint. he's only a dozen times taller than a Lilliputian. They brought me a second hogshead. in a very ingenious manner.728 of our subjects." Elsewhere Gulliver relates: "I had three hundred cooks to dress my victuals. all which the waiters above drew up as I wanted. which I might well do. it surpassed by far the largest ships of their fleet. and placed them on the table.. Figure 221 Figure 222 . and prepared me two dishes apiece. Why should such tiny hogsheads and buckets exist in a country where everything is only 1/12th normal size? Food Allowance and Dinner Lilliputians set the following daily allowance of food for Gulliver: ". I took up twenty waiters in my hand. Are the allowance and appetites compatible with the relative sizes of Gulliver and the Lilliputians ? * The displacement of a ship is the largest load (including the weight of the ship itself) that the ship can support. as we draw the bucket up a well in Europe". some with dishes of meat. which I drank in the same manner. by certain cords. How did they come to fix on that number? And what is the use of all that army of servants to feed just one man? After all. and beat out the top.. but they had none to give to me". sufficient for the support of 1. They slung up with great dexterity one of their largest hogsheads. where they and their families lived. a hundred more attended below on the ground..Problems from Gulliver's Travels Lilliputians. Could you work out the displacement* of the boat in Lilliputian tonnes if its weight-carrying capacity was 300 kilogrammes? Hogsheads and Buckets of Lilliputians Gulliver is drinking: "I made another sign that I wanted drink .. I drank it off at a draught. and some with barrels of wine and other liquors slung on their shoulders. Elsewhere in the book Gulliver describes the Lilliputian buckets as being no larger than a thimble. the said Man Mountain shall have a daily allowance of meat and drink. then rolled it towards my hand. and made signs for more. . that it would have infallibly knocked out my brains. approximately. which very narrowly missed me. one of them hit me on the back as I chanced to stoop. formed like a standing ladder. by which a dozen apples. for it was almost as large as a small pumpkin". and knocked me down flat on my face. So once he was in the gardens of the court under some apple-trees and the Queen dwarf "when I was walking under one of them. shook it directly over my head. The Queen's joiner had contrived.. the lowest end placed at ten foot distance from the wall of the .230-231 Figure 223 Problems from Gulliver's Travels Three Hundred Tailors "Three hundred tailors were employed. It was indeed a movable pair of stairs. each of them near as large as a Bristol barrel. What do you think was the weight of the apples and nuts in Brobdingnag? A Ring of the Giants The collection of rarities brought by Gulliver from Brobdingnag includes "a gold ring which one day she (the Queen) made me a present of in a most obliging manner. the steps were each fifty foot long. a kind of wooden machine five and twenty foot high." Is it possible that a ring from a little finger would fit on Gulliver like a collar and how much. it came with so much violence. taking it from her little finger.. would the ring weigh? Books of the Giants About books of Brobdingnagians Gulliver tells us the following: "I had liberty to borrow what books I pleased.." On another occasion "an unlucky schoolboy aimed a hazelnut directly at my head. came tumbling about my ears. otherwise. to make me clothes." Was this army of tailors really necessary to have clothes made for a man who is only a dozen times larger than a Lilliputian? Gigantic Apples and Nuts In the part "A Voyage to Brobdingnag" devoted to Gulliver's stay in the country of giants we read about some of the hero's trouble-filled adventures. and throwing it over my head like a collar. what number would he require? . consider a problem of this kind that is not directly taken from Gulliver's Travels. and so turned over the leaf. and began the other page on the same manner. after which I mounted again. your collar size is 38. I first mounted to the upper step of the ladder. If Gulliver wished to order some collars in London for a Brobdingnagian. began at the top of the page. and in the largest folios not above eighteen or twenty foot long. and turning my face towards the book. and so walking to the right and left about eight or ten paces according to the length of the lines. for it was as thick and stiff as a pasteboard. You may know that the size of a collar is nothing but the number of centimetres of its length. which I could easily do with both my hands. On average an adult's neck is 40 centimetres round. till I had gotten a little below the level of my eye." Does this make sense? Collars for the Giants Finally. The book I had a mind to read was put up leaning against the wall.Problems from Culliver's Travek chamber. and then descending gradually till I came to the bottom. If your neck is 38 centimetres round. and so the several gradations downwards..e.. . for his bed Gulliver required 144 (i.728 times smaller in volume. and a young girl threading an invisible needle with invisible silk. Crearly. That is why the cart with Gulliver had to be pulled by so many Lilliputian horses. Our cow is about 1. about 150) Lilliputian beds. The bed would however have been exceedingly t h i n . For Lilliputians it was as difficult to transport his body as it would have been to transport 1. the sheep an inch and a half. then its surface "area would be 12 x 12 times smaller than the surface of our bed. and hence as much ighter than ours. Figure 224 Animals in Lilliput were also 1.728 kilogrammes.232-233 i6 Answers Animals of Lilliput It's calculated in the answer to "Food Allowance and Dinner" that Gulliver's volume was 1. less than 1/4 kilogrammes. which to my sight were almost invisible. which was not so large as a common fly. i. he was that many times heavier. A toy cow like this really could be carried about in a pocket.5 metres high and weighs 400 kilogrammes.1 2 times thinner than ours.e. and of course 12 times narrower than a conventional bed. If a Lilliputian bed is 12 times shorter.728 grown-up Lilliputians. I have been much pleased with observing a cook pulling a lark. Accordingly. their geese about the bigness of a sparrow.728 times larger than that of a Lilliputian. till you come to the smallest. Thus even four layers of such beds would not have been soft enough for Gulliver since the resultant mattress was three times thinner than ours. more or less." Hard Bed The calculation is quite correct. Gulliver gives a true account of relative sizes: "The tallest horses and oxen are between four and five inches in height. A cow in Lilliput would be 12 centimetres high and weigh 400/1. to make a round number. We now see the purpose of so many cooks.e. but also 12 times narrower and 12 times thinner than Gulliver. hence the boat displaced 1/3 of our cubic metre. though smaller. Consequently. Today we have ships with displacements of tens of thousands of tonnes ploughing the seas. width. This is clearer if we imagine that each square inch of the surface of a Lilliputian's body corresponds to a square foot on the surface of Gulliver's body. A tonne is the weight of 1 cubic metre of water. We shouldn't forget that Lilliputians were an exact. i.728 of that of Gulliver. N o wonder Gulliver couldn't quench his thirst with two such hogsheads. If we assume that our bucket contains about 60 glasses.a n d 1. and l e n g t h . If the capacity of a Lilliputian bucket is thus a tea-spoonful. about 1/30 of a glass. so a ship with a 575-tonne displacement should not be a wonder. So 1/3 of our cubic metre contains about 575 Lilliputian cubic metres and thus Gulliver's boat had a displacement of 575 tonnes or thereabout since we arbitrarily took the figure 300 kilogrammes. That's why Lilliputians calculated that Gulliver needed an allowance sufficient to support 1. And to support the life of such a body requires respectively more food. Three Hundred Tailors The surface of Gulliver's body was 1 2 x 1 2 . This is just larger than a tea-spoonful but not really much larger than the volume of a large thimble. and their volume was 1/1. however. An accordingly larger number of people is required to haul the load up to Gulliver's table.728 of ours.728 dinners requires no less than 300 cooks taking that one Lilliputian cook can make half a dozen Lilliputian dinners. which can be estimated to be the height of a three-storey building in Lilliput.Gulliver's Boat We know from the question that the boat could carry 300 kilogrammes. that there are 144 square inches in a square foot. i.e. and hence more . replica of conventional people with normally proportioned members. the capacity of a 10-bucket hogshead would not be much larger than half a glass.728. To make 1. they were not only 12 times shorter. But all the linear dimensions in Lilliput are 1/12 of ours. and volumes are 1/1. Food Allowance and Dinner The computation is perfectly correct.728 times smaller in volume. we can work out that a Lilliputian bucket contains only 60/1. Hogsheads and Buckets of Lilliputians Lilliputian vessels were 12 times smaller than ours in every dimensions-height. its displacement was about 1/3 tonne. We should remember though that at the time of writing (early in the 18th century) 500-600-tonne ships were still rare.728 Lilliputians. We know. Thus Gulliver's suit would take 144 times more fabric than that of a Lilliputian. 144 times larger than that of a Lilliputian.e. i. " Quite plausible. Such a gigantic nut might be about a dozen centimetres across. as if I had been pelted with tennis balls. A 3-kilogramme. he would only just survive the blow. the hailstones gave me such cruel bangs all over the body. Thus Brobdingnagian apples are about 173 kilogrammes.728 times heavier than here. Figure 226 . Gigantic Apples and Nuts An apple that weighs about 100 grammes here should correspond to an apple in Brobdingnag that is as many times heavier as it is bigger in volume. i. i. say. then to make 144 suits in a day (or one of Gulliver's suits) may require 300 tailors. 1. e.e. Gulliver thus got off lightly. because each piece of hail in this country of giants must weigh no less than a kilogramme. that I was immediately by the force of it struck to the ground: and when I was down. If such an apple falls from a tree and hits a man on the back. A Ring of the Giants A normal little finger is about 11/2 centimetres across. Figure 225 A Brobdingnagian nut must have weighed 3-4 kilogrammes. hard object thrown with the speed of the nut clearly could smash the skull of a normal-size man. Multiplying this by 12 gives 18 centimetres and a ring of such a diameter has a circumference of 56 centimetres. Elsewhere in the book Gulliver recalls: "There suddenly fell such a violent shower of hail.234-235 Answers working time. one tailor can make one suit in two days. if we take that our nut weighs about 2 grammes. If. the conventional format of books (tomes) was far larger than now. about 3 tonnes. Responding to certain critisisms of his poem Eugine Onegin Alexander Pushkin once noted that in his book "time is calculated with a calendar".e. if a normal ring weighs 5 grammes its counterpart in Brobdingnag must have weighed 8 1/2 kilogrammes! Books of the Giants If we start from the size of books current in our times (about 25 centimetres long and 12 centimetres wide). early in the 18th century. But a real tome of the time might be as large as a newspaper. Figure 227 You could handle a book 3 metres high and 1 1/2 metres wide without a ladder and without having to move to the left or right by 8—10 steps. Assuming that it has 500 sheets. the modest tome we mentioned would in the country of giants weigh 1. * * * We thus see that all the whimsical things in Swift seem to have been carefully calculated. . each of its sheets would weigh about 6 kilogrammes. the giant would need a 40 x 12 = 480 size collar.728 times more than here. It is impossible to read a 4-metre book without a ladder. And if a normal man needs a collar of size 40. which when multiplied by 12 gives 360 x x 240 centimetres. In the days of Swift. 20 x 30 cm formats were not uncommon.Answers it's sufficiently large for a normal head to go through it. then Gulliver's account might appear to be a slight exaggeration. However. As to the weight of such a ring. In exactly the same way Swift could say that all his objects had conscientiously been computed using the laws of geometry. Collars for the Giants The neck of a giant will be 12 times larger than that of a normal man. i. perhaps a bit too much for fingers. the following happened in ancient Rome.. his head down. please award me with money to provide for the rest of my life. He said: "I have won many victories to exalt your grandeur. General Terentius had returned to Rome with booty after a victorious campaign. The general's request plunged him in a deep reverie. "What sum.. Sire. I have had no time to take care of my well-being. Sire. But I'm tired of fighting. He asked." The E m p e r o r ." "Proceed. "Hear me out with indulgence. Finally. Terentius. I have been unafraid of death and if I had many lives.236-237 Stories about Giant Numbers Reward According to legend. But Terentius didn't want this. then may your generosity help me live out the remainder of my days in peace and comfort at home. imbruing my sword with blood. would you consider sufficient?" "A million denarii. I do not seek honour or high office as I would like to retire from power and public life to live peacefully. Back in the capital he was received by the Emperor." The encouraged general went on to say: "If it is your desire to reward your humble servant. Tomorrow at noon you will hear . The time has come for me to retire to my father's home and revel in the joys of domestic life. The general waited." The Emperor grew pensive again. He liked to save money for himself but was miserly with it to others. and to cover your name with glory. The reception was very warm and the Emperor thanked him cordially for his services to the Empire promising to confer on him a high office in the Senate. you are a great warrior and your prodigies of valour have earned you a lavish reward! I will give you wealth. Sire! In all these long years of battle. brave Terentius. I'd sacrifice all of them to you. I.s o the legend goes-wasn't distinguished for his lavishness. Terentius?" the Emperor asked. the Emperor spoke: "Valiant Terentius. Sire. I'm poor. Sire. my youth had passed and my blood flows slower in my veins." "What would you like to receive from me. O n the first day he only brought 1 brass. 16. I will order appropriate coins be produced for you an<} while you have the strength. Nobody may help you. and thirty-two-fold the weight of the first." The Emperor answered: "It's not my intention that such a noble warrior like you should have some miserable reward for his heroic deeds. You kindly promised to reward me. You shall go to the treasury and take one coin. "Sire. on the fifth. Terentius started his daily visits to the treasury. He visualized the multitude of coins. you must rely on your own power only." he beamed. On the following day you shall again go to the treasury. "I'm happy with your favour." Terentius listened eagerly to the Emperor's words. Terentius bowed his head humbly. you will take them from my treasury. that he would bring out of the treasury. On next day at the hour appointed the general came to the Emperor's palace. etc. "Greetings. O n the third day you are to bring a coin worth 4 brasses and on the fourth day bring a coin worth 8 brasses. It was located close to the Emperor's hall so the first trips with the coins cost Terentius very little effort. sixteen-fold. fourfold. brave Terentius!" the Emperor said. II. * A brass is a fifth of a denarius.. "Really generous is your reward!" III. His trips upto the sixth day were also very easy and he brought the coins double." Terentius bowed and walked out. This was a small coin 21 millimetres across and weighing 5 grammes. double the value of the previous coin. then you shall return here and place it at my feet. each one more than another. take a coin worth 2 brasses and place it here near the first one. Listen to me.238-239 Stories about Giant Numbers my decision. You will stop when you notice that cannot move a coin any more and then our deal will come to an end. There are in my treasury 5 million copper brasses. I came to hear your decision. All the coins that you will have managed to bring here will belong to you and you shall keep them as your reward. Figure 228 . He saw that after 12 days only slightly more than 2. Sire.384 unit coins. It was a coin equal to 32.." the general responded grimly wiping his brow. He trudged slowly to the Emperor carrying a huge coin corresponding to 16. On the fourteenth day Terentius had a heavy coin that was 42 centimetres across and weighed 41 kilogrammes. The Emperor who up until that day was very kind to the general now couldn't conceal his triumph. and corresponded to 65. for his visits to the treasury and trips to If a coin's volume is 64 times that of a normal one. On the twelfth day the coin was almost 27 centimetres across and 10 1/4 kilogrammes in weight. This time Terentius's burden was really heavy. on the thirteenth day the brave Terentius brought out a coin that was worth 4. It was 53 centimetres wide and weighed 80 kilogrammes.* On the eighth day Terentius had to carry out a coin that was worth 128 units. there was a roar of laughter. It was 13 centimetres wide and weighed more than 1 1/4 kilogrammes. The fifteenth day came. Further. The general was exhausted and gasping.238-239 Stories about Giant Numbers The seventh coin weighed 320 grammes and was 8 1/2 centimetres across.536 unit coins. It weighed 640 grammes and was about 10 1/2 centimetres wide. the weight of a tall warrior. We should have this in mind when working out the sizes of further coins. "No. . my brave Terentius?" the Emperor could hardly help smiling.096 units. its diameter being 67 centimetres and weighing 164 kilogrammes. When Terentius came to the Emperor the next day. On the ninth day he carried into the Emperor's hall a coin corresponding to 256 unit coins. On the sixteenth day the general staggered with the burden on his back.000 brass units had been brought. He could no longer carry his coin in his hands and rolled it in front of him. The eighteenth day was the last day of Terentius's enrichment. "Are you tired. because 4 x 4 x 4 = 64. then it is only four times wider and thicker. The coin was 84 centimetres and 328 kilogrammes. The Emperor smiled.768 units. It was 34 centimetres wide and weighed 20 1/2 kilogrammes.. 960 8.768 x 2 .120 1. i.535." So the close-fisted Emperor gave the general about 1/20 part of the million of denarii Terentius had requested.560 512 5. The mammoth coin fell thundering at the Emperor's feet.. Enough for me.096 40.072 unit coins.768 327. 32.192 81. g. "Can't do any more.840 32.143 brasses.680 65.1.e.384 163. The result is 65. This time he had to fetch a coin worth 131.. .280 256 2.072 The totals for these columns can be calculated easily using the proper rule.920 16. The Emperor could hardly conceal his pleasure at the total triumph of his ruse. thus the second column totals Each number in this column equals the sum of the previous ones plus one.536 655.480 4. thanks to your generosity the victorious warrior Terentius has got a reward of 262. e. He ordered the treasurer to compute the total of all the brasses brought into the hall by Terentius. when it's necessary to sum u p all the numbers in the column." he wispered. Therefore.048 20. Terentius brought out: Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Coin Weight in brasses in grammes 5 1 2 10 4 20 40 8 16 80 160 32 64 320 640 128 1. It was more than a metre across and weighed 655 kilogrammes.238-239 Stories about Giant Numbers the Emperor's hall ended on that day. The treasurer reckoned quickly and said: "Sire. * * * Let's check the treasurer's calculation and the weight of the coins. we need only find the next number and subtract one. Terentius was completely worn out.360 131. from 1 to 32.240 2. Using his spear as a lever Terentius rolled it into the hall with a huge effort.768.024 10. the king summoned him in order to reward him personally for such a stroke of brilliant insight. named Seta. e. Figure 229 1 16 — 9 7 5 .238-239 Stories about Giant Numbers 262. When the Indian king Sheram got to know about it he was amazed at its ingeniousness and the infinite variety of positions it afforded. You do not need to be able to play chess to understand it. The play of chess was invented in India. 5 million brasses. Legend about Chess-Board I. He was a simply dressed scribe who earned his living giving lessons to pupils. One of these legends I want to relate. it is sufficient for you to know that it involves a board divided into 64 cells (black and white alternately).000 262. The inventor. i. It has been in existence for centuries so it is no wonder that it has given rise to many legends whose truthfulness cannot be checked because of the remotedness of the events. Accordingly. Having learned that the play was invented by one of his subjects.143.143 = 19 times less than he requested. came before the sovereign's throne.000. he got 5. Chess is one of the world's most ancient games. Terentius requested a million of denarii. before going to bed the king Sheram again inquired how long before had Seta left the palace with his bag of wheat. "Sovereign. "Yes. The answer was: "Sovereign." "Enough!" the king was exasperated. At night. II. "Tomorrow. But let me tell you that your wish is unworthy of my generosity. At dinner the king remembered about the inventor of chess and asked if the foolish Seta has collected his miserable reward. ." When the next day Seta came to the throne he amazed the king by the unprecedented modesty of his desire. "You'll get your grains for all the 64 cells of the board according to your wish: for each twice as much as for the previous one." the king said.. Seta said: "Sovereign. for the sixth 32. oh sovereign. I'll name you my wish. upon consideration.. There was a silence. For the second cell let there be two grains. for the third four. left the hall and began to wait at the palace gates. for the beautiful play you invented. By asking for such a miserable reward you show disrespect for my favour. Give me some time to sleep on it. your order is being fulfilled.238-239 Stories about Giant Numbers "I want to reward you properly. Seta. for the fourth eight. order that one grain of wheat be given to me for the first cell of the chess-board." "A simple wheat grain?" the king was shocked.h e wasn't used to having his orders fulfilled so slowly. The court mathematicians are computing the number of grains required. Truly. for the fifth 16." "Why so long?" the king was furious. sovereign." Seta smiled." The king f r o w n e d . your mathematicians are working hard and hope to finish their calculations before dawn. Tomorrow. as a teacher you might give a better example of gratitude for the kindness of your king. "Name a reward that would satisfy you and you'll get it"." the king went on to say. Go away! My servants will bring you the bag of wheat. The sage bowed. "Don't be shy! What's your desire? I'll spare nothing to meet your wish!" "Great is your kindness. "I'm rich enough to fulfil any of your desires. The number is so enormous. oh sovereign!" III.073.. Should all the land be sown with wheat and should the entire yield of these fields be given to Seta. There is now no way of knowing if it's true. I never give my order twice!" First thing in the morning the king was told that the chief mathematician humbly asked to make an important report. Such was the legend.615. There is not sufficient grain in all your barns to give Seta what he wants. "What is this prodigious number?" "18.. to fulfil his wish. order all the seas and oceans dried up. Hence the calculation comes down to multiplying together 64 twos: 2 x 2 x 2 x 2 x 2 . You would not find that many grains in the entire space of the earth. If you use the rule explained at the end of the previous problem. must be given to Seta. "my granaries won't be depleted! The reward is promised and must be given out.-64 times. and order the ice and snowy wastes that cover the far northern lands melted. oh sovereign.4. 1 6 . you can easily obtain the number of grains to be received by the inventor (we double the last number and subtract one).446. Sheram said: "Before you bring out your business I'd like to know if Seta has at last received the miserable reward that he asked for." The old man responded: "It's exactly because of this that I dared to bother you at such an early hour. etc. but that the reward is expressed by this number you could verify by some patient calculations.709. And if you wish to give out the promised reward by all means." "No matter how enormous it is".242-243 Stories about Giant Numbers before I wake up everything.2." "It's beyond your power. etc. And there is not enough in all the barns throughout the kingdom. then he'd receive his reward.8. the king interrupted him arrogantly.744." The king attended to the words of the elder with amazement... The king ordered him in..551. The result of the 63th doubling will be what the inventor should receive for the 64th cell of the board. We've painstakingly worked out the number of grains that Seta wants to have. Starting with unity you'll have to add up number 1. down to the last grain. then order all the kingdoms on earth to be turned into arable fields. 16.238-239 Stories about Giant Numbers To facilitate computation divide the 64 multipliers into six groups with 10 twos in each and one last group with four twos. It's easy to see that the product of 10 twos is 1. and of four twos. but if you summon up all your patience you'll find that one head contains about 3.024 x 1.400 grains in the first 24 hours.576 x 16.073.000 kilometres. A boring business. Consequently.551. Multiplying 1. If you want to imagine the enormousness of this numerical giant just estimate the size of a barn that would be required to house this amount of grain. What follows from this? If there is enough space around our poppy plant with adequate soil. or 12. You see that even if Seta had devoted a lifetime to his counting. If the barn were 4 metres high and 10 metres wide its length would be 300.048.000. if all the seeds germinate? To begin with we should know how many seeds there are in a head.000. It now remains to find x 1.576 x 1.744.024 x 1.024 x 1. How many poppy plants shall we have. he would still have only obtained a miserable fraction of the reward he desired.000 seeds. each seed will produce a shoot with the result that the following .000. In fact. subtract one from the result to arrive at the sought-for number of grains: 18.024 x 16.024.024 gives 1.000 cubic kilometres. In a ten year's time he would have handled about 20 cubic metres.709. the reward of the inventor of chess would occupy about 12.576. He should have suggested to Seta to count off the grains he wanted himself. The desired result is thus 1.000. he could have freed himself of the debt.024 x 1.048. It's known that a cubic metre of wheat contains about 15. twice the distance to the Sun! The Indian king could never grant such a reward. Prolific Multiplication A ripe poppy head is full of tiny seeds.000 grains.576 x x 1. each of which can give rise to a new plant. if Seta kept on counting day in day out he would have counted only 86. A million would have required no less than 10 days of continual reckoning and thus to process 1 cubic metre of wheat would have required about half a year.000 cubic metres.024 x 1. Had he been good at maths.048. 000.000.000. one which yields less seeds.000.000. say.000 = 81.000. because they'll reach the number 81.000 = 243.000 x 3.000. which gives about 100 seeds annually. seeds each.000 .000 poppies will grow.000. i.000.000 x 3.000 plants. all the continents and islands of the earth.000 10.000.000. Let's see what will happen next.000 square m e t r e s . amount to 135. and hence during the following year we are going to have 3.000.000. or 135. A whole poppy field from just one head. with 3.000 x 3.000 1. would lead to the same result with the only distinction that its offspring would cover the lands of the earth in a longer period than five years. the offspring of one plant could engulf the earth in five years so that there were about But the surface area of all the land.000 1. In the fourth year there will be 27. Each of the 3. Such a numerical giant lives in a tiny poppy seed! A similar calculation made for a plant other than the poppy. Having germinated.000.000.244-245 238-239 Stories about Giant Numbers summer 3.000.000 = 9.000.000 times less than the number of the poppy plants grown.000 plants of each square metre of land.000 100.000.000 new plants.a b o u t 2.000 x 3.000 offspring.000.000.e.000 6 7 8 9 10.000. Calculation gives that in the third year the offspring of our initial head will already reach 9. we would have: Year N u m b e r of plants 1 2 3 4 5 1 100 10. Should all of them germinate. the seeds of each head will give 3.000 plants will produce no less than one head (more often several heads).000.000. You see thus that if all the poppy-seeds from one head germinated. In the fifth year our poppies will engulf the earth.000 square kilometres. Take a dandelion.000.000 = 27.000. Before we leave the subject. The oceans would be filled to the brim with fish so that any shipping would be impossible. The number of insects began to drop markedly and before long the sparrows.238-239 Stories about Giant Numbers This is 70 times more than the square metres of land available on the globe. any plant would engulf our planet in a short period. If it were not for death. the whole Earth would be covered by dandelions in the ninth year with about 70 plants on each square metre. we'll consider several real-life examples of uncannily prolific animals placed in favourable conditions. In consequence. Swarms of locust covering huge stretches of land may give some idea of what might happen on earth if death didn't hinder the multiplication of living things. The sparrows liked their new environment. switched to vegetable food and went about destroying crops. or having begun to germinate are suppressed by other plants. for want of animal food.. since there were no birds of prey eating them. The sparrow is known to eat in quantity voracious caterpillars and other garden and forest pests. If there were no massive destruction of seeds and shoots. Why then don't we observe in reality these tremendous multiplications? Because the overwhelming majority of seeds die without producing any new plants. . At one time America was free of sparrows. The bird that is so common in Europe was deliberately brought to the United States to have it exterminate the destructive insects. the offspring of just one couple of any animal would sooner or later populate all the land available. or are eaten by animals. and so they began to multiply rapidly. they either fail to hit a suitable patch of soil and don't germinate at all. In the Hawaii they even completely superseded small endemic birds. And the air would not be transparent because of the mists of birds and insects. too. In two decades or so the continents would be covered with impenetrable forests and steppes inhabited by incountable animals struggling for their place under the sun. This is true not only of plants but of animals. The Americans were even forced to initiate a sparrow control effort which appeared to be so expensive that a law was passed forbidding the import to America of any animals.. fields and plantations. others. Hordes of rabbits soon inundated Australia inflicting enormous damage to agriculture. you'd better stop arguing. In less than a decade they had almost wiped out the rats. The rabbits were brought to Australia in the late 18th century and as there were no carnivores that might be their enemies they began to multiply at a terrifically fast rate. Some suggested that they sit in alphabetic order. but with limited success. It's known that an enemy of the rats in the Indian mongoose. Free Dinner Ten young people decided to celebrate leaving school by a dinner at a restaurant. And when they had multiplied still further they set about devastating orchards. The number of snakes soon dropped all right. an inveterate killer of poisonous snakes. yet others. The island was suffering from an abundance of poisonous snakes. To get rid of them it was decided to introduce the secretary-bird. goat-kids. by age. sit at . the mongooses began to consume whatever came their way and turned into omnivores. He said: "My young friends. or even by their height. So the inhabitants of the island were compelled to start combating their previous allies. They became a plague of the country and their eradication required great expense and effort. A third instructive story comes from Jamaica. But alas. The rats wrought dreadful havoc amongst the sugar cane fields and posed an urgent problem. poultry. and so it was decided to bring four pairs of these animals to the island and allow them multiply freely. Later the same situation with rabbits occurred in California. It was the waiter who made it up between them. The mongooses adapted perfectly to their new land and in a short period of time inhabited the island. having destroyed the rats. by their academic record.238-239 Stories about Giant Numbers A further example. They started killing puppies. There were no rabbits in Australia when the continent was colonized by the Europeans. piglets. but nobody sat down at the table. The argument dragged on. but instead the island got to be infested with the rats that earlier were controlled by the snakes. When all had gathered they started arguing as to how they were to sit at the table. But as we have two pairs. it is 3. Further. (1) D behind the triple. AB and BA. C. Let's label them A. (2) B in front of the pair. In how many ways may we attach D to each of the six arrangements of three? Obviously. but because the number of arrangements was too great. We would like to know in how many ways it's possible to permute them. We argue as follows: if for the moment we put B aside. B. You can see this number of days equals to almost 10. Clearly. the two remaining objects may be arranged in two ways. They didn't live to see it. Let there be four objects A. We may place it in each of three ways: (1) B behind the pair. We'll again put aside one object and make all the possible permutations with the remaining three. there are no other positions for B besides these three. We will now attach B to each of the two pairs. (2) D in front of the triple.238-239 Stories about Giant Numbers the table arbitrarily and listen to me. B. To begin with. and D. (3) B between the members of the pair. We know already that there are six of these. however. and C. until you have tried out all the arrangements possible. say three. we may place it as follows.000 years! It might seem unlikely to you that as few as 10 people might be arranged in such an enormous number of various ways but we can check it. we'll repeat the argument for four objects." The ten set anyhow and the waiter continued: "Let somebody record the order in which you are sitting now. The day after tomorrow you sit in a new order. And not because the waiter didn't keep his word. then upon my word. we must learn how to find the number of permutations possible. When you come to sit in exactly the same order as you are sitting now." The party liked the suggestion. To make our life easier we'll begin with a small number of objects. . It was decided to come every night and try all the ways of sitting at the table in order to enjoy the free dinner as soon as possible. then there are 2 x 3 = 6 ways of arranging the objects. Tomorrow come here again to dine and sit in another order.628. I'll start to treat you to the finest dinners without charge. Specifically.800. and so on. it's somewhat more difficult to work it out. What is the number of ways in which the five girls may occupy the vacant chairs between the boys? Clearly.800.238-239 Stories about Giant Numbers (3) D between the first and second objects. then from his successor. Although the number of the possible permutations is far less in this case. Tnis will in fact give the above-mentioned 3. and so on. For six objects: 1 x 2 x 3 x 4 x 5 x 6 = 720. . too.800. Since the total number of chairs is 10. hence the number of all possible arrangements for the boys is 10 x 24 = 240. The remaining four may only be seated in alternate chairs (leaving the vacant places for the girls) in 1 x 2 x 3 x x 4 = 24 various ways. and 2 = 1 x 2 . Return now to the case of the 10 diners. and since 6 = = 2 x 3 . The above number is smaller by far than the previous one though it would require almost 79 years to work through them all. Combining each of the 240 positions for the boys with each of the 120 positions of the girls we obtain the number of all the possible arrangements: 240 x 120 = 28.628. then the number of permutations may be represented as the product 1 x x 2 x 3 x 4 = 24. the number of permutations is 1 x 2 x 3 x x 4 x 5 = 120. if not from the waiter himself. We thus get 6 x 4 = 24 permutations. 1 x 2 x 3 x 4 x 5 = 120. The calculation would be more complex if among the 10 diners there were five girls who wanted to alternate with the boys. the first boy may be seated in 10 ways. Reasoning along the same lines we'll find that for five objects. The number of permutations possible here is obtainable if we take the trouble of multiplying together I x 2 x 3 x 4 x 5 x x 6 x 7 x 8 x 9 x l 0 . Let one boy seat at the table somewhere. they could get the free dinner. Should the young guests of the restaurant live to be 100. (4) D between the second and third objects. Unity Obtain unity using all ten digits. 12 + 34 . 12.4 + 5 + 67 + 8 + 9 = 100. Use them to obtain the following numbers: 15. Now try and obtain 100 using only three plus or minus signs. With Ten Digits Obtain 100 using all ten digits. Try and find another combination of these digits that would yield 55. e.5 + 6 . 321. you proceed thus: 123 + 4 . You can as above arrive at 100 by inserting a plus or minus six times and get 100 thus: 12 + 3 .5 + 6 7 . Once More with Five Twos Is it possible to obtain 28 using five twos? .Tricks with Numbers Out of Seven Digits Write the seven digits from 1 to 7 one after the other: 1 2 3 4 5 6 7.g. In how many ways can you do it? There are no less than four different ways. It's easy to connect them by the plus and minus signs to obtain 40. It's much more difficult but possible.8 9 = 100. With Five Twos We only have five twos and all the basic mathematical operation signs at our disposal.7 = 40. If you want to use only four plus or minus signs. 11. Nine Digits Now write out the nine digits: 1 2 3 4 5 6 7 8 9. 7. In Four Ways Represent 100 in four various ways with five identical digits. Is that possible? With Five Threes To be sure. 6. It's more of a problem to obtain 15 and 18 using four threes: 15 = ( 3 + 3) + ( 3 x 3). Use four twos to arrive at 111. But can you write 10 with five threes? The Number 37 Repeat the above problem to obtain 37. 2. 8. with the help of five threes and the mathematical operation signs we can represent 100 as follows: 33 x 3 + y = 100. With Four Threes The number 12 can be very easily expressed with four threes: 12 = 3 + 3 + 3 + 3. 18 = (3 x 3 ) + (3 x 3). With Four Fours If you have done the previous problem and want some more in the same vein.250-251 Tricks with Numbers With Four Twos The problem is more involved. 10. try to arrive at all the numbers . 3. 9. And if you were required to arrive at 5 in the same way. 4. you might be not very quick to twig that 5 = Now think of the ways to get the numbers 1. Cross out Nine Digits The following columns of five figures each contain 15 odd digits: . It's more difficult to do this with other sets of identical digits. Could you do this using other sets of three identical digits? The problem has several solutions. With Four Fives Obtain 16 using four fives.256-253 Tricks with Numbers from 1 to 10 with fours.000 with the aid of eight identical digits? Get Twenty The following are three numbers written one below the other: 111 111 999 Try and cross out six digits so that the sum of the remaining numbers be 20. you'll may be able to find several solutions. One Thousand Could you obtain 1. With Five Nines Can you provide at least two ways of getting 10 with the help of five nines? Twenty-Four It's very easy to obtain 24 with three eights: 8 + 8 + 8. Try it. Thirty The number 30 can easily be expressed with three fives: 5 x 5 + 5. This is no more difficult than getting the same numbers with the threes. give more than if multiplied together? The Same Which two integers.252-253 Tricks with Numbers 1 1 3 3 5 5 111 9 9 1 3 5 9 The problem is to cross out nine digits so that the numbers thus obtained add up to 1. give 7? Don't forget that both numbers should be integers. if multiplied together. Other numbers are called composite. if multiplied together. Which year is it? Which Year? In this century. if added up. give the same as if added up? . Add and Multiply Which two integers. therefore answers like 3 1 / 2 x 2 or 2 1 / 3 x 3 won't do. give the same as if added up? Even Prime Numbers You must know that prime numbers are those that are divisible without remainder by themselves only or by unity. What do you think: are all the even numbers composite? Are there any even prime numbers? Three Numbers Which three integers. if multiplied together.111. is there a year such that the number expressing it doesn't change if viewed "upside down"? Which Numbers? Which two integers. In a Mirror The number corresponding to a year of the last century is increased 41/2 times if viewed in a mirror. Maybe you can find several pairs with the same property. Find the number. we get exactly 10 times more than if we add them up: 12 x 60 = 720. You maybe are unaware that there are dissimilar numbers showing the same property. Two Digits What is the smallest positive integer that you could write with two digits? The Largest Number What is the largest number that you can write with four ones? . So that you don't believe that the search would be in vain I assure you that there are many such number pairs. 12 + 60 = 72. Multiplication and Division Which two integers yield the same result whether the larger of them is divided by the other or they are multiplied together? The Two-Digit Number There is a two-digit number such that if it is divided by the sum of its digits the answer is also the sum of the digits. 2 x 2 = 4. though none of them are integers. Think of examples of such numbers.258-253 Addition and Tricks with Numbers Multiplication You've undoubtedly noticed the curious feature of the equalities: 2 + 2 = 4. This is the only case where the sum and product of two integers (equal to each other at that) are equal. Ten Times More The numbers 12 and 60 have a fascinating property: if we multiply them together. Try and find another pair like this. All the digits (save for 0) are used in it once.458. Use the nine digits to obtain the following fractions: 7' 1 1 1 1 J_ J_ J_ J' J' J' 7' 8~' 9 ' Multiplier? What Was the A schoolboy carried out a multiplication. then rubbed most of his figures from the blackboard so that only the first line of the figures and two digits in the last line survived. the fraction is 1/2. As to the other figures.254-255 7ticks with Numbers Unusual Fractions Consider the fraction 6729/13. As is easily seen. only the following traces remained: 235 x #* * * * * + * * * # *56 Could you restore the multiplier? Missing Figures In this multiplication case more than half the figures are replaced by asterisks: x 1 32 •3 + 32 25 1830 Can you restore the missing figures? What Numbers? A further problem of the same sort: . how many of them are there? Mysterious Division What is given below is nothing but an example of a long-division sum where all the digits are replaced by points: . It's remarkable in that each of the nine digits is involved once here. 7. Can you think of any other examples? If so. Determine the result of the division. The problem has only one answer. Not one digit in either the dividend or the divisor is known. .632. . It's only known that the last but one digit in the quotient is 7.260-253 5 x j 2*5 130 *** 477 Tricks with Numbers + Strange Multiplication Cases Consider the following case of the multiplication of two numbers: 48 x 159 = 7. Another Triangle Repeat the previous problem so that each side adds up to 17. Magic Star The six-pointed star shown in Fig. that divides by 11 without remainder. 1 1 + 6 + 8 + 1 = 26.256-253 Tricks with Numbers Another Division Problem Restore the missing figures in the division below: 1 325) * 25* 0* * g** Figure 230 5 Division by 11 Write out a nine-digit number containing no repeated digits (all the digits are different). 4 + 8 + 12 + 2 = 26. 1 1 + 7 + 5 + 3 = 26. too. 1 + 1 2 + 1 0 + 3 = 26. . 231 insert one of the numbers from 1 to 16 so that the sum of the numbers on the side of each square be 34 and the sum of the numbers at the corners of each square be 34. Eight-Pointed Figure 232 Star Into the circles of the figure of Fig. 230 arrange all the nine digits so that the sum of the digits on each side be 20. 232 is "magic" because all the six lines of numbers have the same sum: 4 + 6 + 7 + 9 = 26. What is the largest such number? What is the smallest such number? Triangle of Figures Figure 231 Within the circles of the triangle of Fig. 9 + 5 + 10 + 2 = 26. Trident Figure 234 It's required to arrange the numbers from 1 to 13 in the cells of the trident shown in Fig. Couldn't you improve the star so that the numbers at the points also gave the same sum (26)? Wheel of Figures The digits from 1 to 9 should be so arranged in the circles of the wheel of Fig. and III) and in the line (IV) are the same. 233 that one digit is at the centre and the others elsewhere about the wheel so that the three figures in each line add up to 15.Tricks with Numbers However the numbers at the points of the star add up to another number: Figure 233 4 + 1 1 + 9 + 3 + 2 + 1 = 30. . II. 234 so that the sums of the figures in each of the three columns (I. 5679 " 8 ~ \ etc.3 + 45 .+ 5 \ = 1 0 0 .+ 3 ^ .789°. since any number to the zeroth power is unity. Nine Digits 123 . 1 . 12 . This is the only solution..3 .4 + 56 + 7 = 55. It's impossible to arrive at the same result by using the plus and minus signs less than three times.6 + 7 = 55. j bU 1 38 50 — + 49 — = 100. 2 76 U nity Represent unity as the sum of two fractions: 148 35^_1 Those knowing more advanced mathematics may also give other answers: 123.6 7 = 55.258-283 There are three solutions: Answers Out of Seven Digits 123 + 4 . . 54 6 84 + 9 ^ .= 100. 18 6 27 3 80 — + 1 9 .2 . With Ten Digits The following are the four solutions: 70 + 2 4 ^ . 234.= 100.67 + 89 = 100.5 .45 .456. ^ . .321. The problem is manageable. five sevens. Here is the solution: 222 Y = ill2 = i n x 111 = 12.^ . Now the number 12. or. with any five identical digits. ~ + 2)_\| = 1 5 . (2 x 2)2 — y = 15. however. 3 3 It's worth mentioning that the problem would have had exactly the same solution if we had had to express 10 with five ones. With Four Twos 222 ^==.+ 2 + 2 = 15. in general. And 11 as: 22 — + 2-2=11.+ 2 x 2 = 15. five fours.= 111. it would seem impossible to write this five-digit number with five similar figures. 2(2 + . With Five Threes The solution is: 33 3 ^ . At first sight.Answers With Five Twos Write 15 as: (2 + 2)2 — y = 15.4 = 1 0 . five nines. In fact: 11 1 1 22 =r 1 2 2 44 — 2 4 4 99 — 4 9 9 PtC 9 ' ' . Once More with Five Twos 22 + 2 + 2 + 2 = 28.321. threes and (most conveniently) fives: 111 . (5 + 5 + 5 + 5) x 5 = 100. In Four Ways We can use ones. .260-261 Answers Also. „=y y 2 3 = 1 33 (there are also other ways). 3 3 The Number 37 There are two solutions: 33 + 3 + y = 37. 5 x 5 x 5 .11 = 100. 3+3+3 3 3x3 + 3 4 = 6 = (3 + 3 ) x j . 3x3 =37.5 x 5 = 100. there are other solutions to the problem: 3x3x3+3 3 33 3 _ — + — = 10. 33 x 3 + y = 100. 333 . With Four Threes 33 + . swers We've given the solutions through six only. 8 = 4 + 4 + 4 .. With Four Fours 1 = 44 4+ 4 r 4 4 ' ° 4 ^ 4 ' °r 4 4 + 4x4 474 . 4 x4 4T4 4x4-4 . 2 =4 4' °r 3= 4+4+4 : . too. 4 + 4 4 44 7 = 4 + 4 — —. 10 = With Four Fives There is only one way: 55 — + 5 = 16. etc.4 . 6 = — . may be represented with other combinations of threes.4 .— + 4.. or 4 = 4 + 4 x (4-4). The above solutions. With Five Nines The two ways are as follows: 99 .X n. 5 _ 4x 4+ 4 ~ • * . Work out the remaining ones for yourselves. or . or 9=4+4+ 44-4 4 4 ' 4x4-4-4. 6 = 30. or 9 + 99 9 ~ 9 = 10. Twenty-Four The two solutions are: 22 + 2 = 24. Cross Out Nine Digits The problem permits of several solutions.3 = 24.V = 10. Thirty The three solutions are 6 x 6 . One Thousand 3 3 + 3 = 30.3 = 30. 888 + 88 + 8 + 8 + 8 = 1. We 100 111 011 000 030 330 005 000 000 007 070 770 999 900 000 furnish four: 101 303 000 707 000 1111 1111 1111 1111 . e.262-283 A nswers 99 9 9 9 9 10 ' Those knowing more mathematics may add several other solutions. 33 .g. Get Twenty The crossed out digits are replaced by zeros: 011 000 009 because 11 + 9 = 20. 3 3 .000. 9 + \| . Add and There are many such numbers. Which Year? In the 20th century there is only one such year. There are no other integers. Multiply 1 0 x 1 = 10. 1961. viz.A nswers u In a Mirror The only figures that are not inverted in a mirror are 1. This is because adding one increases a number and multiplying by one does not change it. There are no other numbers. Multiplying 1. The problem has no other solutions. 3x1=3. Even Prime Numbers There is one even prime n u m b e r . the year we seek can only contain these figures. which is 41/2 times more than 1818. hence the first two figures are 18. The Same The numbers are 2 and 2. Accordingly.2 . Three Numbers 1 x 2 x 3 = 6. or 3 + 1=4. 2. we know that the year is in the 19th century. . It's easily seen now that the year is 1818 because in a mirror we obtain 8181. 0. It only divides by itself and 1.g. Besides. In general. e. 1 0 + 1 = 11. and 3 gives the same as adding them up: 1 + 2 + 3 = 6. Which Numbers? The answer is simple: 1 and 7. In fact. and 8. any pair of integers of which one is unity will work. 1818 x 41/2 = 8181. 20 and 20.^ 1 = 7. Number The Two-Digit The number we seek should clearly be a square.01 = 102. then by trial-and-error method we readily find the unique solution.1 1 1/20 = 22 1/20. 21 + 1 1/20 = 22 1/20. 1. 5 + 1 1 / 4 = 6 1/4. 14 and 35. 43 1 = 43. As among the two-digit numbers there are only six squares. 11x110=1. Multiplication 1 1/4 = 6 1/4.01. 1 1/8 = 10 1/8. For example. . and Division There are many correct number pairs. 11 + 110 = 121.1 = 12. Searching for the solutions by trial and error is tiresome and a knowledge of the ABC of algebra would make the process easier and enable us not only to find all the solutions. namely 81: = 8 + 1 8TT - Ten Times More The following are the four other pairs of such numbers: 11 and 110. 11 + 1.210. 20 = 40. The problem has no other solutions. 2x1=2. 9 + 1 1/8 = 10 1/8. 101 + 1. 1. 20 = 400 .01. 2 4-1=2. but also to make sure that the problem doesn't have more than five solutions. 14+ 15 + 20+ 35 = 49.1 = 12. 5 9 11 21 101 X X X X X There are a lot of such pairs. 15 and 30. In fact. 30 = 45. 14 x 15 x 20 x 35 = 490.264-265 Answers Addition and Multiplication 3 x 1 1/2 = 4 1/2. 7 x 1 = 7. 30 = 450. 43 x 1 = 43.01 = 102. etc.1. 7 . Examples are: 3 + 1 1 / 2 = 4 1/2. 000 times more. 2°.429 ' There are many versions. one of which may be either 0 or 5. Accordingly. What Was the Multiplier? We argue as follows. then the upper is 6.381 57.658 ' 3. Unusual Fractions There are several solutions.496 ' 1 9 6.697 13. . 250.394 16. * But the solutions — or 0° would be wrong because they are meaningless. etc.187 25. l l 1 1 is much more.A nswers is f- Two Digits 1.943 17. expressed as follows: 9 7" Many may believe that the number is 10.758 1 4 1 6 1 8 3. the lower figure of the last but one column must be 5 and above it 1. may the upper figure be 6? Testing shows that whatever the second figure of the multiplier.768 2.942 15. because any number to the zeroth power is unity.823 17.111. if the lower one is 0. But. But the number is far from being the largest. it's 1 2 3 4 7' 7' 7' T' etc " up to Those who know some more mathematics may add to these answers a number of others: 1°. 4°. 6 cannot be in the last but one place of the first partial product. The Largest Number The commonest answer is 1. No. up to 9°.469 2. 3°.485 2. But..000. especially the ones for 1/8 of which there are more than 40. One of them is 1 3 1 5 1 7 5. The figure 6 is the result of the addition of two figures. the meaning of the first asterisk in line I becomes clear: it is 4. We have: 235 x 6 1 410 + *5 560 Reasoning further along the same lines we find that Missing Figures the multiplier is 96. We can now guess the meaning of the asterisk in line II. Let's try 6 and this works out all right. Suffice it to multiply together the . This figure must give a number ending in zero when multiplied by 2. Now we determine the value of the last asterisk in line I. Eventually. which follows from the fact that 0 is at the end of line VI. It cannot be 5 as we won't then get 1 in the last but one place. when multiplied by 8. because only 4. and a number ending in 5 (line V) when multiplied by 3. The remaining figures now present no problem. It's 8 because only when multiplied by 8 the number 15 gives a result ending in 20 (IV). For convenience we assign numbers to the lines i x I 32 II III IV V VI 3* 32 + 25 1830 It's easily seen that the last asterisk in line III is 0. The missing figures are restored one after another if we use the following argument.266-261 Answers We can now easily restore some of the missing figures: 235 x + 56* The last figure in the multiplier must be more than 4. otherwise the first partial product will not consist of four figures. gives a result beginning with 3 (line IV). There is only one such figure-5. 396.796. 4 x 1738 = 6.852. 48 x 159 = 7. 27 x 198 = 5. 4 x 1963 = 7.346.632. Mysterious Division 7.346. I II III IV V VI VII For convenience. We get x 325 147 + 2275 1300 325 47775 Strange Multiplication Cases multiplication The patient reader can find the following nine cases where the calculations meet the question's demands.796. They are: 12 x 483 = 5.952.A nswers numbers of the first two lines that have We'll end up with the multiplication: x now been completely determined. too. 18 x 297 = 5. we'll number the lines in the arrangement thus: ) . 42 x 138 = 5.254. 39 x 186 = 7. 28 x 157 = 4. 415 382 830 3320 1245 158530 What Numbers? Arguing as above we uncover the meaning of the asterisks in this case. 996 124 Another Division Problem The answer is: 162 325) 52650 325 2015 1950 650 650 . 10.085 115 10.879. otherwise.964 116 10.480 120 10. gave a difference not less than 100. it wouldn't give a two-digit difference when subtracted from a four-digit number.238 122 11. i.541. Accordingly. viz.601 119 = 90.268. Lines IV and V indicate that Ix (the product of the last but one digit in the quotient and the divisor).118 10. This actually completes the problem as the desired result (the quotient) has now been found. we see that the number in line III is more than 900.117 123 11.905.268-261 Looking at line II we conclude that the second figure of the quotient is 0 as it was necessary to borrow two figures from the dividend. The numbers in I and VII are four digits long hence the third digit in the quotient is 8 and the extreme left and right digits are 9. Further.e. Thus the third digit of the quotient should be 900 —128. more than 7. 899.360.814.206 114"^ 10. it is either 8 or 9.632. The problem doesn't require us to decipher the whole of the arrangement.843 117 10.722.359 121 11. Denote the divisor by x. there are 11 pairs of numbers that satisfy the given arrangement of points and give 7 in the fourth place of the quotient.178. Besides. 10. It's not necessary to go on with the argument to find the dividend and divisor.03.996. Ix cannot exceed 999 — 100. e. i.879. Clearly. when it was subtracted from a number not larger than 999. It is 90. as we wanted the quotient only.087.723. hence x is not larger than 128.451. Take another number-7. By way of example.904. 21 . hence the number divides by 11.586.049. 7 + 4 + 5 + 5 = 21. A number is divisible by 11 if the difference between the sum of the even digits and the sum of the odd digits either is divisible by 11 or is zero. Now we can easily work out the order in which we should write the nine digits so as to arrive at a number that is a multiple of 11 and meets the conditions of the problem.652. Let's test it: 3 + 2 + 4 + 7 + 6 = 22. The sum of the digits in the even places is 3 + 5 + 9 + 4 = 21 and the sum of the digits in the odd places is 2 + 6 + 8 + 0 = 16.347. 235. Of these numbers the largest is 987. The difference (5) doesn't divide by 11 nor is it zero. Figure 235 .16 = 5.413.786. hence the number under consideration doesn't divide by 11. Yet another example is 352. As 11 divides by 11.1 0 = 11.A nswers 1S Division by 11 To solve the problem requires the knowledge of the criterion of divisibility by 11. Triangle of Figures The solution is shown in Fig. 5 + 0 + 9 + 8 = 22. and the smallest is 102. test the number 23.535: 3 + 4 + 3 = 10. the number in question is a multiple of 11.344. The difference is 22 — 22 = 0.658. The figures in the middle of each line can be interchanged to obtain further solutions. Their difference (we subtract from the largest) is 21 . Figure 238 . with each number at the vertex entering twice.e. But as the sum of the three internal pairs (i. On each side we have 26. of the internal hexagon) is known to be 52. Also. but the sum of all the numbers in the star is 78. and for all the three we get 26 x 3 = 78. Now let's look at one of the large triangles. the solution is given in Fig. then the double sum of the numbers at the vertices of each triangle is 78 — 52 = 26. the numbers on the internal hexagon is 78 . Figure 237 Magic Star To make our life easier we'll start off with the following considerations. the single sum is thus 13. The numbers at the points must add up to 26.270-283 A nswers Another Triangle Again. Accordingly. 237.26 = 52. Figure 236 Eight-Point-Star The solution is in Fig. the figures in the middle of each line can be interchanged to obtain further solutions. 236. 240). Wheel of Figures The solution is given in Fig. that neither 12 nor 11 can be at the star points (why?). Hence the tests might be begun with 10. Figure 240 7 9 .A. Figure 239 Trident The following is the desired arrangement (Fig. In that case we immediately determine the two numbers that must occupy the remaining vertices of the triangle: 1 and 2. It's shown in Fig. We know. Moving on after this manner we eventually arrive at the desired arrangement. for instance. Answers The field of search has now been narrowed markedly. 239. 238. The sum of the numbers in each of the four lines is 25. How many are we? How Many Children? Figure 241 I have six sons. hence 4 x 9 = 36. not 56. Place both hands on a table. This living computer will remind you. Further examples: how much is 7 x 9 ? Your seventh finger has six fingers on its left and three on its right. But my sister has two times more brothers than sisters. Suppose you want to multiply 4 by 9. How many children have I? . So you read: 36. that 6 x 9 is 54. for example. Each son has a sister. Cats and Mats Once some cats found some mats. The answer is 81.272-273 Merry Arithmetic Simple Multiplication If you don't remember the multiplication table properly and have difficulty in multiplying by 9. six. then your own fingers might be of help. But if each mat had but one cat there's be a cat without a mat. Your fourth finger gives the answer : on the left of it there are three fingers. How many cats and how many mats? Sisters and Brothers I have an equal number of sisters and brothers. on the right. What is 9 x 9? On the left of the ninth finger there are eight fingers. on the right. The answer: 63. one. your 10 fingers will be your computer. Should each mat now have two cats there'd be a mat without a cat. please tell me how old your son is?" "His is as many weeks old as my grandson is days old. boy my she my will be twice as old as he was two girl in three years will be three was three years ago. And times as old as Who is older. Now guess how old each of us is. boy or my girl? The Age of the Son Now my son is a third my age. How do you account for it? Three Quarters of a Man A team leader was asked how many people there were in his team." "How old are you. how old is he?" "His age is as many months old." Figure 242 Who is Older? In two years my years ago. each having a whole egg." "And your grandson. But five years ago he was a quarter my age. The answer was: "If you take thrice my age in three years and subtract thrice my age three years back." Could you compute the number of people in his team? How Old Are They? "Gran'pa." How old is he now? Three Daughters and Two Sons An uncle visited his two nieces and three nephews. as I am years old. The first to greet him were little Johnny and his . He answered in a rather involved way: "Not many: three quarters of us plus three quarters of a man. that's all. How old is he? His Age A witty person was asked about his age.Merry Arithmetic vP Breakfast Two fathers and two sons breakfasted on three eggs. then?" "Together the three of us are 100 years old. then you'll have my age precisely. When Alexis came from school the father reckoned that both boys together are twice as old as both girls. However." How old was each son and daughter? Two Trade Unionists I remember hearing a conversation between two trade unionists: "So you've been a trade union member twice as long as me?" "Yes." How many years has each of them been a trade union member? How Many Games Three persons were playing draughts. Each day it climbed 5 metres." "And you know what?" the father added. How many days did it take the snail to reach the summit? To the Town A farmer was travelling to a town. "It just occurred to me that my three daughters together are two times older than my sons. How many games had each of them played? Figure 243 Snail A snail was climbing up a 15-m tree." "Two years back? Then that was so. but each night as it slept it slid back down 4 metres. exactly twice. Then Nadine ran out to meet the uncle and her father said that both girls together were twice as old as the boy. you just arrived on my birthday. the second half of the route he . The latest to come was Libby. The first half of the route he went by train. Today I'm 21. 15 times faster than if he had gone by foot. The little chap proudly declared that he was twice as old as his sister.274-275 Merry Arithmetic sister Anne. They had played three games." "But last we met you said that you'd been a member three times longer. she saw the guest and exclaimed happily: "Uncle. but now I've only been twice as long as you. "Give me an apple." How many apples had each initially? Binding Here is an insidious problem. How much time did he save as compared with walking all the way to the town? Figure 244 To the Village From a town to a village the road first goes uphill for 8 kilometres. and ril have twice as many as you. The belt costs 60 kopecks more than the buckle.Merry Arithmetic rode on an oxcart. again non-stop. then 24 kilometres downhill. How much does the binding cost? The Cost of Buckle A belt with a buckle costs 68 kopecks. and spent 4 hours 30 minutes. A bound book costs 2 roubles 50 kopecks. The book is 2 roubles more expensive than the binding. "You give me one then we'll even. How much does the buckle cost? ." replied the mate." "That would be unfair. at half the speed of a walker. How fast could John ride uphill and how fast downhill? Two Schoolboys A schoolboy said to his mate. He also bicycled back. John went there on a bicycle and the non-stop journey there took him 2 hours 50 minutes. 276-277 Figure 245 Merry Arithmetic Casks of Honey In store there were seven casks brim full of honey. Postage Stamps A man bought a 5 roubles worth of postage stamps of three kinds: 50-kopeck stamps. How many single socks and gloves is it sufficient to take from each box to have any one pair of socks and gloves? . How many stamps of each kind did he buy? How Many Coins? A customer got his change of 4 roubles 65 kopecks. and seven empty casks. indicate all those which occur to you. all in 10 and 1-kopeck coins-in all. 42 coins. How can they divide without transferring the honey from one cask into another? If you think that various ways of doing so are available. all belonging to three firms that wanted to divide both the honey and casks into equal shares. 10-kopeck stamps and 1-kopeck stamps-100 pieces. another contains 10 pairs of brown and 10 pairs of black gloves. How many coins of each worth was he given? How many solutions has the problem? Socks and Gloves One box contains 10 pairs of brown and 10 pairs of black socks. seven half-full ones. all told. Figure 246 There are insects that feed on books eating their way through leaves and thus ruining the bulk of the book. One such book worm has eaten through from the first page of the first volume to the last page of the second volume on a bookshelf, as shown in the accompanying figure. There are 800 pages in each volume so, how many pages has the worm ruined? The problem is not difficult but it has a catch. Spiders and Beetles A boy collects spiders and beetles in a box and he now has 8 insects in all. There are 54 legs in the box in total. How many spiders and how many beetles are there? Seven Friends A man has seven friends. The first visits him every night, the second every other night, the third every third night, the fourth every fourth night, etc., through to the seventh friend who comes every seventh night. Figure 247 Is it often the case that all the seven friends get together there on the same night? The Same Problem Continued On those nights when the seven friends get together the host treats them to some wine, and all touch glasses in pairs. How many times do the glasses ring as they touch one another? Cats and Mats This problem is solved in this way. Ask the question: How many more cats would be needed to occupy all the places on the mats the second time than to get the situation we had the first time? We can easily figure that out: in the first case one cat was left without a place, whilst in the second case all the cats were seated and there were even places for two more. Hence for all the mats to have been occupied in the second case there should have been 1 + 2, i. e. three, more cats than there were in the first case. But then each mat would have one more cat. Clearly there were three mats all in all. Now we seat one cat on each mat and add one more to obtain the number of cats, four. Thus, the answer is four cats and three mats. Sisters and Brothers Seven: four brothers and three sisters. Each brother has three brothers and three sisters; each sister has four brothers and two sisters. How Many Children? Seven: six sons and one daughter. (The common answer is twelve, but each son would then have six sisters, not one.) Breakfast The situation is very simple. Seating at the table were three, not four people: a grandfather, his son, and his grandson, l l i e grandfather and his son are fathers, and the son and grandson are sons. Three Quarters of a Man Note that the three-quarters-of-a-man is the last quarter of the team. So the whole of the team is four times the three quarters of a man, i. e. three. In consequence, the team consisted of three men. How Old Are They? We know thus that the son is 7 times, and the grandfather 12 times, older than the grandson. If the grandson were one year old, the son would be seven, and the grandfather 12. Adding the three together gives 20, which is exactly a fifth of the real figure. It follows that in actuality the grandson is five, the son 35, and the grandfather 60. Check: 5 + 35 + 60 = 100. A nswers Who is Older? Neither is: they are twins and each of them at the time is six. The calculation is simple: two years hence the boy will be four years older than he was two years ago, and twice as old as he was then. Hence he was four years old two years ago. Accordingly, now he is 4 + 2 = 6 years old. The girl's age is the same. The Age of the Son If now a son is one third the age of his father, then the father is older in years by twice the son's age. Five years ago the father was, of course, also twice his son's present age older than his son was then. On the other hand, since at that time the father was four times older than the son, he was older by the triple then age of the son. Consequently, the double present age of the son equals the triple then age of the son. Thus, the son is now 11/2 times older than he was five years ago. It follows that five years is a half of the son's previous age, and hence five years ago the son was 10, and now he is 15 years old. Thus, the son is now 15 years and the father 45. Checking this, five years ago the father was 40 and the son was 10, i.e. a quarter the father's present age. His Age Arithmetically the problem has a rather involved solution, but the situation simplifies considerably if we draw on the services of algebra and set up an equation. We'll denote the number of years we're after by x. The wit's age in three years will then be x + 3, and three years ago, x — 3. We'll thus have 3 (x + 3) - 3 (x - 3) = x The equation gives x = 18. So the witty person's age is at present 18 years. Let's check. In three years time he'll be 21 and three years ago he was 15. The difference is 3 x 21 - 3 x 15 = 63 - 4 5 = 18, which equals the present age of the man. Three Daughters and Two Sons We know that Johnny is twice as old as Anne, and Nadine and Anne together are twice as old as Johnny. Accordingly, the sum of the ages of Nadine and Anne is four times more than Anne's age. It follows directly that Nadine is three times as old as Anne. We also know that the ages of Alexis and Johnny combined are twice the combined age of Nadine and Anne. But Johnny's age is double Anne's age, and the ages of Nadine and Anne put together give the fourfold age of Anne. Accordingly, Alexis's age plus the double age of Anne are equal to the eightfold age of Anne. Thus, Alexis is six times older than Anne. Lastly, as stated, the ages of Libby, Nadine, and Anne combined equal the sum of the ages of Johnny and Alexis. For convenience, we'll compile the table: Libby Nadine Johnny Alexis 21 years three times older than Anne two times older than Anne six times older than Anne We can now say that 21 years plus the trebled Anne's age plus an Anne's age are equal to the fourfold Anne's age plus the twelvefold Anne's age. Or, 21 years plus the fourfold age of Anne are equal to the sixteen-fold age of Anne. In consequence, 21 years are equal to the twelve-fold age of Anne and Anne is thus 21/12 = 1 3/4 years. •We can now easily determine that Johnny is 3 1/2, Nadine 5 1/4, and Alexis 10 1/2. Two Trade Unionists One has been with the trade union for eight years, the other for four years. Two years ago the first one had been with the trade union six years, the second two years, i.e. three times as long. The problem is readily solvable using an equation. How Many Games? The commonest answer is that each played once, ignoring the fact that three (and any odd number in general) players cannot each play only once for who then did the third player play? It takes two partners to have a game. If we denote the players by A, B, and C, the three games will be A with B A with C B with C We see that each played twice, not once: A with B and C B with A and C C with A and B So the answer is: each of the three played twice, although three games had been played in all. Snail In 11 days. During the first 10 days the snail had crawled up 10 metres, 1 metre a day. The next one day it climbed the remaining 5 metres, i. e. it reached the summit. (The common answer is 15 days.) To the Town The farmer lost time, he did not save it. The second half of the route took as much time as he would have spent travelling to the town on foot. He thus could not save A nswers time, he was bound to lose time. His loss amounted to 1/15 of the time required to cover half a route on foot. To the Village The solution of the problem follows from the following calculation: 24 kilometres uphill and 8 kilometres downhill took 4 hours 30 minutes; 8 kilometres uphill and 24 kilometres downhill took 2 hours 50 minutes. If we multiply out the second line by three, we obtain: 24 kilometres uphill and 72 kilometres downhill takes 8 hours 30 minutes. A bit of algebra gives that the bicyclist covers 64 kilometres downhill in 4 hours. Hence, downhill he travelled at 64/4 = 16 kilometres an hour. We'll find in much the same way that he travelled uphill at 6 kilometres an hour. Testing the answer is an easy exercise. Two Schoolboys Transferring an apple balances out the number of apples, thus suggesting that one had two apples more than the other. If we subtract one apple from the smaller number and add it to the larger number, then the difference will increase by two and become four. We know that then the larger number will be equal to double the smaller one. Accordingly, the smaller number is 4 and the larger 8. Before the transfer one schoolboy had 8 — 1 = 7 apples, and the other 4 + 1 = 5 apples. Let's check whether or not the numbers become equal if we subtract an apple from the larger and add it to the smaller: 7-1=6; 5 + 1 = 6. Thus, one schoolboy has 7 apples and the other 5 apples. Binding The off-the-cuff answer is usually: the binding costs 50 kopecks. But then the book would cost 2 roubles, i.e. it would be only 1 rouble 50 kopecks more expensive than the binding. The true answer is: the binding costs 25 kopecks, the book 2 roubles 25 kopecks with the result that the book costs 2 roubles more than the binding. The Cost of Buckle Perhaps you've decided that the buckle costs 8 kopecks. If so, you're mistaken, as the belt would then cost only 52 kopecks more than the buckle, not 60 kopecks more. The correct answer is the buckle costs 4 kopecks, then the belt costs 68 — 4 = 64 kopecks, i.e. 60 kopecks more than buckle. Casks of Honey The problem becomes a fairly easy exercise if we note that in the 21 casks bought there were 7 + 3 1/2 = 10 1/2 caskfuls of honey. Each firm must then get 3 1 / 2 caskfuls of honey and seven casks. A nswers We could divide them in the following two ways: First way f 3 full 1st firm i s 1 1 half-full 13 empty ( 2 full 2nd firmS 3 half-full 12 empty f 2 full 3rd firm < 3 half-full I 2 empty 3 full 1 half-full J > . 3 empty f T o t a l : 3 1/2 caskfuls of honey Second way [3 full 2nd firm ^ 1 half-full 3 empty ( 1 full 3rd firmi 5 half-full }• 11 empty There is only one answer: the customer bought 1 x 50-kopeck stamp 39 x 10-kopeck stamps 60 x 1-kopeck stamps Really, there were 1 + 39 + 60 = 100 pieces all in all, and the total cost was 50 + + 390 + 60 = 500 kopecks. How Many The problem has four solutions: I Roubles 10-kopeck pieces 1-kopeck pieces Total 1 36 5 42 II 2 25 15 42 III 3 14 25 42 IV 4 3 35 42 Socks and Gloves Three socks will be enough, as two of them are bound to be of the same colour. But with the gloves the situation is not that simple. These differ from one another not only in their colour, but also in that half of them are right-handed and half left-handed. Here 21 gloves will be sufficient. With a smaller number it might appear that all of them would be right-handed, or left-handed for that matter (10 pairs of brown left and 10 pairs of black left). Book Worm The common answer is that the worm went through 800 + 800 pages plus two covers. But this is not so. Stand two books side by side as shown in Fig. 246, and see how many pages there are between the first page of the first book and the last page of the second book. You'll discover that there is nothing but two covers between them. Thus the book worm had only destroyed the two covers without touching their leaves. Spiders and Beetles To tackle the problem we should first of all remember from your nature lessons how many legs beetles have and how many spiders have. In fact, the numbers are six and eight, respectively. With this in view we suppose that the box only contains beetles, either all told. Their legs would then add up to 6 x 8 = 48, six fewer than given in the problem. Let's now try and replace one beetle with one spider. This will increase the number of legs by two because the spider has two more legs. Clearly three such replacements will bring the total number of legs in the box up to the desired 54. But in that case there will only be five beetles, the rest being spiders. The box thus contained five beetles and three spiders. Let's check: five beetles give 30 legs, the three spiders 24, the total being 30 + 24 = = 54, as required. The problem can also be solved in another way. We may start off assuming that the box only contains spiders, eight of them. The number of legs will then be 8 x 8 = 64, 10 legs more than what was stated. Replacing one spider with one beetle reduces the number of legs by two. We'll have to make five such substitutions in order that to arrive at 54. Put another way, we'll retain only three spiders, with the rest being replaced by beetles. Seven Friends You should easily twig that the seven can only come together in a number of days that divides by 2, 3, 4, 5, 6, and 7. The smallest such number is 420. Consequently, the friends will only get together once every 420 days. The Same Problem Continued All of those present (the host and his seven friends) touch their glasses with those of the remaining seven. The number of combinations 2 at a time totals 8 x 7 = 56. But this counts each pair twice (e.g. the third guest with the fifth and the fifth with the third are considered as different pairs). Hence the glasses ring 56/2 = 28 times. without sorting them out. birches and aspens in the same hectare. Everything depends on what is to be counted. He cannot sort out all the trees according to their species. towels to another. That's what is called not knowing how to count! This way of handling dissimilar objects is utterly inconvenient. then all the birches and then all the aspens? Would you go all round the whole area four times? Couldn't the job be done in a simpler way. should you first count all the pines. Who can't? To utter the words "one". "three" etc. spruces. then all the spruses. It's no problem to count.. But try to place yourself into a forester's shoes who wants to count all the pines. the nails in a box. It's required to find out how many of each there are. etc. in succession doesn't take much genius. perhaps by a single tour of the area? Yes. She first sorts the washing out: shirts go to one heap. get a pencil and a sheet of paper marked out as shown below: Nails Screws . How could you go about it? Would you separate the heap into nails and screws and then count them? This sort of a problem comes up for a housewife when she has to count the washing for laundry. "two". Til illustrate its principle essence referring to our nails and screws. Well.284-285 Count Can You Count? The question might seem to be even insulting for a person more than three years old. And still I'm sure that you're not always equal to this seemingly simple task. And it's only after she had done this tedious job that she begins to count the items in each heap. say. But suppose the box contains screws as well as nails. It's all well and good if you have to count nails or washing: they are fairly easily sorted out into separate heaps. To count the nails and screw at one go. there is such a way and it has been used since time immemorial by foresters. labour consuming and occasionally even completely impossible. only now you'll have four columns or lines. after the first 10 dashes begin a new row. Take out a second piece and repeat the procedure. then a third. So you should begin with a sheet like this: . 250). The arrangement will be approximately as shown in Fig. If it's a nail you make a dash in "Nails". To do so we should not just dispose our dashes one under another. It's convenient to arrange these squares into pairs.Count Figure 248 Now begin counting. e. in the "Nails" column you'll have as many dashes as there are nails in the box. if it's a screw. etc. a fourth. We could simplify the counting procedure. until the box is finished. one plus three dashes. but group them as shown in Fig. 30 + 5 + 3 = 38. not two. then the third.. It only remains to count up the dashes. So they often figures in which each complete square means (Fig. i. lines being more convenient here. i. 248 with five dashes in each group. Figure 249 It's easy to count the dashes thus arranged: you at once that here we have three complete tens.e. Figure 250 see five use 10 When counting trees of different species in a forest area you should proceed in much the same way. 249. and in the "Screws" column as many dashes as there are screws. mark a dash in "Screws". In the end. Other figures are also possible. Take out of the box whatever comes first. and so on. It's a straightforward exercise here to work out the totals: Pines 53 Spruces 79 Birches 46 Aspens 37 . 251.286-287 Count Pines Spruces Birches Aspens Figure 251 Pfnes Spruces Birches Aspens You'll end up with about what is shown in Fig. a good eye. In the novel Anna Karenina by L. leaving several lines for other plants you may come across. Why Count Trees in a Forest? Why is it actually necessary to count the trees in a forest? Some town dwellers even think that it's impossible. without counting. You can see thus that counting is only a simple and easy business when handling similar objects. First write down the names of the plants found and allot a line to each.. thickness and height of its trees were representative of those in the entire forest. of course. When handling dissimilar things the just described procedures are needed. but only those in a definite area. "Count sands or rays from distant planets perhaps some lofty mind could. Selecting a representative sample area requires. 30 cm. . etc. They count not all the trees in a forest. And no peasant will buy. say a quarter or half a hectare that is so chosen that the density. but also the number of trunks of each gauge (say. for example. asked his naive relative who wanted to sell his forest: "Have you counted the trees?" "How can one count trees?" he answers in bewilderment. and proceed as if it were the forest survey. Should you need to count the plants of various species in a meadow you'll now know how to handle the job and do it in the shortest time possible. Now you can imagine how many times it would be necessary to go all round the area if the trees were counted in some other way. 35 cm." "Oh yes? But the lofty mind of Ryabinin (a merchant . Start off.. Tolstoy an agriculture expert.the author) can. with an arrangement like the one in Fig. 251.N. Levin. The report will therefore include more than four entries as it's in our simplified example. composition.)." The trees in a forest are counted to assess the volume of the wood in it.Count The same procedure is used by a medical worker who counts under the microscope red and white blood corpuscles in a blood specimen. The survey involves determining not only the number of trees of each species. then the ones ( 7 x 8 = 56) and add up the results (160 + 56 = 216). Further examples: 34 x 7 = 30 x 7 + 4 x 7 = 210 + 28 = 238. multiply the tens of the multiplicand (20 x 8 = 160). as you would do in a written operation. If one of the numbers to be multiplied together is representable in the form of two factors. When multiplying by a simple number (for example. 2. It would also pay to remember the multiplication table up to 19 x 9 : 2 11 3 33 36 39 42 45 48 51 54 57 4 44 48 52 56 60 12 13 14 15 16 17 18 19 22 24 26 5 55 60 6 66 72 7 77 84 8 88 9 99 65 70 75 80 28 30 32 34 36 38 64 68 72 76 85 90 95 128 144 102 119 136 153 108 126 144 162 114 133 152 171 78 91 84 98 90 105 96 112 96 108 104 117 112 126 120 135 Knowing the table you could multiply say 147 x 8 in your head as follows: 147 x 8 = 140 x 8 + 7 x 8 = 1120 + 56 = 1176. 3. not mechanically. as with written calculations. 27 x 8) don't begin by multiplying the ones.288-289 Fast Reckoning (Simple tricks of mental arithmetic) The following is a collection of simple and easily grasped tricks to speed up your mental arithmetic. Multiplication by Simple Number 1. First. it may be . 47 x 6 = 4 0 x 6 + 7 x 6 = 240 + 42 = 282. If you want to master them you should realize that to be used fully they need to be approached conscientiously. But it pays to master them as they'll enable you to do calculations in your head without error. For example: 6 x 28 = 28 x 6 = 120 + 48 = 168. 1 7 0 . 6. 5. one of them is mentally broken down into tens and ones. 112 x 4 = 224 x 2 = 448.Fast Reckoning convenient to multiply in succession by three factors. (or 41 x 16 = 16 x 41 = 16 x 40 + 16 = 640 + 16 = 656). you double the number twice. multiply by 10 — 2 in the long run): 217 x 8 = 2 . g. 335 x 4 = 670 x 2 = 1. Another way of multiplying mentally by 8 is to multiply the multiplicand by ten and subtract double the multiplicand (that is. When multiplying by 8. To multiply in your head a number by 4. For example: 29 x 12 = 29 x 10 + 29 x 2 = 290 + 58 = 348. This kind of multiplication can be made simpler by reducing it to the conventional multiplication by a simple number.736. Multiplication by Two-Digit Number 4. . 41 x 16 = 41 x 10 + 41 x 6 = 410 + 246 = 656. For example: 225 x 6 = 225 x 2 x 3 = 450 x 3 = 1350. item 3). When the multiplicand is simple. If the multiplicand or multiplier are more readily representable in the head in the form of two simple factors (e.4 3 4 = 1. the number is doubled three times.340.736. For example. 14 = 2 x 7). When both multipliers are two-digit. It's more convenient to break the multiplier down into tens and ones and so get smaller figures. 217 x 8 = 434 x 4 = 868 x 2 = 1. Multiplication and Division by 4 and 8 7. 8. For example. For example: 45 x 14 = 90 x 7 = 630. then this trick is used to reduce one of the initial factors while increasing the other accordingly (cf. it and the multiplier are interchanged and then the procedure of item 1 can be followed. 2 0 0 + 4 = 50.800. 12. This follows from the fact that 100+4 = 25. 11/4. . if the number is divisible by 4.e. To divide mentally by 8. the number is halved twice.290-291 Fast Reckoning Or more convenient still: 217 x 8 = 200 x 8 + 17 x 8 = 1. it's more convenient to halve it first and then add the zero. Thus a zero is ascribed to the number and the result is divided by two.215. For example. 76-1-4 = 38-1-2 = 19. 9. For example. For example. When multiplying by 1 1/2. 74 x 5 = 7 4 0 + 2 = 370.736. 10. For example. 4 But if the division yields a remainder. 23 x 1 1/2 = 23 + 11 1/2 = 34 1/2 (or 34. 34 x 1 1/2 = 3 4 + 17 = 51. If our number is even. In the case of 25. 464 + 8 = 232-1-4 = 116+2 = 58. 243 x 5 = 2. 72 72 x 25 = — x 100 = 1. it is divided by 4 first and two zeros are then ascribed to the result. 236-1-4 = 118-1-2 = 59. then if it's 1 we add 25 to the quotient.600 + 136 = 1. add to the multiplicand its half. For example. 74 x 5 = 2 x 10 = 370. a number is multiplied by 100/4. i. the number is halved three times. Multiplication by 11/2. and 3 0 0 + 4 = 75. Multiplication by 5 and 25 11. For example.5). 3/4 13. 5 1 6 + 8 = 2 5 8 + 4 = 129+2 = 64 1/2.430+2 = 1. For a number to be mentally divided by 4. and if 3 we add 75. 2 1/2. if 2 we add 50. Multiplying by 5 is actually multiplying by 10/2. 4 700 47 x 125 = 47 x 100 x 1 1/4 = 470 + — = 4700 + 4 + 1. 18 x 2 1/2 = 36 + 9 = 45. For example.350. For example.900 18 x 75 = 18 x 100 x 3/4 = 1800 x 3/4 = = 1.875. Another form of the technique consists in subtracting from the multiplicand its quarter or adding to a half of the multiplicand a half of the half of the multiplicand. 48 x 1 1/4 = 48 + 12 = 60. 15. For example. For example. 26 x 125 = 26 x 100 x 1 1/4 = 2. 58 x 1 1/4 = 58 + 14 1/2 = 72 1/2 (or 72. Multiplication by 75 is replaced by multiplying by 100 and by 3/4 (because 100 x 3/4 = 75). add to the multiplicand its quarter. For example. the number is multiplied by 11/2 and divided by two.5).5).Fast Reckoning 14. 16. to find 3/4 of a number). Multiplication by 125 is replaced by multiplying by 100 and by 1 1/4 (because 100 x 1 1/4 = 125).250.175 = 5. add to the doubled number its half. 39 x 2 1/2 = 78 + 19 1/2 = 97 1/2 (or 97. Another technique consists in multiplying by 5 and dividing by two: 18 x 2 1/2 = 9 0 ^ 2 = 45. 125.600 + 650 = 3. 75 17. 18. 18 x 15 = 18 x 1 1/2 x 10 = 270. To multiply by 3/4 (that is. To multiply by 2 1/2. J = . 19.5). Multiplication by 15. 1800 -I. 3 0 + 15 30 x 3/4 = = 22 1/2 (or 22. For example. Multiplication by 15 is replaced by multiplying by 10 and then by 11/2 (because 10 x 1 1/2) = 15). When multiplying by 1 1/4. 45 x 15 = 450 + 225 = 675. 62 = 600 . add a zero to the number and add the multiplicand to the result. For example.250. When multiplying by 11. Some more examples: 25 2 . 87 x 11 = 8 7 0 + 87 = 957. 1 1/2.= 13.42 = 558. 625. Division by 5. add a zero to the number and subtract the multiplicand from the result. 26 x 125 = 130 x 25 = 3. 62 x 9 = 620 .025. 53 + 1 1/2 = 106+3 = 35 1/3.43 = 657.4. 15 22. 4 x 5 = 20. For example. For example.8.6. 24. Dividing by 15 consists in doubling the number and dividing the result by 30.73 = 700 . 23. 2. (or 924+30 = 308-^10 = 30. 6 8 + 5 = ^ .292-291 Fast Reckoning Note: Some of the above examples can be conveniently handled using the technique of item 6: 18 x 15 = 90 x 3 = 270.8). 10 474 2 3 7 + 5 = — = 47. Dividing by 11/2 consists in doubling the number and dividing the result by 3. 240+15 = 480+30 = 4 8 + 3 = 16. For example. To divide by 5 double the number and move the decimal point one place to the left.g. When multiplying by 9. Multiplication by 9 and 11 20. 462+15 = 924+30 = 30 24/30 = 30 4/5 = 30. 21.225). 73 x 9 = 730 . 45 2 . 85) the number of tens (8) is multiplied by itself plus one (8 x x 9 = 72) and on the right of the result 25 is ascribed (in our example this yields 7. To square a number ending in 5 (e. . Squaring 25. For example. 2 x 3 = 6. 36 + 1 1/2 = 7 2 + 3 = 24. Fast Reckoning 145 2 .1) (85 + 1) = 7. This technique can also be applied to decimal fractions ending in 5: 8. 14 X 15 = 210.g. The procedure may conveniently be used calculations of the following type: I 1/2 x 6 1/2 = (7 + 1/2) (7 .225 + 1 + 2 x 35 = 1.25 = 1/4. and 9. The procedure follows from the formula: (lOx + 5)2 = lOOx2 + lOOx + 25 = lOOx (x 4. As 0.021. 4. 84 x 86 = (85 .296. 14. 26. e.5 = 1/2 and 0. 6.25. We mentally represent the multipliers as (50 + 2) (50 — 2) and use the formula: (50 + 2) (50 .1225. Mental squaring can often be simplified using the formula (a ± b)2 = a2 + b2 ± lab. 53 x 57 = (55 . 362 = (35 + l) 2 = 1. Let's multiply 52 x 48.2) (55 + 2) = 3.2 2 = 2. 33 x 27 = (30 + 3) (30 — 3) = 891. for . (70 + 1) = 4.681.224. For example. 30.140 = 4. 21.2 x 70 = 4.901 .761.1) + 25. 41 2 = 40 2 + 1 + 2 x 40 = 1.2) = 502 .601 + 80 = 1. II 3/4 x 12 1/4 = (12 .52 = 210. The procedure is also convenient for numbers ending in 1.52 = 72. This technique can be used whenever one multiplier can be conveniently represented as a sum of two numbers and the other as a difference of the same numbers. the procedure of item 25 can also be used to square numbers ending in the fraction 1/2: (8 1/2)2 = 72 1/4. (14 1/2)2 = 210 1/4. etc.899.496. 28. 27.1/4) (12 + 1/4) = 143 15/16.352 = 0. etc. 69 x 71 = (70 . 69 2 = 70 2 + 1 . Calculations by Formula (a + b) (a — b) = a2 — b2 29.1/2) = 48 3/4. etc.001. 91 x 11 = 1.002. 77 x 39 = 3. 9. We have only discussed the simplest and most convenient techniques of mental arithmetic. 37 x 12 = 37 x 3 x 4 = 444. 37 x 15 = 37 x 3 x 5 = 555.002. 37 x 9 = 37 x 3 x 3 = 333. 91 x 33 = 3. through practice.003. 91 x 22 = Fast Reckoning It Pays to Remember: 37 x 3 = 111 With this in mind we can easily carry multiplication of 37 by 6. etc. 143 x 14 = 2. 37 x 6 = 37 x 3 x 2 = 222. etc. 12.001. etc. work out further procedures to simplify calculations. etc. 143 x 21 = 3. An inquiring mind can. 7 x 11 x 13 = 1. 77 x 26 = 2. 143 x 7 = 1.003. out the out the .001 With this in mind we can easily carry multiplications of the following type: 77 x 13 = 1.003. The smallest magic square has nine cells. a series of new magic squares. the result is always 15. Hence for each line 45-^3 = 15. The following is an example of a 9-cell magic square: Figure 252 4 9 2 3 5 7 8 1 6 In this square we might add up either 4 + 3 + 8. or 2 + -I. i. We only have to divide the sum of all its numbers by the number of its lines.Magic Squares 22 The Smallest Magic Square Since time immemorial people have amused themselves by constructing magic squares.5 -I. It can easily be shown by trials that a four-cell magic square is impossible. If.e. or 4 + 5 + 6. for instance. The problem consists in arranging successive numbers (beginning with 1) over the cells of a divided square so that the numbers in all the lines. or any other line of three numbers. this sum must clearly be equal to thrice the sum of a single line. we have the square given in Fig. On the other hand. or 3 -(. Turns and Reflections Haying constructed one magic square we can readily derive its modifications. Using the same argument we can determine in advance the sum of the numbers in a line or column of any magic square consisting of an arbitrary number of cells.7 + 6. then by mentally turning it by 90° we'll obtain another magic square (Fig. without constructing the square as such: the three lines of the square should contain all the nine numbers and they add up to 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45.7. The result could be envisaged beforehand. 254): . columns and diagonals add up to the same number. 253. Figure 255 depicts the initial square with one of its mirror reflections. 256): Figure 256 (1-3) Figure 256 (4-8) This is the complete collection of magic squares that could be compiled of the first nine figures.b y 180° and 270°-will give two more modifications of the initial square. squares with any odd number of cells: 3 x .296-297 Magic Squares Figure 253 Figure 254 Further t u r n s . Figure 255 All the turns and reflections possible with the 9-cell square yield the following versions (Fig. Each of the new magic squares can in turn be modified by reflecting it in a mirror. Bachefs Method Here's an ancient method of constructing odd magic squares. i. e. The method being suitable for the 9-cell square. The method was suggested in the 17th century by the French mathematician ClaudeGaspar Bachet (1581-1638). 2 5 4 8 : . 7 x 7.. the simplest case. it'll be convenient to begin discussing the method with this. To do so. we'll need to bring the three-number arrangements from beyond . . 7i We transfer the numbers that appear to lie beyond the confines of the square into the square so that they join the lines at the opposite sides of the square. having drawn a square divided into nine cells we'll write the numbers from 1 to 9 in succession arranging them in the oblique lines as shown in Fig. 257. etc.Magic Squares x 3. 6 Figure 257 Figure 258 Figure 259 Let's apply Bachet's technique to a 5 x 5 We'll begin with the arrangement: i—i : 5! r—+i 4 • ! 10 i 3 9 15 2 —(. !1 7 i f—• r 6 —t—i ! 25 \| 13 19 1 ' 12 24 ' 18 17 i 16 ' ' U 8 14 20 \| 11 23 i 22 -- I 21 L It only remains now to bring the numbers outside the confines of the square into it. 5 x 5.. We thus obtain: 9 4 5 3 1 8 square.. So. . and at the bottom in the next column on the right we write 2. Exercise. Now that we have this magic square with 25 cells we can obtain its modifications by using turns and mirror reflections. Note: Having reached the upper right corner cell we go over to the leftmost lower corner cell. If the last occupied cell belongs to the lowermost line. 262). Observing these rules we can quickly construct magic squares with any odd number of cells. By way of example. 260). 6. 3. Read them carefully and then see them applied to a magic square with 49 cells (Fig. The Indian Method 24 12 17 10 23 30 39 48 38 47 46 5 6 7 8 1 10 19 28 9 18 27 29 17 26 35 37 4 14 16 25 34 36 45 3 12 11 20 13 15 24 33 42 44 21 23 32 41 43 22 31 40 49 2 32 41 43 40 49 48 7 8 16 1 9 2 3 12 21 23 11 20 22 31 10 19 28 30 39 18 27 29 38 47 6 14 15 5 13 17 26 35 37 46 25 34 36 45 4 24 33 42 44 The Bachet (or "terrace") method is not the only approach to constructing squares with an odd number of cells. Having reached an occupied cell we skip over it. Having reached the right edge of the square we go over to the extreme left cell in the next line up. 1. It can be briefly couched in six rules. It is possible therefore to construct several squares by this method. The idea behind this simple technique is fairly complicated. We may start from any cell along the diagonal line passing between the middle cell of the leftmost column and the middle cell of the uppermost line. we proceed from the uppermost cell in the column. This will give a 25-cell magic square (Fig. If the number of cells in the square doesnt divide into 3 we may begin the square following a rule other than 1. 4. Obtain other squares by turns and mirror reflections. Worth mentioning among other techniques is a relatively easy procedure that is thought to have been devised in India about two thousand years ago. All the other numbers are placed according to rules 2-5. 261). 5. In the middle of the upper line we write 1.298-297 3 20 7 11 16 9 8 25 13 5 4 22 15 2 19 6 1 18 Magic Squares 21 14 the square ("terraces") to the opposite sides of the square. though the reader can check it practically. Use the Indian method to construct several magic squares with 25 and 49 cells. 2. Having reached the upper edge of the square we go over to the lowest cell of the next column to the right. we provide the following 49-cell magic square (Fig. We write the next numbers successively along the diagonal upwards and to the right. it consists of 4. cells. first and last). the situation has become more complex. however.. then the respective Figure 264 opposite cell will lie in the penultimate line and fourth from the right. etc. We'll explain the procedure referring to 8 x 8 square. give the same sum. e. But the lines and columns of the square give different sums.e. the upper line adds up 49 50 51 52 53 54 55 56 to 36. respectively. the numbers 1. 264). the other by circles. Fig. we'll place all the numbers from 1 to 64 25 26 27 28 29 30 31 32 in the cells in succession (Fig.Magic Squares <•» Figure 263 Squares with an Even Number of Cells These magic squares can't be constructed using any common or convenient rule. 58. 59.e. All the diagonal lines in the resultant square have the 33 34 35 36 37 38 39 40 same sum -260. the number of whose cells is divisible by 16. It is. 8. 263 presents two pairs of opposite cells: one marked by crosses. and 4 are replaced by 57. necessary that the columns. So. X 0 0 X We see that if a cell lies in the second line from the top and fourth from the left. What has been said about the first and eighth lines is also true of the second and seventh. and 60. As an example. 3.) Note that the opposites of cells in a diagonal also lie on the same 9 10 11 12 13 14 15 16 diagonal. just what we want for a 8 x 8 magic 41 42 43 44 45 46 47 48 square (Check!). and the last line adds 57 58 59 60 61 62 63 64 up to 484. the third and sixth. We'll now agree as to what we'll call "opposite" cells. 224 less than required.e. There is one relatively simple procedure for even squares. 224 more than required. i. (The reader is recommended to practise 1 2 3 4 5 6 7 8 finding some other "opposite" cells. we come to the conclusion that the sums of these two lines can be equalized if we replace a half of the numbers in the first line by the corresponding number in the last line. i. 17 18 19 20 21 22 23 24 To begin with. i. To identify the numbers to be exchanged we make use of the following . After the numbers in all the lines have been interchanged we'll obtain a square in which lines have equal sums. For instance. 2. But after rearranging the lines. and in general for any pair of lines equidistant from their respective extremum lines (i. Noting that each number in the last line is 56 more than the number in the same column but in the first line and that 224 = 4 x 56. With the initial arrangement we could have achieved this by the same kind of exchange that we used with the lines. too. or 12. This means that one side of these squares has a number of cells that is a multiple of 4. 266. 4. We now only have to replace the numbers in the 56 55 11 12 13 14 50 49 cells marked by those in the opposite cells. the remaining numbers staying in their previous places. 265. since we've found that only a half of the 8 X numbers need to be exchanged. instead of a double rearrangement (of the lines and columns) we exchange "opposite" numbers. As a result of the permutation we will have obtained 17 47 46 20 21 43 42 24 a 64-cell magic square presented in Fig. however. however.300-297 Figure 265 Magic Squares 1X 2 3 4X 5x 6 7 9 X 10x 11 12 13 14 15 X 17 18* 19 x 20 21 22 x 23 x 25 26 27* 28 X 29X 30 x 31 33 34 35 36 37 38 39 technique. 267. Which of the opposite 16X pairs then are to be exchanged? The following four rules are an answer to this 24 question: 32 1. We divide the magic square into four squares as 40 shown in Fig. 41 23 22 44 45 19 18 48 16 15 51 52 53 54 10 8 58 59 5 4 62 63 9 1 Figure 267 The reader will undoubtedly find many other ways of arranging the crosses in the cells of the upper left square. Then. Using then rules 3 and 4 we can readily derive other magic squares with 64 cells. 41 42 43 44 45 46 47 48 2. 25 26 38 37 36 35 31 32 We could. as shown in Fig. In the right upper square we mark with crosses Figure 266 the cells that are symmetrical about those marked in the 64 2 3 61 60 6 7 57 upper left corner. use many other ways of marking the cells in the left upper square so that rule 2 would 33 34 30 29 28 27 39 40 be fulfilled. . But this rule is not sufficient in itself. 3. an example is shown in the above figure. for example. which could have been applied from the very beginning. This can be done in 57 58 59 60 61 62 63 64 a variety of ways. In the upper left corner we mark with crosses 49 50 51 52 53 54 55 56 a half of all the cells so that each column and line has exactly one half of its cells marked. Whence the Name? The first recorded evidence of the magic square comes from an ancient oriental book referring to 4.000-5. 16 x 16. Astrologists and alchemists believed that a magic square drawn on a piece of wood was able to deliver a man from misfortune. The reader can do this on his own. Indians in ancient times had a better understanding of magic squares. Many famous mathematicians have been interested in their theory and it has been applied in some of the important problems of mathematics.000 B..Magic Squares Arguing along these lines we can construct magic squares consisting of 12 x 12. C. from where the passion for magic squares was taken over by ancient Arabs. there is a way of solving sets of equations in many unknowns that uses results from the theory of magic squares. So. etc. It is from the medieval superstitious perceptions that these squares have derived their unusual name-"magic". such as alchemistry and astrology. . In medieval Western Europe magic squares were the stock-in-trade of representatives of pseudosciences. * * * The construction of magic squares is not just a pastime. who would assign mysterious qualities to these combinations of numbers. cells. Why is it possible to have a continuous chain of 28 bones (a domino piece is also sometimes called a bone) constructed without breaking the rules of the game? Beginning and End of the Chain. Your friend takes one of the dominoes and tells you to build a continuous chain out of the remaining 27 bones. The 28-bone chain ends in 5 points. What is more surprising is that your friend. calls out the number of points at each end of the chain. Figure 268 . He insists that it's always possible whichever bone he takes. Figure 268 shows a square frame made from dominoes whilst observing the rules. although remaining in the other room. How does he know? Why is he confident that any 27 bones can produce a continuous chain? Frame.302-303 23 Arithmetic Games and Tricks Dominoes A Chain of 28 Bones. He leaves you on your own and goes to another room. The sides of the frame may be equal in length but not in the total number of points: the upper and left sides contain 44 points each and the other two sides contain 59 and 32. How many points are there at the other end? Trick with Dominoes. You begin working and see that your friend is right: the 27 bones produced a chain. 271 you see six bones arranged according to the rules of the game but note that the number of points on each (both halves) increases by one. In our case each number is one more than the previous one. namely 13.Arithmetic Games and TYicks Can you produce a square frame such that each side contains the same sum total of points-44? Figure 269 Seven Squares. The Fifteen Puzzle* The well-known tray with 15 numbered square counters has a curious history few people even suspect of. 6. a German mathematician and investigator: "About half a century ago. it spread quickly and owing to the uncountable number of devoted players it had conquered. An example is given in Fig. You are asked to construct several such 18-bone magic squares. in the late 1870s. in * Other Diablotin. Figure 270 shows a square of 18 dominoes that is remarkable in that the sum of the points on any of its lines (be it longitudinal. Beginning with 4. Using a complete set of dominoes. it became a plague. 8. In Fig. transverse or diagonal) is the same. We can select four bones so that these will form a square with the same sum of points on each side. Domino Progression. names are the Boss Puzzle. Domino Magic Squares. Try to construct some other 6-bone progressions. the Fifteen Puzzle bobbed up in the United States. can you build seven such squares? They do not have to have the same common sum of points of their sides. 7. but now with another line sum. Arens. A series of numbers increasing (or decreasing) by the same amount each time is called an "arithmetic progression". and 9. but the difference may be arbitrary. We'll recall it in the words of W. and Figure 270 Figure 271 . For an 18-bone square 13 is the smallest sum whilst 23 is the largest. the series consists of the following numbers of points 4. 5. Jeu de Taquin. 269 in which the points on each side add up to 11. "The same was observed on this side of the Ocean. ' recalls the geographer and mathematician Sigmund Giinter who was a deputy during the puzzle epidemic. but when the latter enquired if it were solvable. he failed to patent his Fifteen Puzzle in the USA.' "In 1880 the puzzle fever seems to have reached its climax. He came to be widely known as an author of amusing problems and a multitude of puzzles.304-305 Arithmetic Games and Thicks Europe. however ingenious the technique applied to solve them. Here you could even see the passengers in horse trams with the game in their hands. But soon the tyrant was overthrown and defeated by the weapon of mathematics. A French author of the day wrote.' Loyd was satisfied with the decision. 'I can still visualize quite clearly the greyhaired people in the Reichstag intent on a square small box in their hands. "In Paris the puzzle flourished in the open air. Curiously enough. "It thus became clear why some problems wouldn't yield under any conditions and why the organizers of the contests had dared offer such enormous rewards for solving the problems. in the boulevards. The inventor was Sam Loyd. 'There was hardly one country cottage where this spider hand't made its nest lying in wait for a victim to flounder in its web. . The editor was a little reluctant so the inventor expressed his willingness to pay his own money. he had to submit a "working model" so that a prototype batch could be manufactured from it. In offices and shops bosses were horrified by their employees being completely absorbed by the game and they were forced to ban the game during office and class hours.000 dollars for its solution. the answer was 'No. Owners of entertainment establishments were quick to latch onto the rage and organized large contests. and proliferated speedily from the capital all over the provinces. the other half were impossible. The game had even made its way into solemn halls of the German Reichstag. According to the regulations. The mathematical theory of the puzzle showed that of the many problems that might be offered only a half were solvable. He posed the problem to a Patent Office official. The inventor of the puzzle took the cake in this respect suggesting to the editor of a New York newspaper that he publish an unsolvable problem in the Sunday edition with a reward of 1. The official therefore reasoned: 'In which case there can't be a working model and without a working model there can be no patent. it is mathematically impossible'. the counters are in numerical order with the 1 in the upper left * The episode was used by M a r k American Claimant. Twain in his novel The . that came to be known as the Fifteen Puzzle." We'll continue the story of the puzzle using the inventor's own words: Figure 272 1 5 9 2 3 7 11 4 8 The normal arrangement of counters (I) 6 10 14 12 13 15 Figure 273 The unsolvable case (II) "The old dwellers of the realm of aptitude will remember how in the early 1870s I made the whole world rack its brains over a tray of movable counters. We'll just confine our discussion to some of the elements as presented by W." * * * We'll now introduce the reader to the beginnings of the game. 273). It was said that navigators allowed their ships to run aground.304-305 Arithmetic Games and Thicks He would perhaps have been more insistent had he foreseen the unprecedented success of his invention. Arens. engine drivers took their trains past stations. The puzzle was to get the counters into the normal arrangement by individually sliding them so that the 14 and 15 were permutated. Funny stories were told of shop-keepers who forget for this reason to open their shops. of respectful officials who stood throughout the night under a street lamp seeking a way to solve it. Nobody wanted to give up as everyone was confident of imminent success. i. The task of the game is normally as follows: using successive movements made possible by the presence of the blank space the arbitrarily arranged squares should be brought to the normal arrangement. e. The fifteen counters were arranged in order in the tray with only 14 and 15 counters inverted as shown in the accompanying illustration (Fig. "The 1000-dollar reward offered for the first correct solution remained unretrieved although everybody was busy on it. and farmers neglected their ploughs. In its complete form it's very complicated and closely related to one of the branches of higher algebra (the theory of determinants). can be brought to /. The normal arrangement is given in Fig. 11. Further. in the next row there should be from left to right the 5. 12. etc. with the blank space ending up back in the lower right corner. 11. It now only remains to arrange a small patch of six spaces. This done. 6. for instance we can push the 12 in arrangement into the blank space. any two arrangements in the same series are transferable one to the other. too. Conversely. the 14 and 15 will be arranged in the last line either in the normal or inverted order (Fig. 8. arbitrarily arranged. After all. Next. Lastly. Any initial arrangement can be brought into either the Fig. and 12 into the normal arrangement. and those in the other series can be brought to arrangement II. In exactly the same way we can. then the 3 and the 4 in the upper right corner. Within this patch we can always bring the 10. we'll denote it by S.. then we can always restore the previous arrangement by the reverse move. If these occasionally are not in the two last columns. 272. and from II any arrangement in the second series.t 306-307 Arithmetic Games and Tricks corner. In the same way we'll also bring the second line into the normal order. 273). 7. followed by the 2 on the right. which the reader can easily test in practice. 272 (/) form or the Fig. 14. Now think of an arrangement with the 15 counters scattered arbitrarily. within the space of the two last lines we'll need to arrange counters 9 and 13. We'll easily find that it's always possible. We thus have two series of arrangements such that the arrangements in one series can be brought to normal arrangement /. Now the upper line is in the normal order and we'll leave it as it is in later manipulations. then the opposite is clearly possible. which is always possible. we can move the 3 and 4 to their normal places. will always yield the following result. the movements are all reversible. 273 (II) form: If an arrangement. If. I can be brought to S. without touching either the 1 or 2. i. A number of movements can always bring the 1 to the place occupied by it in the figure. Could we go further and combine the two 20« . e. we can bring them there and through a number of movements achieve the arrangement sought. without touching counter 1 move counter 2 to the adjacent place on the right. This procedure. and 15. from the normal arrangement we can obtain any arrangement in the first series. of which one is free and the other five are occupied by the 10. i. Mathematics has produced an exhaustive explanation of the game. 273 bring the counters into the numerical order with the blank space in the upper left corner (Fig. If the number of inversions is odd.Arithmetic Games and Tricks 23 Figure 21A 1 5 8 13 2 6 10 11 3 7 14 15 4 9 12 Figure 275 1 4 8 12 5 9 13 2 6 10 14 3 7 11 15 arrangements? We could rigorously prove (we are not going to here) that these arrangements cannot be interchanged. as in the case in hand. Further examination reveals that the 14 precedes three counters (12. it is an insolvable arrangement. it's solvable. the 12 precedes the 11 and the 13 precedes the 11. This procedure is used to determine the total number of inversions for any arrangement with the blank space in the lower right corner. e. then the arrangement can be brought to the normal one. 13. Further. How are we to know whether or not a given arrangement belongs to the first series? An example will clarify this. Let's consider the arrangement shown in Fig. Counter 9 comes before 8. Thanks to the new light shed on the puzzle by mathematics the earlier morbid passion that was shown for the game is now unthinkable. thus giving three inversions (14 before 12. If. as is the second save for the last counter (9). and 14 before 11). in other words. as in other games. This adds two more inversions bringing the total to six. 14 before 13. This amounts to 1 + 3 = 4 inversions. the arrangement belongs to the second series. 275). The outcome of the game is dependent not on chance nor on aptitude. 274. Starting off the arrangement in Fig. the formidable variety of arrangements break down into two separate series: (1) those that can be brought into the normal arrangement. We'll now consider some of the solvable problems with the game that were produced by the resourceful Loyd. Starting off with the arrangement in . This sort of violation of the order is called inversion. The first line is in perfect order. however many moves are used. but on purely mathematical factors that predetermine it unconditionally. one that leaves no loophole. and (2) those that can't and it was for these arrangements that the enormous rewards were promised. Problem II. Problem I. the total number of inversions is even. Therefore. Concerning counter 9 we'll say that here we have one inversion. and 11). Two people play alternately. e. Is there any way of winning the game with certainty? The "32" Game First 32 matches are arranged on a table. 276.308-309 Figure 276 Arithmetic Games and Tricks Fig. i. two or three matches. The game. you see. Then the other also takes one. It's played by two people taking turns. Each player selects his cell so that his opponent couldn't complete a row of three figures (the row may be transverse or diagonal) that add up to 15. And so on. two or three matches. two. One player takes one. or four matches. The player completing such a row or filling in the last cell of the network is the winner. just as he likes. and then the other player also takes as many matches as he chooses. 273 turn the tray 90° to the right and obtain the arrangement of Fig. The beginner draws one. Each player writes a number from 1 to 9 in one of the cells of the network shown below. but again not more than four. Eleven matches (or other objects) are placed on a table. It's more like the well-known "noughts and crosses" game. Could you indicate the "right" way to win? . The "11" Game This is a game for two. is very simple but it is curious in that the beginner can always win if he plays correctly. He who takes the last match loses. How must you play so that you can always win? The "15" Game This game is not to be confused with the Fifteen Puzzle. Now again the first. three. Problem III. arrange the counters so that the sum of the numbers in all directions is 30. and so on. By moving the counters according to the rules turn the tray into a magic square. It's forbidden to take more than three matches at a time. The player taking the last match wins. too. (3) several counters (as many as there are players). not wins. The beginner here is at advantage. In this case. But the object of the game is different: the winner is the one who ends up with an even number of matches.304-305 Arithmetic Games and Thicks The Reverse of the Last Game The previous game can be modified so that the player taking the last match loses. Figure 277 . what is the fail-safe procedure? Arithmetic TYavel Several people may take part in this game. What is the secret of his fail-safe strategy? The Reverse of the Last Game The object of the "27" game can be reversed so that the winner is the one ending up with an odd number of matches. (2) a die (of wood). You'll need: (1) a board (of cardboard). How must you play then to win with certainty? The "27" Game The game is similar to the previous ones. He can so calculate his draws that he always will win. It's also played by two people and also requires that the players alternately take no more than four matches. Games ana The board is a cardboard square, preferably a large one, divided into 10 x 10 cells that are numbered from 1 to 100 as shown in Fig. 277. The die, about 1 cm on side, is made of wood. The faces are sandpapered and numbered from 1 to 6 (or marked with points as dominoes). The counters may be various coloured disks, squares, etc. Taking turns, the players throw the die. If the die shows, say, 6, the player moves his counter 6 squares forward, his next throw takes his counter forward by as many cells as there are points on the die. When the player's counter comes to a cell where an arrow begins, the counter must follow the arrow to its end either forwards, or backwards. The player whose counter first reaches 100 is the winner. Think of a Number Think of a number, follow the procedure given below, and Fll guess the result of your calculations. Should the result differ, check through your calculations since you will have been in error, not I. No. 1 The number must be less than 10 though not zero Multiply it by 3; Add 2; Multiply by 3; Add the number thought of; Cross out the first digit; Add 2; Divide by 4; Add 19. The result is 21 Add 14; Subtract 8; Cross out the first digit; Divide by 3; Add 10. The result is 12 No. 3 The number must be less than 10 though not zero Add 29 to it; Discard the last digit; Multiply by 10; Add 4; Multiply by 3; Subtract 2. The result is 100 No. 2 The number must be less than 10 though not zero Multiply it by 5; Multiply by 2; No. 4 The number must be less than 10 though not zero Multiply it by 5; Multiply by 2; Subtract the number thought of; Add up the digits; Add 2; Square it; Subtract 10; Divide by 3. The result is 37 No. 5 The number must be less than 10 though not zero Multiply it by 25; Add 3; Multiply by 4; Cross out the first digit; Square it; Add up the digits; Add 7. The result is 16 Games and Subtract it from 130; Add 5; Add the number thought of; Subtract 120; Multiply by 7; Subtract 1; Divide by 2; Add 30. The result is 40 No. 8 Any number (besides zero) Multiply it by 2; Add 1; Multiply by 5; Discard all the digits but the last; Multiply it by itself; Add up the digits. The result is 7 No. 6 The number must have two digits Add 7; Subtract it from 110; Add 15; Add the number thought of; Divide by 2; Subtract 9; Multiply by 3. The result is 150 No. 9 The number must be less than 100 Add to it 20; Subtract from 170; Subtract 6; Add the number thought of; Add up the digits; Multiply it by itself; Subtract 1; Divide by 2; Add 8. The result is 48 No. 7 The number must be less than 100 Add 12 to it; No. 10 The number must be three digits long Write the same number on its right; Divide by 7; Divide by the number thought of; Divide by 11; Multiply it by 2; Add up the digits. The result is 8 Games and No. 11 The number must be less than 10 Multiply it by 2; Multiply by 2; Multiply by 2; Add the number thought of; Add the number thought of; Add 8; Discard all the digits but the last; Subtract 3; Add 7. The result is 12 Number Guessing a Three-Digit Think of a three-digit number. Leave aside the last two digits and double the first one. Add 5 to the result, then multiply by 5, add the second digit and multiply by 10. Add the third digit to the new result and tell me what you've arrived at. Fll immediately guess the number you've thought of. Let's take an example. Say your number is 387. It goes through the following sequence of operations. You double the first digit: 3 x 2 = 6; Add 5: 6 + 5 = 11; Multiply by 5: 11 x 5 = 55; Add the second digit: 55 + 8 = 63; Multiply by 10; 63 x 10 = 630; Add the third digit: 630 + 7 = 637. So you tell me the final result (637) and I tell you the initial number. Explain how. Another Number Trick Think of a number; Add 1; Multiply by 3; Add 1 again; Add the number thought of; Tell me the result. When you tell me the result I subtract 4 from it, divide the difference by 4 and obtain the number you thought of. For instance, suppose you thought of 12. Add 1, we get 13. Multiplied by 3, we get 39. Added 1, we get 40. Added the number thought of: 4 0 + 12 = 52. When you tell me the number, 52, I subtract 4 from Games and it, and divide the difference, 48, by 4. I thus get 12, the number you thought of. How does the procedure work? Guessing the Crossed-Out Digit Ask your friend to think a multidigit number and then ask him to do the following: Write the number down; Transpose its digits in an arbitrary order; Subtract the smaller number from the larger; Cross out one of the digits (but not a zero); Name the remaining digits in any order; You will theti tell your friend the crossed-out digit. Example. Your friend thought of 3857. He performed the following: 3857, 8735, 8735 - 3857 = 4878. Your friend crosses out the 7 and tells you the remaining digits in the following order, say: 8, 4, 8. From these digits you can determine the crossed digit. How can this be done? Guessing the Day and Month of Birth Get your friend to write down the day and month of his (or her) birth and to carry out the following operation: Double the day; Multiply by 10; Add 73; Multiply by 5; Add the serial number of the month of birth. When he (or she) tells you the final result of his (or her) calculations, you can tell him (or her) the day and month of his (or her) birth. Example. Suppose your friend was born on the 17 of August, i.e. on the 17th of the 8th month. He does the following: 17 x 2 = 34; 34 x 10 = 340; 340+73 = 413; Games and 413 x 5 = 2065; 2065 + 8 = 2073. Your friend tells you the number 2073 and you tell him his birthday. How can you do this? Guessing Someone's Age You can guess the age of a friend if you ask him (or her) to do the following: Write down side by side any two digits that differ in more than 1; Write any digit between them; Reverse the order of the three-digit number obtained; Subtract the smaller number from the larger; Reverse the digits of the difference; Add the result to the difference; Finally add his age to the sum. Your friend tells you the final result of the operations and then you can tell him his age. Example. Your friend is 23. He performs the following: 25; 275; 572; 5 7 2 - 2 7 5 = 297; 297 + 7 9 2 = 1089; 1089 + 23 = 1112. The number 1112 is the final result and from it you determine the age. How? How Many Sisters? How Many Brothers? You can guess how many brothers and sisters your friend has, if you ask him to do the following: Add 3 to the number of brothers; Multiply by 5; Add 20; Multiply by 2; Add the number of sisters; Add 5. The friend tells you the final result of his computations and you can tell him how many brothers and sisters he has. Games and Example. Your friend has four brothers and seven sisters. He thus does the following: 4 + 3 = 7; 7 x 5 = 35; 35 + 20 = 55; 5 5 x 2 = 110; 110 + 7 = 117; 117 + 5 = 122. The friend tells you the number 122 and you can tell him how many brothers and sisters he has. How can you do this? Trick with a Telephone Directory Here is another impressive trick. Get your friend to write down any number with three different digits. Suppose he writes 648. Ask him to reverse the digits in the number he has chosen and subtract the smaller one from the larger. He will thus write: 846 ~ 648 198 Ask to rearrange the digit of the difference in the reverse order and add both numbers up. Your friend will write: 198 891 1089 These calculations should be done in secret so your friend thinks that the final result must be unknown to you. Now give your friend a telephone directory and ask him to open it on the page whose number is equal to the first three digits of the final result. He does so and waits for further instructions. You then ask him to count the telephone subscribers (down from the top or up from the bottom) until he gets to the one given by * If the difference is a two-digit number (99), it is written with a zero in front (099). Games and the last digit of the number (1089). He thus finds the ninth subscriber and you tell him the name of the man and his telephone number. This naturally amazes your friend: he selected a number at random and you can tell him the subscriber's name and number. What is the trickery here? Guessing Domino Points The trick is arithmetic, based on calculation. Let your friend put a domino piece into his pocket. You promise to guess the number of points if he makes some simple calculations. Let his bone be the 6-3. Ask him to double one of the numbers (e.g. 6) 6 x 2 = 12, and add 7 12 + 7 = 19. Ask him to multiply the result by 5 19 x 5 = 95 and to add the other number of points of the domino piece (i.e. 3) 95 + 3 = 98. He tells you the final result and you in your head subtract 35 to find the points on the piece: 98 — 35 = = 63, i. e. the piece was the 6-3. Why is it so and why one must always subtract 35? Formidable Memory Conjurers sometimes amaze the public by their striking memory: they memorize long series of words, numbers, etc. Each of you can also surprise friends with such a trick. On 50 small paper cards write the numbers and letters shown below: a long number and in the left corner a letter or a combination of a letter and a figure. Distribute these cards among your friends and claim that you remember exactly which number is on which card. They need only tell you the number of the card and you'll immediately tell them the number written on it. You are told, say, "E4" and you can say at once "10,128,224". 130 E6 12.036 E7 13.030 B1 46.112 B5 870.256 E2 3.536 D 510.110. you didn't think you had to learn the 50 long numbers by heart.416 B3 66.114.224 E5 11.432 C9 1.130.318 E4 10.398.104.212 A2 44.718 B 36.050 D1 610.235 D8 13. How can you do it? Mysterious Cubes Make several cubes of paper (e.616 A9 1.234 C2 68.445 E 612.248 E9 15.092.215 D4 A7 954. figure by figure.016 C5 990. But. .128.134.524 B9 1..828 A5 750.215 B6 972.245 D2 7.056. What is the trickery here? Another Memory Thriller Having written a long series of figures (20 or more). And really.060 El 712.296.074. you put up a brilliant performance.025 D6 11.040 CI 58.108.120 C6 1.328 C8 1.126.322-313 A 24.112 C4 888.340 D9 14.224 C7 1. you proclaim that you can without mistake repeat the whole series.132. your power will shock all those present.412 E3 9.354 The numbers being very long and 50 in all.514 A8 1. With these cubes you can show an interesting arithmetic trick.130 D7 12.158.310 D3 8.136..404 A3 278.616 A4 64.318 B7 1. Everything is much simpler.120 D5 10.627 Arithmetic Games and Tricks C 48. despite the fact that the sequence of figures shows no pattern.g.609 B4 768.223 B2 56. four) and write figures on their faces arranging them as shown in Fig.116.421 B8 1.142 E8 14.310 A6 852.020 A1 34.428 C3 786.124.138. On entering the room you need only cast a glance at the column and immediately determine the sum of the figures on the closed faces of the four cubes. The idea behind it is rather complicated and I am not going to dwell on it here. but is cut. How to Find the Sum of Unwritten Numbers You undertake to guess the sum of three numbers of which only one is written. Having received the cards. The trick is performed as follows. stack them neatly. The trick is based on a special selection of numbers in the cards. 279. 278 you would call out the sum 23.t h e first summand.706.318-319 Figure 278 Arithmetic Games and Tricks Ask your friends to put the cubes in your absence one on top of another in any arrangement to form a column. For example. and then give you back only those cards on which there is this number. Trick with Cards Make seven cards as shown in Fig. in the case shown in Fig. put the clean card on the top. One of the cards is left blank. Suppose he writes 84. Now give the six cards with the numbers to your friend and ask him to remember one of the numbers written on the cards. The result will be the number sought. Write the numbers on them and cut them exactly as shown. and add up in your head those figures that are seen through the cuts. You can easily see that it is so. You will hardly crack this nut. Ask your friend to write down any multidigit n u m b e r . Then you leave enough room for the second and third summands and write . 514 184.706 30.705 .705 Then your friend writes the second summand (it must have the same number of digits as the first).Arithmetic Games and Tricks Figure 279 down in advance the sum total of the three numbers: 1st summand 2nd summand 3rd summand Sum total 84.485 69. and you write the third summand yourself: 1st summand 2nd summand 3rd summand Sum total 84.706 184. tat!" by Ivan Turgenev. To Foresee a Sum In earlier times number superstitions were no less widespread than other superstitions. the hero of the story "Rat!. Explain.. A chance coincidence of numbers led him to imagine he was an unrecognized Napoleon.. 1834 1834 21 7 (July is the 7th month) Total 1862 Total 1835 1 8 3 5 Total 17 (!) 1 8 6 2 Total 17(!) Such number fortune-telling was widespread at the beginning of World War I. when it was hoped the outcome could be foreseen using the method.tat!.320-313 Arithmetic Games and Tricks You can see that the sum was predicted accurately. 1811 1811 1 (January month) Total 1819 is the 1st Total 1792 Total 19 (!) Napoleon died on May 5. 1825 1825 5 5 (May is the 5th month) Total 19 (!) Ilya Teglev died on July 21. In 1916 Swiss newspapers initiated their readers into the "mysteries" by the following revelation about the fate of Emperors of Germany and Austro-Hungary: . What the result of such number fads might be is shown by the example of Ilya Teglev. After he had committed suicide a sheet of paper was found in his pocket with the following calculations: Napoleon was born on August 15. 1769 1769 15 8 (August is the 8th month) Ilya Teglev was born on January 7... ) Age Years he's been studying (working. Ask a friend who doesn't know the trick to write the following four numbers on a sheet of paper and add them up: Year of birth Year of ehtering school (factory. but human stupidity. The same year will result if to the year of an emperor's accession you add the years he has reigned. are equal. the prophets didn't twig that if you so much as slightly changed the lines in the calculations. What else could they arrive at? You can use this idea for a funny trick. etc. To muddle up the situation. double 1916. their mysterious character would go up in smoke.) Although you may not know any of the four numbers it's a simple matter for you to guess their sum: you only have to double the current year. whence it was concluded that the year would be fatal for both emperors. Repeating the trick may well expose the secret. introduce several additional numbers you know between the ones you don't.326-313 Year of birth Year of accession Age Years reigned Arithmetic Games and Tricks Wilhelm II 1859 1888 57 28 Franz-Joseph 1830 1848 86 68 3832 Total 3832 The sums. . We can easily see now why the adding up of the four numbers yielded the same result for both emperors. etc. Arrange the lines as follows: Year of birth Age Year of accession Years reigned Now what year would you obtain if you add a man's age to the year of his birth? Of course. the year when you make your calculation. each representing the double of 1916. you see. Blinded by superstition. If you play your cards right. But here we have not just a chance coincidence. each time the result will be different and the secret will thus be more difficult to perceive. The reader might ask how many ways can such a chain or ring be achieved? Without launching into the tiresome details of the computation. our assumption of unequal point-patterns at the ends of the chain isn't valid. 4-2. The remaining 21 bones have each of the point numbers repeated six times. Seven Squares. 4-5. as we see. then: (1) the remaining 27 dominoes will make a continuous chain with open ends. but only slightly.e. Clearly. Beginning and End of the Chain. when the 21 bones are arranged in a continuous line. of course. In the first one (at the top of Fig. 2 squares with sum 9. The solution is shown in Fig. we can always predict the point-patterns at the ends of the chain made up of the remaining bones. In fact.) By the way. all the 28 dominoes appear to be arranged in a line. This. 8. 1-1. hence if we remove a bone from this ring.959. i. 21« . We know that 28 dominoes always make a closed ring. To simplify the task we'll set aside all the seven doubles: 0-0.7. the property we have just proven suggests the following curious consequence: a 28-bone chain can always be joined at the ends to yield a ring. that in a complete set of bones each number occurs eight. etc. Accordingly. even number of. occurs because the points at the corners of the square are included twice. 8. however. if this were not the case. This makes the search for the desired arrangement somewhat easier. Consequently. The points on the sides of the square sought will add up to 44 x 4 = 176. 4-1. the pieces of such a set can be matched to the ends of other pieces until all the set is exhausted. We can without difficulty show that the chain of 28 bones must end in the number with which it began. (2) the end numbers in this chain will be those that are on the bone removed. i.520. Frame.231. i. the 4-point pattern (on one end) is on the following six pieces : 4-0. occurs an even number of times. 8 more than the total in the complete set (168). a complete set of dominoes can be arranged not only in a chain with free ends. 6-6. The answer follows from what has just been said. 1 square with sum 10.322-323 25 Answers Dominoes A Chain of 28 Bones. This done. the rules of the game observed. Having hidden a bone. 3-3.e. It represents the product of the following seven factors: 2 1 3 x 3 8 x 5 x 7 x 4. but also in a closed ring. 4-4. 4-6. For example. the numbers of points at the ends of the chain would appear an odd number of times (inside the chain the numbers must occur in pairs). we insert the doublets between the butts of 0-0. 2-2. (An argument like this in mathematics is termed "proof by contradiction". all the rules being observed. times. 1 square with sum 16. This yields the sum of points at the square vertices. We'll give two of the many solutions possible. 1-1. Thus.229.931.e. 281) we have: 1 square 1 square 1 square with with with sum sum sum 3. So each number. 6. 4-3. we will here only say that this number is e n o r m o u s . We know. 5-5. Trick with Dominoes. 280. Domino Magic Squares. 2 squares with sum 12.Answers Figure 280 Figure 281 In the second solution (at the bottom of Fig. Figure 282 shows an example of the magic square with 18 points in a line. 2 squares with sum 10. 1 square with sum 8. 281): 2 squares with sum 4. Figure 282 . 1. 15. 2. 3. 12. 13. All told. 1-2. 3. 2. 0-2. 13. (b) For progressions with differences of 2: 0-0. The Fifteen Problem I. 2. 4. 11. 8. 3-2. 5. 0-2. 12. 2-2: 2-4\ 4-6. 6. 15. 8. 15. 0-1. 1. 10. 2-3. there are 23 progressions for (a) For unit-difference progressions: 0-0. 12. 4. 14. 10. 8. 4. 1. 8. 0-4. 9. 3-1. 3-4. 1. 1-1. 15. 10. The "11" Game If you start. (b)O--l. 8. then the outcome of the game depends on whether or not your partner knows the secret of the fail-safe play. 10. 4. 12. 7. 11. 15. 4. 12. 4. 6. 3. N o matter how many your partner takes next. 5. 9. 15. 13. 14. 12. 3. 3. 8. 9. 10. 9. you can leave one match and win. 4. 14. 13. 7. And no matter how many of these five your partner takes. 1-2. 4. 6 bones. 14. If your partner begins. 10. 1. 13. 4-5. 10. 5. 3. 2-0. 13. 5. we'll consider two progressions with differences equal to 2: (a) 0-0. 2. 13. 8. The moves are as follows: 12. 9. 2-3. 9. 6. 15. you have to take two matches leaving nine. 2. 13. 7. 4. 3. 13. The initial bones are as follows: 2-1. 10. 1. 14. 3. 9. 9. 3-0. Problem III. 5-6. 7.324-325 Answers Domino Progression. 0-1. 8. 7. 12. By way of example. 8. 0-2. 1. 1-4. 10. 2-4. 14. The aim is achieved by 39 moves: 14. 3. You should easily see that you can always do this. 6. 6. 11. 2. 6. 12. 12. 3-5. 7. 1-3. 5. 8. 5. 12. 3. 11. . 3-4. 14. 3. 2. 4. 8. Problem II. 2. 14. you then have to leave only five matches on the table. 4. 4. 0-3. 6. 1-0. 6. 2. The arrangement Puzzle in the following 44 moves: can be arrived at 14. 10. 2-2. 15. 8. 9. 9. But in which cell? Let's consider the three possibilities one by one.e. Thus. Either way you win using the above rule 5 x y 3. The 5 is in the middle of the right column. 10-x 2. for the game to be a success begin by drawing 2 matches. then after your partner has taken some matches. The last match will be yours without fail. The number 15-5-x. you will have to fill in cell y. In all the cases you win. i. whatever his choice. by your previous draw. 1. if he writes y. and so at the beginning. how can you contrive so that your partner will have to draw from 10? To achieve this your previous draw must leave 15 matches on the table. In this way. Your partner will take either x or y. i. y. z. to z. . to leave exactly 10 matches. is clearly less than 9. you respond with x. to t. then 10. Further. x. But can you contrive so that you could make your the last but one move leave five matches on the table? You'll have. hence you can take after him all the remaining matches. The 5 is written in a corner cell. by subtracting five each time you'll find that earlier you would have to leave 20 matches on the table and before that 25 matches. so that you will always be able to leave to him five. X z 5 y t Your answer to x is t. you can write in the vacant cell in the same row 15-5-x (where x is your opponent's number). and finally five.e. Which ever cell your opponent chooses. to y. if you take the trouble to play it backwards from the end.Answers 23 The "15" Game If you want to win for sure. z. The "32" Game It's fairly easy to find the way to win in this game. Your partner may occupy one of the cells: x. or t. You'll figure out that if your last-but-one draw leaves five matches on the table. begin with 5. then. If he writes x. you must begin by drawing 2 matches. 30 matches. y. 10-x. The 5 is written in the middle cell. take as many as are required to leave 25. next go leave 20. he can't leave you less than six. then your win is a sure thing since your partner may not take more than four matches. two or one matches. 6 or 7. Only you must see to it that your partner doesn't take the initiative. If four are left take three and win. the game will proceed as follows. 18 or 19. This will unfailingly leave the last match to your partner. you must leave five matches to your partner and your win is a cinch. Zero is considered an even number. you must take four of them and win. 17. if three take two and win. your last-but-two draw must leave 11 matches on the table. you must leave a multiple of 6 or the multiple plus one. you must leave on the table a number of matches that is a multiple of 6 minus one. 21. if three take them and win. If you have an odd number of matches. You must start off with the following two considerations: 1. your last draw can leave the last match to him in any event. if you have an odd number. are as follows . Thus. At the beginning you have zero matches (i. If before the final draw you have an odd number of matches. i. 11. If your partner's next draw leaves six matches to you. the next draw of your partner will leave you with four. respectively.326-327 A n s w e r s The Reverse of the Last Game Your last-but-one draw must now leave six matches on the table. 12 or 13. Now you should be able to find the sure way to win without difficulty. Think of a Number No. you can safely leave five matches to your partner in which case he loses all right (see above). If you have an even number of matches. and then follow the previous procedure. If the number thought of is a. not six. therefore in the beginning you must take two or three. you leave a multiple of 6 or the multiple plus one. you must leave to your partner a multiple of 6 minus one. In fact. Then any draw your partner may make will leave from two to five matches. three. 16.e. If you abide by this rule you will win always. i. If he leaves five matches. an even number). or 23. you must take one and. and finally. 2. then the operations (3a + 2) x 3 + a = 10a + 6. now with an odd number of matches. you must leave six or seven matches to your partner. 24 or 25. and 6 matches. He cannot leave less than two. i.e. e. 21. and if one take it and win. This ensures for your win. In fact. if he leaves two you also win. You thus begin by taking 1 match and your later draws leave 26. The Reverse of the Last Game If you have an even number of matches. 5. 1. and 31 matches. therefore your first draw must be to take four matches and leave 23 to your partner. If before the final draw you have an even number of matches. The "27" Game The way to win here is somewhat more difficult than in the previous game. if four take them all and win. 11. if two take one and win. 26.e. and on your earlier draw you should leave 16. the operations are as follows 170 . then by 5 and by 10. we'll end up with the number thought of. if you think of a three-digit number a. 7 x a x 11 The rest is clear. No. by 2 x 5 x 10 = 100. Guessing a Three-Digit Number The first digit was first multiplied by 2. i. In No. i. The rest is self-explanatory. Therefore. 250. to the result. 9. Nos. we'll have the first digit multiplied by 100 plus the second digit multiplied by 10 plus the third digit. for instance. 4. You thus see that in each of the above cases the guessing is based on eliminating the number thought of. Another Number Trick A close examination of the procedure shows that the result must be the four times the number thought of plus 4.6 + a = 144. To write a three-digit number on the right of itself is equivalent to multiplying it by 1. But 1. Thus. the first digit being the number you first thought of. The third one is added as it is. Guessing the Crossed-Out Digit Those who know the criterion for divisibility by 9 will know that dividing the sum of the digits of any number by 9 gives the same remainder as the number itself.001 = = 7 x 11 x 13. Crossing out the first digit eliminates the number first thought of. The rest is self-explanatory. 5 and 8 are modifications of what has just been described. If we thus subtract 4 and divide the rest by 4. we add 5 x 5 x 10.(a + 20) . the second being 6. In short. 10 requires a special procedure. then the operations are a x 1. 6. 2. The second digit was multiplied by 10.g. 3.356). Any two . 356 x 1. e.e. We thus conclude that to guess the number thought of we must subtract 250 from the result of our calculations.001 = 13.001 (e. if we subtract 250 from the result. 7 and 9 use another way of eliminating the number thought of. Besides. Now try and devise some new examples of your own. Nos.001 = 356.Answers 2? The result is a two-digit number. we'll arrive at the number we seek. Clearly.328-329 Answers numbers composed of the same digits must therefore give equal remainders when divided by 9. In fact. the second the number of sisters. the difference will be exactly divisible by 9 as the subtraction will cancel out the remainders. and the preceding digits the number of the day. Guessing Someone's Age If you go through the procedure several times. The first digit of the result gives the number of brothers. Brothers? . So if we subtract one of the numbers from the other. Why? Let K be the number of the day. you'll obtain the age sought. We obtain (2K x 10 + 73) x 5 + N = 100K + N + 365.089. and the number of sisters is b.089 be divided by 9 and then add the age to the result.08. then [(a + 3) x (5 x 20)] x 2 + b + 5 = 10a + b + 75 and we arrive at a two-digit number ab. if you subtract 1. if the number of brothers is a.365 = 1708.75 = 47. and N the number of the month. The trick can only be a success if the number of sisters is not larger than nine. This thus suggests that the digits of the difference your friend obtained add up to a number divisible by 9. 4. and hence the digit crossed-out. Therefore. Since the digits 8. which is 7. Guessing the Day and Month of Birth To work out the date sought we must subtract 365 from the final result. From 1708 we determine the date: 17. How Many Sisters? How Many Subtract 75 from the final result. In our example 122 .089 from the result. Demonstrating the trick several times you might change the procedure so as not to expose the secret. by requesting 1. In our example 2073 . you should notice that at all times you add the age to the same number. subtracting 365 gives a number with K hundreds and N ones. For example. namely 1. 8 that were told to you add up to 20 and you can infer that the nearest number divisible by 9 is 27 you can find the digit needed to get 27. The last two digits of the difference will then be the number of the month. to obtain the number written on the card.. i. It's now clear why the figures of the result give the numbers of points at once. you must remember that A stands for 20. You can easily test this. Suppose you are told the code E4. multiply both digits together: 6 x 4 = 24. Thus beforehand you remember the name and number of the subscriber in the ninth line (from the top or bottom) on page 108. 2. Second. x . B for 30.e. subtracting. C for 40. add up its digits: 6 + 4=10.Answers Trick with a Telephone Directory The point is that you know the final result beforehand. The operations performed could be represented symbolically as + . C3-43. Consequently. Write all the results you obtain in a line 10. we'll obtain as many tens as there are points at one end of the domino. . 64. For example Al-21. the outcome is always the same-1. You handle this number as follows: First. subtract the larger digit from the smaller one: 6 . In addition. Let's discuss it referring to an example.089. Formidable Memory The alpha-numerical code of a card indicates the number written on it. double it: 64 x 2 = 128. From this number you arrive at the long number written on the card following a definite rule. Whatever the three-digit number.4 = 2. if we subtract 35 from the result. i. doubling.e. multiplying. . Therefore the code means some number.128.e. Third. we added 7 x 5 = 35. Adding the points at the other end gives the second digit of the result. i. Finally. Guessing Domino Points Let's trace through the operations to which we subject the first number. We first multiplied it by 2 and then by 5.224. Above all. D for 50. adding. E for 60. by 10. and E5-65. .999 then the result you've written beforehand will work out without fail. then another digit. 5 . 3 + 8 = 11.705. therefore the trick generally amazes people.106. 53 x 2 = 106.999. 184.999 you can immediately write the future sum of all three numbers. Therefore.176. Now you have only to ensure that the second and third numbers on their own add up to 99. i.000-1. 1 appears on the left of the number.e. so you write 69. Since + 30. If you subtract the number on the top face of the upper cube from 28. 100. and the last digit is reduced by 1.999 to the first number + 84. 1. 278). The trick is based on this. 38 x 2 = 76.706 99.215 Code B8: B8 = 38. you'll always get the sum of the numbers on all the seven closed faces of the column. 5 x 3 = 15. to a five-digit number.999.524. The pattern is rather difficult to discover. In order not to strain your memory you can name the numbers as you work them out or else write them slowly on a blackboard.e.330-331 Answers Some more examples: Code D3: D3 = 53 5 + 3 = 8. So if you mentally add 99.485 69.514 99. How to Find the Sum of Unwritten Numbers If you add 99.3 = 2. 8 . 8 x 3 = 24. In our example the second number is 30.3 = 5.514. the numbers on the top and bottom faces of all the four cubes stacked in a column add up to 7 x 4 = 28. Another Memory Thriller The answer is ridiculously simple: write down the telephone numbers of your acquaintances Mysterious Cubes The answer lies in the arrangement of the numbers on the faces of each cube: the sum of the numbers on the opposite faces of a cube is seven in all cases (check in Fig. This is achieved by subtracting mentally each digit of the second number from nine when writing the third number. 8.485. i. crossing each once only? "Some people believe that it is possible. The river flowing around it is split into two branches which are spanned by seven bridges (Fig." What do you make of it? What is Topology? Euler devoted to the Konigsberg bridge problem a whole mathematical investigation that in 1736 he presented to the St. Others think this is impossible.With a Stroke of the Pen (Drawing figures with one continuous The Konigsberg Bridge Problem line) The great mathematician Euler was once interested in a curious problem that he described thus: "There is an island called Kneiphof in Konigsberg. 283). Petersburg Academy of Sciences. Figure 2 8 3 "Is it possible to visit all of these bridges. The work was begun with the following words defining the branch of mathematics to which similar questions might be referred: Now Kaliningrad in the USSR. . and so I have decided to present here by way of example the method I have found of solving the problem. save for two. C. B. Figure 284 . We're not now going to discuss the reasoning of this eminent mathematician but will only confine ourselves to some brief remarks that support his final derivation. and D in the figure odd numbers of paths meet. the localities A. and D) by one of the paths and then leave by another path. His conclusion was that it was impossible to meet the condition of the problem. B." Euler was referring to the Konigsberg bridge problem. The problems in this section of the book belong to only a small part of the branch of topology. for our figure to be "unicursal" every point. B. 283 can be replaced by points marked by the same letters where the paths meet. Therefore. At each of the points A. Leibnitz was the first to mention another aspect that he called the 'geometry of position'. ignoring their sizes. The size of the island and the lengths of the bridges are of no consequence and now we know this is the characteristic feature of all the topological problems. Let's show that it's impossible to do so. The only exception are the initial and final points: since you don't corne from anywhere to start and you don't go anywhere when you leave. C. an aspect that has been developed since ancient times. must meet either two. or four (in general any even number) of paths. C. Nowadays this branch of higher geometry is generally termed "topology" and it has developed into an extensive field of mathematics. This branch of geometry is only interested in the arrangement of the parts of a figure. We must arrive at each of the node points (A. Examination For simplicity we'll replace the river's branches by the scheme in Fig. and D in Fig. It's thus impossible to trace the figure with one continuous path and so it is not possible to cross all the Konigsberg bridges as required. 284. "Recently. Thus.332-333 With a Stroke of the Pen "Besides the aspect of geometry that treats of the quantities and measuring techniques. I heard of a problem referring to the geometry of position. Now the problem is seen to reduce to tracing the figure in Fig. 284 with one continuous path so that no line is drawn twice. wherever you start from. A Bit of Theory Attempts to trace figures 1-6 in Fig. It can be shown (we'll omit the proof) that any figure only has either zero. 285 yield different results. Examples are figures 1 and 5 in Fig. If there are two odd points in the figure. If there are no odd points in the figure. Others can only be drawn if the Figure 285 path starts from definite points.With a Stroke of the Pen Seven Problems Try and draw each of the following seven figures with one continuous path. What is the reason for this difference? Are there any signs that would enable us to predict whether or not a figure is unicursal. 285. or four (in general an even number) odd points in it. it can always be drawn with a single stroke of the pen. Some of the figures can be drawn regardless of where the path begins. We will now refer to those points at which an even number of lines meet as "even" points and to those at which an odd number of lines meet as "odd" points. and some elements of the theory will be presented below. you must only begin from one of the odd points (either one). You will find that . or two. Yet others cannot be drawn at all by one continuous path. and if so what must the starting point be? The theory provides comprehensive answers to these questions. then it can also be drawn in this way. Examples are figures 4 and 7. ACF and BDE. In 6. Examples are figures 2. Therefore. If a figure has more than two odd points. Seven More Problems Trace figures 8-14 with a continuous line (Fig. Now you know enough to identify which figures are unicursal and the points from which you could start your drawing. we'll have to deal with two figures. which both contain four odd points." Suppose. 286). and they are not connected (figure 5 falls apart). over to AFC. for example. you mustn't go along DA but should first trace the path DEED and then follow the remaining line.334-335 With a Stroke of the Pen you'll always finish your drawing at the other odd point. DA. 3. Arens suggests you should be guided by another rule. it's noncursal. Thus. having covered ABCD. having completed figure AFC we won't be able to go over to BDE since there'll be no undrawn lines connecting them. Figure 286 . and 6. you must begin either from point A or from B. for instance. If now we draw in line DA. namely "All the lines that have already been drawn in a given figure should be regarded as absent and when selecting the next line see to it that the figure remains complete (doesn't disintegrate) if the line you've chosen is removed from it. that in figure 5 we've followed the path ABCD. Professor W. the task is feasible and the reader should now be sufficiently armed with knowledge to handle the problem on his own. Figure 287 . Unlike the Konigsberg bridge problem.With a Stroke of the Pen The Leningrad Bridges The puzzle is to take a walk around the region of Leningrad shown in the figure and come back at the starting point whilst crossing each bridge just once. Figure 289 22 — 975 .336-337 24 Answers The figures below give the solutions of respective problems in this Figure 288 section. .m i Figure 290 --m — '— --II " I However. or. These are all well-known household things. The unusual aspects make these objects view outlandish and recognition difficult. try and guess what the figure shows. . Think hard before you look the answer up. What Is Shown Here? Take a look at Fig..-....Geometric Recreations How Many Faces? How many faces has a hexahedral pencil? On the face of it the question is naive. Glasses and Knives Three glasses are so arranged on the table that their mutual separations are larger than the length of a knife Figure 291 . 290. intricate. . anyone good at engineering drawing will make a short work of the task. Essentially. as is the use of anything besides the three glasses and three knives. with three holes in each. make one plug for the three holes of each row. Figure 293 The first row is as easy as pie: clearly the answer is the block shown in the figure. the task comes down to manufacturing a component from its three views. It goes without saying that dislodging the glasses is forbidden. But pay attention to their shape and arrangement and explain how the joiner contrived to connect both parts. you are asked to contrive bridges of these knives such that they connect all three glasses. Using any suitable material. The upper half has tongues that fit in the grooves of the lower half. Figure 292 How Is It Achieved? You see here (Fig. As to the other rows the situation is a bit more difficult. However. 292) a wooden cube made up of two pieces of wood. each being made of a solid block of wood. 291). Nevertheless.338-339 Geometric Recreations (Fig. One Plug for Three Holes Figure 293 depicts six rows of holes. Figure 298 . find a plug to close the three holes in each board. The smallest vessel here is a glass. Two Cups One cup is twice higher than the other. Again. Which holds more? Figure 295 Figure 297 Figure 296 How Many Glasses? Figure 298 depicts three shelves cn which vessels cf three capacities are arranged so that the total capacity cf the vessels on each shelf is the same.•iVSt. Geometric Recreations Further "Plug" Figure 294 Puzzles The accompanying figures show three more boards. Find the capacity cf the ether two kinds cf vessel. 297). but the other is 1 1/2 times wider (Fig. . Half-Full An open barrel contains some water. Arrange them on the pans cf a balance for it to be in equilibrium. But you want to know it for certain and you don't have a stick or any other measuring device to measure the contents of the barrel. How many times heavier is it? Four Cubes Four solid cubes of the same material have different heights: 6 cm. seemingly half its capacity. Which box is heavier? Tripod Figure 301 It's believed that a tripod never rocks. 299). and the one on the right is filled with small steel balls arranged as shown. Which Is Heavier? There are two identical cubic boxes (Fig. even if its legs have different lengths. 300): the one on the left contains a large steel ball with a diameter Figure 300 equal to the box's height. 301)? Not squares but rectangles. Their walls are equally thick but one is eight times more capacious than the other. Is that so? How Many Rectangles? How many rectangles can you identify in this figure (Fig. cf any size. and 12 cm (Fig.340-341 Geometric Recreations Two Saucepans Fijvre 299 Consider two similar saucepans. Find a way out. 8 cm. 10 cm. 303. How many times heavier is the giant? Along the Equator Figure 302 If you could walk all the way along the equator. Are the internal and external triangles similar (Fig. are the internal and external rectangles similar? . In the frame of the picture (Fig. Referring to Fig. 302). What is the weight of a toy brick of the same material with all its dimensions four times smaller? A Giant and a Dwarf Consider a 2-metre giant and a 1-metre dwarf. 3036). What will its apparent magnitude be? Similar Figures This problem is for those who know about the concept of geometric similarity. 303a)? 2. the top of your head would have travelled a longer way than each point on your feet. What would this difference be? Through a Magnifying Glass An angle of 1 1/2° is viewed through a 4 x power magnifying glass (Fig. answer Figure 303 a b the following questions: 1.346-343 25 (2> Chessboard Geometric Recreations How many differently arranged squares could you identify on the chessboard? A Brick A brick weighs 4 kilogrammes. 305). that would be "superflyish". Trace the path a granite block 30 centimetres long. a tower whose height you don't know. But you have got a photograph of the tower on a picture postcard. The Path of a Beatle At the roadside lies 20 centimetres high A beatle is sitting shortest way to B. On the inner wall. how long will be the strip obtained? Figure 304 A Column Now imagine a column produced by stacking all the 1-mm cubes contained in 1 cubic metre. 3 centimetres from the top.342-343 Geometric Recreations The Height of a Tower Suppose there is a tourist attraction in your town. Figure 305 . at point A and wants to find the and find out how long it is. there is a fly (Fig. and all of them are arranged side by side on a straight line. however. and 20 centimetres thick (Fig. Don't hope that the fly could find the shortest way on its own. Trace the shortest path for the fly to get to the honey. and on the outer wall. thereby simplifying the problem. there is a drop of honey. 304). How high would this column be? Sugar JtO Which is heavier: a glassful-of granulated sugar or pressed sugar? The Path of a Fly Consider a cylindrical glass jar 20 centimetres high and 10 centimetres in diameter. This would require a knowledge of gebmetry on its part. How could this picture help you to determine the height? A Strip A bit of mental arithmetic: if a square metre is divided into 1-mm squares. the diametrically opposite. How calculate the area that. Now it goes to the orchard where the bumble-bee yesterday saw gooseberry-bushes in blossom. Fluttering from a flower to flower it spends half-hour here. the fortress could occupy. according to the legend. The orchard lies due west of the hill and it makes a "bumble-bee" line there. From its nest it flies due south. So the citadel of Carthage was built. fled to the north coast of Africa with many of the inhabitants of Tyre. At last. She bought from the Numidian king as much land "as an oxen hide occupies". who lost her husband at the hands of her brother. . crosses a river and after an hour's travel alights on a hill covered with clover. and later developed into a city. the insect takes 1 1/2 hours to visit all of them. The bushes being in full blossom. given that the oxen hide had a surface area of 4 square metres and the belts into which Dido had it cut were 1 millimetre wide. Having concluded the bargain Dido had the hide cut into thin belts and thanks to this trick she got a site big enough for a fortress to be erected. the bumble-bee starts on its return journey and takes the shortest route possible.348-343 A Bumble-Bee's Geometric Recreations Travels A bumble-bee sets out on a long journey. How long has the bumble-bee been away from its nest? The Foundation of Carthage According to a tradition concerning the foundation of Carthage the Tyrian princess Dido. where it arrives 3/4 of an hour later. whereas these prisms should be referred to as triangular prisms. and ignoring the end faces is widespread. When we look at some object we.344-345 CJ) Answers How Many Faces? The problem reveals an incorrect usage of words. If it really had six faces. . A hexagonal pencil doesn't have six faces. If it isn't sharpened. Many people say: trihedral prisms. What is more. namely a block with a rectangular cross section.. Glasses and Knives This is quite possible to achieve by arranging the knives as shown in Fig. 306. according to their cross section. What Is Shown Here? The objects are a razor. it has eight faces.. as can be seen from Fig. quadrangular prisms. tetrahedral prisms. not "hexahedral". etc. 307. Here you were not shown the views that you see habitually and this is enough to render an object almost unrecognizable. a pair of scissors. a pocket watch. The habit of only counting side faces in prisms. a trihedral prism (i. having three faces) cannot exist. it would have quite another shape. all in all: six lateral faces and two small "end" faces. and a spoon. Figure 306 Figure 307 How Is It 2 3 . e. see it projected onto a plane normal to the line of sight. a fork. generally speaking. etc. as may well be believed.975 Achieved? The way out is very simple. The pencil mentioned in the problem should be referred to as "hexagonal". Answers 25 3 One Plug for Three Holes The suitable plugs are shown in Fig. 308. Figure 309 Figure 310 Figure 311 . 309. 311). the plugs are more complicated (Figs. Figure 308 Further "Plug" Puzzles In this case. 310. i. the bottom is well below the surface of the water. If some of the bottom shows above the surface. on the contrary. The answer is therefore that the larger pan is four times heavier.728. however little.346-347 Answers Two Cups The cup that is 1 1/2 times wider would (with the same height) have (1 1/2)2. Since it is only half the height of the other cup. Two Saucepans The two saucepans are geometrically similar. Let's show that the total volume of the three smaller cubes equals that of the largest one.000= 1. the barrel is exactly half-full. Finally. 312). it's obvious that the capacity of one middle-sized vessel equals that of the three small ones. 216 + 5 1 2 + 1. the barrel is more than half-full. e. the weight of a saucepan depends on its surface area. The thickness of walls being the same. How Many Glasses? A comparison of the first and third shelves shows that they differ only in that the third shelf contains one more middle-sized vessel whilst the three small vessels are missing. Given that the larger saucepan holds 8 times more. 2 1/4 times more volume. The total capacity of the vessels on each shelf being the same. If.e. The middle-sized vessel thus equals three glasses. Its surface area must then be 2 x 2 times larger. i. all of its dimensions are twice larger: it's twice higher and wider. It only remains now to determine the capacity of a large vessel. Comparison with the second half yields that one large vessel holds 6 glasses. because the surfaces of similar bodies relate to each other as the squares of their linear dimensions. the barrel is less than half-full. in the final analysis it still holds more than the taller cup. if the upper edge of the bottom is exactly on the water level. Half-Full The simplest way is to tilt the barrel so that the water reaches the edge (Fig. 23* . This follows from the relationship 63 + 83 + 103 = 123. It's easily verified that the balance will be in equilibrium. Four Cubes We must place the three smaller cubes on one pan. and the largest one on the other. By replacing all the middle-sized vessels on the first shelf by the appropriate number of glasses we get one large vessel and 12 glasses on the top shelf. We can readily work out the number of these small balls and cubes: 6 x 6 x 6 = 216. and hence their weight is the same. and 64 unit squares. The total volume of the 216 balls accounts for the same share of the 216 cubes as the big ball relative to the big cube. is purely geometrical and not physical. That is why tripods are so convenient as supports for field instruments and cameras. A fourth leg wouldn't make the support any more stable. you see. How Many 225. and only one at that. This problem. Chessboard The chessboard contains more than 64 squares. 9. 36.Answers Figure 312 Which Is Heavier? Let's imagine the right cube as consisting of small cubes. 25. These must be taken into account as well. 16. Rectangles? . It's easily seen that the large ball occupies the same proportion of the large cube's volume as each small ball occupies of the smaller cube's volume. 49. Apart from the small black and white squares there are the larger squares consisting of 4. This explains why a tripod doesn't rock. because through any three points in space one can draw a plane. It follows that both boxes contain the same amount of metal. Tripod A tripod can always touch the floor with each of its three legs. each containing a ball. 5 If you believe that the magnifying glass will make the angle look as if it were 1 1/2° x x 4 = 6°. i. Through a Magnifying Glass you and 4x 62.348-345 Answers Unit Squares Number on Chessboard 64 49 36 25 16 9 4 i 4 9 16 25 36 49 64 1 Total 204 Thus. 7 x 7 x 7 = 343 or a whole crowd of dwarfs would have to stand on the other to balance. Consequently.e.2 x 3. We thus have 2 x 3. Since human bodies are approximately similar. The smallest dwarf was under 40 centimetres. A Brick If you thought the toy brick weighs 1 kilogramme. about 11 metres.000 — 64 = grammes. not twice as heavy. the result is independent of the globe's radius.e. A Giant and a Dwarf Now you are well equipped to solve this problem correctly. the correct answer is: the toy brick weighs 4. It's not only a quarter the length. Along the Equator We take the man to be 175 centimetres high and denote the Earth's radius by R. if the giant were to stand on one pan of a balance. i. only a quarter lighter. but also a quarter the width a quarter the height of a standard brick.e. the chessboard contains 204 differently arranged squares of different sizes. he was seven times smaller than the Alsatian giant. would be wrong.100 cm. Interestingly enough.14 xR = 2x 3. the giant would be eight times heavier. i. The tallest giant ever recorded was a man from Alsace in Germany. Therefore.14 x 175 = = 1. therefore its volume and weight is 4 x x 4 = 64 times less. a metre higher than an average man.14 x (R + 175) . you put your foot in it. He was 275 centimetres high. Viewing through a magnifying glass doesn't make . It's worth noting that the method . the heightto-base ratio in reality and in the picture are the same. both questions are answered in the affirmative. For triangles to be similar it's sufficient for the angles to be equal and since the sides of the inner triangle are parallel to those of the external one. for rhombs). i. This stands out especially for rectangular frames with Figure 314 wide planks as shown in Fig. the sides of the external rectangle are not proportional to the sides of the internal rectangle. only the triangles are similar. say. however. In the left frame the ratio of the external sides is 2:1. and hence the figures are not similar. with the result that the central angle remains the same (Fig. 314. and of the inner sides 4 : 1 . In any other cases. In the right frame the ratio of the external sides is 4 : 3 . 14 metres.Answers the angle any larger. the arc subtending the angle increases. which is. the tower is 70 metres high. Now measure the base of the real tower.e. Suppose the height in the picture is 95 centimetres and the base is 19 centimetres. but the radius of the arc increases as much. Then you argue as follows. then you conclude that the height of the real tower is five times larger than its base: 14 x 5 = 70 metres. 313). The Height of a Tower To work out the height of the tower we should at first measure as accurately as possible the height of the tower and the length of its base in the picture. In actual fact. The picture and the real tower are similar. For the internal and external rectangles of the frame this is only the case for squares (more generally. It is also necessary that their sides be proportional. and of the internal sides 2 : 1 . the angles are equal. Figure 313 Similar Figures Not infrequently. The first ratio is 95:19 = 5. With other polygons it's not sufficient only to have equal angles (or parallel sides which is mathematically the same). True. what is the enlarged granulated sugar? It's nothing but pressed sugar. A Strip There are 1. a glassful of pressed sugar has the same weight as that of granulated sugar. 1. i. The key thing here is that the pieces of pressed sugar are regarded here as being geometrically similar to the particles of granulated sugar and are at that arranged in a similar manner. Suppose for simplicity that the lumps of pressed sugar are 100 times larger across than the particles of granulated sugar.e. 3156) at a right angle to the upper side of the rectangle and continue it an equal distance beyond the edge. The capacity of the glass would be increased 100 x 100 x 100. Multiplying by the last 1. Each thousand 1-mm cubes stacked one upon another gives a 1-metre column. but it's fairly close to reality if the lumps are irregular. one millionth part of the contents of the giant glass. 315a) 20 centimetres high with the base equal to the circumference of the jar. we obtain 1. The Path of a Fly Let's make the sides of the cylinder jar into a flat surface. the path ADB being the shortest. Each thousand 1-mm squares arrange along a line span 1 metre. 10 x 3 1/7 = 311/2 centimetres (approximately).. Ciearly. Sugar Use your imagination.000 square millimetres in 1 metre.000 metres = 1 kilometre. it will weigh as much as a normal glassful of conventional granulated sugar. On this rectangle we now can mark the positions of the fly ( A ) and honey drop (B). Thus the strip will be 1 kilometre long. the situation wouldn't have changed in the least. one million times. Multiplied by 1.000 this gives 1. as would the weight of the sugar. But then. The assumption is not strict.000 kilometres high. Accordingly. i.350-351 Answers only works with pictures that don't distort proportions which is often the case with inexperienced cameramen.e. There are 1000 x 1000 x 1000 cubic millimetres in 1 cubic metre.e. A Column The answer is striking: the column will be. If we had made the magnification 60-fold instead of 100-fold or any other magnification. ..000. Let's take a normal glassful of this enlarged granulated sugar. and a thousand thousand 1-mm squares give 1. Point D will be where the fly must cross the edge to the other side. We'll draw a line from B (Fig. Now to find the point at which the fly must cross the edge we'll proceed as follows. 1 kilometre.e.000. Let's test it mentally. Now imagine that all the granules in the granulated sugar were enlarged 100 times together with the glass containing them. i.000 metres. i. We'll obtain a rectangle (Fig.000 kilometres. We obtain point C which we connect with a line to A. AB and BC. and finally it flew back to its nest by the shortest path possible. According to the Pythagorean theorem. So the shortest path AB = 50 cm.tfm Answers Figure 315 Having found the shortest way on the rectangle. Then it flew for 45 minutes "due west". 3156). at right angles to the first leg. i. the hypotenuse AC remaining to be determined. AB must be 50 cm. What is Figure 316 SO 30 its length? We have the right triangle ABC. The shortest route then is the line connecting A and B. CB = 30 cm. A Bumble-Bee's Travels The problem would be a "piece of cake". if we knew the time taken by the bumble-bee to cover the distance from the orchard to its nest. along a straight line. We know that it flew at first "due south" for 60 minutes. Let's draw the path of the insect. because 30 2 + 40 2 = 502. e. we'll again make it into a cylinder and find out how our fly must walk to get to the honey drop in the shortest time possible (Fig.e. We thus obtain the right triangle ABC with two known legs. . where AC = 40 cm. i. The Path of a Beatle We'll mentally turn the upper face of the stone so that it lies in the same plane as the front face (Fig. Geometry will help us work this out. 316). 4 kilometres long. or 4 million square millimetres. then the hypotenuse is 15 kilometres. or 4. Total: 3 + 2 = 5 hours.000 metres. Dido had it cut in a spiral) was 4 million millimetres. Stops: 1/2 + 1 1 / 2 = 2 hours. or a round area of 1. the other leg four units long. and so forth. i. and the belt thickness was 1 millimetre. to cover the distance from the orchard to its nest. A belt this long can encircle a square area of 1 square kilometre. The Foundation of Carthage Since the surface area of the hide was 4 square metres. .352-353 Figure 317 Answers Nest BOmin Or char c 45 min Geometry teaches that if one leg of a right-angled triangle is three units long. if legs are 3 metres and 4 metres. the total length of the belt (clearly.e. For example. then the hypotenuse is exactly five units long.e. In our case one leg is 3 x 15 minutes of flight long and the other 4 x 15 minutes long.3 square kilometres. hence the hypotenuse AC = 5 x 15 minutes of flight long. 11/4 hour. We have thus found that the bumble-bee took 75 minutes. if 9 and 12 kilometres. i. Now it's child's play to figure out how long our bumble-bee had been away from its nest: Flights: 1 + 3 / 4 + 1 1 / 4 = 3 hours. then the hypotenuse is 5 metres. It's possible that the stretch of ground you measured does not contain an integer number of paces. if the remainder is shorter than a step. Lay out the tape on a smooth piece of ground and measure a 20-metre stretch. can be conveniently measured by paces. Now walk along the line in your normal way and count the number of paces you have. i. Then. But this does of course require that we know how long our paces are and could count them. we cannot do without a tape-measure. In order not to lose count of paces you can. paces are not always the same: we can walk with short steps or long steps. when we need to. use the following trick. Here. For example. Draw in the line and remove the tape. especially over long distance. for instance during hikes. To find the average length of your pace you should measure the total length of many paces and find the length of one.e. . Dividing the total length of 20 metres by the number of paces gives the average length of one pace. and if we know their average length. if necessary. and then start from the very beginning remembering how many times have we ticked off all the fingers of the right hand. start ticking off the fingers on the right hand. After the five fingers of the left hand have been ticked off. Count up to 10 and then tick off a finger of your left hand. of course. if having covered a certain distance you've ticked off all the fingers of the right hand twice and you end up with three fingers more ticked off on the right hand. it pays to be able to do without one where approximate estimates are sufficient. 50 paces covered.Without a Tape-Measure Measuring by Paces* Since a tape-measure is not always at hand. if it's longer than a step. But still when we walk at a measured pace our steps are about similar. We can in this way count up to 250. it can be simply discarded. Longish distances. and * We will call two steps 1 pace. This number should be remembered so that. the remainder is taken to be a whole step. Admittedly. we can without much error measure distances in paces. it might be used for measuring. 6 nx = n. We can easily show that the rule is only true for one rather large length of pace.800 seconds) he travels 600 nx metres.66 metres. Measure by Figure 318 .6 nx = 1. For this distance to be equal to the number of paces made in 3 seconds the following equality should hold 0. there is an old rule which says that the length of an average step of an adult equals the distance from floor to his eyes.6 nx kilometres. about 175 centimetres. you've made 2 x 250 + 3 x 50 + 4 x 10 = 690 paces. and the number of paces made in 3 seconds be n.pace length be x metres. you can proceed as follows. If the first old rule relating pace length to man's height. Another old practical rule refers to walking speed: a man covers as many kilometres in half an hour as he makes paces in 3 seconds. You should also add the paces you made after the last finger of your left hand has been ticked off. or 0. Then in 3 seconds the walker goes nx metres. then the second rule is only valid for people of average height. or 0. By the way. Let the . Living Scales To measure objects appropriately without a tampemeasure. and in half an hour (1.354-355 Without a Tape-Measure four on the left. Hence x = 1. as shown in Fig. 319a). This "live scale" will enable you to estimate the dimensions of small objects. The latter piece of advice introduces us to the art of measuring "with bare hands". 319d and. 319e. It is also advisable to know the length of your index finger from the base of your thumb.360-355 21 Without a Tape-Measure a stick or a rope the length from the end of your outstretched arm to your opposite shoulder (Fig. Initially. In adults it's about 10 centimetres. Which parts then should be measured? Above all. By way of example. 319b. but it varies from person to person and Figure 319 you should know its exact value. because they might be of help in measuring objects. the width of your outspread palm from thumb to little finger. Another way of getting an approximate metre is to mark off six times the distance from your thumb to forefinger. the Soviet coins have convenient dimensions: . as shown in Fig. its width. Then it pays to know the span between the ends of your middle and index fingers separated as wide as possible (Fig. as shown in Fig. finally. separated as widely as possible (Fig. you should only measure parts of your hand and remember the results. Measuring with Coins It pays to know the size of your national coins. 319c). 318)-in adult it's about a metre. 5 kopeck piece is 21/2 centimetres across. and so on.356-355 Figure 320 Without a Tape-Measure 1 kopeck piece is exactly 11/2 centimetres across. Remember the diameters of your coins! . 322) and make a loose knot on it as shown on the Figure 322 left of the accompanying figure. You'll witness something enigmatic: instead of the 13 lines that were there before the figure will only show 12. give them the right numbers straight away and without so much as a glance at it or your friends. Really. You could surprise your friends by saying that you'll guess the drawn domino's points from an adjoining room. What is the idea behind the trick? Disappearing Line Copy out the figure in Fig. from the adjacent room.Simple Tricks and Diversions 27 Guessing Domino Points The trick is based on a dodge that can't be guessed. Here is a curious trick that could surprise your friends. Add a second loop (see the knot in the middle). For better effect suggest they blindfold you. one of your friends draws the piece and asks you to guess its points and you. One line will have disappeared. Take a piece of string about 30 centimetres long (Fig. 321 very accurately. Cut the ring out. But to be on the safe side we'll make the knot . You're sure to expect that tightening the string now will give you a good double knot. Where from? A Mysterious Knot Figure 321 We'll now turn to trick with things. apply it to the ring in the figure and turn it counterclockwise so that the severed part of each line registers with the remains of a neighbouring one. Where to? The reverse operation brings the line back. So examine the knots in the figure carefully. All the preparations over. Escaping Bind your friends (A and B) as shown in Fig. 324.358-359 Simple Tricks and Diversions smarter by threading one of the loose ends through both loops as shown on the right. Take hold of one end of the string and offer the other to your friend. The trick is a success if only you make the third loop exactly as shown. Is it possible to set the friends free without cutting the strings? Figure 323 B A Pair of Boots Take a sheet of strong paper and cut out a frame. a pair of boots and an oval ring as shown in Fig. 323. The hole in the oval ring is the size of the width of the Figure 324 . we can proceed to the main part of the trick. Pull! You'll discover something neither you nor your friend expected: instead of an involved knot you'll have a smooth piece of string! The knot will have gone. but narrower than the legs of the boots. Stick the paper under the two ribbons. Figure 326 Two Buttons Figure 326 shows a sheet of paper with two long cuts and one small oval hole that is a bit smaller than the separation between the long cuts. Presto! The paper itself emerged from under both papers but (what . say 7 centimetres long and 5 centimetres wide. "Magic Purse" Figure 327 Cut two rectangles out of a sheet of cardboard. You now have your "magic" purse. But it is possible. Therefore. the rectangles being the size of a notebook. Take a piece of paper signed by your friend so that you could not replace it. if you are asked to hang the boots on the frame as shown in the figure. two of them being a centimetre longer than the rectangles' width. then round the outside of the left rectangle and glue its end under this rectangle. Remove the corks from the paper ring. Thread a piece of string through the hole and the cuts and tie a button to each end of the string so that the buttons won't pass through the hole. on which two corks hang suspended from a short piece of string with a wire ring slung on the string as shown in Fig. you can show your friends a fascinating trick that can be dubbed "live paper" or something like that. Glue the ribbons to the rectangles as shown in Fig. How? Corks on a Ring There is a ring of strong paper. Get three pieces of ribbon (paper strips will do as well). Now close the purse. Using it. you'll obviously think that it's impossible. 327. In so doing. and the third a centimetre longer than twice the width of the rectangles. and glue the other ends to the back side of the left rectangle. Glue the end of the longer ribbon to the outside of the right rectangle.Simple Tricks and Diversions Figure 325 frame. bend the ends of the shorter ribbons under the right rectangle and glue them to it. 325. thread the ribbon under it. reopen it. How could he possibly guess? But he did! He just came up to the table and without a moment's hesitation pointed to the match." said Alex arranging matches on a table in a random manner. When you're ready. You'll be a witness. boy! We'll show you an interesting trick. showed it to the student without touching and called out: "Ready!" I didn't believe that Alex would guess the match since I hadn't so much as touched it and all the matches remained in their places. we'll do it this way: when he's thought of a match he'll show it to you. I peered in and saw my brother and his student friend laughing. I was on the verge of bursting into tears as I was dying to know the secret. Let's start. we can't do without it!" "Okay. Going about my business in my room once I heard in the adjacent room some laughter that wetted my curiosity.. "No. "I put ten matches down at random.. Explain." "And he'll say that it's not the right one. "Look here. Well I never! "Want another go?" "Of course!" We did it again and he guessed it again! A dozen times we did the trick and each time my brother indicated the match I had thought of without mistake. call me. Now Til go into the kitchen and you think of a match here. Finally. I made sure that he was gone and couldn't peer into the keyhole. Guessing Matches In my childhood I was much amazed by a trick shown to me by my elder brother. I'll just take a look at the matches and tell you which one it was. "Come in. What was it? 24 975 ." the guest interrupted." That was exactly what I wanted. I even tried hard not to look at it in order not to betray myself. My brother even didn't glance at me and still guessed." My brother left. Then I thought of a match." "That's different.360-359 Simple Tricks and Diversions is beyond belief!) it got under the centre ribbon on the opposite side of the purse. My brother was a great wag. my tormentors took pity on me and revealed the trick. some control is needed here. the trick will work. practice a bit. the slightest jolt will turn the match over. If you are adroit enough. Is It Easy? What do you make of what is shown in Fig. doesn't it? But try to do it yourself and you'll find that it requires patience and practice.366-359 Simple Tricks and Diversions Eleven Matches on One Arrange a dozen matches as shown in Fig. if not. Each of the two partners places his counter at the either end of the path. 328 and try and raise them all by lifting the sticking out end of the Figure 328 lower match. 329: is it easy to lift a match with two other matches? Figure 329 It seems easy as pie. Each partner shifts his counter forward by so many squares as there are points shown by the die. Then they take turns to throw the die (the one with the largest number of points begins). For the game you'll need a die and two counters or draughts (two coins or buttons will also do). On a Narrow Path Draw a narrow path of 15 squares on a sheet of paper (Fig. 330). but he is not entitled to . The rules of the game are simple. g. cut the folded paper along some ornate lines. e. C. The counters thus alternatively appear in the middle of the path or at its extremes. The game ends when one of the partners is forced to leave the path.362-363 Figure 330 Simple Tricks and Diversions skip the square occupied by his opponent's counter. and E. like those shown in the figure. The winner is the one who stays. D. B. Star-Like Patterns Some people maybe don't know that just with a pair of scissors. he must retreat by the excess number of squares. 331. If the die shows more points than there are free squares left. Having Figure 331 reached the stage E. Now unfold and smooth out the paper to obtain . without any drawing instruments it's possible to manufacture an infinite variety of beautiful paper patterns. Take a sheet of white paper and fold it several times as shown in Fig. A. it is trimmed at the thick end along one of the dash lines in Fig. not a circle. the semicircle obtained is then folded four times as shown in Fig. because the semicircle must be folded so as to give five similar segments. When you unfold the paper. Once the circle has been folded correctly. 333. 333B. In the first method. The circle is cut out and folded in two.368-359 Simple Tricks and Diversions a beautiful design that will look yet better when glued on some dark paper (Fig 332). The second method is perhaps simpler as we start with a square. Then three . 333/4. you get a regular five-pointed star with either shallow or deep notches (Fig. Figure 333 This is the most difficult part of the problem as it requires a good eye. Figure 332 Five-Pointed Star Can you cut out a paper five-pointed star? It is not simple and takes some practice. There are two methods of cutting good regular stars. C and D) depending on how you trimmed the semicircle. a circle is drawn on a sheet of paper using a pair of compasses or just a saucer. 334/1) is folded in two. otherwise your star will have unequal points. To begin with. a square sheet of paper (Fig. The dot-and-dash line in Fig. The resultant star is depicted in Fig. B. 334£. 334D indicates the trim line. and D. C. Figure 334 . 334.364-359 Simple Tricks and Diversions more folds are made as shown in Fig. Which words ? Its Simple. mark out the four end points of the Figure 336 two lines.. However. of course. perceive Figure 335 nothing sensible. but you can say that he is standing on his left leg with the same .. you will. 335). But the line is stubbornly unsuccess. Or Is It? Look carefully at the design in Fig. Have you remembered it?. 337 and say which leg the footballer is standing on. if you view the circle in the proper way. Looking at it in the conventional way. At first. He seems to be standing on his right leg.Drawing Puzzles What's Written Here? Something is written in the circle (Fig. The first curve will probably come out adequately. This seemingly easy job does not now appear to be so easy. On Which Foot Look at Fig. Then begin drawing. the right or left. 336 and try to remember it so that you could reproduce it from memory. Okay! Now draw the second curve. you'll be able to read the words. 338). Where are they? . "But which is which. It might seem that the angler has caught nothing so far. The artist has done his job so skillfully that it's impossible to establish which leg is doing the kick and which is supporting the man. How Many Fish? You see a strange drawing here (Fig.366-367 Figure 337 Drawing Puzzles measure of certainty. No matter how long you view the drawing you'll never answer the question. But Figure 338 look very attentively at the figure: three big fish are already here. It will remain an unsolvable mystery for ever. Perhaps you are asking. either. The artist doesn't know. really?" I don't know. Figure 340 . 339)? His portrait does appear in this figure. Find it. Figure 339 Sunset Look at the picture (Fig.Drawing Puzzles Where Is the Tamer? Where is the tamer of this tiger (Fig. The picture contains one incongruity that you should find. 340)-a sunset-and say if it is correct. Figure 341 .368-369 Drawing Puzzles Moonset Figure 341 represents a tropical moonset. Is the picture correct? Perhaps you can see something incongruous about it. In that case." But how about the blanks? It might be denoted by some other word. then your companion utters: "I think this time they are difficult to guess. If the domino is 0-4. that the following words have the meaning: "I".2 "he". Let the piece in question be 4-6. and "my" . " i t " . Figure 342 one will have disappeared. . Figure 342 shows a piece of cardboard with 13 lines.6 These conventions may be illustrated by some examples. namely a 1/12th longer." In the secret language this will be: "we"-4. In this case we can easily see where it has gone since each of the 12 new lines has got somewhat longer than before. friend. The sheet is cut along the diagonal.1 "you". "they"-5.4 "they"." Those uninitiated will never guess that these words contain the secret message: ' T . and "their"-5 "it". what we've thought now.l . and " i t s " . and " o u r " . say. hence 4-6.3 "we". say. and " y o u r " . guess it." Disappearing Line The jist of the trick is better illustrated in a simplified form. your companion calls out: "We've thought of a piece. You've agreed. If you shift one part relative to the other as shown in the figure.6 . friend. A further example: 4-2. If the piece is 1-5.tfm 27 Answers € 6 Guessing Domino Points Here you use a secret language known only to you and one of your friends with whom you've preliminarily worked it out. and " h i s " . then instead of 13 lines you'll get only 12. What "message" should your companion send? Something like this: "Now we've thought of such a piece that you'll never guess. your fellow-conspirator calls out: "Guess. When a sufficient length of the string has already been tucked in. Escaping Yes.370-371 Answers Clearly. The lines in Fig. when shifted one of the lines has been divided into 12 parts each of which went to lengthen the other lines. String A is taken at point C and threaded through loop B in the direction indicated Figure 343 B by the arrow. the friends separate. Figure 344 . refolded and pushed to the bend in the frame. Reverse shifting brings the vanished line back into being by shortening the other lines. 321 are arranged in a circle and possess the same property: shifting the circle through an appropriate angle kills one of the lines (it is "smeared" over the other 12). It now only remains to unfold the frame. it is. hand B is put into the loop formed and. Finally. A Pair of Boots The accompanying figure explains the answer. the ring is slided onto the end. when string A is pulled. Then the unfolded figure of "double boots" is threaded in-between the folded ends. The frame is folded and the ring is put on the folded ends. remove the wire ring by sliding it away to the free end. So the upper match marked the hair. Two Buttons The accompanying figure shows the solution. mouth. the forehead. "Magic Purse" The point is that you open the purse from the opposite side. Figure Fold the paper ring as shown. and on either side the ears. he first of all cast a glance at . and remove the corks. Guessing Matches I was simply made a fool of. nose. the next below. The student who pretended to control the guessing was my brother's conspirator and gave signals to him. this one will be smooth sailing.Answers tfm 27 6 345 Corks on a Ring Now that you know how to solve the previous problem. 347) that the pattern would resemble the outlines of a human face. further down were the eyes. Then thread the strip through the oval hole and remove the buttons through the loop. neck. Fold the paper so that the upper and Figure 346 lower ends of the narrow strip between the cuts will coincide. When Alex walked into the room. chin. It turned out that the matches were arranged not at random: the brother had so arranged them (Fig. But how? That was the trick of it. One fish is one the angler's back. Sunset The incongruity is that the convex part of the crescent faces in the opposite direction from the sun. Figure 348 The letters are extremely elongated and narrow. their width being the same. then turn the circle and you'll now see the word PERELMAN. . How Many Fish? Fll help you discern the catch. because a year never passes without a large number of inverted crescents appearing at the Paris Salon".. hence it by no means can be facing the sun with it dark side. thus indicating which match had been thought of.. 348. The French astronomer Flammarion wrote: "Most of painters are ignorant of this. not towards it. Where Is the Tamer? The tiger's eye doubles as the tamer's eye. This imparts a normal aspect to tht letters. You'll clearly read the words MIR PUBLISHERS. the tamer is looking in the opposite direction. The third is under his feet. thus simplifying reading them. What's Written Here? Bring the ring up to your eyes as shown in Fig. therefore it's impossible to make them out in the conventional way. Another is between the float and the end of the fishing rod. The moon is illuminated by the sun. head down. In the suggested method the letters become much shorter.372-371 Figure 347 Answers the "controller" who touched an appropriate feature of his face with his hand. as shown in the figure. In the higher latitudes the sun and moon (indeed all the luminaries in general) execute their diurnal motion in inclined circles. This is explained as follows. . 341 is depicted correctly.-n ' € Answers Moonset Strange as it may seem. illuminating it from the right or left. But in tropical lands the crescent hangs horizontally in the sky. the crescent in Fig. where the hump of the new moon faces to the right and that of the old moon faces to the left. so that the crescent faces to the right or left. It's a tropical landscape where the position of the crescent differs from that in the higher latitudes. The moon is thus illuminated from below and that is why the crescent has the form of a gondola. But on the equator the celestial bodies move in normal trajectories with the result that the sun illuminating the moon sets below the horizon directly beneath the moon and not to the left or right of it. Therefore during the evening the sun casts slanting rays at the moon. T h e End . Perelman .I.Ya. Sign up to vote on this title UsefulNot useful Master Your Semester with Scribd & The New York Times
Glossary of technical terms ABB glossary of technical terms Although power and automation technologies impact our lives on a daily basis, many of the terms used to describe these fields are not part of everyday vocabulary. The purpose of this glossary is to provide simple explanations for some of the more commonly used terms associated with ABB’s technologies and to open up the world of power and productivity to a wider audience. An online version of this glossary is available at: ABB glossary 3 Actuator: In electrical engineering, the term actuator refers to a mechanism that causes a device to be turned on or off, adjusted or moved, usually in response to an electrical signal. In some literature the terms actor or effector are also used. The term “effector” is preferred by programmers, whereas engineers tend to favor “actuator.” An example of an actuator is a motor that closes blinds in response to a signal from a sunlight detector. Actuators enable computers to control complex manufacturing processes without human intervention or supervision. Advanced process control (APC): In general terms, advanced process control refers to large-scale computer systems that are used to monitor and control processing plants such as cement factories or oil refineries. The systems extend traditional process control, which is used to monitor and control individual processes, by evaluating and controlling multiple processes across the plant. By monitoring multiple processes, APC systems can optimize operations for multiple parameters, evaluating the impact each adjustment will have on neighboring operations by referencing current and historical data. With a broad yet detailed view of an entire plant’s operations, APC applications allow processes to operate closer to their maximum capacity, while maintaining the necessary standards of reliability and safety. Air-insulated switchgear: see Switchgear. Algorithm: A set of (mathematical) instructions or procedures for carrying out a specific task such as defining the steps taken by an automation system. Alternating current (AC): Alternating current is a form of electricity in which the current alternates in direction (and the voltage alternates in polarity) at a frequency defined by the generator (usually between 50 and 60 times per second, ie, 50 - 60 hertz). AC was adopted for power transmission in the early days of electricity supply 4 ABB glossary because it had two major advantages over direct current (DC): its voltage could be stepped up or down according to need using transformers (see Transformer), and it could be interrupted more easily than DC. Neither advantage is as relevant today as it once was because power electronics can solve both issues for DC. (See also Direct current and Transmission and distribution.) Alternator: see Generator. Ampere: The standard unit of electrical current. (See also Current.) Arc flash: An arc flash is caused by current flowing between two conducting surfaces and most commonly occurs in switchgear as a result of faulty equipment or poor work practices. Left unchecked, arc flashes release a tremendous amount of energy in a high-pressure blast of heat and debris, which can result in serious injuries to workers and damage to equipment. Arc welding: A group of welding procedures that fuse metal pieces by melting them together, using heat from an electric arc between an electrode and the work piece. The arc is caused by electrical current flowing though plasma consisting of ionized air molecules and metal ions. Material from the electrode is transferred to the work piece, and the electrode is consumed over time. Arc-welding processes are attractive because of their low capital and running costs. Arc-welding cell: The area of a factory set up to weld metals using electric arcs. ABB provides modular robotic arc-welding cells that are ready to install in a customer’s plant. Asset management: Also referred to as industrial and plant asset management. Asset management systems collect and manage data on the condition and availability of major plant equipment in discrete and process manufacturing plants. This enables plant operators to plan maintenance schedules more effectively (condition-based ABB glossary 5 rudder and stern thruster. This means that generators on either grid can be used to secure the supply of electricity across the extended network. with a minimum of human interaction. In computing. Asynchronous machines: See Machines Azipod: The registered trademark of a family of modular electric propulsion systems for ships. Bandwidth: 1. Since these functions are no longer installed as separate units inside the ship. bandwidth is often a synonym for the rate of information transmitted by a network 6 ABB glossary . The Azipod unit is fitted to the ship’s hull externally in a pod. the first of which was co-developed by ABB in the 1980s. links used to connect neighboring grids are often referred to as “backto-back” connections. and enable power to flow from one grid to another. and combines the functions of a propulsion motor. Azipod units also contribute to improved hydrodynamics. The connections can also improve voltage and frequency stability in the linked grids. which result in fuel savings of around 15 percent compared to conventional propulsion systems. Note: The term “back-to-back connection” is also used to describe a test set-up for electrical devices where a motor and a generator are connected to the same shaft line. indicating that the distance between the two grids is minimal. space onboard can be used for other purposes. avoiding both unnecessary equipment inspections and unexpected breakdowns. B Back-to-back connection: In HVDC terms. which can cause expensive interruptions in production time. including those operating at different frequencies. Such connections are able to link independent power grids. or casing.maintenance). main propeller. Computerized asset management systems gather data in real-time to ensure maximum production uptime and throughput. comprising a single binary digit (ie. The plants that maintain constant levels of production tend to be those that rely on lower-cost fuels and are known as “base-load” power plants. which are derived from ancient organisms. For example. It is measured in hertz (Hz). which means it is capable of transmitting 56. Barges are used as cargo tankers. Base-load power plant: To maintain power supplies as efficiently as possible. crane platforms and support and accommodation bases in offshore drilling. and as submarine pipe-laying vessels. by using local generators. (recently) living organisms. while others are brought online or increase production temporarily to meet transient peaks in demand for electricity. A bit is the smallest unit of computerized data. independently of the larger grid. Bioethanol. Bandwidth in electronic communication is the difference between the highest.connection or interface.) Black-start capability: The ability of a power system (a generator or grid subsection) to restart after a blackout. A blackout may also be referred to as a power outage or power failure. For example. Biofuel: Fuel derived from biomass. corn and similar materials is an example of a biofuel. 2. some power stations run near to full capacity all the time. Reactive power. (See also Carbon cycle.and the lowest-frequency signal in a given transmission medium. equipment and supply carriers. HVDC Light transmission systems can be fitted with small diesel generators to provide auxiliary ABB glossary 7 . a modem’s bandwidth might be described as 56K. Wide-Area Monitoring Systems. a barge is an unpowered multipurpose marine vessel.000 “bits” of information per second. a fuel derived from sugar cane. This does not include fossil fuels such as coal and oil. (See High-current transients. 1 or 0). Barge: In the oil and gas industry. ie.) Blackout: A complete loss of power resulting from damage or equipment failure in a power station. power lines or other parts of the power system. power that can be operational almost immediately in the event of a blackout. in a power plant to connect the generator and the main transformers.) Busbar: An electrical conductor that makes a common connection between several circuits. a wall or other physical barrier. Busbars are uninsulated. to connect electrical installations. They are used in electrical substations to connect incoming and outgoing transmission lines and transformers. C Capacitance: The ability of a device to store an electrical charge (electrical charge is what flows in electric current). It enables a conductor to pass through a grounded enclosure. to feed large amounts of electricity to equipment used in the aluminum smelting process. (See Voltage drop. such as a transformer tank (the physical shell of a transformer). which can damage electrical equipment or cause it to under perform. lights dim. or to distribute electricity in large buildings Bushing: A bushing is a cyclindrical insulating component. Capacitance is used in many different applications. in industry. In the case of a transformer.) The unit of capacitance is the Farad. but are physically supported by insulators. usually made of ceramic. This power enables voltage control to be established and normal operations to be resumed quickly. electrical wire cannot accommodate high-current applications. Brownout: A dip in the voltage level of a power system. though it can also be referred to in Coulombs per volt (Coulomb being the standard unit of electrical charge). eg. Sometimes. for example. that houses a conductor. The Farad is 8 ABB glossary . and electricity must be conducted using a more substantial busbar — a thick bar of solid metal (usually copper or aluminum). (See Capacitor. bushings protect the conductors that connect a transformer’s core to the power system it serves through channels in the transformer’s housing. a very large unit and capacitances are usually on the order of microfarads. these elements also begin to shut down and shift their power load onto other elements. for power factor correction in (inductive) AC circuits. for example). Charging station: An installation at which an electric vehicle can be plugged into the grid to charge its battery.) Carbon cycle: The circulation of carbon through its various forms in the environment. higher current fastABB glossary 9 . Capacitors are used to buffer electricity (smooth out peaks) and to guard against momentary voltage losses in circuits (when changing batteries. Either way. (See also Capacitance. Briefly. pF (1 pF = 10 -12 F). carbon is released into the atmosphere as carbon dioxide and is available again for fixation (ie.) Capacitor bank: A number of capacitors connected in parallel. including low-voltage. for example). “cascading” through parts and systems like a ripple on a pond until the grid collapses. (See also Parallel. and higher-voltage. These then die and rot under the influence of bacteria and fungi or are consumed by higher organisms in the form of food or fuel (burning plant matter or fossil fuels). The resulting surge current can induce ongoing failures and take down an entire power system in a very short time. There are several types of charging station. and so on. carbon dioxide in the atmosphere is fixed (ie. for example. Cascading power failure: A cascade happens when a part of the power grid fails. Capacitor (also referred to as a condenser): A multipurpose device that can store electrical charge in the form of an electric field. incorporation into biomass). Overloaded. µF (1 µF = 10 -6 F) and picofarads. It is used. and shifts its power load to other elements in the grid. lower current installations that charge a battery over a period of several hours (for use in homes. converted into solid matter) by the process of photosynthesis in plants and green algae. 10 ABB glossary . public buildings.). Collaborative production management (CPM): A method of unifying disparate yet interdependent production systems in order to optimize productivity. from a short circuit or a lightning strike. but it is more specific in its responses and is able to deal with a broader range of conditions. which relies on feed forward control). analyze and direct their operations. An example of closed loop control is a driver steering a car. an acronym for the co-generation of heat and power. they are used as an alternative to fuses in the home. The heat is produced by combustion of fuel in the power station to create the steam that drives the generating turbines. A closed system responds to actual system conditions with a range of responses. etc. It would otherwise be released to the atmosphere. to domestic and industrial heating systems.) Circuit breaker: Devices that interrupt high currents to protect electrical equipment from damage caused by current surges.charging stations for a more rapid service in public places (car parks. (See Co-generation. the driver steers right to compensate.) Circuit breakers are typically classified according to the medium they use to inhibit arc formation between the open contacts of the breaker. Co-generation: A particularly efficient method of electricity generation that diverts heat. eg. (On a much smaller scale. sulfur hexafluoride gas. Computerized CPM solutions are software applications that enable process manufacturers to plan. oil and a vacuum. Closed Control System (CCS): This is a system used to regulate a process using feedback control (as opposed to an open control system. CHP: Combined heat and power. It is slower to react to changes in process conditions than an open system. ABB glossary 11 . If the car veers to the left. track. Media used include air. produced as a byproduct of the power generation process. how well a material conducts electricity depends on its atomic structure and chemical consistency. The first is driven by oil or gas. coolers and recycling loops.Combined-cycle power plant: conventional thermal power stations produce steam to drive turbines that generate electricity. a conductor refers to a material that can transmit electricity. the compression train is the entire line of equipment that contributes to process of compressing gas: It includes valves. scrubbers. Inverter. (See also Converter station. Conductivity also depends on how strong the bond is between electrons and the metallic ions with which they are associated. comprising a rectifier and inverter. and waste heat from that process contributes to the production of steam to drive the second turbine Compression train: In the oil and gas industry. Converter: An electrical device. heat or sound. In a combined cycle plant. High-voltage DC (HVDC) converter stations use power electronic devices called thyristors to make these conversions. All metals are conductors (copper is a particularly good one). or vice versa. Plastics are not good conductors. More generally. The weaker the bond. rectifiers or frequency converters.) 12 ABB glossary . Super-conductors. Rectifier. under special conditions. Conductor: An electrical conductor is any substance through which electrical current can flow. Frequency converter). used to alter the voltage and frequency of incoming alternating current in an electrical system. but make good insulators. (See also HVDC and HVDC Light. so electricity can flow indefinitely. the better the conductor. Semi-conductors are materials whose ability to conduct electricity can be controlled. Converter station: Special equipment is needed to convert electricity from alternating current (AC) to direct current (DC). Since electrical current is a process involving the flow of electrons. two turbines are used. offer no electrical resistance. The term may also refer to inverters. for example. the electrons flow through the circuit in one direction. but the development of high-voltage. Overlay DC grids would handle fluctuations and instability in the network better than AC systems and are a part of the “smart grid” concept (see also Smart grid). ABB glossary 13 . It can also be used. If an electric circuit is likened to water flowing through a system of pipes. the current is analogous to the rate at which the water is flowing. Power from such DC grids can be fed into the AC networks as needed.Coupling transformer: A coupling transformer is a device that permits two (usually) separate circuits to influence one another. Such a setup can be desirable for control purposes. As a result. Electric current is measured in amps. D DC grid: Today’s electrical transmission systems are almost exclusively based on alternating current (AC). demand-response technologies are needed to help consumers use power when it is plentiful and reduce their consumption when there is less available. in a DC system. As utilities generate more electricity from intermittent sources of energy such as wind and solar. Direct current (DC): This is electrical current that does not alternate (see Alternating current). making better use of the system’s capacity. DC does not generate reactive power (see Reactive Power). only real (or active) power is transmitted. This means that. direct current (DC) technology has made it possible to build a DC grid (DC transmission network) that can handle bulk power flows over long distances. Demand-response: The term demand-response refers to a variety of technologies required to make demand for electricity more responsive to the supply available. to inject high frequency signals into power lines for communications purposes. Current: The rate at which electrons flow through a circuit is defined as the current. At the other end of the process. Torque is an angular force that causes rotation.In order to transmit electrical power as DC. Distributed generation: This term refers to electricity generating installations that are scattered across the grid. ie. The other situation in which DC transmission is advantageous is when connecting asynchronous grids. over very long distances (~1000 km for overhead lines. as seen for example in a car’s engine. and integrate distributed automation controllers. as happens in some parts of Brazil and the United States). In the conversion between the two forms of power. They tend to be small-scale generating plants – often operating using renewable fuels. the alternating current generated in the power plant must be converted into DC. refineries). as opposed to from a single. known as rectification. rather than placed at a central location.) Direct torque control: A drive system (see Drive) that controls the speed of an electric motor. the DC power must be converted back into AC. centralized control unit. (See HVDC. and fed into the ACtransmission or distribution network. application servers. Microprocessor-based distributed control systems (DCS) originated in continous process industries (eg. The drive works by regulating the amount of power the motor draws from the grid. incurs additional power losses and so it is worth while only when these losses are less than would be incurred by AC transmission. and hence the torque it can produce on a rotating shaft. which turns the vehicle’s drive shaft. ~100 km for underwater). 50 or 60 Hz. where adjoining electricity grids have different frequencies (eg. ie. They also include domestic power generators such as roof-top wind turbines and solar 14 ABB glossary . workstations and other modules necessary to build a complete automation system. The transmission of DC current has very low losses. networks. chemical or other) from a series of strategic positions in the processing plant. Distributed control system (DCS): A control system that regulates a process (manufacturing. factories and elsewhere. often in a thermal power plant. See also Upstream.panels. and microhydro installations. and shipping of those products. ABB glossary 15 . frequency and current the motor draws from the grid. Many motors are controlled by “throttling down. even when a lower speed would suffice. to heat water that is then fed through a communal system. Drives (also referred to as a variable-speed motor drive) can lead to considerable energy savings as most motors are fixed-speed devices that run at full speed.) District heating: a district heating system is one that makes use of heat generated at a central location. distributed generation will become an increasingly common feature of our power systems. Downstream: The oil industry term “downstream” refers to all petroleum activities from the processing of refining crude oil into petroleum products to the distribution. rather than taking your foot off the accelerator. Reducing a motor’s speed by half using a drive can reduce the energy it consumes to one-eighth of its consumption at full speed. Distribution transformers: Distribution transformers are used to regulate the supply of power to residential premises. It works by controlling the power. Drive: A drive is an electronic device used to regulate the performance of an electric motor. delivering heat to homes in the surrounding area. and does not save energy. As more smart technologies are incorporated into the grid. (See also Transformer. It is used to transfer power from a medium-voltage electricity distribution system to a low-voltage distribution system that serves groups of domestic or industrial consumers. marketing. Distribution substation: A distribution substation comprises medium-voltage switchgear.” which is equivalent to slowing a car by using the brake. transformers and low-voltage distribution equipment. enabling local distribution grids to receive as well as deliver electricity. ) E Eco-efficiency: Combining efficiency and ecological aspects in the pursuit of sustainable development. the others being series compensation and dynamic energy storage. The system helps to improve power transmission capacity as well as the overall stability of the grid. (See also Series and Shunt. Electrical units: Quantity Current Voltage Power Name Ampere Volt Watt Symbol A V W Watt = ampere x volt 1. Electrical drivetrain: In the wind power industry.000 A = 1 kiloampere (= kA) 1.Dynamic shunt compensation: A technology used to stabilize voltage by introducing or absorbing reactive power at specific points of a power transmission grid. Large power transmission lines have voltages in the range of 220 .000 W = 1 kilowatt (= kW) 1.000. Electric motor: A device that converts electrical energy into mechanical energy that can be used to drive mechanical equipment.000 V = 1 kilovolt (= kV) 1. converter and transformer.000 W = 1.800 kV. Electrical balance of plant (eBoP): The sum of all electrical equipment required for safe and coordinated operation of various parts of a power plant. Dynamic shunt compensation is one of the three main FACTS (Flexible Alternating Current Transmission Systems) technologies. this term refers to the combination of the a wind turbine’s generator.000 kW = 1 megawatt (= MW) Some examples of electrical units: Voltage: In a home the voltage in the outlets is normally 220 or 110 volts. 16 ABB glossary . Electromagnetic fields: All stationary charged particles are surrounded by an electric field (measured in volts/ meter). an incandescent light bulb (one with a filament inside the bulb) is said to be inefficient because much of the energy it uses (around 95 percent) is converted into heat rather ABB glossary 17 . electrons in an electrical current) are also surrounded by a magnetic field (measured in amps/meter). Note: the terms “electric field” and “magnetic field” are not interchangeable.000 kW (= 3 MW) A large coal or nuclear power station can generate 500 . Alternatives include largescale batteries. A large wind power unit can generate 3.000 MW. The combination of an electric field (around the charged particles) and the magnetic field (generated when the charged particles flow) is known as an electromagnetic field (sometimes abbreviated to EMF). if necessary. Energy cost effectiveness: This is a key performance indicator used to judge the productivity of a proves in terms of financial gain per unit of energy consumed. Energy efficiency: Defined as output energy divided by input energy. The electrical efficiency of an appliance is defined as the amount of that energy that is converted into a useful form. For example. A normal home in North America or Europe consumes power in the range of 1 . and. Charged particles in motion (eg. averaged over time. Radio waves are a form of electromagnetic radiation.1.100 watts. effluents or pollutants into the environment.) Electricity storage: Electricity is difficult to store.10 kW. a process known as pumped storage.4.Power: A typical incandescent (not fluorescent) light bulb consumes 40 . divided by the total energy it draws. Emissions: The release or discharge of substances.3 GW. The most effective way to store surplus electricity in terms of cost and environmental impact is to use it to pump water uphill into the reservoirs of hydropower plants. (Individual nuclear generating units have a capacity of 1 . A fluorescent lamp that works on a different principle is somewhat more efficient because more of the energy it uses is converted into light and less is lost as heat (around 80 percent). network capacity can be doubled. for example arc furnaces. The technologies can be installed in new or existing power transmission and distribution lines. Series Compensation can be fixed or controllable. Thyristor-controlled series compensation is especially useful for damping power oscillation over interconnections between transmission girds. in particular more powerful flicker compensation to stabilize heavy and rapidly fluctuating loads. In some cases. Engineering Procurement and Construction (EPC): Term used to describe contracts in which a company assumes full responsibility for project engineering. ABB’s FACTS devices optimize power flow to maximize the capacity of power lines and improve voltage stability by reactive power compensation (see Reactive power and Power factor compensation). The latter is called Thyristor Controlled Series Capacitor (TCSC). The term is also used for companies contracted to perform these services. and to smooth voltage flicker. Series compensation is a straightforward and cost effective way to improve power transmission capacity and preserve voltage stability. The most advanced version of this technology is called SVC Light and has additional features. material procurement and construction. uses an electrical device (see Static var compensator) to regulate and stabilize voltage in bulk power systems. Examples of FACTS devices are: Static var compensation (SVC). capacity and flexibility of power transmission and distribution systems. The equipment also makes the system more resilient to “system swings” and other disturbances. particularly in bulk transmission corridors. 18 ABB glossary . F FACTS (Flexible Alternating Current Transmission Systems): Refers to a group of technologies that enhance the security.than light. including a zero-voltage dip. Feeders connect distribution substations and consumers. ABB glossary 19 . Frequency converter (frequency changer): At ABB. and to help the system return to normal operation. these devices are used to enable ships. Fault ride-through (FRT): Refers to the ability of an electrical device (such as a wind turbine converter) to respond to a temporary fault or voltage change in the transmission and distribution grid. this term most commonly refers to a device used to adjust the frequency of alternating current. Fuel cell: A device in which chemical energy released by the oxidation of a liquid (such as methanol) or gaseous fuel is converted directly into electrical energy. most of which have onboard electrical systems running at 60 Hz. Frequency converters are a central component in variable-speed drives to control the speed. preventing it from spreading to other areas and causing widespread disruption. Fault ride-through specifications are part of many grid code requirements. natural gas or other materials used as raw ingredients for making gasoline. For example in shore-to-ship power connections. other refined products or chemicals. natural gas liquids. to onshore power supplies that most commonly run at 50 Hz. Frequency converters are also used to connect electrical systems operating at different frequencies.Fault-closing device: A system of circuit breakers that serves to contain a fault in a grid. Feeder: Overhead lines or cables that are used to distribute electrical power to consumers. Feedstock: A term that refers to crude oil. torque or power on the shaft of an electric motor by adjusting the frequency and voltage of the electricity powering the machine. Frequency converters are used to control the rotational speed of wind turbines to stabilize the frequency of the electricity they produce. 20 ABB glossary . Generation mix: The generation mix is a term used to describe the contribution various sources of electricity make to the power supply serving a particular region or population. including wind-turbine generators. that define grid fault and other conditions that must be responded to by wind power plants. A DC generator operates on the same principle as the AC generator. but includes a device (a commutator). Generator: A device that converts rotating mechanical movement into electric power. a loop of wire is placed between the poles of a permanent magnet. The portion of renewable energy in the global generation mix is rising in response to concern over climate change and increasing demand for electrical power. Gearless mill drive (GMD): a system consisting of a ringmotor and its associated equipment such as transformers and control systems. Grid code: This term refers to the requirements developed by power utilities that power generators of all kinds must meet to ensure the proper functioning and stability of the electrical transmission and distribution grid. The magnet is then rotated and the electromotive force produced by the movement of the electric field causes a current to flow in the wire. In a simple AC generator.G Gas-insulated switchgear: see Switchgear. These include regulations such as n-1 and fault ride-through capabilities (see n-1 and Fault ride-through). Grid reliability: Power utilities strive to maintain electricity supplies without unexpected dips or surges that can ABB glossary 21 . which effectively prevents the current from alternating. This is the principle of the synchronous motor and big generators in power plants. ABB manufactures a range of generators. The current generated can be either alternating (AC) or direct (DC). Its main application is to drive (rotate) mills in the minerals or cement industry. compensating for overloaded sections of the grid and even shutting down certain connections to prevent the spread of disturbances or to allow maintenance work to be carried out. The data are transmitted to a central computer. To avoid these problems.cause disruptions ranging from flickering lights to equipment damage. circuit breakers. harmonics are oscillations in the base power frequency. utilities therefore need to control the flow of power under normal running conditions and in emergency situations. Wide-Area Monitoring Systems. which uses them to calculate the settings for the control equipment housed in the substations and generating plants. the base frequency is typically 50 or 60 hertz (Hz) and harmonics occur in multiples of this. if the current is interrupted or if AC current is synthesized in a converter. and monitoring equipment (protection relays. transformers. eg. the temperature of hot power lines. for example 100 Hz. or rapid switching of electrical devices in the grid.) H Harmonics: Generally.) in substations. caused by lightning strikes. (See FACTS. where the base frequency is 50 Hz. thermal line sensors etc) at strategic points on the grid. 150 Hz. 200 Hz. phase monitoring units. etc. In electrical AC systems. This is done by installing sophisticated switching and protection equipment (fuses. This allows power flow to be directed. The monitoring units measure the rate and direction of power flow. Network control. which may cause damage. its stability. etc. Harmonics can be reduced by the use of power filters. High-current transients: Short spikes of high electrical current in a grid. SCADA. and other parameters critical to the normal functioning of the grid. The problem with harmonics is that electrical devices may react differently when exposed to a different frequency than the one they are designed for. Harmonics are an increasing problem in power systems as most power electronics solutions cause harmonics. especially 22 ABB glossary . Harmonics occur whenever there is a disturbance of the voltage or current. Another important aspect of HVDC lines is that they can never be overloaded. or surges.660 kV) UHVDC: 6000-8000 MW (± 800 kV) HVDC Light: 100-1100 MW (± 150 .typically by overhead transmission lines. The conversion is carried out with high-power. In the 1990s ABB developed the HVDC Light technology which made it possible to have long underground transmission (see HVDC Light). In 2006 ABB carried out the first test circuit on +/.400 MW (± 150 . High-voltage direct current (HVDC): A technology developed by ABB in the 1950s to move large amounts of power over substantial distances . This means that the same power can be transmitted over fewer (or smaller) transmission lines than would be required using AC. potentially damaging insulation and leading to short circuits. Because HVDC transmits only active (real) power. and less land is needed to accommodate the lines. Equipment can be protected from highcurrent transients by using a surge protector. An HVDC system takes electrical power from an AC network. Typical power and voltage range are: Classical HVDC: 500 . cause cables to overheat. where it is turned back into AC by using another converter.320 kV) ABB glossary 23 .6. high-voltage electronic semiconductor valves. so the amount of transmitted power and also the direction of transmitted power can be precisely controlled. These transients. no line capacity is wasted on transmitting reactive power.capacitors.800 kV ultrahigh-voltage DC (see Ultrahigh voltage). so the power lines may be built safely closer to human habitation. Transmitting DC power over long distances is more efficient than AC transmission (see Direct current and Transmission and distribution) and is a cost-effective method of connecting two asynchronous grids (grids operating at different frequencies). HVDC induces minimal magnetic fields. converts it to DC at a converter station and transmits it to the receiving point by line or cable. These valves are controlled by a computer system. a feature unique to HVDC systems. but also by way of submarine cables. It is rarely used for power transmissions using overhead lines. Because of its smaller footprint. HVDC Light is environmentally friendly.100 megawatt (MW) (±320 kilovolts).Hoist. Because of its superior ability to stabilize AC voltage at the terminals. Offering both HVDC and HVDC Light systems extends the economical power range of HVDC transmission. HVDC Light: An adaptation of classic HVDC. All hoists are powered using electric motors. friction hoist: In underground mining. underground cable technology and superior controllability. it is the ideal technology for wind parks. strengthening power networks in areas where there is opposition to new overhead lines. Modern hoists are generally equipped with variable speed drives that minimize energy consumption and control the speed of the hoist. By comparison. classic HVDC (see High-voltage direct current) systems typically transmit electricity in the 500 to 8. The superior controllability is achieved by using IGBTs (ie. and delivering power to islands that would otherwise need local generating plants. for example: feeding power into cities and offshore oil and gas platforms. where the variation in wind speed can cause severe voltage fluctuations.000 MW power range. It is the only technology available that allows long-distance underground high-voltage transmission. a hoist or winder is used to raise and lower conveyances within the mine shaft. HVDC Light offers the same benefits as traditional HVDC systems. transistors) as the power electronic device used for the conversion (see Direct current). featuring oil-free cables. 24 ABB glossary . developed by ABB in the 1990s. It can be used to transmit electricity in lower power ranges (tens of megawatts) to an upper range of 1. but also provides more secure power control (superior to classic HVDC) and quick power restoration in the event of a blackout. compact converter stations and cables that can be laid underground (thereby avoiding local planning difficulties associated with overhead lines) as well as underwater. HVDC Light has many more potential applications than classical HVDC. Industrial IT: A series of interoperable software and hardware products and systems from ABB and/or third parties that are designed to communicate with each other and work together as part of a larger system for a specific application. A single communication standard for substation automation removes the need for “translators. including human operators. car. and makes installations easier to expand or modify. The problem is that protocol converters can cause messaging errors and delays.” helps customers lower maintenance and operating costs. New technologies and business models are allowing ABB glossary 25 . printers. I I/O(Input/output): A device that enables communication between electronic equipment and external devices.HVSC: High-voltage shore connections enable ships to draw electricity from onshore power grids while in port to operate onboard equipment such as lighting. For a large cruise ship on a 10-hour stay in port. Manufacturers are under intense pressure to improve productivity and performance to remain competitive. a shore connection can cut fuel consumption by up to 20 tons and reduce carbon dioxide emissions by 60 tons. Industrial productivity: Raising industrial productivity means lowering costs for each unit (eg. which are basically “translators” that help electronic devices using different machine languages transmit information to each other. and avoid losing business to more efficient rivals. etc.) produced. Examples of I/O devices include computer keyboards. instead of burning fuel oil to run onboard generators. ton of paper. cooling and heating systems. sensors and all type of interface cards. IEC 61850: The International Electrotechnical Commission IEC standard for substation automation replaces a great many communication protocols that require the use of use protocol converters. optimizing factories operations. instrument transformers are components of devices used for measurement or monitoring (eg. improving the asset management. research. some kinds of silicon or glass.) Integration of renewable energy: Feeding electricity from intermittent sources of energy such as wind and solar into the power network without causing any disturbance to the power supply. (See also Conductor. Productivity improvements can be achieved by automating operations. often referred to as meters. The term can also refer to a material that does not conduct heat. Insulator: A material that does not conduct electric current. level. temperature and pressure of processes in different industrial applications. Infrared thermography: A method used to measure the status of equipment by analyzing the amount of heat it radiates. They monitor processes in power generation. manufacturing and refining plants. Instrument transformer: In contrast to most transformers (which are used to convert power). to measure voltage or current in transmission lines).establishing new combinations and locations that enable them to work more closely with partners. outsourcing. used to measure the flow. such as plastic. suppliers. and so on . sales. and improving the supply chain management. distribution. Information collected by various instruments is processed by analyzers and used to assess performance. Instrumentation: Electronic or electromechanical devices.companies to restructure their business processes things like procurement. sending alerts if readings are not as expected. For clarity. and customers. the terms thermal insulator and electrical insulator may be used. manufacturing. As they do not actually transform any significant quantities of energy they are usually small and lightweight. 26 ABB glossary . It includes some 20 elements of quality process performance. See also Circuit breaker.) Ionized gas: If a material is exposed to high temperatures or an electrical field. it can become ionized. K Key performance indicator (KPI): A measurable objective used by organizations to monitor progress towards a specific goal. ie. Line thermal monitoring (LTM): Process that measures average power-line temperature and detects temperature ABB glossary 27 . Such measures are commonly used to define and evaluate an organization’s performance against internal benchmarks or those of peer organizations . ionized gases can enable an electric current to jump across a gap in an electric circuit. ISO 14000: International standards for environmental management systems set by the International Standards Organization. L Lights-out factory: An automated factory that requires no light because no people work in it. ISO 9000: International standards for quality assurance set by the International Standards Organization. (See also Rectifier. circuit breakers are equipped with various insulators that inhibit arc formation.Inverter: An electrical device for converting direct current (DC) into alternating current (AC). Also known as plasma. its particles can become electrically charged. quality products to customers. and is a prerequisite for delivering predictable. To avoid this problem. or in some other way improve the stability and reliability of electrical power distribution. Loop flow: Inadvertent transmission of power through an unnecessary diversion in the transmission network. fires and blackouts if they contact treetops etc. The speed of a “synchronous” machine. This means that it maintains its speed irrespective of the load placed on it. Load tap changer (LTC): load tap changers are devices used to adjust the performance of transformers. The speed of a synchronous machine is accurately predictable. (See also Wide-Area Monitoring System. resulting in short circuits. Load management: Controlling loads in a utility system to limit peak demand. the rate at which its shaft rotates. while generators convert the mechanical work of a rotating shaft into electricity. Adjusting the tap changes the voltage of the transformer’s input or output. reduce costs.” Motors are machines that convert electrical energy into mechanical work in the form of a rotating shaft.changes in power lines. they are used in performance-critical applications such as mechanical clocks 28 ABB glossary . M Machines. electric: Motors and generators are collectively referred to as “machines” or “electric machines. improve load factor.) Load: A load in electrical terms is the power consumed by a device or a circuit. ie. Because synchronous motors can maintain a particular speed with extreme accuracy. Load is also used to describe the total of all electricity consumers in a power system. It is undesirable because it serves no purpose and incurs losses. is dictated by the frequency of electricity in the grid to which it is connected. It is important because heat causes wires to expand and sag. Megawatt (MW): One million watts. Synchronous generators are commonly used in power plants. (See also Watt and Watt hour. microgrids may also be connected to the larger-scale grids from which they can draw power if locally generated supplies fail to meet demand. Mechanical drivetrain: In the wind power industry.000 one-hundred-watt light bulbs. Asynchronous motors slow down as their load increases and asynchronous generators change speed with the torque (rotational force) that is applied to their rotors. where their predictable. 1 MWh of electrical power would be used. ABB glossary 29 .) Meters: see Instrumentation. Microgrid: A microgrid is a small-scale power network that comprises generating units and consumers. this term refers to the combination of the turbine’s main rotor shaft and bearings. The speed of an asynchronous machine is slightly slower than the frequency of the electricity it consumes or generates. Manifold: an arrangement of connected pipe and valves used to consolidate multiple pumps. which can be located near a customer load. tanks. Often including renewable power sources such as wind turbines and solar panels.250 kilowatts (kW) generating capacity. gearbox (if used) and generator. One megawatt would be needed to light 10. consistent performance helps to maintain the quality and reliability of power supplies. Megavoltampere (MVA): One million VA (volt-ampere). If those bulbs were powered for 1 hour.and DVD drives. and/or pipelines and a single unit. Synchronous generators are also referred to as alternators. Microturbine: A small turbine generator of 30 . Asynchronous machines are also referred to as induction motors/generators. Megavar (MVAr): One million VAr (volt-ampere reactive). 30 ABB glossary . then 1 ampere of electric current will flow. Model predictive control (MPC): The online control of an industrial process (such as oil refining) that uses a virtual model of the process. which enables either to tap off power in a station (or stations) in the middle or to feed in more power in the middle of the transmission link. Multiterminal: An HVDC transmission with more than two stations. ABB glossary 31 .Mobile substation: A substation that can be transported. Network management: A system that uses network control and asset management to oversee all aspects (operational and maintenance) of a network. a component may be a transmission line. If a 1 volt source is connected to a wire with a resistance of 1 ohm. N n-1 (n minus one) is the operating standard to which European transmission system operators are obliged to work. to temporarily replace equipment at the site of a failure or in the event of planned maintenance. In the case of a power network. a generating unit of a power station. etc. Network control: Network control systems monitor and control the electricity network to keep power flowing and to preserve the balance between power generation and consumption. which allows a computer to predict appropriate control settings. It refers to a system that can maintain normal operations despite the loss of any single component. usually by truck. O Ohm: Unit of electrical resistance. or parallel. viscous form of crude oil).” as opposed to “in series. such as ABB. preventing the loss of lines through physical overloading. paths through the circuit are said to be connected “in parallel” or “in shunt. the electricity would continue to flow through an alternative path. which relies on a number of phasor measurement units (PMUs) to collect data from strategic positions in the grid.) Phase-shifting transformer (also known as a quadratic booster): A specialized type of transformer used on 3-phase power grids (AC) to balance the active (real) and reactive power in the system (see Reactive power. P Parallel: Electrical components that are connected in such a way that the flow of electricity can take multiple. water.Oil sands: Naturally occurring mixture of bitumen (a heavy.) Phase angle monitoring (PAM): A device that monitors power-network stresses caused by heavily loaded lines. (See also Series. Pig: A cleaning device placed that is used to scrape residues from the inner wall of oil pipelines. Using hydroprocessing technology.” If one of the components in a parallel circuit was to fail. sand and clay. bitumen can be refined to yield synthetic crude oil . machines or switchboards. Original Equipment Manufacturer (OEM): Manufacturers who produce an end product such as automobiles. (See also Wide-Area Monitoring System and Phasor Measurement Units. Optimization: The process of making a system as near to perfect or as effective as possible. incorporating components from sub-suppliers. This is part of the Wide-Area Monitoring System. Power factor correction and Three-phase power). A pig is pushed through the pipeline by the pressure of the oil 32 ABB glossary . distribution. higher currents are drawn from the grid. These are points at which pigs can be introduced or removed from the pipeline. As electricity flows through a conductor. causing them to heat up. Most utilities impose penalties on consumers who fail to correct errant power factors. Unless this variation is corrected. but is practically impossible to attain. enabling operators to identify and counteract any instabilities before they spread through the grid. (See also Power factor correction. voltage and current are in phase and the power factor is 1.) Power losses: This term generally refers to electrical energy that is lost to inefficiencies in transmission. Variation in power factor is caused by different types of electrical devices connected to the grid that consume or generate reactive power.” When no reactive power is present. This is the ideal for power transmission. or in the use of electricity. this plastic material has excellent properties of electrical insulation. Power factor: Power factor is the ratio of real power to reactive power in an electric circuit and a measure of whether the system’s voltage and current are “in phase. This heat is lost to the atmoABB glossary 33 . power factor varies.flowing past. Pipelines can be equipped with pig launch sites and pig traps. higher costs and reduced transmission capacity. (See also Power factor. Polyethylene: Also known as polythene. Phasor Measurement Units (PMUs): Monitoring devices that are installed at critical nodes in a power network where they collect data on power flow.) Signals sent from the units via satellite to a central control room. Line thermal monitoring. individual electrons collide with the atoms of the conductor and transfer energy to them. leading to grid instability. (See also WideArea Monitoring System.) Power factor correction (reactive power compensation): Depending on the type of equipment a consumer connects to the electricity supply (whether there is a net consumption or generation of reactive power). Most electrical transmission systems are alternating current at voltages between 110 and 800 kV. there will be four-times the losses). in order to improve productivity by enhancing consistency and minimizing rejects. Losses in an electricity distribution system depend on the length of the cable (the longer the cable. food. chemicals.sphere in the form of thermal radiation. (See also HVDC. and control pharmaceutical manufacturing processes through the measurement of critical process parameters. which affect critical quality attributes. pharmaceutical and chemical production. Such a process can be the manufacturing or treatment of any goods made in a continuous or quasi-continuous manner such as fuel. The concept actually gains a clearer understanding of processes by defining and monitoring their critical process parameters. This reduces the current and therefore the amount of power lost in transmission. the principal purpose of which is to automate or support the operator of a manufacturing process. Process automation: The term process automation is used to refer to an automation system. the square of the current (at twice the current. Therefore. the conductivity of the material (higher resistance means greater losses). analyze. cement. paper. Process Analytical Technology (PAT): as defined by the United States Food and Drug Administration. and the cross-sectional area of the cable.) Process Industry: an industry in which raw materials are treated and converted into products by means of a series of stages (or processes). Some power is also lost to electromagnetic radiation. power should be transmitted at the highest practical voltage. Process industries include oil and gas refining. steel. The data stored by modern historians typically include time-stamped information from a variety of traceable 34 ABB glossary . to minimize losses. water and sewerage treatment etc. Process historian: A process historian is a mechanism for storing data relating to a particular process. PAT is a mechanism to design. the greater the losses). ramping up to full productivity only during periods of high demand. Power capacity: In terms of generation. which are more expensive to run. the capacity of a power plant is the maximum power that installation is capable of producing. They are small.7 percent. The relationship between capacity and output is known as the “capacity factor. or programmable controller): These are electronic devices used to control equipment. Reactive loads in a power ABB glossary 35 .000 megawatt-hours of electricity per year (14. optimization and auditing purposes. especially in automation. such as sensors in a control system. R Reactive power: It is a concept that describes the loss of power in a system resulting from the production of electric and magnetic fields in it.760 hours = 122. which enable them to achieve about 90 percent productivity.” where 100 percent is the theoretical maximum. As an example. The data are used for modeling. such as actuators. and transmit signals to input devices. Nuclear power stations have low maintenance requirements and few shutdowns (as do all “base-oad” power plants). Pumped storage: see Electricity storage. that can effect changes in the control system.640. The Itaipu dam actually produced 91. Gas-fired power stations. the hydropower station on the Itaipu dam in Brazil has a total generating capacity of 14. (See also Base-load power plant.30 percent of the plant’s actual capacity.651.) Programmable logic controller (PLC. programmable units that can receive information from output devices.000 megawatts and could therefore theoretically produce 122. This means that their productivity may be only 20 .sources. often operate well below capacity.6 million MWh). for example.000 MW x 8. It does not account for periods of inactivity due to maintenance work.808 MWh of electricity in 2009. The actual production divided by the theoretical maximum production gives Itaipu a capacity factor of 74. system drop voltage and draw current. but not instantaneous. Reactive power is produced for maintenance of the system. For example. poor management of reactive power can cause major blackouts. which must be fast enough for accurate decisions. Recloser: A circuit breaker designed to interrupt shortcircuit current and reconnect the circuit after interruption. (See also Inverter. Reactive power is significant because it must be provided and maintained to ensure continuous. To ensure a system is real-time. In this way. they will pull it across transmission lines and destabilize the grid. and not for end-use consumption. a system is described as real-time if it will operate in a deterministic manner.) Regenerative braking: A braking method that is used to recoup some of the energy lost as vehicles slow down or brake against an incline (downhill). It exploits the ability of electric motors to work as generators during breaking. Rectifier: An electrical device used to convert alternating current (AC) into direct current (DC). and is measured in Volt-Amps-Reactive (VAR). ie. This enables the mechanical energy from the load to be 36 ABB glossary . as unpredictable response times and reaction delays would effectively destabilize the process. Such systems are sufficiently fast that it can be assumed that critical time limits will not be exceeded. An example would be the communications between an automation system and a business system designed to provide management level information. Real time: In business. Some applications are described as near real-time. If elements of the power grid cannot get the reactive power they need from nearby sources. it must fulfill stringent demands with both hardware and software design. This “imaginary power” or “phantom power” is called reactive power. which creates the impression that they are using up power. safety-relevant systems must always respond within pre-determined time limits. when they are not. Many automation applications are also real-time. steady voltage on transmission networks. it will respond to an input within a defined time limit. converted into electric energy and returned to the electricity supply systems for use either by other vehicles. If an electric circuit is likened to water flowing through a system of pipes. Resistance: Cables and electrical devices resist the movement of electrons that constitute the current passing through them. ABB glossary 37 . The method can be used to improve the energy efficiency of cranes and elevator systems. Ringgeared mill drives (RMD): a system used to drive (rotate) a mill. or any obstacles within the pipe. 2. Relays: 1. high-voltage protection. Resistors are also an important component in instrumentation and are used together with capacitors in power filters to eliminate unwanted harmonics. or by the braking vehicle at a later time if onboard energy storage systems such as batteries or super-capacitors are available. The RMD itself is comprised of motor(s) (synchronous or asynchronous). Resistors can be used to control current and therefore protect a circuit from overload. They are typically used to control and monitor power networks. A switch that can be operated remotely. substation control and communications. Remote Terminal Unit (RTU): Remote terminal units collect data from points around a power transmission and distribution network and transmit the information to a central location. Resistor: A resistor is any electrical component that resists the flow of electrical current. This is known as electrical resistance and is measured in Ohms. automated substation components. They include electronic and electromechanical relays and components. Control and protection relays are switches used to signal and control the operation of electrical equipment and systems. trains and hybrid cars. and are components of supervisory control and data acquisition (SCADA) systems. and distribution relays. the resistance in a wire is analogous to the restriction of the water flow imposed by the diameter of the water pipe. a frequency converter. Ringmotor: also called wrap-around motor. painting.transformers and control equipment. load curtailment and restoration. They are a fundamental component 38 ABB glossary . (See also Machine). which may be either fixed in place or mobile for use in industrial automation applications. Robot. It may perform other functions in power networks. This means that a semiconductor will behave either as an insulator or a conductor of electricity. industrial: An industrial robot is defined by the internatinoal standard ISO 8373 as an automatically controlled. packaging and palletizing. speed. Semiconductor: A semiconductor is a material whose electrical properties can be significantly influenced by physical factors (mostly electrical conditions. distribution automation. manipulator. and precision. and testing. pick and place. pinion(s) and ringgear. oil refineries and water treatment facilities. and facilities management functions. The poles of the motor are directly flanged on the driven equipment. light. depending on the conditions to which it is exposed. ABB developed the first commercially available electric robot almost 40 years ago. product inspection. but also pressure. etc). a ringmotor is a very large synchronous motor. assembly. As opposed to gearless mill drives. reprogrammable. temperature. S SCADA (supervisory control and data acquisition): A SCADA system is a computer system that gathers and analyses data on equipment and processes in industrial processing plants such as pulp and paper mills. such as load management. all accomplished with high endurance. programmable in three or more axes. the motor in RMD is mechanically connected to the mill via a coupling. multipurpose. Typical robot applications include welding. if the circuit is not properly protected. semiconductors are commonly used in sensor systems. It is a measure of its ability to perform safely and. This means that before it can be fed into the local grid. There are four SIL levels. the circuit would be broken and no electricity would flow. in the event of failure. Unlike thermal solar plants. If a device is said to have a short-circuit resilience of 400 amps (A). which absorb the radiation and emit electrons. Ship-to-shore connection: see HVSC Short circuit: An electric contact between parts of an electric circuit.of electronic devices. Because of their ability to respond to external conditions. SIL (Safety integrity level): The safety integration level (SIL rating) of a system indicates the level of risk associated with it. perhaps because of worn insulation.) Series capacitor : See FACTS. with level 4 indicating the highest performance.” as opposed to “in parallel” or “in shunt. This can occur if two live wires come into contact with each other. (See also Inverter). ABB glossary 39 . photovoltaic power must be converted into alternating current using an inverter. photovoltaic power plants generate direct current. Series: Electrical components that are connected in an unbranched line are said to be “in series. Shunt: see Parallel. (See also Parallel. Solar power (photovoltaic): Photovoltaic solar power is generated when the sun’s radiation is “harvested” by specially designed panels. The term is also used when defining the safe operating conditions for electrical devices. increases in temperature and potentially fire.” If any one of the components in a series circuit was to fail. which causes a very high current. that means that it can be subjected to up to 400 A before it will shut itself down. to fail safely. 40 ABB glossary . In the case of thermal solar power. secure. re-establishing balance and maintaining the stability demanded by both endusers and government legislation. based on industrywide standards. which are based mainly on centralized generating plants. The system will cross national and international borders. Thermal solar power is suitable for large-scale generating plants (eg.Smart grid: Smart grids are modern power transmission and distribution systems. and generate steam. Solar power (thermal or concentrating solar power): Solar power is electricity generated using sunlight as its primary energy source. The steam is then used to generate electricity in the same way as it is used in conventional thermal power stations. unidirectional transmission and distribution systems whenever consumers request it. Smart grids are being developed in response to rising demand for power and the increasing need to incorporate renewable or distributed. supplying power via long-established. It must be able to detect and react automatically to disturbances and changes in supply and demand. gas-fired). Desertec) and can be used in combination with conventional generation (eg. Thus smart grids also accommodate customer response management systems that allow utilities to optimize the performance of the grid and to integrate consumption into balancing load and generation. based on an infrastructure of enabling smart grid components. either directly or via a heat-conducting fuid. the sun’s heat is used to heat water. capable of accepting power of any quality from any source and delivering it to consumers of all kinds via a bidirectional supply system. Many of the technologies and standards needed to establish smart grids on a large scale have been the subject of research and development at ABB for some years and many are already in use. ABB’s smart grid concept is of an observable and controllable system. They are an evolutionary development of traditional grids. less predictable generation into the grid. efficient and environmentally sustainable network. providing a stable. ABB glossary 41 . This is achieved by an automation and information technologies infrastructure integrating the whole supply chain from production to consumption. (See also Reactive power. increasing network stability. comprising a frequency converter. such as synchronous compensators (see also FACTS). Substation automation: The various technologies. This includes control and protection functions. Power factor correction. String tests are time consuming and expensive but often reduce time spent on erection and commissioning on the customer’s premises. Storage: see Electricity storage. Submetering: Metering of individual units in multi-unit properties. String tests are performed prior to delivery to verify the performance and functionality of the equipment and to ensure that the units comply with specifications under the working conditions of the destination plant. thereby allowing more power to flow through the network while maintaining safety margins. String test: In a string test.064 MPa (the “critical” point of water). Circuit breaker and Switchgear.Static var (volt amperes reactive) compensator (SVC): A device that provides fast-acting reactive power compensation (see Power factor and Power factor correction) in high-voltage electricity networks. They house equipment for the protection and control of electrical power transmission and distribution. switchgear and measuring equipment.) Supercritical power plant: A supercritical power plant is a thermal electricity generating station that uses steam at extremely high temperature and pressure to generate electricity with improved efficiency. Above 374°C and 22. are tested in a factory situation that simulates site conditions. a complete drive train. water simply 42 ABB glossary . SVC has no rotating parts (it is static). Substation: Substations are key installations in the power grid. including power transformers. methods and equipment used for the automatic operation of substations. It compensates for fluctuations in the voltage and current of an electric grid. such as a pump or a compressor. Cheaper to build and maintain than rotating compensation devices. a motor and an application. it might be necessary to shut off the affected section to prevent the fault spreading). The Desertec project. but it takes up less space and is therefore the preferred option when installing switchgear in urban environments (the substations can be one fifth the size of a conventional AIS substation). Surge protector: Also known as a surge arrester. Operating under such conditions requires the use of extremely robust equipment. Switchgear: Equipment used to control. or for maintenance purposes. the term Supergrid refers to a pan-European subsea power grid. It is often located in substations. protect. These can occur when substations are hit by lightning or as a result of switching operations in high-voltage transmission. for example would rely on a supergrid for the transmission of offshore wind power from European coastlines. which can be used to drive the turbines of a generator more efficiently than steam at a lower (subcritical temperatue). together with hydro power from northern Europe. The term is widely used in the context of renewable energy. but can be associated with any electrical equipment that might need to be isolated for fault correction (eg. Supergrid: Trademarked by Airtricity in 2006. The gas-insulated variety is more costly than the air. The main components of switchgear are circuit beakers. The specifications for products used in supercritical plants are higher than those used in subcritical plants. solar power from northern Africa and southern Europe.exists as super-heated steam. The terms gas.and air-insulated circuit breakers. which interrupt high-voltage current to protect electrical equipment from excessive current. and regulate the flow of electrical power in a transmission or distribution network.and air-insulated switchgear (GIS and AIS) refer to switchgear equipped with gas. if a voltage drop occurred in one part of the grid. this is a device used to protect equipment from damage caused by high-voltage power surges. Synchronous machines: See Machines ABB glossary 43 . and it is used in many industry sectors to oversee and control a wide range of processes. Thyristor: A thyristor is a semiconductor device used in electrical systems. as a high-speed. There is usually one traction motor on each driven axle. Thyristor-controlled series capacitor: see Capacitor Traction motor: A traction motor is typically used to power the driving wheels of a railroad locomotive. It extends the scope of traditional control systems to include all automation functions within a single operations and engineering environment. and to improve productivity. Three-phase is a more efficient way of delivering heavy loads and the three-phase motors it supplies are more efficient. Residential premises. high-power switch. Wiring is simplified because no neutral return path is provided. most transmission lines are three-phase. are supplied with single-phase power. T Three-phase power: A form of electricity used to supply heavy loads (power-hungry electrical equipment) such as industrial air conditioning units. Thyristors are a component used in inverters and rectifiers. however.System 800xA: An Industrial IT-compatible control system that provides a means of achieving measurable productivity and profitability improvements. Traction motors differ from other motors in the scale of their design. Almost all power is generated as three-phase and. The full name is Extended Automation System 800xA. with the exception of HVDC. a tram or an electric train. grinding machines etc. like a subway or light rail vehicle. such as HVDC installations. capable of turning power supplies of many megawatts on within a split second. They must be extremely compact. and highly 44 ABB glossary . smaller and cheaper to build than their single-phase counterparts. This enables plants to perform in a more intelligent and costeffective way. because of the limited space available on the locomotives. (See also Inverter and Rectifier). though not always. usually over long distances. Transmission is the movement of power at high voltage (above ca. Note that the voltage of DC cannot be transformed in the same way as it can for AC. Transformer: A transformer is a device used to transfer energy from one AC circuit to another and to increase (step up) or reduce (step down) voltage as required. mainly for traction. brakes. Transformers are an essential component in an electrical grid. more electrical power is converted to heat and lost to the atmosphere) over a wide area. 1 and 50 kV) over shorter distances to industrial. but also for lighting.) Traction substation: A substation used to feed power into railway electrification systems. Traction transformer: This is a fundamental component of a rail locomotive’s traction lower voltages. housed in substations. (See Alternating current. Distribution is the transport of electricity at medium voltage (between ca. The traction transformer is the unique energy transfer point between high voltage (HV) and low voltage (LV) and therefore must achieve the highest availability and reliability levels to guarantee uninterrupted train service. commercial and residential areas.230 V). passenger information and safety systems such as door blocking. Transformers are generally. ABB glossary 45 . heating and ventilation. which is delivered to homes. Electricity generated in a power station must be stepped up to the appropriate voltage for transmission (between 100 and 800 kV) and then stepped down again to the distribution voltage (110 .) Transmission and distribution (T&D): The term refers to the transport of electricity from the power station to the end user. with fewer losses . (See also Traction transformer. It adapts the catenary (overhead) voltage to the various low voltage levels needed by the train. Raising the voltage allows power to be transmitted more efficiently (ie.reliable as there is no room for any backup systems. 50 kV). signaling and communication. or wind (as in a wind farm). and therefore the power generated. The amount of fuel that can be ignited in the cylinder. a mixture of fuel and air is pumped into the confined space of a piston cylinder and ignited by a spark. UHV transmission using 46 ABB glossary . In an internal combustion engine. agreed by the contractor and the customer before the work has begun. Turnkey project: A turnkey project is one in which the contractor will design. Turbogenerator: a collective term referring to a turbine and the generator to which it is connected. allowing more fuel to be burned.) Turbocharger: An air compressor that is used to boost the oxygen intake of a motor. (See also Generator. using the oxygen in the air. U Ultrahigh voltage (UHV): This term refers to voltages in excess of 800 kilovolts (kV). This expansion pushes the piston out. releasing a huge amount of energy. more completely. leading to more power obtained at higher efficiency and “cleaner” exhaust-emissions. If there is too little oxygen. When it ignites. and the remaining gasses expand almost instantly. more oxygen is made available for the combustion process. not all the fuel will burn. By compressing the air that is fed into the cylinder. water (in a hydro plant). turning the crankshaft that drives the engine. engineer. A lump-sum turnkey project is one in which the contractor undertakes a turnkey project for a set fee. is limited by the amount of oxygen present.Turbine: A propeller-like device that is turned by a stream of hot gas (steam in a conventional thermal power station). gas (in a gas power plant: here the gas burns in the turbine and exhaust gases cause it to rotate). the fuel burns. deliver and commission an installation. taking responsibility for all aspects of the work. The rotation of the turbine drives the generator that converts the mechanical rotation into electrical power. They have exceptionally long life and are virtually maintenance free. Upstream: The oil industry term “upstream” refers to oil and natural gas exploration and extraction activities. Ultrahigh-voltage DC links will make it viable to produce electricity in remote regions and transmit it to centers of demand via energy “superhighways. smaller and more efficient than comparable AC transmission systems.” The efficient transmission of electricity at 800 kV DC power transmission is now feasible over distances as far as 3. Volt: standard unit of electrical “pressure” in a circuit.000 km. (See also Voltage. Vacuum interruption offers the lowest environmental impact of all medium-voltage switching technologies over the entire product life cycle. and it is now also possible to transmit power this way using direct current (DC). Variable-speed drive: see Drive. DC transmission has lower losses and requires fewer overhead lines than AC transmission.) ABB glossary 47 . Excellent switching capabilities. It also insulates the contacts after the arc has been interrupted. Vacuum interruption is seen as the ideal switching technology for medium-voltage applications. V Vacuum interrupter: A vacuum interrupter is a device that uses a vacuum to extinguish the arc formed when a circuit breaker is opened.alternating current (AC) has been possible for several decades. See also Downstream. provide economical switching solutions with virtually no maintenance requirements. The devices perform well in all medium-voltage switching applications required in modern power systems. combined with high reliability and a compact design. UHVDC systems are cheaper. Vacuum interrupters are comprised of materials that are environmentally benign and safe to handle during periodic out-of-service maintenance and at end-of-life disposal. Due to the highly variable composition of the plants’ fuel. respond to voltage drops by working harder to obtain the same power. Devices such as computers often have sensors that warn of suboptimal voltage or excess heating and will shut down automatically in response to a voltage drop. I = current in amperes (amps) and R = resistance in ohms. or the force. Under these conditions. which can cause overheating. Voltage is measured in volts. resistive loads. increased operating costs and the risk of equipment failure. where V = potential difference in volts. Voltage drop: A voltage drop is a reduction in the force that “pushes” current through a circuit. such as light bulbs. Voltage rating: The maximum voltage that can be applied to an electronic device. such as motors. stringent environmental standards are imposed and waste-to-energy plants use sophisticated flue-gas cleaning devices and monitoring devices to ensure emission control. that is pushing electrons between these two points. will give suboptimal performance. Their furnaces cannot easily be ramped up or down and so the plants are not used for peak-load generation. and is directly proportional to the current and resistance of a circuit: V=IR. The watt is also a general unit of power. One watt = 1 joule per second. Inductive loads. W Waste-to-energy plant: A waste-to-energy plant produces energy. Watt (W): Standard unit of electrical power (1 watt = 1 amp at 1 volt). This is Ohm’s law. 48 ABB glossary .Voltage (potential difference): The voltage between two points in an electrical circuit is a measure of the potential difference. It is analogous to water pressure in a water system.lights will flicker or become dimmer because less current is flowing. either heat or electricity using waste as a fuel. as well as cascade tripping that leads to power blackouts. spots and streaks. These monitor stresses (loads and temperatures) on the power lines and send data back to a central control station via a GPS satellite link. Watt-hours are a measure of energy transferred. ie. For example. Rather confusingly. Because of various inefficiencies and the fact that wind blows erratically. The systems can detect and report many types of defects. wind turbines are actually only about 30 percent efficient. 350 MW. ABB glossary 49 . This means that 150 MW (theoretical maximum) x 24 h (number of hours in a day) x 30 percent (efficiency) = 1080 MWh will be produced each day. set up in strategic positions around the grid. This is the capacity of the cable. a 100 watt light bulb (a 100 watt load) uses 100 watt-hours of energy every hour. If the farm was 100 percent efficient.” This is incorrect. Web inspection system (WIS): Web inspection systems are used by the pulp and paper industry to inspect the surface of the paper as it is being produced. a wind farm described as “150 MW” has a peak power output of 150 MW. the maximum amount of power it can carry. it would transfer 150 MW x 24 hours = 3600 MWh to the electricity grid every day. for example. including holes. It comprises a series of phasor measurement units.Watt hour (Wh): 1 watt hour is the amount of electrical energy consumed by a 1 watt load over a period of one hour. WAMS is used in conjunction with phase shifting transformers to protect and stabilize power grids. This allows operators to identify problems at an early stage and prevent widespread disruption of the grid (ultimately rolling blackouts). Cables can also be described as. Wide-area monitoring system (WAMS): WAMS is an advanced early-warning technology for power grids that helps operators prevent system instabilities and overloads. watt-hours are sometimes used to describe “power. a 350 MW cable could (theoretically) deliver 350 MWh of electricity. the product of power (kW) x time (hours). For example. ie. In an hour. Confusion can also arise when describing electricity generation. Notes: 50 ABB glossary . Notes: ABB glossary 51 . com Contact us .abb. All rights reserved www.© Copyright 2009 ABB. 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Thursday, 8 January 2015 JLR teams with Seeing to detect drowsiness JaguarLandRover is working with Seeing Machines and Intel to develop sensing technology able to monitor a driver's face and eyes to reduce distracted and drowsy driving. Seeing Machines, an Australian company, is a world leader in the development of computer vision related technologies that help machines understand people by tracking and interpreting human faces and eyes. The technology is used in underground mining to detect if drivers of vehicles could be on the verge of falling asleep at the wheel. DMS uses attention-monitoring sensors in the dashboard to detect eye and facial movements so it can identify if the driver has become inattentive, either due to drowsiness or distraction. It is so sophisticated it can understand the state of the driver in real world conditions, including bright sunlight and if the driver is wearing glasses or sunglasses. Nick Langdale-Smith, vice president at Seeing Machines, said: "The algorithm we have developed for DMS has the potential to seamlessly enable a host of safety and autonomous driving features and reduce the potential for accidents caused by the driver not paying attention. DMS is unique because it is the only driver monitoring system that can achieve this even if the driver is wearing shades, or in full sunshine.” No comments:
Dark Chocolates – Amazing Health Benefits A new research found that eating a bit of dark chocolate every day cuts the possibilities of heart attack and stroke in high-risk people. Cocoa beans are its basic ingredient, rich in flavanols that guards the body from various infections and diseases. Dark chocolate has higher cocoa content than milk chocolates. Dark chocolate products have 30% to 70% cocoa. In case of extra dark varieties the cocoa content will be upto 80%. Flavanols in dark chocolates will prevents accumulation of cholesterol in blood and improves blood flow. In medium size dark chocolate bars contains about 2grams of protein and 12g of fat, in which 8grams are saturated fat and it contains 180 calories whereas in a white chocolate has 285 calories. Health Benefits: Prevents heart disease: Flavanols, antioxidant substances in dark chocolates prevents the chance of heart attack and completely protects the heart valves from the cholesterol deposit and increases blood flow. Keeps you stress-free: Dark chocolates contains a chemical named phenyl ethylamine (a chemical also produced by brain) stimulates the production of endorphins (chemicals in the brain) that brings your mind to keep happy. Also, it contains the chemical serotonin, which acts as an anti- depressant. Protects our skin: Flavonoids, will absorb UV rays, and helps to protect and increase blood flow to the skin. It improves skin’s hydration and complexion. Helps the insulin to do its duty: When the blood sugar level rises, Insulin is released by pancreas to do the job of escorting the blood glucose into the cells. Repeated release of insulin due to too much sugary food causes the cells to resist the insulin from doing its job. Stops the food cravings: Dark chocolate helps in reducing weight by stopping one’s inclination towards over-eating. Prevents cancer and anti-aging: An anti-oxidant rich food prevents cell damage, and protects from all types of cancer. These anti-oxidant rich dark chocolate prevents anti-aging too. Hardens tooth enamel: Dark chocolate contains theobromine, which hardens tooth enamel. It also prevents the cavities causing tooth decay. Lowers Blood Pressure: Flavanols in dark chocolates lowers the blood pressure level. Researchers proven that dark chocolates help in leveling the pressure of blood. It is good for both low pressure and high pressure patients.
Blog Header Release the Root Causes of Low Energy, Pain, and Disease How to Connect with Your Body and Remain Disease Free When science first began to identify and decode genes, the medical field got really excited and thought we understood the underlying determinants of health. More recently, however, epigenetics – the science that looks at how our environment controls our gene expression – has made discoveries that have overridden the idea that our genes determine our health or disease. It isn’t whether you carry a gene or not that determines your likelihood to develop disease, but whether the chemical environment in your body is one that stimulates your cells to express those genes and become diseased. Since the science of epigenetics is new and has not been incorporated into the foundation of clinical medicine at this time, most doctors are still operating under the belief that your genes dictate your health. What controls your biochemical environment? Your diet and lifestyle play a huge role in determining your biochemistry. However, one the largest determinants of your internal state is the impact of your thoughts. When you have thoughts of fear and stress on a regular basis, you generate harmful biochemicals that stimulate your cells to become diseased. When you have healthy thoughts of joy and appreciation, you generate healthy biochemicals that keep your cells nurtured and healthy and turn off disease genes. Even if you do not think you’re stressed… If you feel overwhelmed, overworked, worried about money, disconnected, like you are on a hamster wheel, or feel like you’re just waiting for the weekend to come… These are stressors that generate harmful chemicals in your body. How do your thoughts control your gene expression? A multitude of research studies has made it evident that our biochemical environment (our hormones, neurotransmitters, peptides and immune cells) alters our cells genetic expression. Stress chemicals like cortisol, epinephrine and norepinephrine, as well as inflammatory mediators that increase when we are stressed, create a biochemical environment that activates the genes for disease to be expressed in the body. This means that genes get turned on or turned off depending on how we think, feel and behave. When you listen to your body and live in harmony with what it needs, disease genes are unexpressed. By listening to the body and honoring its needs, studies show that even patients who carry genes for cancer remain disease free. -Dr. Kim Get the Book Here What Clients are Saying Work with Dr. Kim Programs for Sidebar As Seen In As Seen In... As Seen In As Seen In... As Seen In As Seen In...
Cultural upheavals and the emergence of the counterculture in 1960s America Aslett, James (2007) Cultural upheavals and the emergence of the counterculture in 1960s America. BA dissertation, University of Portsmouth. [img] PDF Restricted to Registered users only Download (104kB) 1960s America saw huge change, politically, culturally and economically; people began to question their government and the ideals that were being relayed to them. During this period there were some significant upheavals that divided American society and caused people to develop a new set of morals and ideals regarding contemporary society. This new set of ideals differed from the mainstream and the disenchanted people that adopted this new consciousness came to be known or to be part of the counterculture. The counterculture was not a political movement but rather a new consciousness that was reacting against mainstream society, Kenneth Westhues argues that a counterculture is a group of people who, because they accept such nonconformist beliefs and values they tend to, drop out of the society (Westhues, 1972, p9), this is true of the 1960s counterculture to an extent but instead of completely dropping out of society, they bought their non-conformist ideals and values into mainstream society and became motivators of change. The values and beliefs that the 1960s counterculture adopted were reactionary against the rigid social norms of the 1950s, the war in Vietnam, segregation in the Deep South and women's rights. People wanted to be free from the government's oppressive ideals; they wanted freedom to create and construct their own values; thus promoting independence and equality. This new consciousness spread to popular culture, musicians took it upon themselves to exploit the fact that they were 'popular' and use it to become the voice of the new counterculture. A new permissive attitude towards sex and drugs was adopted by these musicians and with the globalisation of TV into most American homes; these musicians amongst other popular figures became the voice of the youth. The counterculture didn't spread to the film industry until the end of the 1960s; the film industry adopted a much tighter regime than the music industry where individual expression was readily encouraged. The film industry began to see the influence of this new culture when the influx of young, fresh film school bred filmmakers began to fill their studios. The aging studio moguls had lost control of their audience and couldn't cater for their needs. They reluctantly handed over power to these directors; many were immersed in the counterculture and could give this new youthful audience what they wanted. Elsaesser (2000) identifies this transition with the cultural upheaval "The protests against the Vietnam war, the Civil Rights movement and the emergence of feminism gave birth to an entirely new political culture, acutely reflected in a spate of movies" (p38). This new genre of movie started with Arthur Penn's Bonnie and Clyde (1967), a paradigm of 1960s American counter culture. It had two anarchistic revolutionaries fighting against the Capitalist authority, disillusioned by the false appeal of the 'American dream'. The parallel ideal of transformation and change reflected the socio/political climate which is why this movie received such a cult following; the rising counter culture saw this movie as a stimulus for change in their reckless modern worlds. This film marked a huge turning point in the American film industry; directors had been given the power to explore taboo subjects such as sex, drug taking, extreme violence, homosexuality and other subject matter that would never have been allowed ten years ago. This new type of personal film was branded the 'new Hollywood', it carried on throughout the 1960s and through the better half of 1970s. Many critics believe the demise of the New Hollywood can be attributed to Steven Spielberg with Jaws (Spielberg, 1975) and George Lucas with Star wars (Lucas, 1977); the first two Hollywood blockbusters. To fully understand the impact that these directors and their films had on the industry and American society, one must first examine the social context that they were involved in and what they were reacting against. There are two main aims of this dissertation, firstly to identify the extent to which the films of the New Hollywood reflected the socio/political climate of the time and wh Item Type: Dissertation Depositing User: Jane Polwin Date Deposited: 20 Jan 2011 12:47 Last Modified: 28 Jan 2015 11:13 Actions (login required) View Item Document Downloads More statistics for this item...
Total Pageviews Saturday, December 12, 2009 What is volvox? Volvox is probably the simplest living organism composed of a number of cells that show as common purpose. Volvox (Latin for rolling) is a plant, looking like a tiny green ball as big as this ‘o’,. If you look carefully into the surface of a freshwater pool or pond you will probably see, rolling through the water, tiny green balls-these are volvox. Tuesday, December 8, 2009 What is show-jumping? Show-jumping is a competition to see which horse and rider can best jump a series of walls, fences and other obstacles . Points are won and lost as the horses, one after the other, attempt each obstacles on a specially prepared course. Some times, extra points are awarded to the horse which completes the course successfully in the fastest time. Some of the special walls on a show-jumping course are made of brick, and if the horse kicks any of the bricks off the wall as it goes over the top it will lose its rider points. Fences are often made of wooden poles, and again, none of the poles must be kicked out of place by the horse if its rider is to score full points. Also there are often ditches filled with water, which the horses must be able to clear. If a horse refuses to jump a fence, it will mean a serious loss of points, And if a horse throws its rider out of the saddle, this is worse still. Show-jumping is popular with millions of people today who can see such contests on television. Some show-jumping horse riders are now as famous as racing jockeys. Tuesday, December 1, 2009 What do guide-dogs do? Dogs are what we call Domesticated animals, meaning that for thousands of years they have played a very close and important part in men’s lives. One of the most valuable jobs a dog can be trained for is to act as a guide-dog. These dogs are owned by blind people and lead the way when they want to go out. Such dogs are selected for this job when they are about two years old, and it takes four or five months to train them. They are trained to lead their blind master down a street so that he won’t bump into other people or walk into building or lamp posts. They are also taught to stop at the curb and not lead their master across the road until the traffic has stopped or is a safe distance away. As they are highly intelligent animals, they can even help their masters safely in and out of buses and trains. Sunday, November 29, 2009 Who are the Bedouins? The Bedouins are a nomadic Arab tribe whose name is derived from badawi meaning ‘desert-dweller’. They make up about one-tenth of the population of the Middle East, but cover in their wanderings nearly nine-tenths of its land area. Their Pattern of life is determined by the grazing needs of their flocks which they follow all the year round, living in black goats’ hair tents. Traditionally they despise agricultural or manual work, and happiest tending their herds of sheep, camels and highly-bred horses. Saturday, November 28, 2009 What is Valhalla? The word means Hall of the slain and, in Norse mythology, was the great hall of the dead heroes. The hall had 540 doors, so wide that 800 men could enter side by side, and the guests were seated at long tables where they were served with wondrous food and drink. Valhalla’s walls were of gold, lined with battle shields so highly polished that the light they cast made candles unnecessary, and coats of mail and armour hung from the walls. Thursday, November 26, 2009 What is knur and spell? A word game? A Viking singing duo? A witch’s curse? No, knur and spell is a little-known game that has been played in the Pennine area of Northern England for the last 300 years. The game has a terminology all its own. The knur is a small baked clay ball, sometimes known as a potty. The spell is a wooden structure something like a miniature gallows, from which the knur is suspended. The players-known locally as laikers – must hit the knur with a long sycamore cane, the laiker whose knur travels furthest being the winner. The game had almost died out until recently, but now there has been lots of new interest, and a world championship is planned. Monday, November 23, 2009 What is pall-mall? This game is similar to croquet, played with a wooden mallet and ball. The name derives from the Italian, Palla (ball) and maglio (mallet). Though not played much nowadays, pall-mall enjoyed great popularity in England. Italy and other parts of Europe in the 1600s. Monday, May 25, 2009 What is tropic of cancer ? The farthest northern latitude at which the sun can appear directly overhead, which occurs on the June solstice. North of this line is the subtropics and Northern Temperate Zone. The Tropic of Capricorn is at the opposite latitude south of the Equator. South of the Tropic of Cancer and north of the Tropic of Capricorn are the Tropics. The center line is called Equator. What is an atomic clock? Atomic clock is a special type clock that shows almost accurate time. Atomic clock maintains continuous and stable time scale. the first model of atomic clock was build on 1949 by the U.S National Bureau of standards. First successful atomic clock was designed on 1955 in UK by National physical laboratory. A chip scale atomic clock designed in august 2004 by NIST scientists. Chip type atomic clock consumes only 75 mw current. Major application of atomic clocks are to generate standard frequency and serve time signals to time signal sites. They also installed at navigation transmitters and broadcasting stations. By the help of this atomic clock signals broadcasting stations produces accurate carries frequency. GPS navigation systems base signals are also from atomic clock. Sunday, May 24, 2009 How to download youtube videos to your computer? Every one knows about youtube, we can search and watch a youtube video when the computer is connected to internet. without connected online we cant see a video in youtube unless its streamed. whats the remedy for it. To watch your favorite youtube video in offline just download this software and paste the url of your youtube video and download it to your computer. Watch youtube videos offline with this software Saturday, May 23, 2009 How many languages are in the World? (, whose detailed classified list currently includes 6,809 distinct languages. Thursday, May 21, 2009 Download zoozoo all ads Download vodafone zoozoo Download High Quality Zoozoo in vodafone background music How "Ida" named new fossil help the study about human origins? Ida is a new fossil found in Germany that will help to created a good media attention and will likely continue to make waves among those who study human origins. The paleontologist team that analyzed the 47-million-year-old fossil seen above, suggests Ida is a critical missing-link species in primate evolution. This fossil, reduces the gap between higher primates (monkeys, apes, and humans) and their more distant relatives such as lemurs. Tuesday, May 19, 2009 What is Casimir force? When two uncharged metals are kept micrometers away from each other in a vaccum. There is a quantum force betwen them (repulsion or attraction) depending upon the arrangement of the metals. The repulsion properties of casimir force can be used in levitationg micro objects. Casimir force is very significant in nanotechnology as this helps to reduce the friction between submicromillimeters parts. Since this force is created in vaccum It is also described as force from nothing. What is AVATAR and where does that word came from? Avatar is a word came from Hindu vedas. Avatar means incarnation mostly from an upper spiritual being (God) to a lower spiritual being (Human), also posses supernatural powers mainly objected for a special purpose.Avatar is mainly connected with Vishnu one of the three main Gods of Hinduism. Dasavataram denotes ten avatars of Vishnu in the world for certain purposes. The tenth avatar KALKI is believed to be in our Living age and yet to come. Sunday, May 17, 2009 Latest movie news Sunday, May 3, 2009 What Is Biogas? Biogas is a mixture of carbon dioxide, methane and some other gases. It is produced by some kinds of microorganisms, usually when air or oxygen is absent. (The absence of oxygen is called “anaerobic conditions.”) Animals that eat a lot of plant material, particularly grazing animals such as cattle, produce large amounts of biogas. The biogas is produced not by the cow or elephant, but by billions of microorganisms living in its digestive system. Biogas also develops in bogs and at the bottom of lakes, where decaying organic matter builds up under wet and anaerobic conditions. How to build a biogas generator Visit: Wednesday, April 29, 2009 How can Robots help us ? Robots can help humanbeing in different ways. We can send robots to space, under the deep sea, into the earth for complicated mining process that ordinary people cant done. Robotos can go into extreme temperature and do the tasks correctly without human error. Nasa also use robots to repair space ships and space stations. We can use robots to manipulate the environment. Wednesday, April 8, 2009 How Rice cooker works ? Basically Rice cooker consists of a heating coil and thermostat. A bowl is placed on the heater which contains rice and water. During cooking the temperature will not increase above 100 degree due to the boiling point of water. In final process of cooking, water boiled off and temperature increases in the absence of water and thermostat trips. In market there are electric and microwave rice cookers are available. Rice cookers also included steamer. The new technological rice cookers are Induction Heating, Microcomputer controlled rice cookers. Wednesday, April 1, 2009 Where does vanilla come from? Vanilla falvouring is something we are all familiar with. But did you know that from whrer we get vanilla? We get it from the vanilla orchid, which grows in Madagascar and other islands in the Indian Ocean. What is more, the vanilla orchid is the only orchid which produces a useful product. Thursday, March 5, 2009 When was history made in twelve seconds? The date was 17 December 1903; the scene: the cold windy hills of North Carolina; the name of the place which was to go down in history: Kitty Hawk; the occasion: man’s first powered flight. The aero plane had arrived. Orville Wright was at the controls. The aircraft, powered by a four cylinder engine, careered through space for twelve seconds at 48Km. p.h. airspeed, swept down and landed in soft sand. Orville wrote: ‘This flight lasted only twelve seconds but it was, nevertheless, the first in the history of the world in which a machine, carrying a man, had raised itself by its own power into the air in full flight, had sailed forward without reduction of speed and had finally landed at a point as high as that from which it started’. The Wrights’ aircraft was called flyer. Only five people were there to watch it make history. One photograph recorded the scene. It was not until three years after Kitty Hawk that the Scientific American wrote” ‘In all the history of invention there is probably no parallel to the unostentatious manner in which the Wright Brothers of Dayton, Ohio, ushered into the world their epoch-making invention of the first successful aeroplane flying machine’. Thursday, February 12, 2009 Where do we get the word denim from ? If you have a pair of Jeans you will know that what they are made of is called denim, but do you know where the word comes from? At first, it was used to describe a serge cloth made in Nimes, France – the original name was ‘serge de Nimes’. Gradually, these last two names were shortened and adapted to the word we know as denim, although now denim is made all over the world sand not just in Nimes. Friday, February 6, 2009 How did the Oscar get its name? In 1929, the first awards for best performances in films were made. These awards where shaped like as man, and a secretary at the Academy of Motion Pictures Arts and Sciences on seeing one for the first time, remarked that it looked just like her uncle Oscar. The name stuck, and the awards have been called Oscars ever since. Thursday, January 15, 2009 Quiz 2 1. Who wrote about the Jabberwockey? 2. What is a ‘Kentucky Pill’? 3. Where is the ‘Land of the White Eagle? 4. What does MS stand for ? 5. What is a Naiad? 6. Who hid from his enemies in an oak tree? 7. What is a Palindrome? 8. What is another name for Quicksilver? 1. Lewis Carroll. 2. A Bullet. 3. Poland 4. Manuscript 5. A water nymph. 6. Charles II. 8. Mercury. 9. Aries. Thursday, January 1, 2009 1. Who is the patron saint of travelers? 2. What is the ‘Third Estate’? 4. By what name is Van Dieman’s Land now known? 5. What is wampum? 6. What kind of musical instrument is a xylophone? 7. What is the song of the Yellowhammer? 8. What are the Zingari? 1. St. Christopher 2. The House of Commons 3. Jonas Han way 4. Tasmania 5. Shell bead money used by the North American Indians 6. A percussion instrument. 8. This is the name given to gypsies in Italy.
Go to content Henri IV - An unfinished reign Listen to the the music tracks Ninfe qui tiens tant d’heur Eustache Du Caurroy Source : ‘Henri IV et Marie de Médicis: Messe de mariage’; Doulce Mémoire; dir. Denis Raisin-Dadre; Astrée-Naïve E 8808 (2000). On the subject of the royal wedding, Nicolas Rapin composed these vers mesurés à l’antique. Set to music by Eustache Du Caurroy, Rapin this time addresses the queen Marie de Médicis, by evoking the eventful journey she undertook to her new country, the eagerness of France to discover the charms of the new queen, and its impatience to see the two greatest powers of the humanist Renaissance united and at peace. Eustache Du Caurroy Eustache Du Caurroy was born in 1549 in Gerberoy, at the borders of Picardy, Normandy and the Ile de France. He is considered to be the last great masters of Renaissance polyphony. He probably entered royal service (as a countertenor in the king's chapel) in 1575, the same year he won a musical competition in the town of Evreux, the Puy de Sainte Cécile, with a composition for four voices, Rosette pour un peu d’absence. He won the same competition the following year, with a motet for five voices (Tribularer si nescirem, now lost), and again in 1583 with a song, Beaux yeux dont le pouvoir, also for five voices. In 1578, his name appears in the court account-books, still listed as a countertenor, but also as sous-maître de la Chapelle du roi, one of the most prestigious musical posts in the kingdom. He was also a member of the Chapelle of the queen mother Catherine de Médicis (1585 and 1587) and appeared to have been part of the circle around Marguerite de Valois who, starting in 1605, gathered around her the finest artists at her townhouse in Rue des Augustins (where the École des Beaux-Arts now stands). Starting in 1594, Henri IV set Du Caurroy apart from other musicians. In 1595, Henri named him Compositeur de la Musique de la Chambre – a post he shared with Claude Le Jeune – and Compositeur de la Musique de la Chapelle five years later in 1599. This royal favour was accompanied by a number of ecclesiastical benefits that ensured him a comfortable life. He died in 1609 as he was preparing to publish his works, having signed an agreement with Pierre Ballard, "music printer to the king". He barely lived to see the completion of the project. Most of his surviving works have come down to us in five collections, published starting in 1609. There are two volumes of Preces ecclesiasticæ (1609), dedicated to Henri IV and Marguerite de Valois, which contain fifty-three motets for between three and seven voices; forty-two Fantasies a III, IV, V et VI parties (1610); one volume of Melanges (1610), which contain secular and sacred polyphonic works sung in French; a Missa pro defunctis for five voices. This last was written around 1590, but the only surviving source for it is a re-edition by Ballard from 1636. It was sung at the funeral service for Henri IV, and tradition made it the funeral mass for the kings of France. Three other masses for four voices that he wrote are now lost. Transcription (in French) Ninfe qui tient tant d’heur, que de joindre à la France ta grandeur, Et d’un Roy valeureux prendre le joug amoureux : Quel paresseux démon te retient à Florence si long temps, Sur le sablon toscan, loing de ton Astre nouveau ? Viens combler de faveur notre Mars, qui s’avance devant toy : O ! quelle troupe de Dieux et de Déesses t’attend. Les forts vents de la mer bientôt sur l’onde paroistront, Déjà la Brume revient, qui nous allonge la nuit. Pousse la barque Hymenée nocier, ne retarde ce festin : D’un mutuel flambeau brusle l’Amante et l’Amant, Entre la guerre et paix que la France ait laissé de chanter : O Hymenée, Hymenée ô Hymenée d’Amour. Welcome to our web site devoted to Henri IV /3/ A mobile version is available. Version accessible
If you’ve browsed through our continuously updated documents, you’ll have appreciated their breadth of scope and their seriousness. We have peer reviewed international references that are often overlooked in mainstream media and other climate sites. We have documents that criticise things that haven’t worked, and since we’ve concentrated on science and tried to factor out ideology, some of our documents may seem controversial. If you’d like to help us expand and improve our library, please consider making a donation, for which we thank you in advance. Thanks for your support, The SOP team. documents in the library in the category Agriculture Agriculture: Includes the GHG contribution of various agricultural activities. also in categories carbon capture, causes, economics, effects, forests, mitigation moreless Tropical reforestation (TR) has been highlighted as an important intervention for climate change mitigation because of its carbon storage potential. TR can also play other frequently overlooked, but significant, roles in helping society and ecosystems adapt to climate variability and change. For example, reforestation can ameliorate climate-associated impacts of altered hydrological cycles in watersheds, protect coastal areas from increased storms, and provide habitat to reduce the probability of species’ extinctions under a changing climate. moreless also in categories economics, energy, forests, government, international references, negotiations, plans and scenarios moreless A public database of submitted INDCs. This data can be used to calculate a worldwide mitigation response. These commitments are expected to improve over time. moreless also in categories economics, education and training, effects, government, international references, mitigation, negotiations, plans and scenarios moreless A United Nations overview of climate issues, activities, and science. Gathers and shares information on GHG emissions, national policies and best practices,Launch national strategies and measures for reducing GHGs and adapting to the adverse impacts of climate change, including developing financial and technical support to developing countries, Cooperate in preparation for taking mitigation measures and adaptation measures. moreless also in categories carbon capture, causes, effects, forests moreless A forest is much more than what is seen, says ecologist Suzanne Simard. Her 30 years of research in Canadian forests have led to an understanding of how trees interrelate, often over vast distances. Understand the delicate balance of the forest and the concept of tipping points in forest health. moreless also in categories causes, economics, education and training, effects, energy, forests, government, international references, models, plans and scenarios, sea, technology moreless also in categories causes, community, economics, education and training, effects, energy, forests, government, health, industry, mitigation, models, recycling solutions, technology, transportation, video moreless Frameworks and tools to understand and address climate issues that impact people and their communities. Build resilience to climate impacts, see what others are doing, explore local situations. moreless also in categories biofuel, carbon capture, coal, economics, energy, forests, fossil fuel, french, government, habitation, hydroelectric, industry, natural gas, nuclear, petroleum, plans and scenarios, recycling solutions, solar, technology, transportation, waste, wind moreless Explains how France intends to reduce GHG to 140 Mt (divide by factor 4, 1990 — 2050) in two generations. moreless https://static1.squarespace.com/static/5515d9f9e4b04d5c3198b7bb/t/552d37bbe4b07a7dd69fcdbb/1429026747046/An Ecomodernist Manifesto.pdf also in categories carbon capture, community, economics, effects, energy, forests, government, habitation, industry, nuclear, plans and scenarios, promising technology, technology moreless A revolutionary reevaluation of environmentalism, with a high reliance on technology to provide human needs while providing environmental space for wilderness and wild things. moreless also in categories coal, economics, effects, energy, forests, fossil fuel, habitation, industry, negotiations, plans and scenarios, transportation moreless Nine propositions to take Europe to a post-carbon era before 2050 moreless also in categories biofuel, carbon capture, economics, energy, forests, mitigation, models, nuclear, plans and scenarios, solar, technology, wind moreless MIT RESEARCH MISSIONOur integrated team of natural and social scientists studies the interactions among human and Earth systems to provide a sound foundation of scientific knowledge to aid decision?makers in confronting future food, energy, water, climate, air pollution and other interwoven challenges. Much details on energy alternatives, including costs, safety, and Timeliness of availability. moreless Choose another category
Sunday 30 September 2007 Myth, History And Politics Ever since Ayodhya became a disputed territory, Rama has been at the centre stage of the political mobilisation by Hindu communal forces. The incidents associated with the Rama Katha were invoked one after the other to appeal to the religious sentiments of Hindus. It began with a claim to the birthplace of Rama at Ayodhya, around which Hindu religious sentiments were so aroused as to lead to the destruction of the Babri Masjid. In the movement culminating in this vandalism, several symbols linked with Rama such as Rama Jyoti, Rama Paduka and Rama Shila were floated. Yet, over the years, the political appeal of Rama has waned despite his strong presence in the religious life of believers. The temple issue was indeed kept alive through occasional religious assemblies and demonstrations. Nevertheless, Rama ceased to be of much emotional value that would provide political advantage to Hindu communal forces. In the elections of 2004, the Ram temple did not figure as an issue at all. This can be taken as an indication that believers were inclined to abandon the Sangh Parivar’s aggressive Rama and return to worshipping his benign image, looking upon Rama Katha, as they had for centuries, as an “allegory of the life of the spirit as it journeyed through the world”. Rama was almost lost to the political Hindu and was being resurrected to his rightful place in the religious life of believers. It is in this context that the Ram Sethu project has come in handy for the Sangh Parivar, to revive the appeal of Rama in order to breathe some life into its sagging fortunes. Once again the Parivar is bracing up to claim Rama for the communal cause. In the process it is attempting to turn myth into history, blurring the distinction between the two, in order to gain legitimacy for its political project. The question of whether the Archaeological Survey of India (ASI) should have filed an affidavit in the Supreme Court denying the historical existence of Rama has led to differences of opinion. The government has hastened to disclaim the affidavit and withdraw it, obviously fearing a Hindu backlash. Unlike the Ayodhya issue, even the secular voice has been rather muted. However, implicit in the affidavit is an important question regarding our approach to the past: Is there a distinction between myth and history? Mythic Character The ASI, it appeared, was conscious of this distinction in projecting the mythological character of Rama. The distinction does not imply a counterposition of myth and history as false and true. Myth is a way in which the human mind comes to grips with reality, and therefore, it can be said that it refers to reality. Yet, myth in itself is not reality. What the ASI has tried to state is that Rama was not a historical figure but a mythic character. Similarly, the Ramayana being a literary piece, which was not originally a religious text but only sacralised later, contains many events and incidents that are products of imagination. It would therefore be futile to try to correlate them with historical fact and establish their authenticity. Such a view is not in any way a denigration of Rama or a critical reflection on the Ramayana. The Ramayana’s literary quality, whether in the original Sanskrit or in regional languages, is well known. So are the ethical and moral values it foregrounds, which exercise considerable influence over the life of believers. However, devotion to Rama and the influence of the epic have nothing to do with the historical veracity of Rama Katha. Devotees consider Rama an incarnation and do not test his deeds by the yardstick of historical truth. They are moved by their devotion and hardly approach the epic from a rational viewpoint or try to locate it historically. Whether the Ramayana is historically true or not is not a factor in their devotion. The Sangh Parivar has been trying for long to impute to incidents in the epic a historical quality to legitimise popular belief, under a false notion that belief would be reinforced by historical truth. The panic reaction of the government in withdrawing the affidavit in effect endorses the Sangh Parivar’s attempt to equate myth with history. Like the Sangh Parivar, the government seems to subscribe to the view that ascribing mythic character to Rama and the Ramayana is to undermine their importance and to injure the sentiments of believers. It overlooks the fact that believers consider Rama an incarnation. Traditional religious sources represent him so. The Matsya Purana, for instance, gives the following account: “There is also the account of the pastimes of Lord Rama, spoken by Valmiki – an account originally related by Brahma in one billion verses. That Ramayana was later summarised by Narada and related by Valmiki, who then presented it to mankind.” What accounts for the devotion to Rama and the veneration of the Ramayana are not their historical veracity but their divinity. Many Ramayanas In an attempt to attribute historical authenticity to the epic and its protagonist, the Sangh Parivar has been striving to privilege one single version of the Ramayana. But the Ramayana has several versions. It is difficult to ascertain the exact number as all of them are not written but are orally transmitted, both in India as well as in other Asian countries. A.K. Ramanujan has argued that these different “tellings” – a term he prefers to versions or variants as these imply an invariant or original text – differ from one another. They are not mere divergences from Valmiki’s rendering but entirely different tellings. Highlighting the multivocal existence of Rama Katha, Paula Richman has drawn attention to the many Ramayanas, of which Valmiki’s composition is one, Tulsi’s another, Kamban’s another, the Buddhist Jataka yet another and the Jaina tradition yet another. Along with them, there are also innumerable folk narratives, extant not only in India but also in almost all the countries of Asia. They were not Valmiki’s Ramayana adapted to local conditions but substantially different from one another, both in form and content. In the Buddhist version, Rama and Sita are originally brother and sister, a fact that once aroused the ire of the Sangh Parivar. Women’s folksongs from Andhra Pradesh challenge the accepted values of a male-dominated society by questioning the integrity of Rama and foregrounding the theme of the suffering that husbandly neglect causes a wife. Thus, the Rama Katha prevalent in different communities is vastly different and defies any attempt to identify a universally applicable text. All of them draw upon locally specific cultural traits, which impart to them a distinct character. Recent studies on different Rama Katha traditions demonstrate the different tellings of Rama’s story that vary with regional literary tradition, social location, gender, religious affiliation, colonial context, intended audience, and so on. K.R. Srinivasa Iyengar’s edited work highlights the Asian variations of the Ramayana, and the essays in the volume edited by Avadesh Kumar Singh focus on the way the epic has found expression in regional languages. The many Ramayanas connote that the events and incidents in the different versions of the epic are not historical facts but mythical representations or literary imaginations. The debate on whether the Ramayana is a true story or whether Rama is a historical figure is, therefore, off the mark. The issue of Ram Sethu requires to be situated in the general context of the mythological character of the Ramayana. The Sethu Bandhan encapsulates within it several qualities of Rama and the character of the epic. Sethu Bandhan was a humanly impossible task that was made possible only by the divine powers of Rama. The description of Sethu Bandhan in one version of the Ramayana is as follows: “During the first day of construction, monkeys laid a hundred and twenty miles of rocks, which floated upon the ocean. They worked very swiftly, and were happy to see the bridge take shape. The second day, they set down a hundred and sixty miles of rocks; the third day, a hundred and sixty-eight miles; and the fourth day, their strength increasing, they completed a hundred and seventy-six miles. On the fifth and final day, the monkeys constructed a hundred and eighty-four miles of bridge, up to Mount Suvala on the northern shore of Lanka. Thus when the bridge was finished, it was eighty miles wide and eight hundred miles long.” Obviously, a vanar sena would not have achieved this feat. The question, however, is not its possibility or impossibility but how it enriches the mythical and divine quality of Rama. Obviously Sethu Bandhan is a myth. But then, when myths become part of the belief system, they can be put to use for different purposes. Nobody in India has understood this better than the Sangh Parivar as is evident from the manner in which they have manipulated the myth and history of Ayodhya. Ram Sethu is an opportunity they are unlikely to let go of easily. The distinction between history and myth is well recognised. Myths are in a way the opposite of historical facts, in the sense that, unlike historical facts, what constitutes a myth is not verifiable. Despite this, myths and history cannot be counterpoised as true and false. In fact, myths also represent reality but represent it symbolically and metaphorically. Yet, myth masks reality. Therefore, myths are illusory representations of man and his world. Given their illusory nature, myths may not help to unravel the historicity of an event. Most myths are in a way timeless. Nevertheless, myths being a reflection of reality constitute a source of historical reconstruction and a means to understanding reality. Given this overlap, myths are used for a variety of purposes. They often serve as an agency of legitimisation, as in the case of Parasurama reclaiming land from the sea. They may also be employed for explaining a natural phenomenon, as in the case of Helios’ chariot in Greek mythology. The use of myths has been integral to the politics of the Sangh Parivar. Beginning with the movement for the construction of the temple at Ayodhya, the Sangh Parivar has been engaged in providing authenticity to various myths surrounding the life of Rama. The central issue of the Ayodhya movement was the identification of the exact birthplace of Rama, which was difficult to ascertain owing to the lack of evidence. Local tradition identifies Ayodhya through a popular myth, which runs as follows: “After Treta Yuga when Ram was supposed to have been born Ayodhya could not be located. While Vikramaditya was looking for Ayodhya, a saint told him to leave a calf loose and the place at which the calf secreted milk would be the place where Ayodhya was located. Vikramaditya did as he was told, and where the calf secreted milk he located Ayodhya.” This mythical story became the basis for the identification of Ayodhya as well as the birthplace of Rama. In the accounts given by leaders of the Vishwa Hindu Parishad (VHP), the place of birth becomes an indisputable fact of history. Following this identification, the VHP accorded historical status to a series of myths. These include the existence of the Ram temple at the site of the Babri Masjid and the attempts by Hindus to reclaim the temple through 77 battles against the Muslims in which 300,000 sacrificed their lives. These myths have now become authentic histories; not only are they paraded as historical facts, they have found place in textbooks as authentic history. Over a period of time, many of these facts could become part of popular history also. The politics of the Sangh Parivar is essentially irrational. The attempt to turn myth into history and to use it for political advantage is rooted in irrationality. Now that Ayodhya is no more a potent force, Ram Sethu has emerged as a possible alternative. The Sangh Parivar is gearing up to exploit it. Would the ruling establishment take a rational and scientific stand and not succumb to the fear of the irrational? By K.N.Panikkar (K.N. Panikkar, a former professor of history at Jawaharlal Nehru University and a former vice-chancellor of Sree Sankaracharya University of Sanskrit, is currently the chairman of the Kerala Council for Historical Research.) Copyright © 2007, Frontline No comments:
Mythology, Fairies, Witches The mythology of the British Isles is probably less well known than Classical or Norse mythology but plants are central to many of its themes. The Celtic warrior Cuchulainn was said to be bathed in baths of meadowsweet to cure his terrible rages and the Gaelic name for the plant ‘crois cuchulain’ (belt of Cuchulain) reflects this. Blodeuwedd (flower face) was created out of the flowers of meadowsweet, broom and oak to become wife of Welsh hero LLew Llaq Gyffes, but was turned into an owl for her infidelity. The gods, goddesses and heros of Greek and Roman mythology are closely connected with wild plants and give many of our plants their scientific names, such as Artemisia (mugwort) for the goddess Artemis/Diana, and Andromeda (bog rosemary) for the maiden rescued by Perseus. The sacred ash tree Yggdrasil was central to Norse mythology and mistletoe was said to be banished to the tops of trees for its role in the death of Baldur. Fairies have long been associated with particular plants such as the fairy cap (harebell) and the stone bramble (Subh nam ban sithe – the fairy woman’s strawberry in Gaelic), and the flower fairies created by Cicely Mary Barker have held their popularity for over a hundred years. Some of our best loved and less known fairy tales have plants at their core, such as Rapunzel, the Wild Swans, Cap O’ Rushes and Rushen Coatie. Similarly witches and witchcraft have an intimate connection with wild plants. Elspeth Reoch was tried as a witch in Orkney in 1616 for collecting yarrow in a ritualised manner, and plants such as foxgloves are known as ‘witches thimbles’. Certain plants are believed to give protection against witches, such as the wreaths of ivy, rowan and honeysuckle hung over barn doors on the Western Isles to keep the livestock safe. Please download our factsheets to find out more about wild plants and mythology, fairy tales, and witches. British and Irish Mythology Classical Mythology Norse Mythology Fairies and Witches
Censorship by Charles E. Corry, Ph.D. © 2002 Equal Justice Foundation \| EJF Home \| Join the EJF \| Comments? \| Get EJF newsletter \| EJF Newsletters \| \| Courts, Veteran Courts, And Civil Liberties \| Contents \| Index \| \| Chapter 3 — What Happened To Civil Rights? \| \| Next — There Ought Not To Be A Law by Wendy McElroy \| \| Back — Rural Cleansing By Endangered Species by Ted Miller \| Censorship is an essential component of war. Ship and troop locations and movements must be kept secret. Communications must be monitored and spies intercepted. Events, even disasters, must be presented in a favorable light in order to ensure the support of the populace. Disinformation and propaganda are as essential as secrecy. But the temptation to censor or classify information in order to cover incompetence, fraud, waste, theft, and other crimes virtually always overcomes some government officials. Napoleonic France had a saying: "To lie like a bulletin," regarding official communiques. Hitler openly used the idea that a lie repeated often enough by officials would inevitably be believed, and that the Big Lie is more likely to be believed than small fabrications. Simply withholding information is also an effective method of censorship. It is reported that in Russia Stalin used the method where 100,000 books favorable to Communism were published but only 2,000 books presenting opposing views were printed. Today, with regard to the hysteria surrounding domestic violence we find a "lace curtain" has been drawn by the publishing industry wherein only violent men are portrayed in print and screen, and all women are innocent "victims." In the wake of the Nixon Watergate scandals Congress passed the Freedom Of Information Act (FOIA) to reduce the amount of information the government could withhold from citizens. That act has been hailed as one of our greatest democratic reforms. Naturally, the FOIA has proved to be of great embarrassment to many government officials. But far be it from any bureaucrat to use the information to correct their misconduct. Instead, the natural inclination of such creatures is to crawl back under their rock and make it illegal to turn over rocks in the future. The tragic events of 9-11 provided perfect cover for U.S. Attorney General John Ashcroft to issue a memo without fanfare on October 12, 2001, in which he vigorously urged federal agencies to resist most FOIA requests made by American citizens. Rather than asking federal officials to pay special attention when the public's right to know might collide with the government's need to safeguard our security, Ashcroft instead asked them to consider whether "...institutional, commercial and personal privacy interests could be implicated by disclosure of the information." Continuing in an even more chilling vein, he wrote: Attorney General Ashcroft's actions to derail the FOIA under cover of war were soon followed by an executive order by President Bush on November 1, 2001, that allows him to seal all presidential records since 1980, despite laws that require such records to be made available after twelve years. What are they hiding? And past experience suggests that looking under these rocks won't yield pleasant surprises. Governments are not the only ones interested in presenting only their side of the story. Many groups with an ideologic agenda find it convenient, if not essential to their survival, to ensure that only their side of the story is told. Communism and Naziism are recent historical examples. Gender feminism today, with its "politically correct" agenda, seeks to provide only one side of the issues, as supported by "advocacy research" in which the outcome is determined by the ideology rather than the facts. Opposing feminism is painted in propaganda as denying Mom and apple pie. As a result, a "lace curtain" has been drawn by the media across such issues as child abuse and domestic violence. Such censorship is felt to be essential in order to protect the vast public funding these groups now receive. The "lace curtain" maintains its integrity by various means. For example, in August, 2001, several groups were flown to Houston, Texas, to film a segment on "Good Girls Gone Bad" for the Debra Duncan show on an ABC affiliate station. However, one abusive ex-wife from Maine apparently heard about the show and threatened to sue. Even though this woman has been arrested for knocking the man's current wife to the ground, the ABC network attorneys lacked backbone, or held to the feminist ideology, and the show was never aired. As in times of yore, censorship involves banning the book in Boston, or better yet ensuring it is never printed. If it is printed, then "politically correct" groups across the country can be counted on to steal it off the bookshelves or from libraries. On university campuses across the country newspapers expressing unpopular, i.e., not "politically correct," opinions are taken from newsstands and trashed to prevent the spread of unpopular ideas. Nor are such actions limited to college campuses. In Eagle, the conservative paper Speakout! has been trashed by school teachers after their competence was called into question. And book burning is still a popular past time, as in the case of the Harry Potter fad. While we presently don't engage in burning heretics at the stake for refusing to accept the current ideology or religion, such prominent women as Erin Pizzey have been driven into exile by death threats and harassment for daring to publish a book showing that women are as violent as men in the home. But the problem of censorship isn't as simple today as it once was. With the advent of the Web, most current information is available globally via the Internet. So ensuring the local paper or radio stations don't carry an item of information doesn't mean the populace won't hear of it. Thus, other means of censorship have come into play. Everyone has heard of "computer hacking" but few are aware of the extent to which it is occurring and how successful it is. In the year 2000 the US military is estimated to have received about 250,000 computer attacks, of which approximately 65% were at least somewhat successful. At present they often receive that many attacks in a single day and they most certainly don't advertise how vulnerable they are. To defend against such attacks is an essential component of modern warfare but such methods also lend themselves to censorship. On the personal level, I receive a minimum of two attacks a day with five or six the norm. Commonly these attacks occur immediately after I log on to the Internet, or go to a particular Web site. Even Macintosh, previously nearly immune to hacks, are successfully attacked today unless firewall software is installed. Thus, if your computer doesn't have firewall protection it is a virtual certainty your computer is being invaded if you are connected to the Internet. The possibilities for controlling the information you can see and hear are therefore immense and growing. The Clinton administration wanted to put a microchip in all computers to monitor them, and at the same time the FBI developed its Carnivore program to monitor your e-mail. Such techniques are fundamental to censorship and, of course, in wartime we don't hear about what is currently being done. Without the FOIA we are not likely to learn. Another form of modern censorship that is constantly attempted is "denial of service" and that takes many forms. One method is to send viruses, worms, and trojan horses hoping to control or disable our computers, or to spread these viruses through mailing lists. Companies often receive hundreds of such attacks a day, and many individuals using e-mail receive several a week. Anyone who doesn't update their virus definitions at least once a week is almost sure to be infected eventually as viruses grow and multiply. I have known companies claim to be free of viruses when in fact more than fifty trojan horses, worms, and viruses existed on virtually every machine in their network. Problems of hacking and viruses are of particular concern when one looks at such fundamental activities as computer voting. Since access can often be had from anywhere in the world, the results of an election may depend more on the whims of a teenage hacker, or the will of a foreign government, than the wishes of the electorate. Another method of censorship used against unpopular Web sites is to notify the service provider that a copyright violation exists on the site. As that violates the service rules for virtually all ISP's, as well as the law, the site will commonly be taken down without further investigation. Ideologically-driven groups have also been know to claim a Web site they dislike is being used for sending or generating spam (unwanted commercial email). For example, a group of about 40 people, apparently centered in New Zealand, did that in October, 2001, and shut the www.dvmen.org site down for several days. The fact that the site cannot possibly be used to generate spam is irrelevant in dealing with self-appointed censors. Note that these methods work regardless of location. A Colorado Web site is readily censored from New Zealand. A voting machine is infected from China via Texas. So the means and methods of ideologically-driven groups, whether government or private, of controlling information, and basic freedoms such as a secret election, continue to grow despite the freedom of information provided by the Internet. It is said the Soviet Union was defeated by fax, copy machines, and microchips. Since then the means and methods of tyranny and oppression have grown. However, the opportunities to spread ideas and truth have never been greater. For example, it is a rare scientist these days who doesn't maintain a Web site to make their results public and communicate with their colleagues. The job then of dominating and controlling free men and women has been infinitely multiplied. Thus, it is unlikely such actions as sidestepping the Freedom of Information Act will succeed but tyrants are unlikely to stop trying to censor what we see and hear. \| Chapter 3 — What Happened To Civil Rights? \| \| Back — Rural Cleansing By Endangered Species by Ted Miller \| This site is supported and maintained by the Equal Justice Foundation. Last modified 3/2/15
List Of Social Psychology Theories • Attribution theory - is concerned with the ways in which people explain (or attribute) the behaviour of others. The theory divides the way people attribute causes to events into two types. External or "situational" attributions assign causality to an outside factor, such as the weather. Internal or "dispositional" attributions assign causality to factors within the person, such as ability or personality. • Cognitive dissonance - was originally based on the concept of cognitive consistency, but is now more related to self-concept theory. When people do something that violates their view of themselves, this causes an uncomfortable state of dissonance that motivates a change in either attitudes or behaviour (Festinger, 1957). • Drive theory - posits that the presence of an audience causes arousal which creates dominant or typical responses in the context of the situation. • Motivation crowding theory - suggests that extrinsic motivators such as monetary incentives or punishments can undermine (or, under different conditions, strengthen) intrinsic motivation.[1] • Observational learning (social learning) - suggests that behaviour can be acquired by observation and imitation of others, unlike traditional learning theories which require reinforcement or punishment for learning to occur. • Positioning theory - focuses on the moral orders that occur in conversations as a result of the interplay between the speech-acts uttered, the positions taken and the developing story-line. • Self-perception theory - emphasizes that we observe ourselves in the same manner that we observe others, and draw conclusions about our likes and dislikes. Extrinsic self perceptions can lead to the over-justification effect. • Self-verification theory - focuses on people's desire to be known and understood by others. The key assumption is that once people develop firmly held beliefs about themselves, they come to prefer that others see them as they see themselves. • Social comparison theory - suggests that humans gain information about themselves, and make inferences that are relevant to self-esteem, by comparison to relevant others. • Social identity theory - was developed by Henri Tajfel and examines how categorizing people (including oneself) into ingroups or outgroups affects perceptions, attitudes, and behavior. • Social penetration theory - proposes that, as relationships develop, interpersonal communication moves from relatively shallow, non-intimate levels to deeper, more intimate ones.[2] The theory was formulated by psychologists Irwin Altman and Dalmas Taylor in 1973 to provide an understanding of the closeness between two individuals. • System justification theory - proposes that people have a motivation to defend and bolster the status quo, in order to continue believing that their social, political, and economic systems are legitimate and just. • Terror management theory - suggests that human mortality causes existential dread and terror, and that much of human behavior exists as a buffer against this dread (e.g., self-esteem and worldviews). 1. ^ Frey, B.S. and Jegen, R. (2001) "Motivation Crowding Theory" Journal of Economic Surveys 15(5):589-611 2. ^ Griffin, E. (2006). A first look at communication theory (6th ed.). New York: McGraw-Hill. US Cities - Things to Do
Katy Ferguson Katy Ferguson: The Woman Who Loved All Children In about 1774, Catherine Williams was born on a schooner. Her mother, a slave from Virginia, was being sent to a new owner in New York when she gave birth to the little girl who would soon be known as Katy. That child would show what a person with determination and generosity--and very little else--can accomplish. At an early age, Katy's mother taught her what she knew about Christian scripture, and it made a deep impression on her. Even after the two were separated, when Katy was eight, the child went to church services and became a member of the Murray Street Church in New York City. She was not, however, taught to read and write. When she was sixteen, Katy was purchased by a white abolitionist, who gave her half of her $400 purchase price as a wage for one year's work. A merchant named Divee Bethume helped her get together the other half and, by the time she was eighteen, she was free. Almost immediately, she got married and began to have children. Both of the babies she gave birth to died when they were infants. Her husband died not long after the children. In the meantime, Katy had begun to make a living as a caterer and as a launderer of lace and other fine fabrics. But she was not satisfied with her modest financial success. Katy Ferguson had other concerns. She lived in a poor neighborhood near an almshouse. All around her were children whose lives must have wrenched her heart. In 1793, when she was little more than a child herself, Ferguson started a Sunday school. She took forty-eight children into her home once a week to give them lessons in scripture and in the practical skills of life. She also did her best to find them homes. Soon, the pastor of her own church, Dr. John M. Mason, heard about Ferguson's work and offered her space in his basement. He also provided assistants who could provide the basic education that she, still unable to read and write, could not. Under Ferguson's supervision, the Murray Street Sabbath School continued for forty years. It was New York's first Sunday School. Katy Ferguson died of cholera in New York in 1854. In 1920, the city of New York opened a home for unwed mothers and named it the Katy Ferguson Home.
Tom Vath Jr. No Comments Dew point is defined as the atmospheric temperature below which water droplets begin to condense and dew can form. When you put a cold glass in a humid room, condensation forms on the glass. This is because the glass has a temperature below the dew point in the room. The same goes for a floor during a coatings job. If the slab of concrete is at a temperature that is lower than the dew point of the room, condensation will form on the concrete, creating all sorts of issues with your coating such as compromised bond and possible finish issues such as fisheyes and color inconsistencies. Below is a table showing the relationship between temperature, humidity and dew point. dew point and floor coating As you can see, if the air temperature is 75 degrees and the relative humidity of the room is 35%, the dew point would be 45 degrees. This means that if your floor temperature is 45 degrees or lower, coating the floor is a risk. This is why most technical data sheets will say not to coat a floor within 5 degrees of the dew point. The concrete slab can contain condensed moisture on the surface, causing adhesion, cure, and film issues. Also, it is worth noting for complete understanding that at 100% humidity, the dew point is equal to the air temperature. This is because when the relative humidity is at 100%, moisture can no longer evaporate into the air because it is completely saturated. For example, in 100% RH, if you put a wet rag outside, even if the temperature is 85 degrees, it will never dry because the air is already completely saturated with moisture and the moisture from the rag has nowhere to go. A common misconception… “The weather man says the dew point is 40 degrees today and my slab is 50 degrees, so I’m good to coat.” In some cases, this is correct. If the floor is outside, or in an outside garage, or in new construction with no influence of HVAC, this statement is true. However, the temperature and relative humidity outside is not always the same as inside. The relative humidity and temperature need to be taken in the environment you are coating. If the temperature outside is 60 degrees and the relative humidity is 50%, the dew point would be (according to the chart) 41 degrees. This is the dew point the Weather Channel would have listed. If your slab was 50 degrees, you would be good to coat. However, if you go inside in a temperature controlled environment and now the temperature of the air is 70 degrees with the same 50% RH, suddenly the dew point is 50 degrees and you are at risk with your 50 degree slab. Usually, in a temperature controlled environment the concrete slab has been acclimated to a temperature close to the air temperature and RH is kept at a comfortable level, so dew point is rarely an issue, but it is a common mistake to watch the weather channel and use their outdoor related dew point for a temperature controlled environment. What do I need to measure the correct dew point where I am coating? There are many dew point meters on the market and choosing the right one in your price range is up to you. Or, if you use the table above, all you need is an instrument that measures humidity and temperature. Remember to make sure whatever you’re coating is at least 5 degrees above the dew point of the environment you are coating in. Do you have a flooring project, but don’t know where to start? Our Industrial Flooring Self-Assessment Tool can help you determine the ideal solution for your unique application. Tom Vath Jr. Tom Vath Jr. R&D Lab Technician at Protective Industrial Polymers Tom Vath, Jr. is an R&D Lab Technician at Protective Industrial Polymers, a company that manufactures high-performance resinous floor coatings for industrial manufacturing environments, which has a keen focus on developing unique solutions for managing electrostatic, microbial, chemical, explosion and safety risk concerns. He has nearly a decade of field, quality-control and lab experience. Tom works closely with PIP staff and application contractor partners to test product, develop samples, technical literature and training materials. You can follow Tom on LinkedIn, email him at, or contact Protective Industrial Polymers at 866-361-3331. Tom Vath Jr.
15 Amazing Historic Cities in Europe These beautiful medieval towns have stood the test of time. The medieval period was one of the most significant periods in the history of Europe. Gothic-themed buildings were constructed during this period. Unfortunately, the majority of the buildings and monuments have been destroyed after years of warfare, earthquakes, neglect, and vandalism. However, in some European cities, monuments have been perfectly preserved and attract millions of tourists who visit to admire the ancient medieval architecture. 15. Delft, Netherlands A panorama of the old buildings of Delft. Delft is a city in the province of South Holland in the Netherlands, located several miles north of Rotterdam. Delft is famous for its rich history and attracts thousands of tourists every year who are drawn to the well-preserved medieval buildings and monuments. Some of the monuments include the Old Church (Oude Kerk), the 13th century New Church (Nieuwe Kerk), and the Eastern Gate which was constructed in 1400. 14. Bergen, Norway A view of Bergen's historic buildings. Bergen is a city on the west coast of Norway. The city is Norway’s second-largest city with a population of over 278,000 residents. Bergen is surrounded by mountains and is also known as “the city of seven mountains.” The city was founded in 1070 by the Norwegian king Olav Kyrre and grew to become Norway’s capital city for many years. The city has several surviving buildings and monuments of the medieval period including the St. Mary’s Church which was built in the 12th century. 13. Chester, England A view of historic Chester. Chester is an old city located in Chesire, England and is also the most populous city in the region with a population of 332,200 residents. Chester is one of the few walled cities in England, and its city walls are among the best preserved in Europe. The city was founded in the 1st century AD as a Roman fort. The city has few medieval monuments with the majority of the buildings in Chester being from the Victorian Era. Some of the medieval monuments include Chester Castle as well as the Chester Racecourse of the 16th century. 12. Ptuj, Slovenia The cityscape of Ptuj. Ptuj is a small city in the northern part of Slovenia and has a population of about 18,000 residents. The city is one of the most visited cities in the country due to several well-preserved old monuments spread across the city which include the Parish Church which was constructed in the 14th century but was built upon an older, 9th-Century structure. Other famous ancient monuments include the Ptuj Castle, the Dominican monastery, and the Orpheus Monument. 11. Siena, Italy Siena, Italy. Siena is a city in Tuscany, Italy and is the provincial capital of the Italian province of Siena. While the city is relatively small with a population of just over 52,000 people, Siena is one of the most popular tourist destinations in the entire country with more than 163,000 visitors annually. The main attraction of the city is its rich history with the historic center of Siena which was inscribed as a UNESCO World Heritage Site. The city is home to some of the best-preserved pieces of medieval architecture including the Siena Cathedral which was built in the 12th century, the Piazza Salimbeni, and the historic Siena Synagogue. 10. Bruges, Belgium Beautiful Bruges, Belgium. Bruges is a city located in the Flemish region in Belgium and is the provincial capital of the West Flanders Province. The city has a population of about 120,000 residents and covers an area of 53.44 square miles. Bruges has a rich history, and the historic center of Bruges was inscribed as a UNESCO World Heritage Site in 2000 due to the many medieval monuments located in the city. Some of the key medieval attractions in the city include the Church of Our Lady and a 13th-century belfry which houses a municipal carillon. 9. Toledo, Spain The ancient Spanish city of Toledo. Toledo is a city in central Spain and is the provincial capital of the province of Toledo. The city has a rich history because it was once the court of the Holy Roman Emperor Charles V. The city has great religious and cultural significance and was once known as the “City of the Three Cultures” attributed to the co-existence of Jewish, Islamic, and Christian religions in the city over hundreds of years. The Old City of Toledo was listed as a UNESCO World Heritage Site in 1987 due to its perfectly preserved monuments including the medieval castle, Castillo de San Servando, the 13th-century Gothic Cathedral, and the Tomb of Saint Beatrice of Silva. 8. Tallinn, Estonia An example of a typical street in Tallinn's old town. Tallinn is the largest city in Estonia and is also the country’s capital. It is located on the Gulf of Finland and the city is among the most visited cities in Estonia attracting thousands of tourists annually. The city's old town is the main attraction which has some of the best-preserved medieval monuments in Europe. The Old City of Tallinn was established in the early 13th century and has numerous monuments which are several centuries old including the 16th century St. Olaf’s Church, the medieval Toompea Castle (which houses the Estonia National Assembly), and the Church of the Holy Ghost. 7. Obidos, Portugal The beautiful village of Obidos. Obidos is a Portuguese town located in the Oeste Subregion of Portugal. It is a small town with a population of only 3,100 residents and covers an area of 54.65 square miles. However, Obidos is one of the leading tourist destinations in Portugal with visitors being fascinated by the well-preserved medieval monuments. Some of the famous ancient monuments include the Obidos Castle as well as its streets which feature medieval Gothic architecture at its best. The Obidos Castle hosts a “Mediaeval Market” every July for two weeks where locals recreate a medieval theme and sport medieval style clothing. 6. Prague, Czechia Prague's old town and famous old clock. Prague is the largest city in the Czech Republic (now officially Czechia) and is also the nation’s capital city. The city is a popular tourist destination particularly due to its rich history receiving more than 6.4 million visitors per year. The old part of Prague known as the Praha is packed with numerous perfectly preserved monuments and buildings dating back several centuries including the Staronova Synagoga which was constructed in 1270, the Strahov Monastery which was established in 1149, as well as the world’s largest ancient castle, the Prague Castle. The Old Town of Prague is a UNESCO World Heritage Site and was inscribed in 1992. 5. Ohrid, Macedonia A view of Ohrid's ancient amphitheatre and historic city center. Ohrid is a city situated in the Lake Ohrid region of Macedonia. The city is the eighth largest city in Macedonia with a population of over 42,000 residents. The city is world-famous for its ancient monuments which are perfectly preserved including one of the oldest universities in the western hemisphere, the Plaosnik Monastery, and numerous churches. Ohrid was a religious center of ancient Macedonia with legends claiming that the city had 365 churches, one for each day of the year. 4. Dubrovnik, Croatia Dubrovnik, Croatia. Dubrovnik is a city located in the Dalmatia region in Croatia bordering the Adriatic Sea. With a population of only 42,615 people, Dubrovnik is a relatively small city. However, the city is one of the most famous tourist destinations in the Mediterranean region. The earliest recorded mention of the city was in 1189 in the Charter of Ban Kulin. The city gained prominence in the 16th century when it became the capital of the ancient republic of Ragusa. Several monuments and buildings from this period still exist including the Big Onofrio’s Fountain as well as the world’s oldest Arboretum, the Arboretum Trsteno. 3. Torun, Poland The old town of Torun, Poland. Torun is a Polish city situated in the northern region of the country and is the capital of the Kuyavian-Pomeranian Voivodeship. The city is one of the oldest cities in Poland with Torun being established in the early 13th century. The old part of the town was listed as a UNESCO World Heritage Site in 1997 and became one among the Pomnik historii or official national Historic Monuments of Poland on September 16th, 1994. Torun is a popular tourist attraction which visitors can get a feel of the mediaeval era in the old city. Some key attractions in the city include the old town hall, the Torun Castle, and the Cathedral Basilica of St. John the Baptist and St. John the Evangelist. 2. Carcassonne, France The old town of Carcassonne. Carcassonne is a town located in the Occitanie region in France. The town is relatively small with a population of about 48,000 people. However, Carcassonne is world-famous as it is one of the best preserved ancient towns in Europe. Inhabited since the Neolithic period, Carcassonne is famed for its medieval buildings including the Cite de Carcassonne, a fortress which is a UNESCO World Heritage Site. Thousands of tourists visit Carcassonne to view the medieval architecture in the ancient fortified city. Other key attractions in the town include the 12th-Century Basilica of Saints Nazarius and Celsus and the 13th-Century Carcassonne Cathedral. 1. Nordlingen, Germany Nordlingen, Germany. Nordlingen is a German town situated in Swabia, Bavaria and is one of the most famous old towns in the country. The town is among the earliest habited urban centers in Europe with Nordlingen first being mentioned in 898 AD making the town over a thousand years old. The city is perfectly preserved with many buildings in the city which are several centuries old. One such building is the town hall whose construction is traced back to the 13th century. The city is also one of only three in Germany to have a medieval city wall. More in Travel
If you are having trouble swallowing, pain during swallowing, chronic heartburn, or chest pain, your doctor may order an esophageal manometry test to discover the source of your problem. The test measures the ability of the esophagus to move food down in to the stomach and also the function of the lower esophageal sphincter (a valve that prevents the acid in your stomach from coming back up into your esophagus). Before testing you should discuss any medications, including vitamins, you take with your doctor and be sure to follow the provided instructions. During the test, you will be given some numbing medicine to minimize discomfort, and a small tube will be inserted through your nose and down your esophagus into your stomach. Then the tube is slowly removed; during the removal your doctor will direct you to swallow at specific intervals. The strength of the lower esophageal sphincter is measured as well as the strength of the muscle contractions along the esophagus. The tube is removed at the end of the test and you should be able to resume normal activities.
Tuesday, April 5, 2011 What was she thinking? Inside the head of a historical character A common ‘truisim’ that historical novelists maintain is that, whatever the era, people still essentially love, hate, grieve, etc. in the same ways. That’s true, of course, but the way we express those feelings, and even the way we think about things is regulated to an extent, I contend, by our culture. These differences exist in our very own time – why else are we looking with respect and awe at the dignified behaviour of the Japanese people in the wake of such terrible disasters? Closer to home (for me), having moved from London to the American South, I often encounter thought processes and assumptions that mystify me (and I’m sure I return the ‘compliment’). In teaching early American literature, one thing I have to impress upon my students is that they have to try to get out of the habit of approaching works with a post-Romantic mind. A simple example I give is our widespread use of the question, “How do you feel?” Quite frankly, this continual focus on the self would not fly for seventeenth century Calvinists, who are community-, not individual- oriented. So how do we reflect what our characters might be thinking, and is it OK to have that ‘rebel’ with modern sensibilities? Spending time with your nose in the popular books of the day, as I suggested in a previous blog, is a good way to pick up the sensibilities of the period. Diaries, letters and journals are a help, bearing in mind that people may still create personas for what were often seen as semi-public works. Poetry has a wonderful way of capturing emotions and ideas in a nutshell. If you work in an era where newspapers exist, you have a goldmine of opinion to gather. You must first and foremost know your period, and then you’ll feel more confident about guessing what your character may or may not think. Can you make your character a freethinker and still sound authentic? Of course. There have always been those who think outside the cultural box and are not afraid to hide it; there must also be countless others who think but do not dare to act. But still, those thoughts come from within a particular culture. An example that comes to mind is a YA novel about the Salem witch trials that I recently reviewed. Something about the young heroine just struck me as inauthentic – while I accepted the premise she was a rebel, I found it hard to swallow that she questioned absolutely everything about the world around her, from wearing stays to the existence of the devil. When I did a little research on the author’s website, I found that she had been undergoing her own spiritual crisis. Suddenly, my nagging doubts became crystal clear: the author had clearly transposed her own feelings onto her character, and, for me at least, it just did not fit. So this, I think, is the key. A character who has nothing in common with his culture is probably not authentic. This is true even for the greatest rebels. Thus an eighteenth century atheist would usually still call himself a Deist; Oscar Wilde spoke only in veiled terms of “the love that dared not speak its name” (a phrase he borrowed from his lover, by the way); George Elliot openly lived with George Henry Lewes, but she was a slave to nineteenth century notions of duty (and did of course marry her second partner). In the next post, I’ll list some recommended secondary reading for getting inside the heads of your characters. Suggestions welcome! 1. Interesting post, Susan. I love reading the diaries I've bought written by Victorian women. They are so helpful for getting into the spirit of the times. 2. I think you make a good point Susan. Our society does influence us whether one wants to admit it or not. I think being true to your audience and the character is a fine line to draw for historical novelists. How much authenticity is too much for modern sensibilities? 3. How interesting Susan. There are quite a few historical romances that have kick ass heroines ignoring the mores and constraints of the society in which they live, unfortunately. I reviewed a book which had a strong Victorian heroine who made only small inroads into freeing herself from those constraints. It was believable enough for me to enjoy it. And Only To Deceive by Tasha Alexander. 4. I made my hero the epitome of 17th Century man in his attitude and behaviour - and my critiquers hated him for his chauvinism, and his lack of emotion. I'll aim for a middle ground next time! 5. Religion was important in the lives of those born in previous centuries. Governments were so much harsher, and money so much harder to come by. How we'd react such harsh lives would dictate how we thought about things, don't you think? So maybe our easier lives only mask our real feelings? Maybe I'm not explaining my self very well! 6. Rebels. Yes, they do exist. My favourite medieval author, Wolfram von Eschenbach, was way out of step with his contemporaries when it came to the themes of his romances (the brotherhood of man, no matter what race or religion). But look how he fit those ideas into story lines that are so typically 12th century! He didn't break out of the box, just bent its sides a little. While getting into a character's head is essential, I think Anita makes a good point. As authors of historicals, these days we're treading a thin line between authenticity and political correctness. We're also stuck with what readers believe to be correct for a period, whether or not it actually is accurate. Having said that though, I think we still have some wiggle room to create the kind of characters our readers today crave while maintaining some level of authenticity. + Male characters can start out as domineering, cold, unfeeling, insensensitive, etc., and through their interaction with the heroine (if its a romance) or the things that happen to them, change. + By the way, the cold, unfeeling stuff doesn't start until the Victorian Era. Men before that were allowed to show their emotions. But most men are still boys, even as adults, and let's face it, boys are callous. The sensitive male that today's romance reader responds to is a figment of her imagination, for the most part (and yes, they do exist, but not as extensively as we'd like.) + There are rebels in every society -- or those whose thinking is more advanced. But they also still carry with them a pile of baggage from their own time period. They're usually only out-of-synch in one aspect of their lives. + When people's thinking goes against social norms, they have to pay the cost. This includes self-doubts. (Which can add to the black moment.) We read historicals not to be transported to some alien realm, but rather to find in the experiences of others in the past validation of our own feelings and experiences. The trick for the historical author is finding the connection between the genuine experience of the past and the reader's experience today. 7. Thank you for opening up the subject. I suppose we have to tread that fine line between authenticity and our own era's perception of a historical period - a thing you all do so well!
Nerdy Fact #1434: Wonder Woman was originally based on two women: the wife of creator William Marston and one of his former students that both he and his wife had sexual encounters with. How about you actually name ‘em? Elizabeth Holloway Marston and Olive Byrne were among a number of women who contributed to the original Wonder Woman, and they’re fascinating people in their own right. Elizabeth Holloway Marston was a brilliant woman. She earned three university degrees in psychology and law at a time when few women received any tertiary education. She was a successful career woman who assisted her husband with his work and was frequently the breadwinner of the family. The main reason she was able to continue working after having children? Olive Byrne, who was not simply a casual “sexual encounter”, but the Marstons’ lover and life partner. To enable Elizabeth to work, Olive stayed at home and raised both her and Elizabeth’s children. She also wrote for Family Circle and contributed to Marston’s research. Elizabeth is credited with pushing her husband to create a female superhero, and after his death she worked hard to preserve his vision for the character, urging DC to employ her as the comic’s editor (she was ignored). Wonder Woman’s bracelet’s are Olive’s bracelets: Olive was known for wearing a pair of wide silver bracelets, and Marston had these in mind when he envisioned Diana’s bullet-deflecting accessories. Marston died in 1947, but Elizabeth and Olive continued to live together until the end of their lives. Wait. Clarification please. Are you telling me that the creator of Wonder WOMAN WAS IN A POLY-AMOROUS RELATIONSHIP? Yep! They were in a poly relationship and had four children together, two by Elizabeth and two by Olive. (And for those who’ve asked about sources, the Marstons’ story is covered in detail in The Secret History of Wonder Woman by Jill Lepore and Wonder Woman: The Complete History by Les Daniels) Leave a Reply You are commenting using your account. Log Out / Change ) Twitter picture Facebook photo Google+ photo Connecting to %s
John Turner obituary He developed theories of social change and intergroup behaviour John Turner John Turner began to appreciate the power of groups through workplace union activities John Turner obituary He developed theories of social change and intergroup behaviour How do individual minds make possible groups and society, and how does society change individual minds? For four decades, the social psychologist John Turner, who has died aged 63 after a lengthy illness, confronted his discipline's central challenge. The simplicity of Margaret Thatcher's 1987 assertion about society – "There is no such thing! There are individual men and women and there are families" – is politically and/or scientifically attractive to some. Others favour a no-fault social determinism, in which the individual mind falls helpless victim to social pressure. John's immense contribution lay in his development of a precise, testable and now strongly supported theory that explains how mind and society create each other. In the research that led to his PhD (1975) at Bristol University, he was supervised by Henri Tajfel, who had observed that once people make a division into categories, they tend to emphasise the similarities within groups, and the dissimilarities between them. Together, the two developed social identity theory, pointing to people's tendency to categorise themselves into groups in order to gain a greater sense of who they are, with consequences for self-esteem, prejudice and stereotyping. These insights generated a new psychology of intergroup behaviour and social change. Now it dominates the field, and is used to address everything from the Arab spring to football hooliganism and anti-cuts protests. Lecturing posts followed at Bristol, and in 1982-83 John was a scholar at the Institute for Advanced Study in Princeton, New Jersey. He moved to Macquarie University in Sydney, and then, in 1990, to the Australian National University in Canberra. There, he was professor of psychology until retiring as emeritus in 2008. His book Rediscovering the Social Group (1987), produced in collaboration with his PhD students Michael Hogg, Penny Oakes (his second wife), Steve Reicher and Margaret Wetherell, explores the relationship between the individuality of the person and the social reality of group identity and action. John made a characteristic break with received wisdom in insisting that rather than the group being a distortion and simplification of people's individuality, it reflects the true nature of humanity. "We" is often a more useful and valid expression of self than "I". Stereotyping and Social Reality (1994), written with Penny Oakes and Alex Haslam, explores the radical implication that, far from being unresponsive caricatures, our stereotypes of self and others reflect our relationships with those others and vary as social reality changes. "We Londoners", for example, can mean different things – and self-categorisation as a Londoner engenders different norms and behaviour – in peacetime and war, and if London is compared with another British city rather than the capital of another country. John showed that shared social identity is necessary to social co-operation, cohesiveness and leadership. Only when we come to see another person as "us" rather than "them" are we motivated to help, collaborate with, and follow them. The route to sustainable social and behavioural change – in health, in dysfunctional communities, in the planet's survival – is through the group, and the crafting of relevant identities. As he explained in one of his last major papers, it is through working together in shared identity that we create our own fate. Born in south London, John was raised in a small council flat, the eldest of eight children and the only one educated beyond secondary school. At the age of 11, he gained a scholarship to Wilson's grammar school in Camberwell. While his working-class background did little to prepare him for such an environment, he excelled at Latin and English. Nor did he find it easy at Sussex University (1965-71). He dropped out several times, going home to help his dad fit windows in tower blocks around London, and then got a job in a Fleet Street printing factory. Through involvement in workplace trade union activities, he began to appreciate the power of groups, both politically and personally. Reinvigorated, he completed his social psychology degree and went on to Bristol. A charismatic and charming figure, John drew large numbers of students to his cause. Immensely knowledgable about politics and history, he was a congenial rebel, both passionate and principled. He changed the landscape of social psychology, in part through his students, who now occupy senior posts around the globe, and in part through inspiring social scientists to apply his ideas in fields as diverse as politics, economics, geography and theology. However, John could be difficult to deal with. For him, academic rituals of politeness did not trump getting it right. He was involved in a battle of ideas with real political consequences, and did not tolerate the dilution or misuse of his contributions. With this intellectual intensity went a troubled personal life. John found people a source of great joy but also of great pain, and was married and divorced three times. His 20-year relationship with Penny produced two daughters, Jane and Isobel, who survive him. John Charles Turner, social psychologist, born 7 September 1947; died 24 July 2011
Definition - What does So'ham mean? So'ham, or So'hum, is a Hindu mantra that can be translated as "I am He/That." It is derived from the Sanskrit, Sah, meaning "He," and Aham, meaning "I." It is a universal and natural mantra because it is present within everybody as the breath, with the sound of "so" during inhalation and "ham" during exhalation. As such, So'ham is a mantra that is chanted just by concentrating on the breath because the breath chants it naturally. There is also an inverted version of this mantra: hamsa, meaning "white swan," which stands for the inner Self. Yogapedia explains So'ham The So'ham mantra has been used for thousands of years to identify oneself with the Universal Reality. In Tantra and Kriya yoga, it is known as ajapa japa - a constant awareness of the mantra, without chanting it. It is also believed that So'hum is an answer to Koham, meaning "Who am I?" The universe answers this question with So'hum, communicating that "You are the same as I am." As a combination of Sah and Aham, So'hum also symbolizes the power of Shiva and Shakti, forming the male and female powers of the universe. Share this:
Governor Macquarie's Rum Hospital 1850s sketch of the Rum Hospital The rum trade was influential in the new colony. When government funds were insufficient to build a new hospital, Governor Macquarie persuaded a consortium of businessmen to undertake the task. In return they were granted a monopoly on rum imports. The contract allowed them to import 45,000 gallons of rum, later increased to 60,000 gallons. Convict labour was also provided for the building works. The Rum Hospital, in Macquarie Street, accepted its first convict patients in 1816.
Accessibility. Accessibility is the ease with which a person may enter a library, gain access to its online systems, use its resources, and obtain needed information regardless of format (Reitz 2010). Desktop computer. A desktop computer is a personal computer or any microcomputer designed for individual use, usually in a personal workspace or in travel, consisting of a CPU and associated peripheral devices. Laptops are small, portable battery-operated personal computers (Reitz 2010). Interface. An interface is the point or process that joins two components of a data processing system, for example, the screen display that functions as intermediary between a software program and its human users (Reitz 2010). Mobile device. A mobile device is a wireless handheld device or a durable, lightweight computer small enough to be held comfortably in the hand, designed to be used in a wireless network for applications requiring mobility (Reitz 2010). M-learning or Mobile learning. Any sort of learning that happens when the learner is not at a fixed, predetermined location, or learning that happens when the learner takes advantage of the learning opportunities offered by mobile technologies (Wikipedia contributors). M-library or Mobile library. M-library is a short form term to denote mobile library. A mobile library is a library in mobile digital form (Hahn 2008). Mobile technology. Mobile technology is a collective term used to describe the various types of cellular communication technology (Wikipedia contributors). Mobile web. The World Wide Web which as accessed through a mobile device ranging from a cellular phone to an iPod Touch mobile app (Kroski 2011). Website. A group of related, interlinked Web pages installed on a Web server and accessible 24 hours a day to Internet users equipped with browser software (Reitz 2010).
Health Benefits of Proper Hydration You know that drinking water is good for you, but did you know that every system in your body depends on water? Here are 10 reasons why drinking water is good for you and why you should make drinking 8-10 glasses of water part of your daily routine. 1. Get healthy skin. Drinking water moisturizes your skin from the inside out. Water is essential to maintaining elasticity and suppleness and helps prevent dryness. 2. Lose weight. Increased water consumption can help you control weight by preventing you from confusing hunger with thirst. Water will also keep your body systems working properly, including metabolism and digestion, and give you the energy (and hydration) necessary for exercise. 3. Flush toxins. By helping to flush toxins, appropriate water intake lessens the burden on your kidneys and liver. 4. Reduce your risk of a heart attack. Researchers at Loma Linda University in California studied more glasses a day. 5. Cushion and lube your joints and muscles. Water makes up a large part of the fluid that lubricates and cushions your joints and muscles. Drinking water before, during, and after exercise can also help reduce muscle cramping and premature fatigue. Home Page Site Map Click Here To Find Out More Discover the Power of Health Through Hydration!
Saturday - Sep 23, 2017 Binding Stone To Concrete: Impossible, Right? Wrong The idea of binding concrete to stone might inspire fear in the hearts of even the most experienced builders. It can seem impossible to bind concrete and stone because of the physical composition of concrete and the fact that stone is porous, meaning it is covered in little holes that create an irregular surface. What techniques are there to provide a solution in this situation? Two-stage Epoxy Solutions The majority of products on the market are epoxy adhesives, which usually contain two components that have to be combined to bind the stone and concrete together. The method of application involves sanding down the surfaces to remove any irregular facets. This is followed by applying a layer of the first chemical, usually polyester- or styrene-based, to both faces, pressing them together and waiting, and then repeating with the second preparation, the epoxy adhesive. Such two-stage industrial adhesives have the downside of taking a long time to set – sometimes up to a week. The setting and curing process can also fail due to temperature changes or movement. This makes them rather inflexible in a construction environment, where different materials respond differently to temperature, expanding and contracting at different rates. Additionally, if the two components aren’t added in the exact quantities specified, the adhesive effect will fail, making this solution frustratingly temperamental. One-stage Adhesive Solutions More recent developments in adhesive technology have led to single-stage concrete-stone binding solutions. These products are usually polymer-based and bond the two surfaces together far more quickly. This adhesive solution also has the benefit of compensating for the varying expansion rates of different materials, providing flexibility alongside a permanent bond. Polymer-based adhesives produced by companies such as ct1 can also be applied in cold conditions or on damp surfaces, although this can reduce the strength of the fixing in vertical applications. When used carefully, however, polymer-based solutions can save time and work more effectively. The chemical composition also allows for a far greater range of applications. Uses in construction include the fixing of stone lintels around windows, where the fast-setting effect helps reduce labour time. Increasingly popular stone facades are traditionally time-consuming constructions, but polymer-based one-stage applications help cut down the work time required. It is expected that more and more construction companies will be applying them in new builds over the next few years.
Game Development Reference In-Depth Information angles internally, and those that don't still often represent orientations to the user as Euler angles. Unfortunately Euler angles are almost useless for our needs. We can see this by looking at some of the implications of working with them. You can follow this through by making a set of axes with your hand (as described in section 2.1.1), re- membering that your imaginary object is facing in the same direction as your palm— along the Z axis. Imagine we first perform a pitch, by 30 or so. The object now has its nose up in the air. Now perform a yaw by about the same amount. Notice that the yaw axis is no longer pointing up: when we pitched the object, the yaw axis also moved. Remember where the object is pointing. Now start again, but perform the yaw first, then the pitch. The object will be in a slightly different position. What does this mean? If we have a rotation vector like 0 . 3 0 . 4 0 . 1 in what order do we perform the rotations? The result may be different for each or- der. What is more, because the order is crucial, we can't simply use regular vector mathematics to combine rotations. In particular, r 1 · r 2 = r 2 · r 1 where r 1 and r 2 are two rotations. In case you think that the problem is caused by moving the rotation axes around (i.e., keeping them welded to the object rather than fixed in the world), try it the other way. Not only does the same problem still occur, but now we have another issue—gimbal lock. Gimbal lock occurs when we rotate an object such that what started as one axis now aligns with another. For example, assume we're applying the rotations in the order X, then Y, then Z. If we yaw around by 90 (i.e., no X rotation, 90 Y rotation), the front of the object is now pointing in the negative X direction. Say we wanted to have the object roll slightly now (roll from its own point of view). We can't do that: the axis we need (the local Z axis) is now pointing in the X direction, and we've already passed the point of applying X rotations. So maybe we should have applied a little bit of X rotation first before rotating in the Y direction. Try it: you can't do it. For this particular problem we could perform the rotations in a different order—ZYX, for example. This would solve the problem for the previous example, but there'd be new orientations that this ordering couldn't represent. Once rotations of around 90 come into play, we can't achieve all desired orientations with a combination of Euler angles. This is called “gimbal lock.” There are some ways to mitigate the problem, by using combinations of axes, Alternatively we can repeat rotations around some axes. There are a lot of different Search Nedrilad :: Custom Search
Presentation is loading. Please wait. Presentation is loading. Please wait. English Pronunciation Practice 英语语音技巧突破 Similar presentations Presentation on theme: "English Pronunciation Practice 英语语音技巧突破"— Presentation transcript: 1 English Pronunciation Practice 英语语音技巧突破 Lecture 4 Liaison and Assimilation 连读与同化 2 Liaison(or Sound-linking) 连音 3 Liaison In English one word is not separated from another by pausing or hesitating; the end of one word flows straight on to the beginning of the next , e.g. first of all /'fә:st◡ әv ◡ 'ɔ:l/ some of us /'sΛm◡ әv◡ әs/ The linking of words in connected speech may be divided into the following types: 4 1.consonant + vowel Examples: put it on /'puti'tɔn/ look at it /'lukәtit/ think of it /'θiŋkәvit / 5 2.vowel + vowel a) ending with an unrounded-lip sound, add a /j/ sound. Examples: the other /ði◡j◡'Λðә/ he is my uncle. /hi: ◡j◡ iz mai◡j◡ 'Λŋkl/ she ate some./ ʃ i: ◡j◡әt sәm/ 6 b) ending with a rounded-lip sound, add a /w/ sound. Examples: two others /'tu: ◡w◡'Λðәz/ do it /'du: ◡w◡it/ how old /'hau◡w◡'әuld/ 7 3. r-linking 3) When a word ending with “r” or “re” goes before a word beginning with a vowel sound /r/ is usually pronounced as a link. Examples: for ages /fәr 'eiʤiz/ her own /hә:r 'әun/ share out /'ʃεә r 'aut/ far away /'fa:rә 'wei/ 8 However, there are special circumstances in which a final “r” is silent even when the following word begins with a vowel. a) When there is a /r/ in the same syllable, e.g. a roar of laughter /ә 'rɔ : әv 'la:ftә/ a rare animal /ә 'rεә 'æniml/ nearer and nearer /'niәrә әn 'niәrә/ b) when a pause is permissible between the two words (even if no pause is actually made) .e.g. He opened the door and walked in. /hi: 'әupnd ðә 'dɔ: әnd 'wɔ:kt in/ 9 4) some English people link a final /ә/ or even /a:/ and /ɔ:/ to an initial vowel in the same group by inserting a /r/ sound even if there is no letter r in the spelling. The /r/ sound added in this way is called “intrusive r”. Its existence should be known but not imitated. Examples: China and Japan /'ʧainәr әn(d) ʤә'pæn/ drama and music /'dra:mәr әn(d) 'mju:zik/ law and order /'lɔ:r әn(d) 'ɔ:dә/ I saw a man /ai 'sɔ:r ә 'mæn/ 10 Assimilation In connected speech, sounds, under the influence of their neighbors, are replaced by other sounds. Sometimes two neighboring sounds influence each other and are replaced by a third sound which is different from both the original sounds. This process is called assimilation. 11 3 types of assimilation Progressive(顺同化) Regressive(逆同化) Reciprocal, or double(相互同化) 12 Progressive The assimilated sound is influenced by the preceding sound. For example: What’s this? /'wɔts 'ðis/ 13 Attention ! The strong voiceless consonant of a pair replaces the weak voiced consonant in the closely connected speech, but do not make it a general rule to replace the weak voiced consonant by the strong voiceless in other cases. A voiceless plosive (爆破音) or fricative (摩擦音) is not assimilated to a voiced plosive or fricative which follows it. 14 Examples： not very /'nɔt 'veri/, not /'nɔd 'veri/ black door /'blæk 'dɔ:/, not /'blæg 'dɔ:/ this boy /'ðis 'bɔi/, not /'ðiz 'bɔi/ if they come /'if ðei 'kΛm/, not /'iv ðei 'kΛm/ 15 Regressive The preceding sound is influenced by the one following it. For example,: /z/ news /nju:z/ /s/ newspaper /nju:speipә/ 16 Reciprocal or Double Assimilation the neighboring sounds influence each other. For example: /t/ /w/ twenty /twenti/ 17 The usage of assimilation Assimilation changing the work of vocal cords(声带). Examples: /z/→ /s/ is/iz/ It’s easy./its 'i:zi/ has/hæz/ What’s happened? /'wɔts 'hæpnd/ used/ju:zd/ I used to. /ai 'ju:st tu/ 18 2. Assimilation changing the position of the lips: Before the bilabial sounds/m,p,b/,/n,t,d/ change to /m,p,b/ respectively. For example: in /in/ in bed /im 'bed/ ten/ten/ ten minutes /'tem 'minits/ don’t/dәunt/don’t be late./'dәump bi 'leit/ good/gud/ good-bye/gub bai/ 19 3. Assimilation changing the place of articulation: Before the velar sounds /k,g/, /n,t,d/ change to /ŋ,k,g/ in /iŋ/ in case /iŋ 'keis/ don’t /dәunt/ I don’t care. /ai 'dәuŋk 'kεә/ good /gud/ good girl /gug 'gә:l/ 20 b) Before /ʃ,j/, /s,z/ change to /ʃ,ʒ / respectively. this /ðis/ this shape /'ðiʃ'ʃeip/ this year /'ðiʃ'jiә/ has /hæz/ has she come /'hæʒ ʃi 'kΛm/ where’s yours /'wεәʒ 'jɔ:z/ 21 c) The combinations of sounds /tj/ and /dj/ have changed into /ʧ/and/ʤ /in an unstressed syllable: education /,eʤukei'ʃn/ not/,edjukei'ʃn/ situation /,siʧuei'ʃn/ not /,sitjuei'ʃn/ I’m glad to meet you. /aim 'gæld tә mi:ʧu/ Did you like it? /'diʤu 'laik it/ Download ppt "English Pronunciation Practice 英语语音技巧突破" Similar presentations Ads by Google
Saturday, February 22, 2014 Ways to count the dead By Persis Karim, poet and professor at San Jose State University "Keeping track of the Iraqi death toll isn't the job of the United States," a student said, "and besides, how would we count the dead?" Take their limbs strewn about the streets - multiply by a thousand and one. Ask everyone in Baghdad who has lost a brother. Cousin. Sister. Child - to speak their name in a recorder. Go to every school, stand at the front of the class, take roll: for every empty desk, at least two dead. Find every shop that sells cigarettes - ask how many more cartons they've sold this year. Go to the bus station and buy ten tickets - offer them free to anyone who wants to leave. Go see the coffin-maker. Ask how much cedar and pine he's ordered this month. The dead don't require much. They don't speak in numbers or tongues, they lie silent waiting- to be counted. The War- Painting by Taha Malasi 1. It is worry some. How do we teach the value of life to people on both the sides? I don't think I will find an answer in my life time. There is beast in the form of humans on both the sides. Here, we are hearing that a lot of times, two sects of the same religion are at war with each other. Also we are told that revolutionary groups instigate violence and get retaliated by the governments in each of the suffering countries. We are here making a living, working hard and raising kids in spite of hardships. The difference is that we try to pick up the pieces after being discriminated against every step of the way, yet try not to give up. We do begin to see the blessings. I hope that some day people in every country become strong enough to see clearly through storms that one day the sky will be blue and sun will come out. How ever they will have to look and see and find out what they can do. 2. Maybe they cannot be counted. But least, they can be and should be respected. 3. I second Aiza :/ This is heartbreaking :( 4. Oh God this is sad. There are a lot more ways. Millions of them. And thoughts are running in my mind to write of all the ways to count dead. 5. This poem is very powerful and moving. War is senseless. I thought you had written this one at first. I see now it was written by a professor, but I have been reading your work enough to know that I wouldn't have been surprised to see something as good as this come out of your pen. I have been MIA for a while now, but I'm slowly returning to my blogging world. Looking forward to reading more of your recent posts! 6. This is actually so hard to read, for all the emotions those words transfers to your soul. Really well written. Contact Form Email * Message *
world's largest Pirate Myths. Pirate Myths. There are many different myths surrounding pirates. Did they really have parrots? And peg legs? And hooks? Below find some debunkers of these myths! Stories such as “Treasure Island” popularized the idea that pirates walked around with parrots all the time. In actuality, this probably isn’t true. Pirates seem to be much too practical to be concerned with pets and parrots would cause a mess on the ship (and the shoulder’s of the Captain!) A parrot might interfere with work being done on the ship or get lost at sea in times of hard voyages. Although this myth is exaggerated in most people’s minds, there is a bit of truth to it. If a pirate was injured in the leg, sometimes the only option was to amputate. Doctors were not usually part of the crew on a pirate’s ship and so it was usually the ship’s cook that was called to perform the operation. However these operations weren’t usually successful as the inexperienced cook could not usually stop the bleeding. The pirate might also die from infection. Later, a substitute would be required for the missing leg. This was usually something that could be found on the ship such as a long piece of wood. The common idea that pirates had hooks on one of their hands probably stemmed from “Peter Pan.” But again, there is some truth to the thought. Pirates would often lose a hand in battle and want to fashion something that could be useful around the ship as well as in future battles. A hook was a good substitute as pirates could hold onto things when working aboard as well it became another weapon for battle. A hook could easily be fashioned by fitting a wooden bowl around the stump. A hook could be constructed with extra metal lying around the ship and this could be fastened to the bowl. The contraption could be attached to the arm with leather. Pirate Myths mythology. The myth of Pirate Myths. Page Sponsored By: Convert AVI to MPEG
Browse Definitions: Contributor(s): Cesar Souza Liedke Humanware is hardware and software that emphasizes user capability and empowerment and the design of the user interface. The process of building humanware generally consists of these steps: 1. Define users (age, mindset, environmental context, previous product experience and expectations, and so forth) and what they really want to do 2. Identify tasks they will need to do or capabilities they will want 3. Specify usability objectives (if possible, these should be measurable, such as how long to do something or how many mouse clicks to get to a specified task point) for each task or capability 4. Build a prototype of the user interface (it can be a paper or simulated prototype if time is short) 5. Test and verify or correct the prototype 6. Provide the prototype and usability objectives to the program designers and coders 7. Test the code against the prototype and objectives and, if necessary, redesign or recode the software 8. Test the product with users or valid test subjects and revise as necessary 9. Get feedback from users and continually improve the product Philips Research uses the term for both software and hardware that is specially designed to interact with users, including its speech synthesis and speech recognition microchips. This was last updated in October 2005 Start the conversation Send me notifications when other members comment. Please create a username to comment. File Extensions and File Formats Powered by: • pure risk (absolute risk) • risk assessment • audit program (audit plan) • insider threat • ransomware • hacker • business continuity and disaster recovery (BCDR) • business continuity plan (BCP) • call tree • 3D XPoint • RRAM or ReRAM (resistive RAM) • Google Cloud Storage • RESTful API • cloud storage infrastructure
Total Number of words made out of Fusile =50 Fusile is a 6 letter medium Word starting with F and ending with E. Below are Total 50 words made out of this word. Also see:- Words starting with Fusile 5 letter Words made out of fusile 1). fuels 2). flies 3). files 4). fusel 5). fusil 6). flues 7). lieus 8). ileus 4 letter Words made out of fusile 1). lieu 2). lies 3). isle 4). fuse 5). lief 6). leis 7). fuel 8). flus 9). fils 10). slue 11). self 12). seif 13). feus 14). lues 15). file 16). life 17). flue 3 letter Words made out of fusile 1). sei 2). lis 3). sel 4). sue 5). use 6). lie 7). efs 8). elf 9). els 10). feu 11). fie 12). fil 13). flu 14). lei 15). ifs 16). leu 2 letter Words made out of fusile us el si ef es is if li Fusile Meaning :- Same as Fusil- a. Note There are 3 vowel letters and 3 consonant letters in the word fusile. F is 6th, U is 21th, S is 19th, I is 9th, L is 12th, E is 5th, Letter of Alphabet series. f, fu, fus, e, le, ile, f uf sf if lf e e le ie se ue f
National Potato Day 2017 Why is it important to celebrate National Potato Day? After wheat, corn, rice and sugarcane, potatoes occupy fifth position in food crops for its popularity and consumption. Because of its delicious taste and high nutritional value, people from all over the world include this in their diet almost every day. With an aim to highlight the importance of its health benefits, every year potato lovers celebrate National potato day on August 19. Even though potato has some thousands of years of heritage history, it had its first recognition at National Organic's 'commitment to biodiversity' event sixteen years back in UK. Why there is a need for potato day celebrations? Despite being delicious with high nutritional and medicinal values, potatoes have less importance among vegetables due to its high dietary carbohydrate content. Moreover, as potatoes are considerably cheap and abundantly available, this vegetable is losing its importance day by day. National potato day highlights the significance of world famous spuds and promotes its consumption in healthy diet forms. How to celebrate National Potato day: Lot of potato lovers from the community come together, form a group, and celebrate this festival with hundreds of varieties of potato spuds. National potato day provides a great opportunity for the farmers to understand the old heritage varieties of potatoes from different places and get awareness on new cultivating methods. Apart from getting exposed to several best varieties of potato seeds on National potato day, you can also enjoy some endless potato cuisine items such as – baked potato, mashed potato, home fries, French fries, potato puddings etc. Being a part of such community related potato event is really lot of fun for both small children as well as adults. National Potato Day 2017
Effective Speech Writing The secret to effective speech writing is being concise - saying the most you can in the fewest words. If I asked you to write a list of memorable speeches, chances are that the Gettysburg Address would appear on that list. So it's quite remarkable to consider that that particular speech is less than 300 words long (272 to be precise!). In only 272 words, Lincoln was able to convey sorrow, respect, patriotism, determination, hope and more... an outstanding feat, and one that few of us could hope to achieve! But we can take away an important lesson from the Gettysburg Address in terms of effective speech writing, and that's that conciseness matters. Effective speech writing Unnecessary 'waffle' in a speech not only bores your listeners, it can also confuse your message. Aside from its historical context, Lincoln's speech was so memorable because it was tightly focused. To deliver a message that really makes an impact, you need to make sure that your speech uses the fewest words possible, and that each words supports your overall theme. Effective Speech Writing - How to Keep Your Presentation Concise (and your audience interested!) Use everyday language that's easy to understand Compare these - which do YOU think is better? "The purpose of my presentation here today is to ponder the wisdom of permitting casual attire in our workplace, rather than the high standard of dress currently expected." "Today I'd like to talk about the campaign to change the office dress code." The two sentences are saying essentially the same thing - one uses 28 words, the other only 14! Keep your sentences short Once you've written your speech, go back through it and look for lo-o-ng sentences that could easily be divided into two (or more!). "The current climate is one of uncertainty, with more and more people out of work because of the closure of the largest factory in the area." "The current climate is one of uncertainty. More and more people are out of work because of the closure of the largest factory in the area." See how the second example has more impact than the first? Shorten your phrases We use overly long phrases so often, that we don't even realize we're doing it! For example... "In a situation in which the front door is locked, you may enter via the side gate." Could be... "When the front door is locked, you may enter via the side gate." "In light of the fact that our guests were disappointed by the lack of choice, we have changed the menu." Could be... "Because our guests were disappointed by the lack of choice, we have changed the menu." "It is necessary for us to all abide by the rules." Could be... "We must all abide by the rules." Keep on topic! The tendency to 'waffle' comes in when we deviate from the subject at hand. When you are editing your work, check that everything you have written relates in a clear way to the main message of your speech. Avoid the passive voice It tends to make sentences longer, more confusing, and greatly reduces their impact. Not sure what this means? With the passive voice, the subject of a sentence becomes the object (or is missing altogether). For example... The artist displayed his painting. (Active) The painting was displayed by the artist. (Passive) The active sentence has 5 words - the passive has 7! And the overall message is simply clearer in the active voice. If you struggle to identify the passive voice in your work, then I highly recommend the Hemingway App (it's free!). Hemingway was famed for his simple, unadorned use of words and the app will help you adopt this style in your own writing. Use visual aids There is much truth in the old idiom 'a picture is worth a thousand words'. Pie charts and diagrams can help you present a great deal of information - that would otherwise be boring! - in a very easy-to-understand way. Avoid being TOO brief... It's very important that your speech includes all the key points. This is why I recommend that you DON'T worry about being concise in your initial draft - instead, write freely, then edit your words. That way, you will see that all the main points are there and you can focus on paring away the unnecessary words and details. And if there are no time constraints on the length of your speech, remember the wise words of the Academy award winning actor Sir John Mills - 'Be sincere, be brief, then be seated.' Recommend This Page! Finding Good Speech Topics Home page Our Facebook Page Like Best Speech Topics? Click the like button and let everyone know!
Oil spill may slow grain exports That could affect grain prices for the United States and overseas markets, according to Iowa State University Extension grain markets specialist Chad Hart. Hart, assistant professor of economics, says that if the oil slick enters the shipping lanes there could be a slowdown in shipping traffic. "If the oil slick got into what is called the Southwest Passage — which is a canal that goes from New Orleans out to the Gulf of Mexico — we would be looking at severe delays in getting our corn and soybeans shipped overseas," said Hart. Ships can sail through the oily water, but would need to be cleaned when they enter port. "When a ship comes into port, it would have to be cleaned if it went through the oil slick," said Hart. "And then when it goes to their destination, it would have to be cleaned again when it arrives." The result would be much slower movement of grain out of the Midwest to foreign markets. More than 60 percent of United States grain goes through the port of New Orleans, according to Hart. Right now, according to Hart, the oil spill is moving mainly to the east, so there has been little impact on the shipping lanes, which lay to the west of the slick. "If we end up with a bottleneck down there, we could see prices in the U.S. fall from 10 to 50 cents (per bushel)," said Hart. "Katrina had a similar impact. If that happens, people will start to look at alternative shipping routes. For instance, right now, most of our soybeans that are going to China, go through New Orleans. People may start shipping overland to the Pacific Northwest by rail to ship over to China. That is more expensive, but it is an alternative if the Gulf slows down." As long as the spill stays clear of the shipping lanes for the next few months, Hart doesn't feel there will be a huge impact on prices. "In some ways we were lucky on the timing," said Hart. "We ship most of our grain earlier in the year, so right now there are smaller amounts of grain moving." Hide comments Plain text • No HTML tags allowed. • Lines and paragraphs break automatically.
The Origin of Halloween EACH YEAR millions around the world observe the strangest of all festivals, Hallowe'en -- All Hallows Evening. Especially so in Great Britain, Scandinavia and the United States. Every autumn, young and old alike anticipate its revels. It's a night of frolicking fun and frivolous foolishness. All kinds of nonsense and superstitions are associated with this festival. But Why? threat associated with Hallowe'en. Buildings are desecrated, windows broken and other fooleries are resorted to. WHY do so many keep Hallowe'en? What useful purpose does such a celebration fulfill in this "enlightened" scientific twentieth century? What purpose did it ever serve? Is it merely a harmless celebration to amuse our children? It's about time we checked into this observance to see WHERE and WHEN it really originated and FOR WHAT PURPOSE it was established. Not Christian Yes, Hallowe'en long antedates Christianity! It was only later introduced into the professing Christian world -- centuries AFTER the death of the Apostles. Notice! "The earliest Hallowe'en celebrations [in Britain] were held by the Druids in honour of Samhain, Lord of the Dead, whose festival fell on November 1" (see Halloween Through Twenty Centuries, by Ralph Linton, p. 4). "It is clearly a RELIC OF PAGAN TIMES"! (The Book of Days, Chambers, v. 2, p. 519.) Further, "It was a Druidical belief that on the eve of this festival Saman, lord of death, called together the wicked spirits that within the past 12 months had been condemned to inhabit the bodies of animals" (Enc. Brit., 11th ed., v. 12, pp.857-8). Read what this November celebration was like! It was a pagan belief that on one night of the year the souls of the dead return to their original homes, there to be entertained with food. If food and shelter were not provided, these spirits, it was believed, would cast spells and cause havoc towards those failing to fulfill their requests. "It was the night for the universal walking about of all sorts of spirits, airies, and ghosts, all of whom had liberty on that night" (Highland superstitions, Alexander Macgregor, p. 44). Literal sacrifices were offered on this night to the spirits of the dead, when, so the belief went, they visited their earthly haunts and their friends. According to the Roman calendar it was the evening October 31 -- hence, Hallowe'en -- the evening of All Hallows. Observed Everywhere Hallowe'en, or "All Souls Eve," was kept throughout the ancient pagan world. The observance was widespread. "There was a prevailing belief AMONG ALL NATIONS that at death the souls of good men were taken possession of by good spirits and carried to paradise; but the souls of wicked men were left to wander in the space between the earth and moon, or consigned to the unseen world. These wandering spirits were in the habit of HAUNTING THE LIVING ... BUT THERE WERE MEANS BY WHICH THESE GHOSTS MIGHT BE EXORCISED" (Folklore, James Napier, p. 11). firmly believed that on All Hallows Eve the spirit of a departed person was to be seen at midnight on every crossroad and every stile" (Folklore and Folk-Stories of Wales,, Marie Trevelyan, p. 254). In Cambodia people used to chant: "O all you our ancestors, who are departed, deign to come and eat what we have prepared for you, and to bless your posterity and to make it happy" (Notice sur le Cambodge, Paris 1875, E. Aymonièr, p. 59). This sort of Hallowe'en festival was strenuously observed throughout the non-Christian world. Pagans would pray to their false gods to prevent "DEMONS" and "witches" from molesting them. Notice! "The Miatecs of Mexico believed that the souls of the dead came back in the twelfth month of the year, WHICH CORRESPONDED TO OUR NOVEMBER. On this day of All Souls the houses were decked out to welcome the spirits. Jars of food and drink were set on a table in the principal room, and the family went out with the torches to meet the ghosts and invite them to enter. Then, returning to the house they knelt around the table, and with their eyes bent on the ground, prayed the souls to accept the offerings" (Adonis, Frazer, p. 244). This, then, is the way the heathen world celebrated their Hallowe'en, their "All Souls Day". Although some aspects of the Hallowe'en festival varied with each country, the overall pattern and purpose remained the same. Hallowe'en "Christianized" But how did the professing Christian world come to accept and keep such a day? Here is what you, probably, haven't been told. In 607 A.D. the Roman Emperor Phocus defeated the Barbarians who were in control of Rome. The Pantheon in Rome, a pagan edifice which had been wrested from the barbarians, was given to pope Boniface IV. Originally, Emperor Hadrian built the Pantheon -- around 100 A.D. He dedicated it to the pagan goddess Cybele and to the other Roman deities. This temple became the central place in Rome where the pagans honored and commemorated their gods. With this splendid edifice now falling into the hands of professing Christians, the question was, What should be done with it? The pagans had dedicated it to Cybele and all their gods. But the Roman bishop now CONSECRATED IT TO THE VIRGIN MARY AND ALL THE SAINTS of both sexes (see The Mysteries of All Nations, Grant, p. 120). Thus this pagan building became "holy." No more did the pagan Romans use this edifice to pray for their dead. It was now the professing Christians who employed the Pantheon in praying for their dead. This May 13 commemoration of the dead saints was known by the name of "All Saints Day." It continued to be held in May for over two centuries -- until 834 A.D. In that year the NAME and the DATE WERE CHANGED. Notice! "The time of celebration was altered to the FIRST OF NOVEMBER,and it was then called ALL HALLOW" -- from where we get the name Hallowe'en, ALL HALLOW merely meaning ALL HOLY, and the "een" is a contraction of evening (Folklore, James Napier, p. 177). Thus in 834 A.D. the Church in the Middle Ages began tocelebrate Hallowe'en on the FIRST OF NOVEMBER for the first time. This was the very same day the Druids in Britain, the Norsemen in Scandinavia, and the pagan Germans among others were keeping their festival of ALL SOULS EVE, in commemoration of Saman, lord of death, and his demons. Reason for Change Why did the church change the date to November 1st, thus coinciding with the pagans' feast of ALL SOULS? There is a reason! It was a general practice of the restored Roman Empire, now professing Christianity, to "convert" the pagans within the empire as quickly and on as large a scale as possible. Changing dates of festivals often made it easier to influence newly conquered peoples. Ever since the time of Constantine -- who made a state religion out of Christianity -- the Roman emperors realized how essential it was to have a UNIFIED empire, in which as many as possible would be of ONE MIND. The civil and religious leaders saw how important it was for the sake of unity to ALLOW ONLY ONE RELIGION within the restored Roman domain. It became therefore a stringent state policy to force all non-Christians to accept the new state religion. Here is how the plan was carried out. Conversion of Germans When the German Frankish king Charlemagne invaded and conquered parts of Eastern Germany, he compelled the conquered German king, Wittekind, to be baptized and to accept Christianity. Having no choice and seeing his life was at stake, this heathen ruler who knew little or nothing about Christ -- was forced into this "conversion." And with him his entire people. This policy brought complex problems. These pagans, who were usually baptized EN MASSE, were still pagans at heart. Even though they became nominal Christians, they still yearned for many of their heathen practices, which they were expected to discard. With Wittekind's baptism, for example, a vast number of barbarians were suddenly added to the roll call of the church. Wittekind's Germans, now professing Christians, and other conquered pagans, had a profound influence on the ecclesiastical affairs of the church in the early 800's A. D. These barbaric and uncultured people brought with them many outright pagan practices and celebrations, Hallowe'en merely being one of many. They were fervent in clinging to their past ceremonies and observed them openly -- yet supposedly converted to Christianity. What was the church to do? There remained only one other way. Let the recently converted pagans keep certain of their heathen festivals, such as Hallowe'en or All Souls Day -- but label it "Christian." Of course the Germans were asked not to pray to their ancient pagan gods on this day. They must now use this day to commemorate the death of the saints. Throughout history, the Christian-professing world has resorted to this action. We have the theological explanation of this given to us by Pope Innocent. He refers to a heathen festival the pagans kept in the early part of the Roman Empire and explained how the professing Christian world should treat this day: "The heathen dedicated this month [2 Feb.] to the infernal gods ... In the beginning of this month the idolaters walked about the city with lighted candles, and as some of the holy fathers COULD NOT EXTIRPATE SUCH A CUSTOM, they ORDAINED that Christians should carry about candles IN HONOUR OF THE "VIRGIN MARY" (Folklore, James Napier, p. 181). If a pagan practice or festival could not be forbidden, it was reasoned, "let it be tamed." Thus many were persuaded to TRANSFER devotion from their former gods to the Christian God. So it was with the festival of ALL SOULS EVE. Notice this admission: "Thus, at the first promulgation of Christianity to the Gentile nations ... THEY COULD NOT BE PERSUADED TO RELINQUISH many of their superstitions, which, rather than forego altogether, they chose to blend and INCORPORATE with the new faith" (Popular Antiquities of Great Britain, John Brand, p. xi). What About Our Time? Now come down to the twentieth century. You'll be surprised to what extent we have inherited pagan rites and ceremonies from our forefathers, so obvious in the celebration of Hallowe'en. Note this classic example. "In many Catholic countries the belief that the DEAD RETURN on this day is so strong, that food is left on the tables and people still decorate the graves of the dead [on this day]" (Dictionary of Folklore, Funk and Wagnalls, v. 1, p. 38). In Protestant countries many pagan superstitious beliefs and practices have become an integral part of each year's celebration. In many parts of Britain, BONFIRES are set alight on the eve of Hallowe'en. Of course fire has nothing to do with praying for dead saints. The original reason for the fire, however, was to frighten away witches and evil spirits on this night. Fire has always been an essential part of Hallowe'en in Great Britain. You and Your Children What about you and your children? What comes to your mind when thinking about Hallowe'en? The truth of the Bible? Not at all! Instead, weird and FRIGHTENING MASKS -- persons PORTRAYED AS WITCHES AND DEMONS. Pumpkins and turnips hollowed out in the shape of EERIE-LOOKING faces! Lighted candles are placed inside to help bring out the more frightful side of these carvings. Dough is baked into small figurines RESEMBLING WITCHES AND SPIDER'S WEB CAKES are baked by the dozen for this occasion. Children, dressed up in the most revolting garments, are let loose on the neighbors, trying to scare the daylights out of them. Let's be honest. I have before me the Good Housekeeping's Book of Entertainment, which my wife picked up from the local library. On page 168 of this much-read book, there is a section on what to do on Hallowe'en. Notice the astonishing advice given! "Halloween decorations are quite as important as the food. When planning them, remember that if the room is to be dimly lit (preferably by candle and FIRELIGHT) the decorations must be bold to be effective. Orange, black and red, THE DEVIL'S COLOURS, are the colours associated with Halloween and THIS SCHEME SHOULD BE CARRIED OUT as far as possible ... Have paper streamers and lanterns hanging from the ceiling, or, if you would like to have something less usual, you could make a giant SPIDER'S web with black and orange strings, or in narrow strips of crepe paper coming from the four corners of the room, complete with a LARGE SPIDER -- one of the DEVIL'S FAVOURITE FOLLOWERS." Notice where the stress lies! Read further of the black magic associated with this festival. "To decorate the walls, make large silhouettes of CATS, BATS, OWLS AND WITCHES ON BROOMSTICKS ... For the supper table small WITCHES WITH BROOMSTICKS can be made by using lollipops on 4-inch sticks." Weird lanterns, witch-balls, and witches' cauldrons are some other objects, the book suggests, which must fit into the evening somehow. How pagan can you get? NOWHERE does the Bible command us to observe Hallowe'en. Hallowe'en and other common festivals which people observe in the Christian-professing world have NO BIBLICAL BASIS. They originated in paganism. The testimony of history stamps Hallowe'en as a HEATHEN festival. It's built on a PAGAN FOUNDATION. Your Bible warns: "For other foundation can no man lay than that is laid, which is Jesus Christ" (I Cor. 3:11). Which is the BASIS of YOUR practice and belief? Turn to Deuteronomy 12:29-31 and read God's condemnation of Hallowe'en! Hits 401 Rating: 3 What is the origin of holloween?, The origin of holloween
The language of business Business practices English is, by far, the dominant language of the Falkland Islands, although there are also some Spanish speakers. Falkland Islands English is distinct in accent, as well as word usage. While colloquialisms found in the United Kingdom and its territories are often in use, a few words are distinct to the islands. For example camp, derived from the Spanish word for countryside, refers to all parts of the Islands that are not the town of Stanley. Please login / register to read full article.
Devastating Computer Viruses That Could Rival Stuxnet Power can never be innocent and while nuclear power can be used for various beneficial purposes, we’ve seen the horrors it can cause in the past. Similarly, computer coding and programming can also be used for both good and bad purposes. Unfortunately, ‘the bad’ often becomes horrific beyond expectations and takes the entire world by surprise. Reader’s might already be familiar with the digital superweapon Stuxnet, that was used in military attack by US and Israel. This malevolent virus, later found its way into black market and has spawned a number of equally destructive cousins that have plagued the internet. Since it’s 2016 and malware attacks have become far more prevalent than ever, it would be interesting for readers to know about some of the most destructive computer viruses ever. 1. Iron Gate This virus operates similar to Stuxnet as evident by its fondness for Siemens Industrial Control Systems. It uses MitM (Man in the middle) style attack pattern to gain entry inside the host system and severs user’s connection to the server. This involves replacing a DLL file with one with malicious code that allows it to take legitimate control over a system. But what Irongate lacks in complexity, it makes it up with its ability to affect sandboxed environments. This can very well be utilized to render all developmental and experimental data useless and essentially blow a company’s research and development department to smithereens. See Also: 7 Biggest Ransomware Threats of 2016 1. Conficker First reported in 2008, Conficker worm has affected more than 15 million computers worldwide. It’s list of victims include government offices, corporations and users from over 190 countries across the globe. This virus is notorious for employing a vast number of malware techniques that make it extremely hard to detect and eliminate once it’s on your system. It can turn your computer into a zombie botnet that will be used to launch more phishing attacks. It also makes any anti-virus or anti-malware websites inaccessible so it becomes extremely difficult to find any online help. See Also: Most Vicious Computer Hacks That Left Everyone Bewildered 1. CryptoLocker The name that essentially coined the term ‘RansomwareCryptoLocker is one of the most malicious viruses floating across the internet. Once this virus enters your computer, it will launch itself in a termination-proof process and encrypts various files. The encryption is usually AES-256 that makes these files impossible to recover without the original decryption key. Since CryptoLocker is labeled as a Ransomware, it then asks the system owner to make a payment (usually in bitcoin) to recover their hijacked data. This is impossible to remove once it gets on your system and makes data essentially irrecoverable. See Also: How Ransomware Attacks your System? 5 Tips to Prevent it 1. Flashback Just when you thought that Mac users are safe from viruses and malware attacks, comes a virus specifically designed to shatter that notion. Named as Flashback, this virus was first reported in 2011 and infected Mac systems by exploiting vulnerabilities in JavaScript. Once it transfers its infected file to the system, a malicious code is initialized from a remote location. Its name is a reference of it being disguised as update for Adobe Flash Player. Once your Mac is infected with Flashback, it exposes all your internet activities and be used to leak sensitive personal information to hackers. This virus has affected more than 500,000 mac systems with a majority of victims based in US and Canada. 1. SQL Slammer If there’s one thing that you hate the more than viruses, it is certainly slow internet speed. And when you make a program that can slow the internet down, you know there’s no refuge from this evil. Surfacing in early 2003, SQL Slammer is notorious for launching massive Denial-of-Service attacks. It typically sends bulk of fake service requests from untraceable locations, causing them to eventually overload and fry. This can pretty much render your internet connection useless and lockdown online databases from being accessed and a crawling internet connection that would make you pull your hair out. A horrid creation of a true evil genius! Programmers and computer coders work their socks off to create new software and systems, used by millions of users worldwide. But there’re always two sides to a story as ‘Power Can Never Be Innocent’ (-Lex Luthor). Hence, it is essential that we must gather more and more knowledge about these looming digital monstrosities, and protect our internet privacy. Akshay Peter Leave a Reply
Introducing Voltage Regulators If you’re keen to build out a circuit on a breadboard that runs under its own steam, whether it be a simple arrangement of LEDs and buttons, or something more complex involving an ATmega then you might need a Voltage Regulator. A Voltage Regulator does what it says on the tin. It’ll take an unstable or unusable high voltage from a power source, typically batteries or a DC mains adaptor, and regulate it down to a stable, usable voltage. 3.3v and 5v are typical useful voltages, and you can get regulators for both of these. Picking a Voltage Regulator Before you select a voltage regulator, it’s crucial to take into account the voltage you want out of it ( probably 3.3v or 5v ) and the voltage you’ve got available to put into it. Every voltage regulator has a number of properties that let you know if it's suitable for your particular use, the most important of these is probably Dropout Voltage. Dropout Voltage Every voltage regulator will have what’s known as a “dropout” voltage. This is the smallest possible difference between the output voltage, and the input voltage required for it to function. For example: * A 5v voltage regulator with a 2v dropout requires an absolute minimum of 7 volts to function correctly. * A 3.3v voltage regulator with a 1.1v dropout voltage requires an absolute minimum of 4.4v to function correctly. From this you can decude that a trio of AA batteries ( 1.5v each ) will give you 4.5v, which is just enough to run a 3.3v regulator. To run a 5v regulator you’ll need a minimum of 5 AA batteries, or a single 9v battery. Mains DC Supply If you decide to use a mains supply and it’s already at the voltage you need, and a decent supply, then you wont need a regulator. If, however, you want to regulate a 5v supply to 3.3v then you'll need two things: 1. A way of connecting the power supply to your project 2. A voltage regulator circuit Female terminal block To connect a 5v supply with a 2.1mm jack, you can use a female 2.1mm Plug to Screw Terminal adaptor - Connecting Batteries As you might have guessed, you’ll need a 9v battery clip or a 3xAA or 4xAA battery holder if you plan on using batteries. Battery Holder A 9v battery will give you a good solid 5v out of a 5v regulator, and 3xAA will do you proud for 3.3v. Rechargeable batteries are a good bet, since they’re less wasteful and maintain a more stable voltage as they drain. 4x1.2v rechargable AA will give you 4.8v which you can also regulate down to 3.3v with no problems. Using a Voltage Regulator Wiring up a Voltage Regulator is simple. They have 3 pins; an input, an output and a ground pin. Looking at the front of one of our 3.3v Voltage Regulators ( LD33V ), the pins will be 1, 2 and 3 from left to right. These are Ground, Output and Input respectively. Our 5v Voltage Regulators ( L7805CV ) have a slightly different pinout, they are Input, Ground and Output respectively. As you might have guessed, you want to put your input voltage into Input ( making sure it’s at least output + dropout ), connect your breadboards Live rail to the Output, and connect the Ground of both your input power supply and breadboard to the central Ground pin. Voltage regulator on a mini breadboard The above shows a 3.3v regulator seated on a 170pt breadboard. If you use a larger breadboard you can connect the output of the regulator directly to the provided ground/live rails. Voltage regulator on a mini breadboard And the image above shows a 5v regulator. Note that the Voltage In is now the left-most pin, Voltage Out the right most, and Ground the middle pin. The capacitors are there to help filter any undesired noise from your power supply and prevent it reaching your circuit. They aren't essential in many hobbyist setups, the regulator will work fine without them, but it's always best to get into good habits. Diagnosing a circuit and finding it's a noise problem because you left out capacitors is never fun! Shopping basket Breadboard (Mini) Blue £2.00 Breadboard (Mini) Green £2.00 Breadboard (Mini) Yellow £2.00 Breadboard (Mini) Red £2.00 Breadboard (Mini) White £2.00 Breadboard (Mini) Black £2.00 Breadboard (Mini) Cyan £2.00 Voltage Regulator 3.3V £1.00 Voltage Regulator 5V £1.00 Voltage Regulator 12V £1.50 2.1mm Plug/Jack to Screw Terminal Block Male £2.50 2.1mm Plug/Jack to Screw Terminal Block Female £2.50 4xAA Press-Stud Battery Holder Raspberry Pi, Electronics Phil Howard
8 Ways of Learning I really enjoyed reading about the 8 Aboriginal ways of Learning. It’s very insightful and I’m sure it is very much an eye opener for many teachers to see it presented in such a way. The Best Aboriginal Pedagogy section gives a clear indication of how to use Aboriginal perspectives to present core aspects of teaching units rather than as peripheral stories of ‘fun’ anecdotes that do little to include the Aboriginal students a teacher may have in the class. Of particular interest was the way in which each school, of varying groups of Aboriginal peoples interpreted and adapted the 8 ways for their own educational purposes. There is a strong link between the seen aspects of Aboriginal culture and the unseen, deeper knowledge. It’s more than just a presentation of artifact or stories, it’s more about the deeper understanding of lore and culture and practice of these that gives relevancy to the perspectives that teachers are including in their lessons. Educators must be aware of the restrictions of knowledge between genders. There must be a balance between the handling of secret knowledge and the non-sexist climate that schools must have. Of particular interest was the guide for displays of Aboriginal Culture: 1. Story 2. Learning Maps 3. Non-verbal objects and items 4. Symbols and Images 5. Land Links 6. Non-linear information 7. Deconstruct/Reconstruct community profiles 8. Community Links The 8 Ways philosophy has begun to be interpreted as a way to observe 4 key aspects of local Aboriginal culture, namely: • values • systems • protocols • processes and the integration of these into the local school system. What is important to remember is that this is a very generalistic guide and that ‘one size does not fit all’ when it come to implementing the 8 ways into a classroom. Of greatest interest to me personally was the Personal Identity Reflection Questionnaire at the end of the website. Did you try it? If not, here it is for all to try. It’s a very challenging experience, if you answer it completely honestly. It shows that there is “a strong link between culture and the way people think and learn”. (Your Identity Map – https://8ways.wikispaces.com/Your+identity+map) The Questionnaire 1. Ways of being. Where do you belong? Who do you belong to? How do you know that something is real? List some categories of the things you know are real in this world. From the following sets, select the land orientations you feel most comfortable with: Saltwater / freshwater High ground / low ground Hills / plains / ridges / mountains / coast Open country / forest Wet / dry Red soil / black soil Sand / dirt / rock Warm / cool Fur / feathers / scales / fins Wood / rock / earth / wind / fire Where are your ancestors from and how do you connect with them? How are you accountable for maintaining relationships with ancestors, people and the environment? (What are your personal consequences for damaging these relationships?) How will the knowledge you have learned in this life be passed on, and to whom? What things in your life-world must change, and what things must always stay the same? 2. Ways of knowing. How did you know the answers to the questions so far – how did you learn these things? Sketch a diagram of the way you solve problems. What shape does this take for you? When you access knowledge from memory, what form does that take in your head? (e.g. images, sounds, print, language, shapes) What are the stories that have had the biggest impact on how you relate to the world around you? (Might be books, films, oral histories, fables etc.) What symbols are most meaningful for you? (e.g. crucifix, tag, icon, flag) How do these symbols inform your life and work? What sorts of things do you know implicitly, without having to be taught? Do the answers to any of these questions make you want to change any of your answers back in section 1? (Because our ways of knowing shape our ways of being.) 3. Ways of doing. Do you learn new knowledge best with others, for others, alone, or for yourself? Do you internalise new knowledge through dialogue, reflection or both? Do you achieve learning outcomes at the end of a process, or during the process? What are the signs you look for to know if what you are doing is right? What does it usually take for you to change your mind about something? What tools do you use for teaching and learning? What are your main cultural practices, your ways of expressing your culture (e.g. singing, sport, events, rituals)? How do these cultural practices impact on the way you do your work? 4. Ways of valuing. What is truth? What would be your top three rules for living? Top three for learning? What is the most important thing in the world to you? How did you learn your values? Where did they come from? Now, track back through your responses and find the points that relate to: 1. Stories and histories 2. Knowledge pathways/processes 3. Unspoken/instinctive/ancestral knowledge 4. Metaphors and symbols 5. Land and place 6. Non-linear/contradictory/irrational/creative ideas 7. Wholes vs parts / Macro vs micro / Communal vs independent 8. Family, community, cultural base These points relate your identity to the 8ways framework. Match these with the 8ways diagram and reflect on your identity within this framework (starting top left with story sharing, then working anti-clockwise). Overall, it must always be remembered that this is a guide across many Aboriginal cultures and by no means is a complete representation of all, or any Aboriginal Culture. As part of the reflection its important to examine how we can, as teachers, incorporate these aspects of culture into our teaching for all students who have the whole cross-section of learning styles. We must remember not to stereotype our Aboriginal students by the mere fact of Aboriginality. Being Aboriginal isn’t a guarantee of having Aboriginal learning styles. For me personally, and this must not reflect on other Aboriginal people in any way, my Aboriginality is only one facet of who I am. I have German heritage, I have British, I have Arab, Russian, Spanish, French and I have West African background. I can talk about percentages and genetics, but the fact remains that I am of very mixed background and that makes me an individual. It rankles me when people. upon hearing that I have Aboriginal heritage, give the all knowing “Ohhhhh!” exclamation, as if that explains everything about me. How little they know. So we must treat all of our students as individuals and ajust our teaching to cater for ALL learning styles and remember to be culturally sensitive and, most importantly, inclusive in our teaching of Aboriginal culture. As an anecdote…. From 2004 to 2006 I was the AERT at Narrandera High and Primary schools. My background is Anaiwan/Kamilaroi from northern NSW. I was expected to teach Wiradjuri language classes in the schools. The students knew that I’m not Wiradjuri and questioned me on every word meaning and pronunciation. I was an outsider trying to teach them about themselves. This is where community contacts come into play. Involving community, especially Aboriginal Elders as part of the learning process is vital. It gives authenticity to the teaching if the involvement follows the 8 ways and is not just a fun distraction from other lessons. Keep the elders involved. Get the whole class used to having cultural components in everything you teach. Make the cultural aspect as equally valued a part of learning as every other part and cater to all learning styles wherever you can. All works refer to: 8 Aboriginal Ways of Learning. (2009). 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top button Flag Notify Connect to us Facebook Login Site Registration Why to Join Facebook Login Site Registration Print Preview Running a command line program and reading the result as it runs in Python +1 vote import subprocess p = subprocess.Popen("D:PythonPython27Scriptspip.exe list -o", for line in p.stdout: print line posted Aug 22, 2013 by Satish Mishra Share this question 2 Answers +1 vote Is the program actually producing output progressively? I just tried your exact code with "dir /ad /s /b" and it worked fine, producing output while the dir was still spinning (obviously setting shell=True to make that work, but I don't think that'll make a difference). It may be that pip buffers its output. Is there a parameter to pip to make it pipe-compatible? answer Aug 22, 2013 by Deepak Dasgupta If I run pip in the command window I can see it's output appearing line by line rather than on one block. I tried the code with the dir command but it's too fast for me to be sure if it's working or not. I tried again using the command "ping" instead since I know that output's slowly and it something that everyone should have. In the command window I can see that the output appears over time, but from python I get nothing for a while and then suddenly get all the output in one rapid go. Can you think of anything else I can look at? A lot of programs, when their output is not going to the console, will buffer output. It's more efficient for many purposes. With Unix utilities, there's often a parameter like --pipe or --unbuffered that says "please produce output line by line", but Windows ping doesn't have that - and so I'm seeing the same thing you are. You should be able to see the time delay in dir by looking for some particular directory name, and searching from the root directory. Unless you're on a BLAZINGLY fast drive, that'll take Windows a good while! +1 vote When file object is used in a for loop it works like an iterator and then it uses a hidden read-ahead buffer. It might cause this kind of blocking. You can read more details here (description of method next): So basically non-blocking loop might look like this: while True: line = p.stdout.readline() if not line: break print line answer Aug 22, 2013 by Anderson Similar Questions +1 vote Something that just sends a screen directly to the printer without having to involve Notepad or the like? I am unable to find a search function on the updated Yahoo group. +2 votes I want to install Python on a PC with the 64 bit version of Windows 7. I want Python to be able to use as much as possible of the RAM. When I install the 64 bit version of Python I find that sys.maxint == 231 - 1 Whereas the Pythpon installed on my 64 bit linux system returns sys.maxint == 263 - 1. It looks to me as though 32 and 64 bit versions of Python on 64 bit Windows are both really 32 bit Python, differing only in how they interact with Windows. So I wouldnt expect 64 bit Python running on 64 bit Windows to allow the large data struictures I could have with 64 bit Python running on 64 bit linux. Is that true?I have spent a couple of hours searching for a definitive description of the difference between the 32 and 64 bit versions of Python for Windows and haven't found anything. +2 votes Any sample example would be helpful, I want to use all files from a directory and want to apply certain operation on it. 0 votes I am writing a command line tool in python to generate one time passwords/tokens. The command line tool will have certain sub-commands like --generate-token and --list-all-tokens for example. I want to restrict access to certain sub-commands. In this case, when user tries to generate a new token, I want him/her to authenticate against AD server first. I have looked at python-ldap and I am even able to bind to the AD server. In my application I have a function def authenticate_user(username, password): pass which gets username and plain-text password. How do I use the LDAPObject instance to validate these credentials? Useful Links with Similar Problem Contact Us +91 9880187415 #280, 3rd floor, 5th Main 6th Sector, HSR Layout Karnataka INDIA.

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