Question: How do we know there isn't a final number for pi, but that it goes on forever?

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 How do we know there isn't a final number for pi, but that it goes on forever?

At the most basic level, the most common way to prove a number is irrational is to first assume that it's actually rational (i.e. can be written as a/b where *a* and *b* are both whole numbers) but show that this assumption leads directly to a contradiction (e.g. 0 = 4 or similar). As for the specifics to pi, there's several different proofs that pi is irrational, but unless you're quite familiar with university-level math (calculus and beyond), they're neither easy to understand nor intuitive. Here is one such proof by [Timothy W. Jones of the University of Washington]( URL_2 ). That said, I believe Lambert was the first person to prove pi is irrational, in 1761. Essentially, he showed that: * tan(x) = x / (1 - x^(2) / [3 - x^(2) / (5 - x^(2) / [7 - ...])]) where tan(x) is [the tangent function]( URL_0 ) which you might remember from geometry classes in middle school or high school. Basically, the above expression is a continued fraction. It may be difficult to parse out in-line like that, but it should look [something like this]( URL_1 ). Lambert also proved in a separate result (unfortunately I don't think I can really ELI5 this part) that if *x* is any non-zero rational number then the above expression is irrational. If we assume that pi is rational then it follows that pi/4 must be rational as well. However, tan(pi/4) = 1 and 1 is not irrational, so we've reached a contradiction and thus we know our assumption is false.


Question: What exactly is 'Youtube-dl' , why was it taken down by RIAA and what does the DMCA takedown of youtube-dl affect?

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 What exactly is 'Youtube-dl' , why was it taken down by RIAA and what does the DMCA takedown of youtube-dl affect?

Youtube-DL is a little program that downloads videos and/or audio from basically anywhere that hosts them. This means you could go on YouTube and download videos with it. This is a form of digital piracy and technically also falls under hacking; you're using a website in an unauthorized manner and making digital copies of something you do not own. For example, you could pay the $2.99 rental fee on any of the movies hosted on YouTube, and then you could download that video and own a copy. You aren't authorized to make a copy, and you're bypassing legitimate channels to purchase and own that movie. You could also go to somewhere like Netflix and download anything you like off of that. Again, bypassing the legal channels that you would otherwise be required to use. It's all very much like going into a movie theater with a video camera and recording the movie you're watching, except this is in HD. The takedown just means that Youtube-DL had to be taken off of Github (the place it was hosted and downloaded from). That's it. You can't harass people who use the program (because it's basically impossible to track), but you can make it harder to download the program.


Question: How do blood and nutrients get to cells that aren't right up against blood vessels and capillaries?

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 How do blood and nutrients get to cells that aren't right up against blood vessels and capillaries?

Blood as a whole doesn't normally get out of blood vessels, if the vessels are intact. Blood *cells*, on the other hand, sometimes do, especially white blood cells. They do this by being able to change their shape enough to fit through small gaps between the cells lining the blood vessel (called the "endothelium"). Nutrients (and other stuff that's not cells) can use the same route, or be transported *through* the endothelial cells in a process called "transcytosis" (basically, the nutrient / stuff enters a cell, passes through it, and exits on the other side). EDIT: Formatting.


Question: Why is there such a thing as a “feels like” temperature? For example, in NYC, it’s 91 degrees today but the weather app says it “fees like” 99 degrees

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 Why is there such a thing as a “feels like” temperature? For example, in NYC, it’s 91 degrees today but the weather app says it “fees like” 99 degrees

A large portion of that has to do with the humidity in the air. 90⁰ with 10% humidity feels way different than 90⁰ with 95٪ humidity. The air can only absorb so much moisture based on its temperature. If it's hot and humidity, it's hard for the sweat on your body to evaporate. Since it's not evaporating and cooling you, it feels hotter than it would if the air was dry.


Question: Why do CFL bulbs turn on almost instantly, but tradition fluoro tubes still need to flicker on?

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 Why do CFL bulbs turn on almost instantly, but tradition fluoro tubes still need to flicker on?

Good question. The design is basically identical to fluoro tubes: A tube containing a mercury vapour, with heated electrodes at both ends. The answer is that the technology has progressed from the old-fashioned switch-start, magnetically controlled systems, and has moved to electronic starting and control. Fluoro tubes equipped with a modern electronic start and control system, start very rapidly and don't flicker, and are also dimmable, etc. The difference is that in a tube system, the start and control system is in the light fitting. In a CFL, the tube and control system are integrated into a single replaceable unit. The result is that people with fluoros tend to keep the same light fitting, and just change the tube, so the old technology stays around longer. The traditional control system worked by routing power through a magnetic ballast - the job of the ballast is to limit the power available to the tube. While a filament bulb takes a fixed amount of power from the mains, a fluoro tube doesn't, and without some sort of system to throttle the power, it would explode due to overload. Fluoro tubes also have another problem, which is that they need a very high voltage to start - thousands of volts. So, if you just connected a tube to the mains, nothing would happen, because the tube needs a kick to start. To help with starting the tube electrodes are warmed up to red-heat in order to get the starting voltage down to a sensible level (about 1000 volts). So, there is a specific sequence to starting a fluoro tube: 1. Warm up tube electrodes 2. Generate high voltage pulse 3. Apply throttled power to tube 4. If tube is not active, go back to 1. Every time, a high voltage pulse is applied to the tube, the tube flashes. The magnetic system, is controlled by a very clever mechanical switch system, which is quite complex so I won't describe it here. However, the mechanical control of the magnetic system isn't able to give a consistent voltage pulse or a consistent electrode heat-up time. Sometimes, you get a small pulse, sometimes you get a large one. Sometimes, the electrodes are well heated, sometimes they're a bit cold. This means it often takes 2 or 3 attempts, before you get a good start. Because the system is mechanical, the timings are quite slow, so you see visible flashing, each time the system tries a start (and also the tube electrodes get a chance to cool down between attempts). With an electronic system, a microprocessor carefully controls the timing of the electrode heaters, and then triggers an electronic pulse generator which applies a very fast constant stream of pulses to the tube until it starts.


Question: How can my external battery fully discharge when charging my phone's battery?

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 How can my external battery fully discharge when charging my phone's battery?

A lithium ion battery has a nominal village of 3.7V. When you use an external battery pack to charge your phone, a circuit pulls power from the battery, converts it into 5V (for the standard USB voltage) and sends it to the USB port. Your phone takes that 5V and converts it to a specific voltage to charge the battery, usually around 4.2 volts. So, there is at least two circuits in between the batteries, not counting protection (to prevent overheating or overcharging). The external battery only sees the load imposed on it by the 3.7 to 5 volt converter. If you took two bare lithium batteries and connected them positive to positive, negative to negative, current will flow from the higher voltage battery into the lower voltage battery until they are the same voltage. (And then they'll both self-discharge due to internal resistance) One more thing, a lithium ion battery is fully discharged around 3.5-3.6 volts. There's almost no more usable energy, but the chemistry inside still produces a voltage. TLDR; there is circuitry between the batteries controlling the flow of electricity.


Question: What would happen if you introduced a flame to a gas giant planet?

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 What would happen if you introduced a flame to a gas giant planet?

The flame would likely go out very rapidly. I know this sounds like a cop out but.. yeah. The flame would go out due to lack of oxidizers. The centres of gas giants are likely hot due to immense pressures and friction down below the top lawyers of gas. So if they were to ignite or something then I. Suppose it would already have happened. (I take from your question you wanted to know if the gas giants would set on fire)


Question: What is an elementary function?

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 What is an elementary function?

The elementary functions are a set of well known functions such as powers of x, roots of x, exponentials, trigonometric functions and their inverses, and most importantly any combinations of them, for example e^sinx + x^(2). Non elementary functions are those that can't be written like that. For example if I define the function: f(x) = 1 if x is rational and f(x) = 0 otherwise Then f is a non elementary function. This function has a specific name - Dirichlet function - but most non elementary functions don't have a name or an easy way to describe them.


Question: What's the difference between an adverbial and a complement?

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 What's the difference between an adverbial and a complement?

Typically the defintion is that an adverbal is "optional" remove it and the sentence still makes sense. He got through. Makes sense. He got through *the window* so "the window" is an adverbial phrase. Complements, on the other hand are required for the sentence to make sense. He is getting. Does not make sense. He is getting *angry* therefore "angry" is the complement.


Question: How do companies/brands work out how many grams is equivalent to one portion, and how many calories in the product?

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 How do companies/brands work out how many grams is equivalent to one portion, and how many calories in the product?

Calories are just a way of measuring energy. Scientists use calorimetry to determine caloric content, where, say, a gram of the substance is burned and the resulting heat carefully measured, giving you the calories of energy that substance contains per gram. From there , you would refer to the appropriate government serving size guidelines and calculate how many grams (calories) constitute a serving.


Question: Why do cooked noodles and rice not continue to absorb water/liquid in soups?

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 Why do cooked noodles and rice not continue to absorb water/liquid in soups?

I think everyone kind of missed the point. Yes, noodles have a certain limit for how much they can absorb, but what decides that limit? The porosity (small holes) that a material has and its [chemical properties]( URL_0 ) decides how much water it can hold. Think of a sponge for the porosity part. The chemical part is a little more complicated, but the atomic structure (atoms are the tiny building blocks of everything) decide if the materials attracts or repels water, hydrophilic or hydrophobic respectively. So, noodles and rice have an ability to absorb water. The porosity (small holes) and chemical properties mean that there is a maximum amount of water that can go into the noodles. If you go over that limit, then the noodles and water around them will be out of balance. If there's too much water in the noodles, then the water will leave the noodles. If there's too much water around the noodles, then the water will enter the noodles. This will happen until the noodles and water are at "equilibrium," and where this equilibrium point exists is defined by porosity and molecular properties.


Question: Why is the esophagus not lined with the same tissue type as the stomach, to prevent damage from acid reflux or vomiting?

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 Why is the esophagus not lined with the same tissue type as the stomach, to prevent damage from acid reflux or vomiting?

Ultimately because we're not engineered, we just happened. People misunderstand evolution. It doesn't create advantageous or clever mutations, it creates essentially random mutations, and beneficial ones often (not always) take hold. Detrimental ones die off, and neutral ones sometimes come through as well in a minority of the population. So first of all, there may never have been a mutation that would line the esophagus. If that doesn't happen, then it doesn't happen. Secondly, if it did occur, then it has to happen in the right circumstances to propagate - and has to be generally beneficial to eventually dominate in the populace. There are definite benefits to vomiting - it gets toxic stuff out of the system before it kills us. Maybe we evolved *away* from having a lined esophagus.