text stringlengths 1 81 | start float64 0 10.1k | duration float64 0 24.9 |
|---|---|---|
>> I could just turn one into 1.0, and
10 into 10.0, which would, indeed, | 4,471.12 | 7.31 |
have the effect of converting
them into floats-- still hopefully | 4,478.43 | 3.96 |
the same number. | 4,482.39 | 0.79 |
Or it turns out there's something
we'll see again before long. | 4,483.18 | 2.7 |
You could cast the numbers. | 4,485.88 | 1.29 |
>> You can, using this parenthetical
expression, you can say, | 4,487.17 | 2.71 |
hey, computer, take this
10, which I know is an int. | 4,489.88 | 2.68 |
But treat it, please,
as though it's a float. | 4,492.56 | 2.1 |
But this feels unnecessarily complex. | 4,494.66 | 2.02 |
>> For our purposes today,
let's just literally | 4,496.68 | 2.36 |
make them floating point values
with a decimal point, like this. | 4,499.04 | 3.66 |
Let me go ahead and rerun, make
imprecision, good, dot slash | 4,502.7 | 4.36 |
imprecision, enter. | 4,507.06 | 1.81 |
OK, we're looking good. | 4,508.87 | 2.12 |
>> 1 divided by 10, according to my
Mac here, is, indeed, 0.100000. | 4,510.99 | 7.204 |
Now, I was taught in grade school there
should be an infinite number of 0's. | 4,518.194 | 3.166 |
So let's at least try
to see some of those. | 4,521.36 | 1.791 |
It turns out that printf is a little
fancier still than we've been using. | 4,523.151 | 3.619 |
It turns out you don't have to specify
just percent f, or just percent i. | 4,526.77 | 4.12 |
You can actually specify
some control options here. | 4,530.89 | 2.94 |
>> Specifically, I'm going
to say, hey, printf, | 4,533.83 | 2.64 |
actually show me 10 decimal points. | 4,536.47 | 3.19 |
So it looks a little weird. | 4,539.66 | 1.16 |
But you say percent,
dot, how many numbers | 4,540.82 | 2.025 |
you want to see after the
decimal point, and then f | 4,542.845 | 2.125 |
for flat, just because that's
what the documentation says. | 4,544.97 | 3.37 |
Let me go ahead and save that. | 4,548.34 | 1.74 |
>> And notice too, I'm getting
tired of retyping things. | 4,550.08 | 2.38 |
So I'm just setting the up and
down arrow on my keys here. | 4,552.46 | 3.44 |
And if I keep hitting up, you
can see all of the commands | 4,555.9 | 2.81 |
that I made, or incorrectly made. | 4,558.71 | 2.38 |
>> And I'm going to go ahead now and
not actually use that, apparently. | 4,561.09 | 3.54 |
Make imprecision, dot
slash imprecision-- so | 4,564.63 | 6.786 |
what I was taught in
grade school checks out. | 4,571.416 | 1.874 |
Even if I print it to 10 decimal
places it, indeed, is 0.10000. | 4,573.29 | 5.72 |
But you know what? | 4,579.01 | 0.83 |
>> Let's get a little greedy. | 4,579.84 | 1.31 |
Let's say, like, show me 55
points after the decimal. | 4,581.15 | 2.84 |
Let's really take this
program out for a spin. | 4,583.99 | 2.17 |
Let me remake it with make
imprecision, dot slash, imprecision. | 4,586.16 | 5.01 |
>> And here we go. | 4,591.17 | 1.22 |
Your childhood was a lie. | 4,592.39 | 2.03 |
Apparently, 1 divided by 10 is indeed
0.100000000000000005551115123-- | 4,594.42 | 13.99 |
>> What is going on? | 4,608.41 | 1.33 |
Well, it turns out, if you kind of
look far enough out in the underlying | 4,609.74 | 3.62 |
representation of this
number, it actually | 4,613.36 | 2.59 |
is not exactly 1/10, or 0.1 and
an infinite number of zeros. | 4,615.95 | 4.45 |
Now, why is that? | 4,620.4 | 1.23 |
>> Well, even though this is a simple
number to us humans, 1 divided by 10, | 4,621.63 | 4.62 |
it's still one of infinitely many
numbers that we could think up. | 4,626.25 | 4.66 |
But a computer can only represent
finitely many so numbers. | 4,630.91 | 3.58 |
And so, effectively, what the
computer is showing us is its closest | 4,634.49 | 4.22 |
approximation to the number
we want to believe is 1/10, | 4,638.71 | 4.23 |
or really 0.10000 ad infinitum. | 4,642.94 | 4.82 |
>> Rather, though, this is
as close as it can get. | 4,647.76 | 2.665 |
And, indeed, if you look
underneath the hood, | 4,650.425 | 1.875 |
as we are here by looking
55 digits after the decimal, | 4,652.3 | 4.75 |
we actually see that reality. | 4,657.05 | 2.94 |
Now as an aside, if you've
ever seen the movie-- | 4,659.99 | 2.62 |
most of you probably haven't--
but Superman 3 some years ago, | 4,662.61 | 3.17 |
Richard Pryor essentially leveraged this
reality in his company to steal a lot | 4,665.78 | 3.72 |
of fractions and fractions of pennies,
because the company-- as I recall, | 4,669.5 | 4 |
it's been a while-- was essentially
throwing away anything that didn't fit | 4,673.5 | 3.71 |
into the notion of cents. | 4,677.21 | 1.58 |
>> But if you add up all these
tiny, tiny, tiny numbers again, | 4,678.79 | 2.69 |
and again, and again, you can, as in
his case, make a good amount of money. | 4,681.48 | 3.48 |
>> That same idea was ripped off by
a more recent, but still now older | 4,684.96 | 3.05 |
movie, called Office Space,
where the guys in that movie, | 4,688.01 | 2.49 |
did the same thing, screwed it up
completely, ended up with way too much | 4,690.5 | 3.001 |
money in their bank account. | 4,693.501 | 1.165 |
It was all very suspicious. | 4,694.666 | 1.134 |
But at the end of the day,
imprecision is all around us. | 4,695.8 | 3.49 |
>> And that, too, can be
frighteningly the case. | 4,699.29 | 2.95 |
It turns out that Superman 3
and Office Space aside, there | 4,702.24 | 3.35 |
can be some very real
world ramifications | 4,705.59 | 2.87 |
of the realities of imprecise
representation of data | 4,708.46 | 3.83 |
that even we humans to
this day don't necessarily | 4,712.29 | 2.48 |
understand as well as we should,
or remember as often as we should. | 4,714.77 | 3.46 |
And, indeed, the following clip is
from a look at some very real world | 4,718.23 | 4.72 |
ramifications of what happens if you
don't appreciate the imprecision that | 4,722.95 | 4.78 |
can happen in numbers representation. | 4,727.73 | 2.335 |
>> [VIDEO PLAYBACK] | 4,730.065 | 1.235 |
>> -Computers, we've all come to accept
the often frustrating problems that | 4,731.3 | 4.32 |
go with them-- bugs, viruses,
and software glitches, | 4,735.62 | 4.69 |
for small prices to pay
for the convenience. | 4,740.31 | 2.82 |
But in high tech and high speed
military and space program applications, | 4,743.13 | 4.67 |
the smallest problem can
be magnified into disaster. | 4,747.8 | 5 |
>> On June 4th, 1996, scientists prepared
to launch an unmanned Ariane 5 rocket. | 4,752.8 | 6.1 |
It was carrying scientific
satellites designed | 4,758.9 | 2.32 |
to establish precisely how the
earth's magnetic field interacts | 4,761.22 | 3.38 |
with solar winds. | 4,764.6 | 2.81 |
The rocket was built for
the European Space Agency, | 4,767.41 | 3.39 |
and lifted off from its facility
on the coast of French Guiana. | 4,770.8 | 3.57 |
>> -At about 37 seconds into
the flight, they first | 4,774.37 | 3.17 |
noticed something was going wrong. | 4,777.54 | 1.73 |
The nozzles were swiveling in
a way they really shouldn't. | 4,779.27 | 2.98 |
Around 40 seconds into the flight,
clearly, the vehicle was in trouble. | 4,782.25 | 4.33 |
>> And that's when they made
a decision to destroy it. | 4,786.58 | 2.27 |
The range safety officer, with
tremendous guts, pressed the button, | 4,788.85 | 3.93 |
blew up the rocket, before it could
become a hazard to the public safety. | 4,792.78 | 5.37 |
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