[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:05.25,Default,,0000,0000,0000,,Pretend you're me and you're in math class. Actually... nevermind, I'm sick so I'm staying home today
Dialogue: 0,0:00:05.25,0:00:10.45,Default,,0000,0000,0000,,so pretend you are Stanislaw Ulam instead. What I am about to tell you is a true story.
Dialogue: 0,0:00:10.45,0:00:13.78,Default,,0000,0000,0000,,So you are Stan Ulam and you're at a meeting but there's this really boring presentation so
Dialogue: 0,0:00:13.78,0:00:17.58,Default,,0000,0000,0000,,of course you're doodling and, because you're Ulam and not me, you really like numbers...
Dialogue: 0,0:00:17.58,0:00:20.83,Default,,0000,0000,0000,,I mean {\i1}super{\i0} like them. So much that what you're doodling is numbers, just counting
Dialogue: 0,0:00:20.83,0:00:25.38,Default,,0000,0000,0000,,starting with one and spiralling them around. I'm not too fluent in mathematical notation so
Dialogue: 0,0:00:25.38,0:00:29.49,Default,,0000,0000,0000,,so i find things like numbers to be distracting, but you're a number theorist and if you love numbers
Dialogue: 0,0:00:29.49,0:00:32.93,Default,,0000,0000,0000,,who am I to judge? Thing is, because you know numbers so intimately,
Dialogue: 0,0:00:32.93,0:00:37.59,Default,,0000,0000,0000,,you can see beyond the confusing, squiggly lines you're drawing right into the heart of numbers.
Dialogue: 0,0:00:37.59,0:00:40.82,Default,,0000,0000,0000,,And, because you're a number theorist, and everyone knows that number theorists are
Dialogue: 0,0:00:40.82,0:00:44.33,Default,,0000,0000,0000,,enamoured with prime numbers( which is probably why they named them "prime numbers"),
Dialogue: 0,0:00:44.33,0:00:50.13,Default,,0000,0000,0000,,the primes you've doodled suddenly jump out at you like the exotic indivisible beasts they are...
Dialogue: 0,0:00:50.13,0:00:54.82,Default,,0000,0000,0000,,So you start drawing a heart around each prime. Well... it was actually boxes but in my version
Dialogue: 0,0:00:54.82,0:00:59.00,Default,,0000,0000,0000,,of the story it's hearts because you're not afraid to express your true feelings about prime numbers.
Dialogue: 0,0:00:59.00,0:01:02.83,Default,,0000,0000,0000,,You can probably do this instantly but it's going to take me a little longer... I'm all like -
Dialogue: 0,0:01:02.83,0:01:08.17,Default,,0000,0000,0000,,"Does 27 have factors besides one and itself? ... o.0 ... Oh yeah, it's 3 times 9, not prime."
Dialogue: 0,0:01:08.17,0:01:10.38,Default,,0000,0000,0000,,"Hmmm what about 29...? pretty sure it's prime."
Dialogue: 0,0:01:10.38,0:01:14.91,Default,,0000,0000,0000,,But as a number theorist, you'll be shocked to know it takes me a moment to figure these out.
Dialogue: 0,0:01:14.91,0:01:20.09,Default,,0000,0000,0000,,But, even though you have your primes memorised up to at least 1000 that doesn't change that
Dialogue: 0,0:01:20.09,0:01:22.55,Default,,0000,0000,0000,,primes, in general, are difficult to find.
Dialogue: 0,0:01:22.55,0:01:26.89,Default,,0000,0000,0000,,I mean if I ask you to find the highest even number, you'd say, "that's silly, just give me
Dialogue: 0,0:01:26.89,0:01:30.46,Default,,0000,0000,0000,,the number you think is the highest and i'll just add 2.... BAM!!"
Dialogue: 0,0:01:30.46,0:01:39.71,Default,,0000,0000,0000,,But guess what the highest prime number we know is? 2 to the power of 43,112,609 - 1.
Dialogue: 0,0:01:39.71,0:01:44.51,Default,,0000,0000,0000,,Just to give you an idea about how big a deal primes are, the guy that found this one won
Dialogue: 0,0:01:44.51,0:01:47.03,Default,,0000,0000,0000,,a $100,000 prize for it!
Dialogue: 0,0:01:47.03,0:01:50.82,Default,,0000,0000,0000,,We even sent our largest known prime number into space because scientists think
Dialogue: 0,0:01:50.82,0:01:54.68,Default,,0000,0000,0000,,aliens will recognise it as something important and not just some arbitrary number.
Dialogue: 0,0:01:54.68,0:01:57.42,Default,,0000,0000,0000,,So they will be able to figure out our alien space message...
Dialogue: 0,0:01:57.42,0:02:00.16,Default,,0000,0000,0000,,So if you ever think you don't care about prime numbers because they're 'not useful',
Dialogue: 0,0:02:00.16,0:02:04.81,Default,,0000,0000,0000,,remember that we use prime numbers to talk to aliens, I'm not even making this up!
Dialogue: 0,0:02:04.81,0:02:10.31,Default,,0000,0000,0000,,It makes sense, because mathematics is probably one of the only things all life has in common.
Dialogue: 0,0:02:10.31,0:02:14.34,Default,,0000,0000,0000,,Anyway, the point is you started doodling because you were bored but ended up
Dialogue: 0,0:02:14.34,0:02:18.20,Default,,0000,0000,0000,,discovering some neat patterns. See how the primes tend to line up on the diagonals?
Dialogue: 0,0:02:18.20,0:02:21.99,Default,,0000,0000,0000,,Why do they do that?... also this sort of skeletal structure reminds me of bones so
Dialogue: 0,0:02:21.99,0:02:25.82,Default,,0000,0000,0000,,lets call these diagonal runs of primes: Prime Ribs!
Dialogue: 0,0:02:25.82,0:02:29.77,Default,,0000,0000,0000,,But how do you predict when a Prime Rib will end? I mean, maybe this next number is prime...
Dialogue: 0,0:02:29.77,0:02:32.69,Default,,0000,0000,0000,,(but my head is too fuzzy for now this right now so you tell me.)
Dialogue: 0,0:02:32.69,0:02:35.92,Default,,0000,0000,0000,,Anyway...Congratulations, You've discovered the Ulam Spiral!
Dialogue: 0,0:02:35.92,0:02:38.04,Default,,0000,0000,0000,,So that's a little mathematical doodling history for you.
Dialogue: 0,0:02:38.04,0:02:41.22,Default,,0000,0000,0000,,Yyou can stop being Ulam now... or you can continue. Maybe you like being Ulam. (thats fine)
Dialogue: 0,0:02:41.22,0:02:46.72,Default,,0000,0000,0000,,However you could also be Blaise Pascal. Here's another number game you can do using
Dialogue: 0,0:02:46.72,0:02:50.06,Default,,0000,0000,0000,,Pascal's triangle.(I don't know why I'm so into numbers today but I have a cold so
Dialogue: 0,0:02:50.06,0:02:55.08,Default,,0000,0000,0000,,if you'll just indulge my sick predelections maybe I'll manage to infect you with my enthusiasm :D
Dialogue: 0,0:02:55.08,0:02:59.12,Default,,0000,0000,0000,,Pascal's Triangle is the one where you get the next row in the triangle by adding two adjacent
Dialogue: 0,0:02:59.12,0:03:03.78,Default,,0000,0000,0000,,numbers. Constructing Pascal's Triangle is, in itself a sort of number game because it's not just
Dialogue: 0,0:03:03.78,0:03:07.38,Default,,0000,0000,0000,,about adding, but about trying to find patterns and relationships in the numbers so you
Dialogue: 0,0:03:07.38,0:03:09.16,Default,,0000,0000,0000,,don't have to do all the adding.
Dialogue: 0,0:03:09.16,0:03:12.61,Default,,0000,0000,0000,,I don't know if this was discovered through doodling but it was discovered independantly in:
Dialogue: 0,0:03:12.61,0:03:16.60,Default,,0000,0000,0000,,France, Italy, Persia, China and probably other places too so it's possible someone did.
Dialogue: 0,0:03:16.60,0:03:19.44,Default,,0000,0000,0000,,Right... so I don't actually care about the individual numbers right now.
Dialogue: 0,0:03:19.44,0:03:24.75,Default,,0000,0000,0000,,So, if you still Ulam, you pick a property and highlight it(e.g. if it's even or odd)
Dialogue: 0,0:03:24.75,0:03:29.75,Default,,0000,0000,0000,,If you circle all the odd numbers you'll get a form which might be starting to look familiar.
Dialogue: 0,0:03:29.75,0:03:33.12,Default,,0000,0000,0000,,And it makes sense you'd get Sierpinski's Triangle because when you add
Dialogue: 0,0:03:33.12,0:03:35.41,Default,,0000,0000,0000,,an odd number and an even number, you get an odd number.
Dialogue: 0,0:03:35.41,0:03:38.24,Default,,0000,0000,0000,,(odd + odd) = even and (even + even) = even... So it's just like the
Dialogue: 0,0:03:38.24,0:03:42.94,Default,,0000,0000,0000,,crash and burn binary tree game. The best part about it is that, if you know these properties, you can
Dialogue: 0,0:03:42.94,0:03:45.70,Default,,0000,0000,0000,,forget about the details of the numbers
Dialogue: 0,0:03:45.70,0:03:50.48,Default,,0000,0000,0000,,You don't have to know that a space contains a 9 to know that it's going to be odd.
Dialogue: 0,0:03:50.48,0:03:55.80,Default,,0000,0000,0000,,Now, instead of two colours, let's try three. we'll colour them depending on what the remainder is
Dialogue: 0,0:03:55.80,0:03:57.94,Default,,0000,0000,0000,,when you divide them by three(instead of by two).
Dialogue: 0,0:03:57.94,0:03:59.30,Default,,0000,0000,0000,,Here's a chart! :)
Dialogue: 0,0:03:59.30,0:04:03.33,Default,,0000,0000,0000,,So, all the multiples of three are coloured red, remainder of one will be coloured black and
Dialogue: 0,0:04:03.33,0:04:07.86,Default,,0000,0000,0000,,remainder of two will be coloured green. The structure is a little different from Sierpinski's Triangle
Dialogue: 0,0:04:07.86,0:04:12.36,Default,,0000,0000,0000,,already but I'm tired of figuring out remainders based of individual numbers, so
Dialogue: 0,0:04:12.36,0:04:16.05,Default,,0000,0000,0000,,Let's figure out the rules... If you add up two multiples of three you always get
Dialogue: 0,0:04:16.08,0:04:21.20,Default,,0000,0000,0000,,another multiple of three( which is the sort of fact you use everday in math class)
Dialogue: 0,0:04:21.20,0:04:22.94,Default,,0000,0000,0000,,However, here this means (red + red) = red.
Dialogue: 0,0:04:22.94,0:04:26.40,Default,,0000,0000,0000,,and when you add a multiple of three to something else, it doesn't change it's remainder.
Dialogue: 0,0:04:26.40,0:04:30.88,Default,,0000,0000,0000,,So, (red + green) = green and (red + black) = black.
Dialogue: 0,0:04:30.88,0:04:34.71,Default,,0000,0000,0000,,(remainder 1 + remainder 1) = remainder 2, (remainder 2+ remainder 2) = remainder 4
Dialogue: 0,0:04:34.71,0:04:40.29,Default,,0000,0000,0000,,and the remainder of 4 divided by 3 is one and (1+2) = 3 remainder 0. (whew...)
Dialogue: 0,0:04:40.29,0:04:43.58,Default,,0000,0000,0000,,The bottom line is you're making up some rules as to what coloured dots combine to
Dialogue: 0,0:04:43.58,0:04:46.28,Default,,0000,0000,0000,,produce which other coloured dots and then you're following those rules to their
Dialogue: 0,0:04:46.28,0:04:49.34,Default,,0000,0000,0000,,mathematical and artistic conclusion...
Dialogue: 0,0:04:49.34,0:04:52.52,Default,,0000,0000,0000,,The numbers themselves were never necessary to get this picture.
Dialogue: 0,0:04:52.52,0:04:56.75,Default,,0000,0000,0000,,Anyway, those are just a couple of examples of number games that are out there but you should
Dialogue: 0,0:04:56.75,0:05:00.77,Default,,0000,0000,0000,,also try making up your own. For example, I have no idea what you'd get if you
Dialogue: 0,0:05:00.77,0:05:04.06,Default,,0000,0000,0000,,highlighted the prime numbers in Pascal's Triangle, maybe nothing interesting(who knows...)
Dialogue: 0,0:05:04.06,0:05:07.90,Default,,0000,0000,0000,,Or, what happens if, instead of adding to get the next row, you start with a two(and a sea of invisible ones)
Dialogue: 0,0:05:07.90,0:05:10.91,Default,,0000,0000,0000,,and multiple two adjacent numbers to get the next row.
Dialogue: 0,0:05:10.91,0:05:13.52,Default,,0000,0000,0000,,I've no idea what hapens there either or if it's already a 'thing' people do.
Dialogue: 0,0:05:13.52,0:05:16.32,Default,,0000,0000,0000,,(Hmmm? o.0 Powers of two...)
Dialogue: 0,0:05:16.32,0:05:19.20,Default,,0000,0000,0000,,I know another way to write this. Ok, that makes sense.
Dialogue: 0,0:05:19.20,0:05:24.24,Default,,0000,0000,0000,,Then there is also a thing called Floyd's Triangle where you put the numbers like this...
Dialogue: 0,0:05:24.24,0:05:25.60,Default,,0000,0000,0000,,Maybe you can do something with that as well.
Dialogue: 0,0:05:25.60,0:05:26.89,Default,,0000,0000,0000,,... Man, it seems like everyone has a triangle these days...
Dialogue: 0,0:05:26.91,0:05:28.00,Default,,0000,0000,0000,,I'm going to take a nap... ZZZzzz...