Some silly number systems

Silly little video about silly little (and some very big) base systems.

[RandomAndgit]

Hey guys (said gender neutrally of course). Here are a couple very minor corrections:
-Quite a major mistake on my part: when doing the calculations for base -i for 5:47, I forgot to place parenthesis around -i, which lead the results to being equal to -1(i^x) rather than "-i, -1, i, 1..." like it should have been. That's completely my mistake.
-I used the wrong spelling of whether at 6:03
-I said at 4:53 that phi was the number that satisfied the equation sqrt(x) = x - 1when the real answer is (sqrt(5) + 3)/2. The correct form of that equation would be that 1/phi = phi - 1. It's a very minor mistake but still important to point out.
-At 2:42 I say that base 18, 446, 744, 073, 709, 551, 616 was for a 64 by 64 grid but that base only satisfies all possible combinations of an 8 by 8 grid. A real 64 by 64 grid base would be closer to 1.322112e+123.
-The Japanese "100" symbol at 3:07 is slightly malformed, it needs an extra line at the bottom.
-I use the term irrational at 4:30 which may have confused some people. The term irrational technically only refers to weather a number can be expressed as a fraction but it is a very useful way of describing a number with infinite, non-repeating digits.
-I accidentally refer to what is called a multiplicative system as a bijective system instead.
-I, in my foolishness, have made the music too loud. D:

I promise there aren't always this many mistakes! Sorry!

[EdKolis]

In base infinity, every number has its own unique symbol! Sort of like writing numbers with words...

[jandor]

- Let's try to write something in nullary
- So we have zero symbols, so we can't write anything
- Rejects to elaborate further
- Leaves

[MiScusi]

For anyone curious, the background music is the third movement from Beethoven's 14th sonata

[glowing_aurora]

i cant believe when we learned expanded form to express numbers in 3rd grade we were peeking into the abyss that is the mathematical bases

[dawg]

"NOOOO WE NEED TO USE BASE 6 ITS THE FUTURE" - Some mathematician, probably

[bow-tiedengineer]

Base 12 is my favorite base. It isn't inconveniently large, and is divisible by 3 and 4. We used to use it on a large scale as well before the Arabic numerals became the standard, that's where the dozen comes from, and is why eleven and twelve have unique names instead of being lumped in with the 'teens.

[tlatai]

I once read this SCP where an AI was created to devise better compression algorithms for the Foundation's archives, only to remove itself from existence. While the documents in the affected archives had practically disappeared, it was somehow still possible to access them. It turns out the AI figured out how to use nullary: this base can only be understood from a certain frame of reference (Q) which is incompatible with that of normal human thought (K). And a researcher trying to find where the data went ends up becoming nonexistent as well, so yeah we better not let number exist in nonexistence

[lagomoof]

4:34 - Common misconception. Rational numbers (including integers) are still rational regardless of whether they have an infinitely long, seemingly random representation. The failing is in the base, not the number. You could say "they appear irrational to people who are familiar with how irrational numbers look in more commonly used bases", but that's about all. They're still rational no matter how they look.

Rational means "can be written as the ratio of two integers". This says nothing about how the number or the integers in its ratio happen to look when that writing is done.

[lockaltube]

- Do you know that you can use different radix for every position?
- What a silly idea! Nobody would use such a system!
(this comment was written at second 2024 10 11 00 19 41 given place value [31558149.8, 525969.163, 86400, 3600, 60, 1], sidereal year and some timezone)

[TrimutiusToo]

Not even mention of base64 and base85 which are both actually used in computer science... (64 for obvious reasons and 85 is actually just the number of printable ASCII characters, so it uses all of them as symbols for the base)

[zerid]

Why use base Infinite when you could just use base -1/12?

[ferenccseh]

"You think you're doing some damage?
2 plus 2 is-... 10
IN BASE 4, I'M FINE"
- GLaDOS

[jerichaux]

I wrote a “big number” program once, which used base (2**64) (meaning every “digit” was a 64-bit digit).

So, instead of 0-9, it was
0-18, 446, 744, 073, 709, 551, 615.

One of the fun things (?) was figuring out a system for overflow-proof multiplication, while still remaining as performant as possible. You could get some ludicrously big numbers with that thing.

For example, it’s much like how the “2” in the tens-position of the decimal number 23 represents (2 * (10 ** 1)), giving us 20, to which the 3 in the ones-position is then added for the final result of 23.

But, in this case, [2, 3] in base (2 ** 64) - and I’m representing the digits in an array, to avoid confusion - means we have:
• (2 * ((2 ** 64) ** 1)
= 36, 893, 488, 147, 419, 103, 232
plus
• (3 * ((2 ** 64) ** 0)
= 3
for a total of:

36, 893, 488, 147, 419, 103, 235

In decimal, if we have [1, 0, 0], we get 100. In base (2 ** 64), [1, 0, 0] is instead:

• (1 * ((2 ** 64) ** 2))
= 340, 282, 366, 920, 938, 463, 463, 374, 607, 431, 768, 211, 456

So, you can see how these numbers quite readily get very out of hand!

If you had a 1 in the 64th digit position base 10, and zeroes in the rest, that would be pretty crazy! It would be a 1 followed by 63 0s!:

1, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000

That’s a lot of number!

But, if you did the same thing with base (2 ** 64), you get something a little more insane:

56, 616, 434, 707, 392, 290, 493, 830, 608, 686, 343, 291, 913, 914, 207, 267, 329, 621, 488, 609, 504, 077, 443, 092, 998, 260, 469, 825, 507, 336, 856, 810, 827, 911, 261, 368, 707, 758, 178, 809, 587, 148, 432, 632, 037, 424, 161, 064, 675, 500, 873, 383, 487, 082, 580, 173, 608, 658, 838, 616, 501, 128, 049, 812, 714, 217, 651, 328, 283, 024, 830, 073, 412, 384, 889, 815, 432, 597, 905, 927, 601, 958, 951, 314, 543, 937, 080, 343, 085, 064, 110, 993, 312, 334, 723, 049, 547, 437, 731, 770, 779, 823, 050, 760, 639, 880, 425, 500, 165, 204, 989, 981, 997, 213, 399, 871, 161, 087, 661, 501, 312, 220, 225, 137, 504, 516, 172, 823, 917, 738, 211, 300, 299, 807, 381, 757, 818, 984, 800, 273, 856, 795, 211, 620, 996, 748, 504, 363, 142, 690, 436, 276, 062, 613, 301, 784, 444, 812, 913, 670, 500, 602, 718, 367, 796, 525, 145, 427, 307, 300, 283, 865, 951, 803, 998, 808, 065, 639, 029, 170, 703, 022, 449, 468, 190, 319, 930, 507, 340, 988, 677, 523, 066, 084, 721, 639, 425, 495, 152, 552, 125, 131, 611, 082, 991, 384, 744, 696, 522, 708, 197, 306, 203, 186, 569, 928, 692, 274, 528, 086, 558, 201, 803, 207, 638, 020, 888, 691, 121, 265, 434, 197, 293, 907, 218, 384, 095, 520, 560, 555, 896, 947, 150, 944, 133, 055, 863, 397, 615, 648, 411, 112, 470, 754, 656, 110, 748, 811, 237, 653, 374, 788, 477, 716, 072, 552, 588, 609, 616, 376, 430, 894, 096, 481, 364, 501, 294, 655, 654, 823, 142, 548, 823, 259, 752, 215, 716, 293, 351, 999, 419, 717, 562, 306, 177, 064, 929, 632, 050, 689, 015, 014, 405, 578, 694, 408, 614, 353, 540, 180, 649, 410, 108, 905, 523, 548, 191, 355, 424, 055, 272, 181, 142, 840, 177, 487, 296, 189, 764, 022, 300, 385, 934, 884, 483, 982, 341, 901, 658, 184, 426, 332, 624, 776, 972, 085, 905, 793, 515, 459, 600, 620, 068, 183, 625, 181, 327, 963, 636, 494, 799, 582, 466, 830, 531, 258, 661, 325, 767, 796, 742, 142, 353, 530, 480, 288, 174, 823, 736, 291, 072, 477, 683, 720, 590, 971, 289, 642, 787, 198, 230, 081, 364, 301, 868, 392, 910, 675, 871, 538, 608, 754, 231, 607, 296

That’s a number 1, 214 digits long when represented in base 10!

[dancinswords]

We all use base 0 far more than we do base 10; whenever you're not writing numbers, you're using base 0

[lotgc]

When I was in basic training I invented a base 60 system, and I'm actually amazed by how easy it is to use

It basically functions like the Mayan system. There's a handful of symbols that you combine to get a value up to 60. A dot is one, a bar is 5, a triangle with it's point up is 15, a triangle pointed down is 30, an equal sign looking thing is 0, and a circle is 60.

You combine them, largest to smallest, top to bottom, but you can subtract smaller numbers from bigger ones by writing the smaller number above the larger one. For example, you can write 27 like this

∆ 15
_ +5
_ +5
.. +2

Or you can save a bit of time and space by writing it like this

... -3
V 30 (pretend V is a triangle)

This system would probably be very good for teaching math to kids because you can visually see what's happening when you do basic arithmetic.

[SheshadriMondal]

7:06 I love the fact that O and Z are technically saying the same thing

[KarlFredrik]

Hard to beat p-adic as a crazy base while still being useful.

[AntoineADubai]

I doesn't really matter, from their point of view, all bases are base-10.

[mrhalp]

There is also a number system based on Fibonacci numbers, it is quite exotic and rare, but no less interesting