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 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!
Another minor correction: base -𝒾 does not cycle in the same direction as base 𝒾, but in the opposite direction: (-𝒾)² = -1, (-𝒾)³ = 𝒾, (-𝒾)⁴ = 1, and so on. If I may do some armchair inference, I believe you might have forgotten your parentheses when calculating base -𝒾, and instead calculated the negative of base 𝒾, which indeed cycles in the same direction.
Not trying to dogpile you further but: • What you describe as a bijective number system is actually a multiplicative system. • The Japanese/Chinese character for 100 is 百; you missed a line on the bottom. • Honestly I really like the music! I wouldn’t lower it too much I still really like the video though; I’m subscribing for sure. Plus I love your artstyle; reminds me of Typoman.
Why not order the things in this comment so that when watching the video the viewer can easily see when the next correction is? (Though any major mistake can stay at the top or something)
@@randy-x They probably meant using Chinese characters as numerals, not just the Chinese numerals. That being said, that's still not base-∞, "only" base-3500 or base-6500.
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)
Hexadecimal (base 16) is much more common, at least by humans who work with computers, than base 64. The main reason for its utility is that each "digit" of Hex can be directly translated into 4 "digits" of binary because 16 is equal to 2^4. Thus you can easily convert between them as needed, taking advantage of using fewer digits when writing long numbers, but being able to break down individual binary bits when needed.
- 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)
@@lockaltube The only thing that remains constant, is the modernist interpretation of the idea of constancy, hypothetically existing outside of personal interpretation; I'll be honest, I have no idea what I'm talking about, but you've read this far ☺Edited: to show I edit therefore am not bot, unless...what if I was a robot and didn't know it?
You missed part where negative base can represent all integers(positive and negative). A base with some negative digits can also do that. Like balanced ternary.
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.
A lot of ink has been used to explain "intuitive" concepts in rigorous mathematical detail, precisely because of how often our intuition is wrong in fringe cases. I remember going through my master's level number theory course where they rigorously defined what natural numbers are (using set theory; it's crazy how complicated you have to be with it to fit how they're actually used in the real world while also satisfying everything they need to be mathematically). It's important to remember that literally everything in math is a construct, so in another timeline we could have defined integers (and therefore rational numbers) differently such that the statement would have been correct. But yeah, as things stand the base we choose to represent them in does not change whether a number is rational or not.
For the primes "base" instead of using the "tally" method to indicate how many factors of each prime is included in a number, we use a "meta" base or system to count the factors of each prime along with the new prime symbols to indicate the prime being counted. Say that we use base 10 for our meta base and a=1, b=2, c=3, d=5, e=7, etc for our prime symbols. Them we would get: 1 = 1a 2 = 1b 3 = 1c 4 = 2b 5 = 1d 6 = 1b1c 7 = 1e 8 = 3b 9 = 2c 10 = 1b1d Etc. Of course we could nest this by using a version of this system as the "meta" base. Suppose that we use capital letters in the meta base, and omit the use of the symbol "1" Then 1 = 1a = Aa 2 = 1b = Ab 3 = 1c = Ac 4 = 2b = Bb 5 = 1d = Ad 6 = 1b1c = AbAc 7 = 1e = Ae 8 = 3b = Cb 9 = 2c = Bc 10 = 1b1d = AbAd 48 = 4b1c =2BbAc Etc.
This video is very entertaining for a math video, i have a critic however. The volume of the music is louder than the voice, maybe you can lower the volume of the music. Other than that it is very good and underrated.
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
base sqrt(2) includes all integers + all multiples of sqrt(2). For example, 111 is 1+sqrt(2)+sqrt(2)^2, or 3+sqrt(2). I don't expect that's particularly useful, but there you go.
Very interesting to learn about these weird bases but on a more practical note, base six or base twelve is infinitely better than base ten. Ten though not the worst is far from the best choice for base of everyday numbers. Of course, for computers, the only base that works is binary.
I don't know what the deal with those 2 dots over the numbers is supposed to be, but I can type some symbols like ö, ä, and ë so that might be it, I have seen other languages use those dots.
@@jackcraftsolar Ah, excellent query. With regard to the numbers, it's just to make them look a little more like little creatures but in other languages, the dots act as accent markers to slightly change the sound that a vowel makes.
@@jonasgajdosikas1125That’s not really true. You’re getting it mixed up with counters, which are more like units, or like “head” in “head of cattle”. With only a few exceptions, everything gets counted with the same sino-Japanese numerals
eu já testei a base 64K, precisa de apenas 4 letras para ser equivalente exatamente a um numero em 16E(~18.5quintilhões), então técnicamente já brinquei com essa base, com a função python asseguir dá para fazer a conversão bidirecional apartir de um inteiro, o python limita (10^10^4300); I have already tested the base 64K, it only needs 4 letters to be equivalent to 16E (~18.5 quintillion), with the following python function you can do the bidirectional conversion from an integer, python limits (10^10^4300); --- import sys sys.set_int_max_str_digits(0) def NK(n: float) -> str: """Converte um número de ponto flutuante para uma string codificada em base de caracteres imprimíveis.""" if n == 0: return p(0) integer_part = int(n) fractional_part = n - integer_part # Convertir parte inteira Bn_integer = '' while integer_part > 0: remainder = integer_part % 65536 Bn_integer = p(remainder) + Bn_integer # Usar função 'p' para pegar o caractere imprimível integer_part //= 65536 # Convertir parte fracionária Bn_fractional = '' precision = 10 # Ajuste a precisão conforme necessário while precision > 0 and fractional_part > 0: fractional_part *= 65536 digit = int(fractional_part) Bn_fractional += p(digit) # Usar função 'p' para pegar o caractere imprimível fractional_part -= digit precision -= 1 # Adicionar ponto decimal se houver parte fracionária if Bn_fractional: return Bn_integer + '.' + Bn_fractional else: return Bn_integer if Bn_integer else p(0) def KN(Bn: str) -> float: """Converte uma string codificada em base de caracteres imprimíveis de volta para um número de ponto flutuante.""" if '.' in Bn: integer_part, fractional_part = Bn.split('.') else: integer_part = Bn fractional_part = '' # Converter parte inteira n = 0 for ch in integer_part: oc = ip(ch) # Usar função 'ip' para pegar o índice do caractere imprimível n = n * 65536 + oc # Converter parte fracionária fractional_value = 0 base = 1 for ch in fractional_part: oc = ip(ch) # Usar função 'ip' para pegar o índice do caractere imprimível fractional_value = fractional_value * 65536 + oc base *= 65536 # Adicionar parte fracionária ao número final return n + fractional_value / base def p(index): """Converte um índice de 0 a 65535 para o caractere Unicode imprimível correspondente.""" count = 0 for code_point in range(0, 0x10FFFF + 1): char = chr(code_point) if char.isprintable(): # Salta caracteres não imprimíveis if count == index: return char count += 1 raise ValueError("Índice fora do intervalo imprimível.") def ip(char): """Converte um caractere imprimível para seu índice (de 0 a 65535).""" count = 0 for code_point in range(0, 0x10FFFF + 1): if chr(code_point).isprintable(): if chr(code_point) == char: return count count += 1 raise ValueError(f"Caractere '{char}' não encontrado na lista de imprimíveis.") just a small excerpt, 4tuple number, power|root: 55|37: W|37|W|55.0 ැ|bd1|'.澘𗉿빗|7.416198487095663 "軴|289e7|#.퍯俬㮍蔍|3.802952460761391 Îꖽ|8ba0a1|".뼉㫸र蔍|2.7232698153315003 ∶螤|1dff8297|".㾠⌞蛩엡|2.2288073840335185 &盲ᄑ|671e50e71|!.𔐔퍰蓦𐬫|1.9501160121288659 ƥ絃ḕ|16278361a47|!.쮭秜𒓢ኪ|1.7726510055204765 儴殺ꬉ|4c27d39fa541|!.걖떿䫮𓄉|1.650233260885109 0憛籙蘄|105c8e774c80f7|!.钣틾䰷𓄉|1.5608947941283693 Ϗ𑂌ꚟ뫲|383e29ba16fb511|!.茼𓋯퉴𐬫|1.4929190815424387 윶땐든𑜧|c155af6faeffe6a7|!.疐엚谏䔍|1.4395103439519596 I蹵뛟鸇鋮|298968b0fe98fa8de1|!.檋짭⼎⑥|1.3964655427646133 ৈ誋ܦ𐠣聤|8ec857e06b2ddd47b57|!.慺쩍說뗡|1.3610499158553278 !𒂫돴畺꺇蒾|1ead0ae13706da8a67fb1|!.姤䐻𖣓蔍|1.3314094056752328 «矢欺⯷䃒琔|6972d5662d278f3bc56f07|!.卲𗇋㬈𐬫|1.306243611083104 ᧷놹𔒍蓒ﻷ𐌶|16a7abd8f3b37fc5d76ada81|!.䷩籷筟⑥|1.2846140513341386 $𐡛𒅷悝碎䴁𓋀|4de05eb9c5b90738147f4f1b7|!.䤚㸮씥𐬫|1.2658267695799341 Ŏ뤦ꎧ뇩횧窬𒒞|10bb3459e97ac08d0c6759fee51|!.䓢𑰹눲𓄉|1.2493577526586888 㺐褂ᕙ𖡷𐍝䩩㡴|398383f51295f5e4daa3455c3367|!.䄩∍旄𐬫|1.234804024542171 ,恎庳𗓌ﭝ𖽄𑠓ആ|c5b4159a6fe37d42af913e6cf0b21|!.㷘㧏菫헡|1.2218506789057486 ˪ꀚ䟭ꌎ驈術鮈椤|2a79b0a42e09dfe953b8346967b6417|!.㫟ퟭ퉜ኪ|1.2102481119331794 霏呁捎𓊻ተ㤷妏藾|92024f345e41f1b20fc9342a548280f1|!.㠲ﬥ፭뗡|1.19979595929973 ?掌Ҍ䔷𒌜楇㨥ⱳ릨|1f5e7f0440402aed41643a35182809b3c7|!.㗆陾穯⑥|1.1903315450666772 ܱ剖𑶘켙𖼽趎洽鼢ꓝ|6bd4d49e9cdc938f90c888168309a159fc1|!.㎒僄䩍锍|1.181721431964663 !瞸鿮䁃䁊蚾壚松ṳ垄|172ab9ae13b363b3d81b153cd62711aa55277|!.ㆀ쬰敤⑥|1.1738551443853251 oꡋ䭰뺇쀗𐚺ţ⪱뽥뵲|4fa2de4663b8a6ba36dd190120264cb984b791|!.⽿𓎰䯤㔍|1.1666404398336823 [...] I want to make it clear that the 64k printable characters used is not the same as utf-16le which uses 16b and also 64k characters, but not all of them are printable; *For obvious reasons, chaGPT did not learn or manage to do any math with this base (I even have the intuition that it learns by the average of what is already used, without anything new) *my purpose with this was to use it in a 64k^64k sudoku expressed in equations
Problem with base pi is that it still sucks even for pi, if you were to write 4pi in base pi, it would be a decimal too. 30 would be equal to 3pi, 33 would be 3pi+3, but the next number, 100 would be pi^2
I'm pretty sure phi isn't special when it comes to irrational bases. I have this gut feeling that any root expression for a base can express integers in finitely many digits Like. If I set the base R = sqrt(2) + 1 then I have the relation R^2 = 2R + 1, which manifests in the base as 100 = 021 So a number like 3 would be written as 10.11, and 12 as 200.02 Not too sure since I haven't tested anything from nested roots or cubics or anything higher degree but I feel like it should hold Funny enough, you need ten symbols for base S = sqrt(6) - 1 because S^2 = 2S + 9 (100 = 029) So 0-9 is still 0-9 but 10 (actual Ten) would now be written as 9.29 and 11 would be... uhhh... huh. no clue, actually
I prefer base 12 (a high composite number) instead of 10. by the way, phi isn't the only irrational number that has that property that makes it easy to write any natural number with finite digits. any of the metal ratios (golden ratio, silver ratio, broze ratio, ...) has this property.
@@RandomAndgit I disagree on base 16. base 16 is only useful because it's a power of 2 and powers of two are easy to manage with computers but 16 only has a single divisor (2) while bases 6 and 12 have two possible divisors (2 and 3)
@@WilliamWizer one reason that people say bases 6 and 12 are better than base 10 is because of the expansions of fractions (specifically reciprocal primes) fraction = decimal = seximal = dozenal = hex, terminating expansions are in italics, repeating expansions are truncated after one full pattern 1/2 = _.5_ = _.3_ = _.6_ = _.8_ 1/3 = .3... = _.2_ = _.4_ = .5... 1/5 = _.2_ = .1... = .2497... = .3... 1/7 = .142857... = .05... = .186A35... = .249... 1/11 = .09... = .0313452421... = .1... = .1745D... 1/13 = .076923... = .024340531215... = .0B... = .13B... 1/17 = .0588235294117647... = .0204122453514331... = .08579214B36429A7... = .0F... 1/19 = .052631578947368421... = .015211325... = .076B45... = .0D79435E5... while hex may have a lot of repeated digit fractions, it usually has relatively short digit patterns compared to bases 10, 6, and 12
I'm disappointed you didn't mention the mixed-radix base-factorial system, where every natural number is written like xyz.abc = ... + x*3! + y*2! + z*1!/1! + a/2! + b/3! + c/4! + ... (where z
obscure numbering system: tic-xenotation (TX): - 2 is written as : - (n) is the nth prime number (1-indexed, starting from 2) - every number is written as its factors 2 : 3 (:) (the 2nd prime) 4 :: 5 ((:)) (3rd prime) 6 :(:) 7 (::) (4th prime) 8 :: 9 (:)(:) 10 :((:)) it's possible to write any integer greater than 2 in this fashion. very impractical since the system is based on factors (even basic addition is impossible without rewriting into a modulus-based system).
I came up with the exact same thing, except instead of using : to denote 2 you just have a blank number represent 1. And if you substitute 1 and 0 for ( and ) you get a very, very cursed form of binary
I love the videos, very interesting stuff! 1 constructive criticism is that the background music was a tiny bit too loud, Its a little distracting. Might just be me though, keep up the work man!
Much too loud! Why is it there at all? Much as I like Beethoven I would rather listen to him without the distraction of the video and I would rather watch the video without the distraction of the music. It's a long time since I was in an education establishment. Is it now normal to have background music in the classroom.
Why is a base 7 number hard to divide? For instance 15 is a perfectly fine base 7 number. It can be divided by 2, 3, 4, and 6. More? 33 can be also be divided by 13 (and 2, 3, 4 and 6 as well).
While that's true, there are a couple of reasons why it's still terrible. -A lot of fractions that would be pretty easier to write become a bit more annoying. (1/2 is now 0.333...) -A lot of smaller, more useful numbers like 2, 3, 4, 5 and 6 get much longer patterns. Also I think you might have misunderstood how bases work because you seem to either be suggesting that 33 is divisible by 13 (which it isn't) or that 24 is divisible by 10 (which it isn't).
7:20 zero to the power of something is equal to zero but at the same time (0!) zero multiplied by NOTHING is equal to one mathematicians still haven't made friends with logic
would that make language, such as say the english language, a base (26 add any symbols such as full stops, brackets etc) - or does language also include all numbers? Basically does your keyboard contain all the subjects (idk to call it) of the language?
Random Bases That Might Exist With Random Order Base G64 Base Tree(3) Base Tree(4) Base 10^100 Base 10^10^100 Base Omega 0 Base Zeta 0 Base Epsilon 0 Base Eta 0
@@Psi_Fan123 I think you actually _could_ have omega as a number system. It'd mean assigning a different symbol to every natural number less than omega, which is every natural number. I'm no set theorist but I figure it might end up looking something like Cantor normal form, where the rightmost digit is the finite component, the second digit is the factor of omega, the third is the factor of omega^2, etc.
@@Psi_Fan123 It's weird but I feel like you could still make it work. Maybe it'd end up looking like the surreals or something. Granted, you wouldn't be able to express (say) 0.5. But you could still end up with a self-consistent ordered ring, maybe even an ordered field.
0:13 "...which means me use ten symbols..." Comment:: it does not mean that. It means we use groups of ten, and the need of such ten symbols is a consequence but wow! I would have thought of using any other base than naturals >= 2. I´ts hard to thing in "groups" of pi or 1+ 3i 😆 Other interesting bases are 60 for time 64 widely used in cryptography to represent "human readable" binary data. Any base will do but 64 was chosen since it represents large amounts of data in a relatively short strings 12 for commerce since it has more divisors than 10 Although mentioned I guess it must be more strongly stated that In any base, 1 will be represented as 1, and 0 as 0 In any base, the base it self will always be represented as 10 Why we use base 10? I always ask this to my students when we start learning about number systems. When they begin to 🤔 I sardonically say "don't think, you have the answer in your hands"
Well, the general idea is that, because exponents and roots of phi directly tie to natural numbers, you can always express an integer using them. The actual algorithm to do this is quite complicated though and I don't think I understand it well enough to give a full explanation.
I like your little typographic guys living their best typographic lives. Did you by any chance get inspiration from the reddit community r/constantscript ?
I've never heard of r/constantscript until this very moment but I might have to go and look at it right now because I *am* quite the fan of silly little typography guys.
Oh, yes, you're quite right! Thank you. The actual size of that base, just for interest, is 1,044,388,881,413,152,506,691,752,710,716,624,382,579,964,249,047,383,780,384,233,483,283,953,907,971,557,456,848,826,811,934,997,558,340,890,106,714,439,262,837,987,573,438,185,793,607,263,236,087,851,365,277,945,956,976,543,709,998,340,361,590,134,383,718,314,428,070,011,855,946,226,376,318,839,397,712,745,672,334,684,344,586,617,496,807,908,705,803,704,071,284,048,740,118,609,114,467,977,783,598,029,006,686,938,976,881,787,785,946,905,630,190,260,940,599,579,453,432,823,469,303,026,696,443,059,025,015,972,399,867,714,215,541,693,835,559,885,291,486,318,237,914,434,496,734,087,811,872,639,496,475,100,189,041,349,008,417,061,675,093,668,333,850,551,032,972,088,269,550,769,983,616,369,411,933,015,213,796,825,837,188,091,833,656,751,221,318,492,846,368,125,550,225,998,300,412,344,784,862,595,674,492,194,617,023,806,505,913,245,610,825,731,835,380,087,608,622,102,834,270,197,698,202,313,169,017,678,006,675,195,485,079,921,636,419,370,285,375,124,784,014,907,159,135,459,982,790,513,399,611,551,794,271,106,831,134,090,584,272,884,279,791,554,849,782,954,323,534,517,065,223,269,061,394,905,987,693,002,122,963,395,687,782,878,948,440,616,007,412,945,674,919,823,050,571,642,377,154,816,321,380,631,045,902,916,136,926,708,342,856,440,730,447,899,971,901,781,465,763,473,223,850,267,253,059,899,795,996,090,799,469,201,774,624,817,718,449,867,455,659,250,178,329,070,473,119,433,165,550,807,568,221,846,571,746,373,296,884,912,819,520,317,457,002,440,926,616,910,874,148,385,078,411,929,804,522,981,857,338,977,648,103,126,085,903,001,302,413,467,189,726,673,216,491,511,131,602,920,781,738,033,436,090,243,804,708,340,403,154,190,336.
base of x is a pretty silly system. You have no idea what system your using. Also base 0.1 would be great. Infinite digits to memorize. Sign me up. Ok, who decided to have a negative number of symbols. How would that even work?
I just can't watch your videos with that music... Too loud and too distracting... Lasted almost 2 minutes before I paused and moved on... PLEASE change the background music !
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 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!
another small error is at 5:50 in the corner "weather" is written instead of whether, still loved your video though!
Another minor correction: base -𝒾 does not cycle in the same direction as base 𝒾, but in the opposite direction: (-𝒾)² = -1, (-𝒾)³ = 𝒾, (-𝒾)⁴ = 1, and so on.
If I may do some armchair inference, I believe you might have forgotten your parentheses when calculating base -𝒾, and instead calculated the negative of base 𝒾, which indeed cycles in the same direction.
@@TheBasikShow You are precisely right, yes, thank you. That really is quite a comically foolish oversight of mine. Thanks very much.
Not trying to dogpile you further but:
• What you describe as a bijective number system is actually a multiplicative system.
• The Japanese/Chinese character for 100 is 百; you missed a line on the bottom.
• Honestly I really like the music! I wouldn’t lower it too much
I still really like the video though; I’m subscribing for sure. Plus I love your artstyle; reminds me of Typoman.
Why not order the things in this comment so that when watching the video the viewer can easily see when the next correction is? (Though any major mistake can stay at the top or something)
In base infinity, every number has its own unique symbol! Sort of like writing numbers with words...
chinese base
@asheep7797 uh no, Chinese is actually base 10 too
@@randy-x They probably meant using Chinese characters as numerals, not just the Chinese numerals. That being said, that's still not base-∞, "only" base-3500 or base-6500.
@@adiaphoros6842I think it would be closer to base-50000
Well, not really like words? Numbers are already written like words. It's just that they're very logical and predictable in how they're spelled
- Let's try to write something in nullary
- So we have zero symbols, so we can't write anything
- Rejects to elaborate further
- Leaves
"NOOOO WE NEED TO USE BASE 6 ITS THE FUTURE" - Some mathematician, probably
And then another mathematician says that we should use base 12 instead, starting world war III.
and then some more say base 2
jan misali:
That probable mathematician is jan Misali. See their video "a better way to count".
base 37 🗿
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)
Hexadecimal (base 16) is much more common, at least by humans who work with computers, than base 64. The main reason for its utility is that each "digit" of Hex can be directly translated into 4 "digits" of binary because 16 is equal to 2^4. Thus you can easily convert between them as needed, taking advantage of using fewer digits when writing long numbers, but being able to break down individual binary bits when needed.
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
That's the good part of mathematics, everything is derivable from everything; and what isn't, you can construct it.
7:06 I love the fact that O and Z are technically saying the same thing
lmao average 0 factorial
What’s more, they’re both correct!
r/unexpectedfactorial moment
so you're telling me, that upside-down-u is saying, that 0^0 = undefined factorial?
It's 0.5 end of story
- 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)
_(please don't remind me that every place value in this system is actually a function of N-body problem in distorted spacetime, not a constant 🥲)_
@@lockaltube The only thing that remains constant, is the modernist interpretation of the idea of constancy, hypothetically existing outside of personal interpretation; I'll be honest, I have no idea what I'm talking about, but you've read this far ☺Edited: to show I edit therefore am not bot, unless...what if I was a robot and didn't know it?
Base 0 is just the best though.
Yeah, counting in it is fun: 0, 0, 0, 0, ... oh.
You missed part where negative base can represent all integers(positive and negative). A base with some negative digits can also do that. Like balanced ternary.
bro got the blue comment
TTT, TT0, TT1, T0T, T00, T01, T1T, T10, T11, TT, T0, T1, T, 0, 1, 1T, 10, 11, 1TT, 1T0, 1T1, 10T, 100, 101, 11T, 110, 111
(-13 to 13 in balanced ternary)
Peter Griffin: “Who could think of such a horrible thing?!”
Also loved the video and i could actually kind of understand it
I'm glad to hear it! Number systems are a pretty complex topic so I'm pleased the video isn't totally incomprehensible.
There is also a number system based on Fibonacci numbers, it is quite exotic and rare, but no less interesting
Ooh, do elaborate! That sounds very interesting indeed.
oof, ghosted… that’s the worst.
Commenting to get notified if someone answers
There's a Wikipedia article on "Fibonacci coding" that looks relevant, but I don't know if that's the same thing or not.
@@Faroshkassame
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.
A lot of ink has been used to explain "intuitive" concepts in rigorous mathematical detail, precisely because of how often our intuition is wrong in fringe cases. I remember going through my master's level number theory course where they rigorously defined what natural numbers are (using set theory; it's crazy how complicated you have to be with it to fit how they're actually used in the real world while also satisfying everything they need to be mathematically). It's important to remember that literally everything in math is a construct, so in another timeline we could have defined integers (and therefore rational numbers) differently such that the statement would have been correct. But yeah, as things stand the base we choose to represent them in does not change whether a number is rational or not.
Yeah, infinite digits to the right of the decimal point isn’t the same as irrational, otherwise 1/3 would be irrational in base 10
For the primes "base" instead of using the "tally" method to indicate how many factors of each prime is included in a number, we use a "meta" base or system to count the factors of each prime along with the new prime symbols to indicate the prime being counted.
Say that we use base 10 for our meta base and a=1, b=2, c=3, d=5, e=7, etc for our prime symbols. Them we would get:
1 = 1a
2 = 1b
3 = 1c
4 = 2b
5 = 1d
6 = 1b1c
7 = 1e
8 = 3b
9 = 2c
10 = 1b1d
Etc.
Of course we could nest this by using a version of this system as the "meta" base. Suppose that we use capital letters in the meta base, and omit the use of the symbol "1"
Then
1 = 1a = Aa
2 = 1b = Ab
3 = 1c = Ac
4 = 2b = Bb
5 = 1d = Ad
6 = 1b1c = AbAc
7 = 1e = Ae
8 = 3b = Cb
9 = 2c = Bc
10 = 1b1d = AbAd
48 = 4b1c =2BbAc
Etc.
I really enjoyed this video! I definitely noticed some similarity with TodePond's style, but also it's definitely unique in many more ways, subscribed
formulaic base: every time it goes to the next digit place, the base is different according to some formula
This video is very entertaining for a math video, i have a critic however. The volume of the music is louder than the voice, maybe you can lower the volume of the music. Other than that it is very good and underrated.
"AWWWWW WE NEED TO USE BASE 7 ITS THE FUTURE" - Some mathematician, will get probably
I'm pretty sure that no mathematician in history would ever use base 7 willingly.
this was the snack i needed from trig. woah woah what about base sin?
Base sin is a hilarious concept, actually.
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
base sqrt(2) includes all integers + all multiples of sqrt(2). For example, 111 is 1+sqrt(2)+sqrt(2)^2, or 3+sqrt(2). I don't expect that's particularly useful, but there you go.
Very interesting to learn about these weird bases but on a more practical note, base six or base twelve is infinitely better than base ten. Ten though not the worst is far from the best choice for base of everyday numbers. Of course, for computers, the only base that works is binary.
Yes, base 10 is just an awkward workaround for us not to happen to have 12 fingers. Which had more divisors.
can you do quaternion bases? great vid btw
base 0 is genuinely my favorite
You don't have to do any maths at all with base 0 because you physically can't.
YESS ANOTHER MATH VIDEO AND I GOT IT EARLY
I'm subscribed because this is good content
I don't know what the deal with those 2 dots over the numbers is supposed to be, but I can type some symbols like ö, ä, and ë so that might be it, I have seen other languages use those dots.
@@jackcraftsolar Ah, excellent query. With regard to the numbers, it's just to make them look a little more like little creatures but in other languages, the dots act as accent markers to slightly change the sound that a vowel makes.
I guess you can heart replies now? Is this new or not!? Sorry for being off topic but I want to know
@@RandomAndgit oh I see the eyes now
I don't understand anything, but i like your videos
3:05 it should be 百 I think. Unless there's something weird going on I don't know
That's quite possible, I'm nowhere close to fluent in Japanese so I'd be willing to bet that I just got it wrong. Sorry about that!
iirc they also have different numbers depending on the type of object you are counting so it could also be that
@@jonasgajdosikas1125That’s not really true. You’re getting it mixed up with counters, which are more like units, or like “head” in “head of cattle”. With only a few exceptions, everything gets counted with the same sino-Japanese numerals
4:32 Not irrational, just with non-repeating decimal expansions (although that conception of "irrational" does work for integer bases)
eu já testei a base 64K, precisa de apenas 4 letras para ser equivalente exatamente a um numero em 16E(~18.5quintilhões), então técnicamente já brinquei com essa base, com a função python asseguir dá para fazer a conversão bidirecional apartir de um inteiro, o python limita (10^10^4300);
I have already tested the base 64K, it only needs 4 letters to be equivalent to 16E (~18.5 quintillion), with the following python function you can do the bidirectional conversion from an integer, python limits (10^10^4300);
---
import sys
sys.set_int_max_str_digits(0)
def NK(n: float) -> str:
"""Converte um número de ponto flutuante para uma string codificada em base de caracteres imprimíveis."""
if n == 0:
return p(0)
integer_part = int(n)
fractional_part = n - integer_part
# Convertir parte inteira
Bn_integer = ''
while integer_part > 0:
remainder = integer_part % 65536
Bn_integer = p(remainder) + Bn_integer # Usar função 'p' para pegar o caractere imprimível
integer_part //= 65536
# Convertir parte fracionária
Bn_fractional = ''
precision = 10 # Ajuste a precisão conforme necessário
while precision > 0 and fractional_part > 0:
fractional_part *= 65536
digit = int(fractional_part)
Bn_fractional += p(digit) # Usar função 'p' para pegar o caractere imprimível
fractional_part -= digit
precision -= 1
# Adicionar ponto decimal se houver parte fracionária
if Bn_fractional:
return Bn_integer + '.' + Bn_fractional
else:
return Bn_integer if Bn_integer else p(0)
def KN(Bn: str) -> float:
"""Converte uma string codificada em base de caracteres imprimíveis de volta para um número de ponto flutuante."""
if '.' in Bn:
integer_part, fractional_part = Bn.split('.')
else:
integer_part = Bn
fractional_part = ''
# Converter parte inteira
n = 0
for ch in integer_part:
oc = ip(ch) # Usar função 'ip' para pegar o índice do caractere imprimível
n = n * 65536 + oc
# Converter parte fracionária
fractional_value = 0
base = 1
for ch in fractional_part:
oc = ip(ch) # Usar função 'ip' para pegar o índice do caractere imprimível
fractional_value = fractional_value * 65536 + oc
base *= 65536
# Adicionar parte fracionária ao número final
return n + fractional_value / base
def p(index):
"""Converte um índice de 0 a 65535 para o caractere Unicode imprimível correspondente."""
count = 0
for code_point in range(0, 0x10FFFF + 1):
char = chr(code_point)
if char.isprintable(): # Salta caracteres não imprimíveis
if count == index:
return char
count += 1
raise ValueError("Índice fora do intervalo imprimível.")
def ip(char):
"""Converte um caractere imprimível para seu índice (de 0 a 65535)."""
count = 0
for code_point in range(0, 0x10FFFF + 1):
if chr(code_point).isprintable():
if chr(code_point) == char:
return count
count += 1
raise ValueError(f"Caractere '{char}' não encontrado na lista de imprimíveis.")
just a small excerpt, 4tuple number, power|root:
55|37: W|37|W|55.0 ැ|bd1|'.澘𗉿빗|7.416198487095663 "軴|289e7|#.퍯俬㮍蔍|3.802952460761391 Îꖽ|8ba0a1|".뼉㫸र蔍|2.7232698153315003 ∶螤|1dff8297|".㾠⌞蛩엡|2.2288073840335185 &盲ᄑ|671e50e71|!.𔐔퍰蓦𐬫|1.9501160121288659 ƥ絃ḕ|16278361a47|!.쮭秜𒓢ኪ|1.7726510055204765 儴殺ꬉ|4c27d39fa541|!.걖떿䫮𓄉|1.650233260885109 0憛籙蘄|105c8e774c80f7|!.钣틾䰷𓄉|1.5608947941283693 Ϗ𑂌ꚟ뫲|383e29ba16fb511|!.茼𓋯퉴𐬫|1.4929190815424387 윶땐든𑜧|c155af6faeffe6a7|!.疐엚谏䔍|1.4395103439519596 I蹵뛟鸇鋮|298968b0fe98fa8de1|!.檋짭⼎⑥|1.3964655427646133 ৈ誋ܦ𐠣聤|8ec857e06b2ddd47b57|!.慺쩍說뗡|1.3610499158553278 !𒂫돴畺꺇蒾|1ead0ae13706da8a67fb1|!.姤䐻𖣓蔍|1.3314094056752328 «矢欺⯷䃒琔|6972d5662d278f3bc56f07|!.卲𗇋㬈𐬫|1.306243611083104 ᧷놹𔒍蓒ﻷ𐌶|16a7abd8f3b37fc5d76ada81|!.䷩籷筟⑥|1.2846140513341386 $𐡛𒅷悝碎䴁𓋀|4de05eb9c5b90738147f4f1b7|!.䤚㸮씥𐬫|1.2658267695799341 Ŏ뤦ꎧ뇩횧窬𒒞|10bb3459e97ac08d0c6759fee51|!.䓢𑰹눲𓄉|1.2493577526586888 㺐褂ᕙ𖡷𐍝䩩㡴|398383f51295f5e4daa3455c3367|!.䄩∍旄𐬫|1.234804024542171 ,恎庳𗓌ﭝ𖽄𑠓ആ|c5b4159a6fe37d42af913e6cf0b21|!.㷘㧏菫헡|1.2218506789057486 ˪ꀚ䟭ꌎ驈術鮈椤|2a79b0a42e09dfe953b8346967b6417|!.㫟ퟭ퉜ኪ|1.2102481119331794 霏呁捎𓊻ተ㤷妏藾|92024f345e41f1b20fc9342a548280f1|!.㠲ﬥ፭뗡|1.19979595929973 ?掌Ҍ䔷𒌜楇㨥ⱳ릨|1f5e7f0440402aed41643a35182809b3c7|!.㗆陾穯⑥|1.1903315450666772 ܱ剖𑶘켙𖼽趎洽鼢ꓝ|6bd4d49e9cdc938f90c888168309a159fc1|!.㎒僄䩍锍|1.181721431964663 !瞸鿮䁃䁊蚾壚松ṳ垄|172ab9ae13b363b3d81b153cd62711aa55277|!.ㆀ쬰敤⑥|1.1738551443853251 oꡋ䭰뺇쀗𐚺ţ⪱뽥뵲|4fa2de4663b8a6ba36dd190120264cb984b791|!.⽿𓎰䯤㔍|1.1666404398336823 [...]
I want to make it clear that the 64k printable characters used is not the same as utf-16le which uses 16b and also 64k characters, but not all of them are printable;
*For obvious reasons, chaGPT did not learn or manage to do any math with this base (I even have the intuition that it learns by the average of what is already used, without anything new)
*my purpose with this was to use it in a 64k^64k sudoku expressed in equations
Base I0 cardinal
Base α + βi + γj + δk + εe' + ζi' + ηj' + θk
Base x
Base sin(-0) = -sin 0
cos(-0) = cos 0
tan(-0) = -tan 0
cot(-0) = -cot 0
sec(-0) = sec 0
cosec(-0) = -cosec 0
Base x > x’
Oh wow, this is deeply cursed. I didn't even think to do quaternion bases but this... this is the work of some deranged mathematical witch.
@@RandomAndgit yipppeee :33
@@RandomAndgitBASES IN 16-DIMENSIONAL SEDENIONS
"NO WE NEED TO USE BASE 6!!!!!!!!" - jan Misali
Binary is actually still good, in base 10 we use powers to represent huge numbers lik 10^100, blah blah, we can do that in base 2 too!
By no means is it bad! Far from it. Binary is enormously useful. It's just not useful for us humans on the day-to-day so much.
@@RandomAndgit yea it is. theres an hour long video called "the best way to count" arguing why binary is the best base for humans
Problem with base pi is that it still sucks even for pi, if you were to write 4pi in base pi, it would be a decimal too. 30 would be equal to 3pi, 33 would be 3pi+3, but the next number, 100 would be pi^2
I'm pretty sure phi isn't special when it comes to irrational bases. I have this gut feeling that any root expression for a base can express integers in finitely many digits
Like. If I set the base R = sqrt(2) + 1 then I have the relation R^2 = 2R + 1, which manifests in the base as 100 = 021
So a number like 3 would be written as 10.11, and 12 as 200.02
Not too sure since I haven't tested anything from nested roots or cubics or anything higher degree but I feel like it should hold
Funny enough, you need ten symbols for base S = sqrt(6) - 1 because S^2 = 2S + 9 (100 = 029)
So 0-9 is still 0-9 but 10 (actual Ten) would now be written as 9.29
and 11 would be... uhhh... huh. no clue, actually
3:12 Base 1, my beloved
4=1111
2=11
90=111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
I don't usually comment but this channel is really underrated! I hope your content reaches many people in the future :D
Thank you! That's very kind of you.
Intentional Stanley parable reference?
I do rather like the Stanley parable.
1:47 Rainworld refrence... Nice.
I was hoping someone would catch it!
Oh you sneaky devil
I prefer base 12 (a high composite number) instead of 10.
by the way, phi isn't the only irrational number that has that property that makes it easy to write any natural number with finite digits. any of the metal ratios (golden ratio, silver ratio, broze ratio, ...) has this property.
I quite agree, both base 12 and 6 and even 16 are vastly better than base 10.
@@RandomAndgit I disagree on base 16. base 16 is only useful because it's a power of 2 and powers of two are easy to manage with computers but 16 only has a single divisor (2) while bases 6 and 12 have two possible divisors (2 and 3)
@@WilliamWizer one reason that people say bases 6 and 12 are better than base 10 is because of the expansions of fractions (specifically reciprocal primes)
fraction = decimal = seximal = dozenal = hex, terminating expansions are in italics, repeating expansions are truncated after one full pattern
1/2 = _.5_ = _.3_ = _.6_ = _.8_
1/3 = .3... = _.2_ = _.4_ = .5...
1/5 = _.2_ = .1... = .2497... = .3...
1/7 = .142857... = .05... = .186A35... = .249...
1/11 = .09... = .0313452421... = .1... = .1745D...
1/13 = .076923... = .024340531215... = .0B... = .13B...
1/17 = .0588235294117647... = .0204122453514331... = .08579214B36429A7... = .0F...
1/19 = .052631578947368421... = .015211325... = .076B45... = .0D79435E5...
while hex may have a lot of repeated digit fractions, it usually has relatively short digit patterns compared to bases 10, 6, and 12
I'm disappointed you didn't mention the mixed-radix base-factorial system, where every natural number is written like xyz.abc = ... + x*3! + y*2! + z*1!/1! + a/2! + b/3! + c/4! + ... (where z
obscure numbering system: tic-xenotation (TX):
- 2 is written as :
- (n) is the nth prime number (1-indexed, starting from 2)
- every number is written as its factors
2 :
3 (:) (the 2nd prime)
4 ::
5 ((:)) (3rd prime)
6 :(:)
7 (::) (4th prime)
8 ::
9 (:)(:)
10 :((:))
it's possible to write any integer greater than 2 in this fashion. very impractical since the system is based on factors (even basic addition is impossible without rewriting into a modulus-based system).
It appears that at least 8 came down the wire wrong. Did you just invent this btw?
I came up with the exact same thing, except instead of using : to denote 2 you just have a blank number represent 1. And if you substitute 1 and 0 for ( and ) you get a very, very cursed form of binary
2+2 is 10.. IN BASE FOUR IM FINE!
4:53, isn't 1/phi equal to phi-1? the sqrt of phi is. 1.272...
Oh, yes you're completely right. My mistake.
I still think hex is the most aesthetically pleasing base
I love the videos, very interesting stuff!
1 constructive criticism is that the background music was a tiny bit too loud, Its a little distracting. Might just be me though, keep up the work man!
Thanks so much! Yeah, I've gotten a lot of people saying that the music is too loud, really sorry. I'll be sure turn it down a notch next video.
@@RandomAndgit ngl i iked the music being like that...added drama too a math vid that added an unusual amount of suspense...
Much too loud! Why is it there at all? Much as I like Beethoven I would rather listen to him without the distraction of the video and I would rather watch the video without the distraction of the music. It's a long time since I was in an education establishment. Is it now normal to have background music in the classroom.
at least its not the typical bad music most channels use 😊
Another excellent video !
base 30 would be absolutely perfect
base 2, 4, 6, 8, 12 and 30 :3
Why is a base 7 number hard to divide?
For instance 15 is a perfectly fine base 7 number. It can be divided by 2, 3, 4, and 6.
More? 33 can be also be divided by 13 (and 2, 3, 4 and 6 as well).
While that's true, there are a couple of reasons why it's still terrible.
-A lot of fractions that would be pretty easier to write become a bit more annoying. (1/2 is now 0.333...)
-A lot of smaller, more useful numbers like 2, 3, 4, 5 and 6 get much longer patterns.
Also I think you might have misunderstood how bases work because you seem to either be suggesting that 33 is divisible by 13 (which it isn't) or that 24 is divisible by 10 (which it isn't).
7:20 zero to the power of something is equal to zero
but at the same time
(0!) zero multiplied by NOTHING is equal to one
mathematicians still haven't made friends with logic
Technically, _all_ base systems are base 10
In base 10, the number 10 has 10 digits
would that make language, such as say the english language, a base (26 add any symbols such as full stops, brackets etc) - or does language also include all numbers? Basically does your keyboard contain all the subjects (idk to call it) of the language?
Is that a swaggy dapper fish?
Swaggy? Possibly. Dapper? Yes. Fish? Who knows? There's no such thing as a fish.
Random Bases That Might Exist With Random Order
Base G64
Base Tree(3)
Base Tree(4)
Base 10^100
Base 10^10^100
Base Omega 0
Base Zeta 0
Base Epsilon 0
Base Eta 0
Omega cannot be a number system, because it is an ordinal, it has no value, so it cannot have digits
@@Psi_Fan123 oh
@@Psi_Fan123 I think you actually _could_ have omega as a number system. It'd mean assigning a different symbol to every natural number less than omega, which is every natural number.
I'm no set theorist but I figure it might end up looking something like Cantor normal form, where the rightmost digit is the finite component, the second digit is the factor of omega, the third is the factor of omega^2, etc.
@@rtg_onefourtwoeightfiveseven 1/omega seems wrong because it's a cardinal devided by an ordinal
@@Psi_Fan123 It's weird but I feel like you could still make it work. Maybe it'd end up looking like the surreals or something.
Granted, you wouldn't be able to express (say) 0.5. But you could still end up with a self-consistent ordered ring, maybe even an ordered field.
3:45 A symbol is a symbol, you can't say it's only a half 😉
Precisely.
0:13 "...which means me use ten symbols..." Comment:: it does not mean that. It means we use groups of ten, and the need of such ten symbols is a consequence but wow! I would have thought of using any other base than naturals >= 2. I´ts hard to thing in "groups" of pi or 1+ 3i 😆
Other interesting bases are
60 for time
64 widely used in cryptography to represent "human readable" binary data. Any base will do but 64 was chosen since it represents large amounts of data in a relatively short strings
12 for commerce since it has more divisors than 10
Although mentioned I guess it must be more strongly stated that
In any base, 1 will be represented as 1, and 0 as 0
In any base, the base it self will always be represented as 10
Why we use base 10? I always ask this to my students when we start learning about number systems. When they begin to
🤔 I sardonically say "don't think, you have the answer in your hands"
How do you write any integer in Base ɸ?
Well, the general idea is that, because exponents and roots of phi directly tie to natural numbers, you can always express an integer using them. The actual algorithm to do this is quite complicated though and I don't think I understand it well enough to give a full explanation.
I love how the background song is nyaw
You and Ludwig should live apart.
We already do, actually. We're both in different countries.
@@RandomAndgit
Oh, of course. Maybe, just ditch the collab, then. ;)
Cheers :)
4:32 ALMOST all integers? Whats the integers that ARENT?
You can actually do 1, 2 and 3 with base pi because it doesn't get irrational until the second digit.
@@RandomAndgit Oh right, lol.
How about base 0.1?
Kind of works (?) but you need to give yourself a symbol because otherwise you wouldn't have any symbols at all.
In nullary 1=0 actually... And it is the only number...
3:05 Japanese uses bijective decimal with extra symbols for powers of ten.
isn't that what they said?
@@BryanLu0 bijective need not have the extra symbols
I like your little typographic guys living their best typographic lives. Did you by any chance get inspiration from the reddit community r/constantscript ?
I've never heard of r/constantscript until this very moment but I might have to go and look at it right now because I *am* quite the fan of silly little typography guys.
It would be better if you use sub digits for the base so it doesn't look like you're saying a hundred is equal to 2.25
Yes, that's quite a good point.
2:24 shouldn't it be 8x8 if you wanted every possible grid of pixels to be a unique digit?
64*64 = 4096 and 2^4096 is a bit larger than 18 quintillion
Oh, yes, you're quite right! Thank you. The actual size of that base, just for interest, is 1,044,388,881,413,152,506,691,752,710,716,624,382,579,964,249,047,383,780,384,233,483,283,953,907,971,557,456,848,826,811,934,997,558,340,890,106,714,439,262,837,987,573,438,185,793,607,263,236,087,851,365,277,945,956,976,543,709,998,340,361,590,134,383,718,314,428,070,011,855,946,226,376,318,839,397,712,745,672,334,684,344,586,617,496,807,908,705,803,704,071,284,048,740,118,609,114,467,977,783,598,029,006,686,938,976,881,787,785,946,905,630,190,260,940,599,579,453,432,823,469,303,026,696,443,059,025,015,972,399,867,714,215,541,693,835,559,885,291,486,318,237,914,434,496,734,087,811,872,639,496,475,100,189,041,349,008,417,061,675,093,668,333,850,551,032,972,088,269,550,769,983,616,369,411,933,015,213,796,825,837,188,091,833,656,751,221,318,492,846,368,125,550,225,998,300,412,344,784,862,595,674,492,194,617,023,806,505,913,245,610,825,731,835,380,087,608,622,102,834,270,197,698,202,313,169,017,678,006,675,195,485,079,921,636,419,370,285,375,124,784,014,907,159,135,459,982,790,513,399,611,551,794,271,106,831,134,090,584,272,884,279,791,554,849,782,954,323,534,517,065,223,269,061,394,905,987,693,002,122,963,395,687,782,878,948,440,616,007,412,945,674,919,823,050,571,642,377,154,816,321,380,631,045,902,916,136,926,708,342,856,440,730,447,899,971,901,781,465,763,473,223,850,267,253,059,899,795,996,090,799,469,201,774,624,817,718,449,867,455,659,250,178,329,070,473,119,433,165,550,807,568,221,846,571,746,373,296,884,912,819,520,317,457,002,440,926,616,910,874,148,385,078,411,929,804,522,981,857,338,977,648,103,126,085,903,001,302,413,467,189,726,673,216,491,511,131,602,920,781,738,033,436,090,243,804,708,340,403,154,190,336.
5:50 -i doesnt cycle in that order, why did you put that there
Oh, no, my mistake. I forgot to place parenthesis around the -i part so I seem to have calculated -(i^x) rather than (-i)^x
@@RandomAndgit oh lol
@@lizzycoax 'tis a very lol moment. This is why you should always check your answers. (Or, why I should always check my answers)
Now do base undefined
For all of us Classical Music imbeciles out here, does anyone know the name of the background song?
Beethoven's Moonlight Sonata 3rd Movement (Piano Sonata No.14, Op.27 No.3)
I love phinary
I wish we used base 12 instead. So much easier to do math with. Especially with division and multiplication
Personally I prefer base -sqrt2i.
4:44 best of
imo
1:44 rain world?
Bro i cant focus bc my brain has been rotted by geometry dash (look up change of scene) good vid!
I WAS WAITING FOR A INCARDINALITY VIDEO
Please have patience. Googology is actually not my area of expertise and infinite numbers past the cardinals is absolutely brain bending.
@@RandomAndgit Ok. Tip: Google it and *try* to convert it to a script that your brain can handle.
binary best base !!!
Why do you say that the powers of -i turn clockwise?
Because, when calculating it, I forgot to put parenthesis around -i so accidentally calculated -1(i^x).
I didn't know you are a number that represents 14 ( 1:44 )
base of x is a pretty silly system. You have no idea what system your using. Also base 0.1 would be great. Infinite digits to memorize. Sign me up.
Ok, who decided to have a negative number of symbols. How would that even work?
Sqrt(phi) is not phi-1. 1/phi is phi-1
Read pinned comment please.
very silly
Great background music, but it's drowning out your voice.
Very few people are going to understand this but, Change of scene
If you know you know ;)
yeah the song is a remix of moonlight sonata 3rd mvt
Could you re-upload without the piano? It looks like it would be worth that.
List of perfect powers (n < 1000)
1
4
8
9
16
25
27
32
36
49
64
81
100
121
125
128
144
169
196
216
225
243
256
289
324
343
361
400
441
484
512
529
576
625
676
729
784
841
900
961
1000
😮
phi = 1.618...
√phi = 1.272...
Gotta be honest. I don't believe √phi = phi-1
Base X
I just can't watch your videos with that music... Too loud and too distracting... Lasted almost 2 minutes before I paused and moved on...
PLEASE change the background music !
Sorry! It sounds fine to me but a lot of people have said that.
The moonlight sonata in the background is really distracting and annoying.
Great content. Music is too loud and annoying.
Gah! I'm so sorry, I never can seem to get the music volume right.
@@RandomAndgiti personally found it fine but yea i can see where they came from, probably a bit quieter and itll be fine
yoo i'm the 100th comment
GET RID OF THAT ANNOYING MUSIC
First
Omg really
4th, I'm afraid. Still impressive though.
@@RandomAndgit Correct, I was the first to get the 4th reply
@@keamu8580 Yes! You were.
@@RandomAndgit Wait, perhaps we shouldst nae use the past tense. For I can assure you, I am still the first to get the 4th reply!