the best way to count

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  • Опубліковано 25 лис 2024

КОМЕНТАРІ • 4,2 тис.

  • @HBMmaster
    @HBMmaster 11 місяців тому +3400

    really well put together video! these are some very compelling arguments for binary. you're right that I dismissed it for superficial reasons without second thought in my videos; the immense advantages it has for arithmetic and information density shouldn't be overlooked, and there definitely is a case to be made that these may matter more than the things I focused on. in the few contexts where the notion of an "objectively best base" actually makes mathematical sense as a thing to care about, binary is a clear winner.
    I don't think I'm completely convinced that binary is necessarily the absolute best choice for a human-scale base (the "coincidental" advantages seximal has for working with small primes are just too good) but I am convinced that it can work as a human-scale base to begin with, which I hadn't even properly considered before. it definitely deserves a seat at the infinite table with the other SHCN bases.

    • @ThiagoGlady
      @ThiagoGlady 11 місяців тому +219

      please do a responde video! not only. for exposing more of your points but also for giving this guy more attention here on youtube

    • @wilh3lmmusic
      @wilh3lmmusic 11 місяців тому +37

      I think the answer then would be some more usable power of two such as 8 or 16

    • @Booksds
      @Booksds 11 місяців тому +4

      +

    • @leggyjorington3960
      @leggyjorington3960 11 місяців тому +72

      @@wilh3lmmusic thats basically what the video said, you can combine 2 or 3 digits of binary to make it shorter like base 8, but with all the advantages of base 2

    • @Salsmachev
      @Salsmachev 11 місяців тому +33

      @@leggyjorington3960 Not exactly. The grouping system in the video is distinct from hex or octal in a few ways.
      First of all, if you just want to use hex, then the notation suggested is very inefficient. I'm not a big fan of how we usually write hex (0,1,2,3,4,5,6,7,8,9,a,b,c,d,e,f) but it's much more efficient than iiii iiil iili iill... etc. The same is basically true for octal.
      Second of all, the advantage of his system is that it isn't hex or octal, it's both (and any other 2^x base). You can very easily re-analyse a number as any of those bases to get its benefits. Sevens aren't great in hex, but they are easy in octal, so just group by three bits. Octal sucks at fives, so just group bits by fours and treat it like hex.
      Wilh3lm is, imo, correct that the benefits of the more flexible system are outweighed by the practical issues with actually writing these numbers. I spent several months using almost exactly the notation suggested in the video and it simply isn't practical.

  • @westwardquest
    @westwardquest 10 місяців тому +210

    I frequently see children using this system to express the number 4 to me when a school bus drives past. It's truly amazing to see something adopted with such enthusiasm at a young age and gives me a lot of hope for future generations.

    • @mehulpandya4761
      @mehulpandya4761 10 місяців тому +14

      Wouldn't they also be expressing the numbers 128 and 132?

    • @westwardquest
      @westwardquest 10 місяців тому +37

      @@mehulpandya4761 The most avid mathematicians on the back seat usually flaunt their counting skills in this way.

    • @mronewheeler
      @mronewheeler 5 місяців тому +5

      New euphemism just dropped!

    • @binauraltreatments6178
      @binauraltreatments6178 9 днів тому

      Finally, Something More Creative Than "But 4 Tho"

  • @undeniablySomeGuy
    @undeniablySomeGuy 11 місяців тому +551

    drama in the counting community

  • @HBMmaster
    @HBMmaster 11 місяців тому +2788

    I'm a bit excited

    • @aenz7352
      @aenz7352 11 місяців тому +29

      a

    • @AHumanBeingNamedAlex
      @AHumanBeingNamedAlex 11 місяців тому +115

      Because Vötgil has so many vowels

    • @EladKaminsky
      @EladKaminsky 11 місяців тому +35

      I am waiting for a formal debate

    • @flyingduck91
      @flyingduck91 11 місяців тому +26

      vötgil :3

    • @gooburr411
      @gooburr411 11 місяців тому +34

      Because this episode is a first in a few ways

  • @sorenallen
    @sorenallen 11 місяців тому +134

    Hi, not sure if anyone’s mentioned this yet but your use of pitches following the harmonic series to accentuate numbers you’re talking about is absolutely incredible and I didn’t want it to go unnoticed.

  • @malharmanagoli
    @malharmanagoli 11 місяців тому +192

    "Seximal may win a sprint, but binary wins the marathon."
    So that's why you made a 1-hour video to counter jan Misali's 18 min one.

    • @katie-ampersand
      @katie-ampersand 11 місяців тому +6

      i'm not sure you understand how a response works

    • @Taib-Atte
      @Taib-Atte 11 місяців тому +19

      youre missing the point but its still funny

    • @theblinkingbrownie4654
      @theblinkingbrownie4654 11 місяців тому +17

      Guys it's a joke, don't take it as him being serious

    • @otesunki
      @otesunki 11 місяців тому

      kekw

    • @katking9574
      @katking9574 10 місяців тому +7

      @@katie-ampersand
      short vid = sprint

  • @martinshoosterman
    @martinshoosterman 10 місяців тому +125

    Another fun fact, since microprocessors out number humans, and most of them do arithmatic significantly more often than the average person does,
    technically binary is the most often used base currently.

    • @CrushedAsian255
      @CrushedAsian255 5 місяців тому +7

      My phone did arithmetic to like ur comment

    • @foggy8298
      @foggy8298 Місяць тому +1

      I mean the term “use” implies some sort of conscious input so no

    • @0m3gA_o3
      @0m3gA_o3 11 днів тому

      We use computers which uses binary​@@foggy8298

    • @NamsaRay
      @NamsaRay День тому

      ​@@foggy8298 I mean, when we use a computer, they use binary. So...

  • @codeman99-dev
    @codeman99-dev 11 місяців тому +151

    59:03 Excuse me, but four bits is a *nibble* (half a byte!). I will not drop the cute name. I love it.

    • @im-radio
      @im-radio 11 місяців тому +16

      fr agree, how wouldnt you wanna say 8DEC as "a nibble"
      "gimme a nibble burgers"
      "i would like a nibble kilo of ice cream"

    • @oyungogdfrust4136
      @oyungogdfrust4136 9 місяців тому +2

      "give me nibble apples"

    • @blurbutnerd8355
      @blurbutnerd8355 6 місяців тому +1

      @@im-radio "Can I just have a nibble of your sandwiches?"
      "NO!"

    • @jlewwis1995
      @jlewwis1995 6 місяців тому +2

      If you wanted to keep it monosyllabic you could shorten it to "nib" :P

    • @peridotisthegoat96
      @peridotisthegoat96 5 місяців тому

      ​@@im-radio36332 right?

  • @jonyloco4134
    @jonyloco4134 11 місяців тому +143

    I think I found my favorite genre of videos: the hour long math rabbit hole.
    Videos such as this one, "HACKENBUSH: a window to a new world of math" by Owen Maitzen, or " The Continuity of Splines" by Freya Holmer.
    Really loved the use of music and sound in this one.

    • @codenamelambda
      @codenamelambda 11 місяців тому +4

      I love both of the videos you mentioned so much, if you have any other similar ones to share I'd love to know! I can also go through my favourites and find similar ones if you want me to tomorrow ^^

    • @mskiptr
      @mskiptr 11 місяців тому

      @@codenamelambda The recent 3b1b explanations of light slowing down when travelling through matter are definitely a must-watch, if you haven't seen them already. Oh, and also the "Why can't you multiply vectors?" by Freya Holmer

    • @thebestwaytocount
      @thebestwaytocount  11 місяців тому +18

      we're honored to be compared to videos like these! glad you enjoyed

  • @Delvokian
    @Delvokian 11 місяців тому +140

    I just appreciate how unnecessarily hostile the video is. It's honestly hilarious.

    • @dolphin2.0.
      @dolphin2.0. 10 місяців тому +25

      Yes, and it makes the thesis so much more compelling
      One cute fraud.

    • @icedqq
      @icedqq 6 місяців тому +8

      yooo wikipedia bisexual lighting skeleton

    • @interbeamproductions
      @interbeamproductions 3 місяці тому +3

      having beef with base four for over an hour

  • @subtlewolf
    @subtlewolf 10 місяців тому +52

    Some fingers are significantly harder to extend individually than others. This applies both physiologically and culturally.

    • @axxeny
      @axxeny 10 місяців тому +7

      Ah yes, the four (l..) finger ;)

    • @OMGYavani
      @OMGYavani 8 місяців тому +2

      This point is addressed in the video. Using just three fingers on each hand still lets you go further than seximal, and binary is the only base where you can use any amount of fingers for finger counting

    • @nate_storm
      @nate_storm 5 місяців тому

      @@OMGYavanithree fingers per hand still means you can flip someone off, and arbitrarily skipping the middle finger would introduce ambiguity.

    • @nate_storm
      @nate_storm 5 місяців тому

      finger counting 19+113 💀💀

    • @g-ray7121
      @g-ray7121 3 місяці тому

      i can do it just fine, so... skill issue

  • @davidjones8047
    @davidjones8047 11 місяців тому +31

    The amount of times I got caught by the “‘well actually’ -You“ moments scared me. Every time I felt like I had a valid argument to make, there was a direct response to it.

  • @sehr.geheim
    @sehr.geheim 11 місяців тому +108

    James Grime convinced me of 12, almost 12 years ago
    Misali of 6, almost 6 years ago
    You just convinced me of 2
    Who said there was no progress in history?

    • @LucasFerreira-gx9yh
      @LucasFerreira-gx9yh 11 місяців тому +30

      in 2 years some will convince you of base 1 and then 1 year later someone else will tell you base 0 is better, on which there will be a imediate response claiming base -1 is optimal, while then you realized that you actually had memories of someone claiming 1 year ago that base -2 was better and so on

    • @4thalt
      @4thalt 8 місяців тому +2

      2 months ago

    • @samueldeandrade8535
      @samueldeandrade8535 5 місяців тому +1

      ​@@LucasFerreira-gx9yh he may end it up studying Gaussian integers. Hahahahaha.

    • @smoceany9478
      @smoceany9478 2 місяці тому

      the pattern shows that in 6 years youll be learning base .5

    • @rsyvbh
      @rsyvbh Місяць тому

      ​@@smoceany9478 12/(t/6)!?

  • @keyofamajor
    @keyofamajor 11 місяців тому +58

    +1 for playing overtones behind fractions

    • @asliuf
      @asliuf 11 місяців тому +2

      i loved that

  • @jamiee7367
    @jamiee7367 10 місяців тому +62

    Finaly managed to crack the text at 8:20 on my own.
    The substitution is 啊 = A, 痹 = B, 雌 = C, 低 = D, 婀 = E, 付 = F, 佮 = G, 喝 = H, 乙 = I, 咳 = K, 刕 = L, 冪 = M, 妳 = N, 我 = O ,仳 = P, 儿 = R, 絲 = S, 偍 = T, 無 = U, 予 = V, 劸 = W, 牙 = Y.
    And the actual text is that one comment from jan Misali's Ido video:
    " YOU HAVE GOT TO BE ABOUT THE MOST SUPERFICIAL
    COMMENTATOR ON CON-LANGUES SINCE THE IDIOTIC
    B. GILSON.
    DID I MISS THE ONE WHERE YOU SAID WHICH CONLANG
    YOURE FLUENT IN AND READ AT LEAST THREE TIMES A
    WEEK AND CAN READ NEW BOOKS IN EVERY WEEK OF
    EVEN ONE YEAR OR LISTEN TO RADIO SHOWS IN EVERY
    WEEK? NEW RADIO SHOWS? "

    • @LuaShine
      @LuaShine 10 місяців тому +4

      this is gold. thank you.

    • @char8169
      @char8169 9 місяців тому +2

      interestingly the characters pronounced in chinese are close to the sound of their corresponding letters

    • @yuvalne
      @yuvalne 9 місяців тому

      amazing dedication

  • @Eurn0
    @Eurn0 Місяць тому +48

    Drama in the black background white text youtuber community

  • @seazeiscool
    @seazeiscool 11 місяців тому +50

    honestly, this video has now converted me into a true binary supporter
    also i did not expect all of the arithmetic stuff with binary to be SO simple and easy to do

    • @poorlydrawncactus1178
      @poorlydrawncactus1178 11 місяців тому +5

      no way its the crystal garden golden person

    • @goodknyght4319
      @goodknyght4319 11 місяців тому +1

      i frogelined and peacelined

    • @meta04
      @meta04 11 місяців тому +1

      oh hey it's the |..|eg guy

    • @akeem2983
      @akeem2983 2 місяці тому

      I did not expected that usage of binary in human scale is not only possible, but pretty convenient too and it has a lot of advantages

  • @Gestersmek
    @Gestersmek 11 місяців тому +81

    I really don't like the way that binary is proposed to be written in this video. The bottom connection thing is actually really nice, but the whole "short ticks for 0, long ticks for 1, and downward short ticks for the radix point" thing seems like it'd be really prone to accidental slip-ups and unnecessary ambiguity, especially without some sort of guide on the paper.

    • @polymloth
      @polymloth 11 місяців тому +10

      Agreed. A good way to distinguish them could be to write 0 like the lowercase Greek gamma and 1 like the cursive lowercase L. It would be fast, less prone to errors and easy to read.

    • @duncanw9901
      @duncanw9901 11 місяців тому +8

      ​​@@polymloth I just sat down to try and find a system based on this comment, and this was what I came up with lol, connecting adjacent characters like cursive. This is a pleasing analog of chiral topology, something like over- and under-crossings in a knot diagram.
      You can use word breaks to indicate digit groups, and a slash to indicate fractions as usual (I don't actually think having a positional notation for fractions gets you much idk).

    • @duncanw9901
      @duncanw9901 11 місяців тому +1

      I also think it would pay to write numbers little-endian.

    • @polymloth
      @polymloth 11 місяців тому +1

      @@duncanw9901 Exactly what I had in mind!

    • @yuvalne
      @yuvalne 9 місяців тому +4

      the thing is, if natural languages have no issue making this distinction (take the word יוון in Hebrew), this shouldn't be an issue with numbers.
      we can also always take inspiration from Hebrew crossword solvers and turn the short tick to a short cross.

  • @rarebeeph1783
    @rarebeeph1783 11 місяців тому +67

    re: chapter six. i'm not sure your naming scheme really does a great job here. it definitely feels like "ninety one" is less information to parse than "four one hex, two four, three", and in general, standard names tend to feel less cumbersome. perhaps there's a less mathematically elegant, but more linguistically practical, way of handling binary number naming.

    • @d.l.7416
      @d.l.7416 11 місяців тому +8

      "four one hex, two four, three" is more analogous to "nine ten one" like some languages do.
      For me it's more natural with -s on the things that should be plural, so four one hexes two fours three. (like "nine tens one")
      I think something that could help solve the cumbersomeness is basically doing base 16. So make all numbers less than hex compound words, so you can treat each as a single unit.
      Like ninety one would be four-one hexes two-fours-three.
      Compared to base 10 English, the digits are more syllables, but that happens in other languages. Like in greek the numbers up to 10 are all 2 or 3 syllables. With this system the numbers up to 16 are all 1, 2 or 3 syllables.
      The fact that it's base 16 means it's actually less cumbersome than base 10 for large numbers.
      It also keeps all the elegance, since it's just a conceptual reframing to help interpretability.
      There's still a slight problem that, for example, "four-one hexes two-fours-three bytes hex one"
      could be read as "four-one hexes" + "two-fours-three bytes hex one", you'd need to say "(four-one hexes two-fours-three) bytes hex one" somehow. I think this is just a problem that comes with the b^(2^n) system, you might have to switch to b^(kn), maybe 2^(4n) so powers of hex. Tho you could have the power names be like hex, byte, hex-byte, short, hex-short, byte-short, hex-byte-short, int and so on, so it'd be "four-one hex-bytes, two-fours-three bytes, hex, one".

    • @rarebeeph1783
      @rarebeeph1783 11 місяців тому +1

      @@d.l.7416 in written form, using the 2^(2^n) system, your latter example isn't technically ambiguous. but when spoken it's unclear what order of magnitude is being referred to at any point until the number ends, because at any point while telling you the number, someone could just say "short" and suddenly the number you were thinking of is 16 orders of (base 2) magnitude too small, etc.

    • @jfb-
      @jfb- 11 місяців тому +1

      my proposal for naming numbers is to simply read off the bits, using short syllables that can be flexibly strung together and said quickly. If 1 is pronounced like "wun" or "nun", and 0 like "oh", "wo", or "no", then a sequence like 1101 1001 becomes "wununowun wunowowun"; and you could optionally insert the magnitude words like hex between gaps. This mirrors the written form and retains its advantage of being able to group digits into whatever sized chunks are most convinient.

    • @suomeaboo
      @suomeaboo 11 місяців тому +4

      Hearing "nine ten one" in English is a little hard to parse, but in my native Hokkien where numbers work exactly like this, it's perfectly natural (九十一 káu-tsa̍p it). I think this just goes to show that it's all a matter of getting used to it. The "four one hex two four three" system is perfectly fine.

    • @Salsmachev
      @Salsmachev 11 місяців тому +10

      @@jfb- I think that would become very confusing very quickly. People already mishear fifteen (wunununun) and fifty (wununo nowuno) in decimal numbers, and you're expecting them to parse wununowun from wunonunun in fast speech (not to mention that both of those numbers are a mouthful). At the very least I think you should pick sounds with greater contrast. Maybe something like ko and mi, where the sounds of each differ in as many features as possible. You'd probably still have people getting mimikomi and mikomimi mixed up if you rattled off a couple of mikokoko-bit numbers, but it would be an improvement.

  • @Prometheus_Alt
    @Prometheus_Alt 10 місяців тому +44

    I got converted to binary after seeing the square root algorithm, knowing how complex it is in base 10

    • @mx_ae
      @mx_ae 10 місяців тому +2

      gd guy

    • @g_vost
      @g_vost 10 місяців тому +2

      its funny cuz the main narrator kepe also made yBot, small world huh

    • @mx_ae
      @mx_ae 10 місяців тому

      @@g_vost WHAT

  • @twixerclawford
    @twixerclawford 11 місяців тому +41

    The bit about the square root algorithm made me literally get up out of my chair, scream "what??" at my phone multiple times, and roam around my apartment for several minutes rethinking life

    • @Subroutine7901
      @Subroutine7901 11 місяців тому +5

      I shared your astonishment when I realized there's an algorithm for that. It just shows how the compactness of binary makes it so versatile.

    • @PinkeySuavo
      @PinkeySuavo 16 днів тому

      When it is? I am too lazy to watch all of it

    • @g_vost
      @g_vost 14 днів тому

      ​@@PinkeySuavothe final section of chapter three goes over the method. pretty neat

  • @feisty-trog-12345
    @feisty-trog-12345 11 місяців тому +72

    Sadly, any way of speaking base-2 numbers will be non-portable. Some ancient cultures will say that int is 2^16, while modern ones say 2^32. And then there's the oft-forgotten cultures where byte (or char, as they'd say) is e.g. 2^31. Instead the names for the double powers of two should follow a simple and memorable system, e.g. 2^16 could be "int underscore least sixteen underscore tee". Since that's a mouthful you should also introduce "intmax underscore tee" as shorthand for "the biggest power of two I feel like thinking of right now".

    • @yoctometric
      @yoctometric 11 місяців тому +12

      Devastatingly nerdy comment, love it

    • @rubixtheslime
      @rubixtheslime 11 місяців тому +5

      just use the x86 names: byte, word, dword, qword / quad, and dqword / double quad. i can't remember what the next two were but i could've sworn it was ddqword and qdqword. super convenient and not confusing at all

    • @the_cheese_cultist
      @the_cheese_cultist 11 місяців тому +3

      @@rubixtheslime after qword is either oword (octa) or xmmword (128 bit simd register)
      after oword is xword (hexadeca) or ymmword (256 bit simd register)

    • @Celastrous
      @Celastrous 10 місяців тому +2

      Based and Embeddedpilled

    • @lassipulkkinen273
      @lassipulkkinen273 5 місяців тому +2

      More like "the biggest power of two I feel like thinking of right now, except I must never change my mind or everything I've said before will break".

  • @flamingpi2245
    @flamingpi2245 11 місяців тому +87

    I have to say. I was extremely skeptical at first, but the elegant way of writing binary numbers you came up with really sold me

    • @Salsmachev
      @Salsmachev 11 місяців тому +8

      Try it for a month and you will change your mind. It's a nice idea, but I can tell you from experience that it doesn't work in practice.

    • @paper2222
      @paper2222 11 місяців тому

      @@Salsmachevthis video's been out for like 3 days

    • @mrosskne
      @mrosskne 11 місяців тому +4

      it's just too bad they're completely unreadable at a glance

    • @starstufs
      @starstufs 11 місяців тому +1

      @@mrosskne I'm curious if you're saying this having used that notation for a while or not

    • @mrosskne
      @mrosskne 11 місяців тому +1

      @@starstufs I literally just said "at a glance"

  • @jargontrueseer
    @jargontrueseer 10 місяців тому +21

    I'm incredibly surprised this video didn't mention that the GREATEST advantage binary has, is that it's a system we could ACTUALLY switch to without nearly as much hassle as any other system.
    I'll be honest, I went into this video thinking "huh, interesting. Id like to see a new point of view", got to the twist reveal that it's about binary and went "ok, this is either a joke or I'm in for an interesting if unconvincing response", but now you've really convinced me. Holy cow, I had no idea what I was in for. The counting is fun too since I don't have to remember so much, and somehow these numbers are easier to understand with my dislexia too. They could also be made easier to understand for dyslexic people with a few simple tweeks so that's comforting. And on top of all that, binary numerals would be so fun to make fonts for, as you can pretty much make the symbols whatever you want as long as one is "less" in some way than the other. Hollow/full circle, down/up arrow, Mario/Luigi, literally infinate options lol.
    Anyways awesome video, please make more! I'd absolutely love more specific video lessons on how to use binary with your numeral and naming systems!!

    • @akeem2983
      @akeem2983 2 місяці тому +1

      STOP DOING BINARY
      "Hello, I would like 🙆🙅🙆 apples please!"
      *They have played us for absolute fools*

  • @romeolz
    @romeolz 11 місяців тому +28

    The fact that the little sound effects match with the number on screen and the harmonic series is a very nice touch

  • @BloodEyePact
    @BloodEyePact 11 місяців тому +22

    Programmers and hardware engineers have been doing this forever, using 8 or 16 as the "compressed" written format, but dropping back to bits for actual arithmetic, especially when making machines to do so. Anyone in those groups worth their salt can convert from 0-F their binary quartets and back intuitively, and when learning to do that, often use fingers in ways that resemble your grouped bits. The main problem with binary as a written or spoken system is that its hard to read at a distance, and the octal/hexidecimal are "error correcting" in that a smudge on a piece of paper or a dent in a sign makes simple tally marks unreadable, but leaves letters and hindu-arabic numerals mostly in tact.

  • @masonskiekonto590
    @masonskiekonto590 11 місяців тому +16

    In my humble opinion this video goes into the youtube's mathematical hall of fame.
    A deep and new point of view shedding light on a topic that everyone can relate to yet few thought consciously before.
    I have no other words than to thank you for your work.

    • @mikechad27
      @mikechad27 11 місяців тому +3

      npc ahh comment

    • @lunarna
      @lunarna 8 місяців тому

      ​@@mikechad27npc reply

  • @notexactlysiev
    @notexactlysiev 8 місяців тому +53

    Back for a rewatch. This is levels of autism I strive for

  • @bideoVames
    @bideoVames 11 місяців тому +36

    She truly made a channel and a dedicated trailer for the counting video essay. Dedication like that deserves my full attention and like!

    • @timperkin9
      @timperkin9 11 місяців тому +15

      Check the credits! The writer/editor has a feminine name and isn't the narrator

    • @bideoVames
      @bideoVames 11 місяців тому +9

      @@timperkin9 thanks! I fixed it in the original comment :) I never check the description or anything so I missed that one :(

  • @nycki93
    @nycki93 11 місяців тому +22

    I always felt, instinctively, that binary "should" be the best base, but it just seemed too cumbersome to use in practice. Thanks for your excellent work.

  • @doorhanger9317
    @doorhanger9317 11 місяців тому +93

    You present your arguments well, however: I am nonbinary.
    So I'll have to stick with Seximal, or maybe Balanced Ternary for the small number and negative advantages

    • @lemoneer7474
      @lemoneer7474 11 місяців тому +24

      Perhaps you would like base negative two, or negabinary? It uses alternating negative and positive powers of two so negatives can be written just like positives without the need of a minus sign.

    • @Schockmetamorphose
      @Schockmetamorphose 11 місяців тому +11

      This comment is pure perfection.

    • @Salsmachev
      @Salsmachev 11 місяців тому +5

      @@lemoneer7474 Wouldn't nonabinary be base 18?

    • @Anonymous-df8it
      @Anonymous-df8it 11 місяців тому +7

      I'm non-decimal. It's a shame no-one supports me! /jk

    • @sehr.geheim
      @sehr.geheim 10 місяців тому

      ​@@lemoneer7474base √-1 -1 (called i-1) works well too

  • @qwertek8413
    @qwertek8413 6 місяців тому +157

    There are 10 types of people, those who understand binary, and those who don't

    • @ensi.creator
      @ensi.creator 6 місяців тому +5

      Underrated comment

    • @yuvalamir3226
      @yuvalamir3226 6 місяців тому +17

      And those who weren't expecting a ternary joke

    • @MuzikBike
      @MuzikBike 6 місяців тому +9

      There are 10 types of people, those who understand the hexadecimal system, and F the rest.

    • @peridotisthegoat96
      @peridotisthegoat96 5 місяців тому

      ​@@MuzikBikethats still 2 #binaryandseximalareslaynumbersystems

    • @leo848
      @leo848 5 місяців тому +2

      Wrong, there are |. types of people

  • @ckafi1011
    @ckafi1011 11 місяців тому +43

    I think the proposed method on how to say the binary numbers has a couple of major drawbacks:
    1) The recursive, non-linear conversion between words and symbols makes it hard to dictate, and non-trivial to write a dictated number down.
    2) The symbolically easy doubling becomes unintuitive, e.g. 3 4 1 doubled becomes H 2 4 2
    3) It can bury the most significant part towards the end, for example 3 4 2 H 3 4 2 B. You have to listen to all of the spoken numbers to make sure you're even in the right order of magnitude.

    • @thebestwaytocount
      @thebestwaytocount  11 місяців тому +20

      as far as I can see, these are all issues with existing spoken number systems. this system isn't much different than the one we use for decimal

    • @d.l.7416
      @d.l.7416 11 місяців тому +6

      i think 1 and 3 come from the fact that it's a 2^2^n system instead of a 2^kn system.
      you could instead make it a 2^4n system (powers of hex), but name the powers using the 2^2^n system. So hex, byte, hex-byte, short, hex-short and so on.
      like you'd say for example, three-fours-one hex-bytes three bytes hex two-fours, which is basically just how standard english base 10 words.

    • @nice3294
      @nice3294 11 місяців тому +22

      @@thebestwaytocount These issues are much more significant in binary since they show up much earlier on than in something like decimal

    • @duncanw9901
      @duncanw9901 11 місяців тому +2

      Recursive algorithms are simple algorithms. No one that has any experience reasoning about procedures thinks any different.

    • @tristanridley1601
      @tristanridley1601 11 місяців тому +10

      Take a cue from the world of programming, where our spoken numbers are base 16 but our math is base 2. If we used the numerals from this video it would make the conversion trivial.

  • @ulrikof.2486
    @ulrikof.2486 10 місяців тому +17

    In the end, it's not about "which system is generally better", but "which system is better after I came to a conclusion which were my criteria and priorities".

    • @simonwillover4175
      @simonwillover4175 10 місяців тому

      Nah. It's more about "which system am I already using".
      However, I think binary wins when we start talking about how to TYPE these numbers out.

  • @karakaaa3371
    @karakaaa3371 11 місяців тому +43

    As a programmer seeing hex byte short int used as power names is both horrifying and amazing

  • @CielMC
    @CielMC 10 місяців тому +18

    I audibly laughed at 5 in the morning when you proposed “a stack” for 8^2, but it sounds only fair when you think about it

    • @geekjokes8458
      @geekjokes8458 10 місяців тому +1

      MINECRAF???!?!??!!

    • @m9l0m6nmelkior7
      @m9l0m6nmelkior7 10 місяців тому

      wow I didn't get it on the spot that's just super funny x'D

  • @Memzys
    @Memzys 11 місяців тому +32

    TLDR: binary > every other base because binary < every other base

  • @sashagornostay2188
    @sashagornostay2188 11 місяців тому +17

    I like how we all do this research but will still all ever only use decimal casually

  • @eugenebebs7767
    @eugenebebs7767 9 місяців тому +22

    This feels like an induction into a religion. Now I see how things should be, and my duty is to convert the non-biners to the true light of one and zero.

  • @shiinondogewalker2809
    @shiinondogewalker2809 10 місяців тому +11

    I went into this with a strong preference for hex. I got pleasantly surprised by the suggestion of binary, and when you started grouping the bits it's essentially a multi base system around binary. Hex is really just groups of 4 bits, which is why it's good. I think the naming would sound more natural if it's done for groups of bits instead of what's suggested here

  • @sophiatrocentraisin
    @sophiatrocentraisin 11 місяців тому +25

    I feel like I've stumbled on a piece of forbidden knowledge.
    The funniest thing was trying to come up with some counter-arguments while noticing I had already used a binary representation of octal (tri-octal to be more precise) to convert an alphabet, and already figured on my own how easy it was to apply a vigenaire cypher mentally on it thanks to how trivial it is to do arithmetics on it

  • @geneticdriftwood
    @geneticdriftwood 11 місяців тому +14

    I love the notation system you created and the grouping shorthand, it’s very elegant and also makes the fundamental patterns you discuss visually obvious at a glance, without having to translate into numbers, even for someone totally new to the notation without having built base specific intuition. I could easily learn to do a lot of that math with your binary notation without converting into or out of decimal, which makes an excellent argument for it’s naturalness and simplicity

  • @dexiedoo_octo
    @dexiedoo_octo 2 місяці тому +33

    things heating up in the counting fandom

  • @KyleTheFolf
    @KyleTheFolf 11 місяців тому +26

    missed opportunity to title it "The best way two count"

  • @redder358
    @redder358 11 місяців тому +38

    The best base is base 10
    Get it? Not base "ten", but base "one zero" where the base of that number is whatever you want. For me that's base "two" too.

    • @neoieo5832
      @neoieo5832 11 місяців тому +2

      don't explain the joke

    • @mrosskne
      @mrosskne 11 місяців тому +10

      explain the joke

    • @whoblue5792
      @whoblue5792 11 місяців тому +1

      @@mrosskne 10 is 2 in binary

    • @tkava7906
      @tkava7906 11 місяців тому +1

      @@mrosskne 10 is 6 in base 6

    • @fazaazfgd
      @fazaazfgd 11 місяців тому +2

      ​@@mrosskne10 is 10 in base 10

  • @samuraiJno
    @samuraiJno 11 місяців тому +32

    This video is exactly 200 minutes in seximal. Cheeky.

    • @Arbarano
      @Arbarano 11 місяців тому +1

      Are minutes a seximal unit?

    • @itistheworstchannel
      @itistheworstchannel 11 місяців тому +1

      @@Arbarano(kinda sexagesimal)

  • @valacejo
    @valacejo 3 місяці тому +8

    The thing that fascinates me the most is that base 2 is every base 2ⁿ at the same time, so it is capable of using properties from all of them.
    Amazing video.

  • @trbz_8745
    @trbz_8745 11 місяців тому +26

    Don't you love it when you have that one really strong opinion that no one else cares about, but then you stumble across an hour long video essay about it at 3 am

    • @rcapt
      @rcapt 11 місяців тому +1

      It's my favourite feeling tbh

    • @zairaner1489
      @zairaner1489 11 місяців тому +1

      > that one really strong that
      I think the noun is missing.
      Regardless, yes.

    • @trbz_8745
      @trbz_8745 11 місяців тому

      @@zairaner1489 oops

    • @binauraltreatments6178
      @binauraltreatments6178 9 днів тому

      Me But One's Compliment Notation.

  • @gretarreynisson3280
    @gretarreynisson3280 11 місяців тому +19

    My jaw dropped when I saw that square root algorithm. Fuckin’ black magic 👍

  • @typecasto
    @typecasto 11 місяців тому +11

    Amazing. Genuinely, i was amazed multiple different times. I'm a computer science major myself, I had already discovered the bit about multiplication, but the section on factoring? I had never thought to do that, and it blew my mind. Division? So much better than base 10. Your notation is beautiful, I'm definitely adopting it for when I do binary work, and I'm geniunely strongly considering switching to binary in my everyday life.

  • @ultrozy
    @ultrozy 10 місяців тому +34

    Great video. Although the "speaking system" is quite flawed. So i made a new one.
    Firstly, the biggest flaw is recursiveness. It's new and neat, but when you want to say a number to other person, it's better to convey number's magnitude right away. For example in decimal you would say "world population in 1975 was 4 billion and dot dot dot". However in binary it would be "three four three hex two BYTE two four one hex four three SHORT dot dot dot", and only when you say SHORT the person can sense the magnitude.
    As a follow up, what if the person is writing the number down? For example when he hears "four int two..." how many zeroes should he put before writing down "two"? If the number is "four int two short" then 14 zeroes. If it's "four int two byte" then 22 zeroes. If it's "four int two byte short" then 6 zeroes.
    Secondly, phrases are a bit bigger. A small number in decimal (255 - "two hundred fifty five") would be "three four three hex three four three": 22 symbols versus 37 symbols (or 6 syllables versus 7 syllables). We sometimes omit hundreds, so it's minus 2 syllables.
    Thirdly, "speaking/writing system" interferes with the idea of grouping bits into groups of 2, 3 or 4 bits. System works with groups of 2 and 4, but does not with groups of 3. As it's said in video there is a learning curve, where person first learns arithmetic on group2 then group3 then (maybe) group4. But what if he considered group4 arithmetic too complex and stopped at group3 ? After he's done calculations on group3 he has no choice rather than regroup the whole thing and only then say the number out loud.
    For the first problem I'd kinda go traditional method (millions, billions, trillions etc.)
    For the second problem I'd compress numbers up to hexadecimal digits
    For the third problem I don't know. Either group3 people will have to regroup, or make another speaking system for group3 representations (which is quite bad).
    The digits
    Imho it would be worse to use digit name, that we already use, so I gave new names, trying to reflect "binariness". Also these numbers should be fast and easy to pronounce and phonetically distinct from each other , because they will be used a lot in speech. I'm not a conlanger, but I tried my worst
    wan du ti ro
    rówan ródu róti ko
    kówan kódu kóti kro
    krówan kródu króti hes
    Here ó is a stressed o. These words represent names for following hexadecimal numbers:
    1 2 3 4
    5 6 7 8
    9 A B C
    D E F 10
    I used "hes" instead of "hex" for sixteen, because I think it's faster to pronounce it this way. For 0 we could use "zero"
    I think "r" prefix for 4 and "k" prefix for 8 work quite good with binary.
    With this system we can count up to 255 (in a similar way we count up to 999 in decimal without involving power names, such as thousands, millions, billions).
    "hes" is used as a connecting word between quartets (similar to "hundred" in decimal). If the right half of number is zero, "hes" is omitted.
    ........ - zero
    .....|.| - rowan
    |||||||| - kroti-hes-kroti
    ...|.... - hes
    ..|..... - du-hes
    |..|.||. - kowan-hes-rodu
    Now for power names.
    Let's call collection of 8 bits as bunches (not bytes cuz we will use this keyword). Bunch in decimal would be 3 digits.
    Every bunch in decimal is followed by a power name (thousand, million, billion...)
    If we do the same in binary with suggested names (byte, short, int, long, overlong, byteplex), these "power names" (technically power phrases) will be like that:
    256 ^ 1 = byte
    256 ^ 2 = short
    256 ^ 3 = short byte
    256 ^ 4 = int
    256 ^ 5 = int byte
    256 ^ 6 = int short
    256 ^ 7 = int short byte
    256 ^ 8 = long
    (We suppose that most significant words come first)
    Here I would suggest other naming system (which in general will have more syllables). However each power name will be represented with one word, pronouncing these names I think will be easier, since "int" "short", "long" are not pronounced well together. Also every name will end on "-yte", indicating, that it is indeed a power name:
    256 ^ 1 = byte -> byte
    256 ^ 2 = short -> plyte
    256 ^ 4 = int -> fryte
    256 ^ 8 = long -> ksyte
    256 ^ 16 = overlong -> znyte
    (I did not come up with an alternative for byteplex)
    Now instead of "overlong long short byte" we would get "znyte ksyte plyte byte". But we need to combine these words. The rules are:
    1) Last word gains prefix "o-"
    2) Other words turn into prefix form
    The prefix forms are:
    plyte -> pil
    fryte -> fer
    ksyte -> kas
    znyte -> zun
    So by these rules "znyte ksyte plyte byte" will convert into "zun-kas-pil-o-byte", or "zunkaspilobyte". Here are first 14 power names:
    byte
    plyte
    pilobyte
    fryte
    ferobyte
    feroplyte
    ferpilobyte
    ksyte
    kasobyte
    kasoplyte
    kaspilobyte
    kasofryte
    kasferobyte
    kasferoplyte
    And now one example with all of this: distance to the Sun in nanometers:
    |... ...|||.. ...|.||. .||..||. ||..||.. .|.|.|.. .|.||... ..|..||. .|.|.||.
    "ko ksyte wan-hes-kro ferpilobyte wan-hes-rodu feroplyte rodu-hes-rodu ferobyte kro-hes-kro fryte rowan-hes-ro pilobyte rowan-hes-ko plyte du-hes-rodu byte rowan-hes-rodu"

    • @livingpicture
      @livingpicture 10 місяців тому +5

      I'm pretty sure if we had developed binary & hexadecimal counting, we would not be translating numbers from base 10, or from metric, especially since considering the metric system was developed in a world where base 10 was well-estsblished. What if we had established a measuring system based on 100,000 [in hex) of the diameter of the earth through the poles? The "hex stick," if I may, would be about 16 cm in length. A little small, but still usable. As much as we like to make up words, I'm sure we'd still have million and billion, or an equivalent in hex language & a little different in magnitude. Mil & bil are kind of arbitrary labels, but if hex had an equivalent, you could again feel the magnitude. Let's just pretend for a bit that hun, thou, mil, & bil applied to the number in the 3rd, 5th, 7th, and 9th digit respectively.
      Distance to the Sun would be about 37 milhex, if I may. A population of 4 billion would be EE milhex, which is just under 1 bilhex. Magnitude problem solved. 🙂

    • @ultrozy
      @ultrozy 10 місяців тому +3

      @@livingpicture Well yeah, we solved magnitude problem in our ways. But thou, mil, bil are names for 3*n hex digits (or nibbles) which is kinda arbitrary. I tried to follow the idea in the video: to establish names only for 2^n digits. The traditional approach (3*n digits) is probably easier to remember, but idk, I didn't learn my system :)

    • @yuvalne
      @yuvalne 9 місяців тому +1

      someone please like this comment later today so I remember to come back to this amazing comment

    • @Gelatinocyte2
      @Gelatinocyte2 6 місяців тому +2

      I kinda prefer this (but what do you guys think about this?):
      0 = zero
      1 = one
      10 = 2 = two
      100 = 4 = four
      1000 = 8 = eight | 1111 = 15 = fifteen (there should be alternative names for 10[dec] to 15[dec])
      1,0000 = 16 = *hex*
      10,0000 = 32 = two hex | 1111,0001 = 241 = fifteen hex one
      1,0000,0000 = 256 = *byte*
      1111,0111,0101 = 3,957 = fifteen byte, seven hex five (fun fact: this is 3 syllables shorter than its decimal name)
      1,0000,0000,0000 = 4096 = hexabyte (or hexbyte?)
      1111,1110,0100,1001 = 65,097 = fifteen hexbyte, fourteen byte, four hex nine
      1,0000,0000,0000,0000 = 65,536 = *"short"* (there's probably a better alternative name for this we can borrow from Computer Science)
      This gets absurd...
      10,0000,0000,0000,0000 = "two short"
      1,0000,0000,0000,0000,0000 = "hex short"
      1,0000,0000,0000,0000,0000,0000 = "byte short"
      1111,0000,0000,0000,0000,0000,0000,0000 = "fifteen hexbyte short"
      Maybe we should think of an alternative for "hexbyte"?

    • @interbeamproductions
      @interbeamproductions 3 місяці тому

      @@Gelatinocyte2we already have:
      ten
      eleven
      twelve
      draze
      eptwin
      fem

  • @hikingpete
    @hikingpete 11 місяців тому +13

    I really appreciated jan misali's introduction to the advantages of seximal, and have considered myself a convert for many years. You present a strong case here, and it's certainly convenient that your choice happens to be binary. One of the two systems that I have to know anyway. I'd like to see separate (short) videos on some of the topics here. How to write binary numbers. How to speak binary numbers. How to divide binary numbers. Etc.

  • @KaitlynBurnellMath
    @KaitlynBurnellMath 11 місяців тому +22

    I think language is the part where I'm least impressed here.
    There are studies suggesting that languages that express numbers in fewer syllables lead to people doing faster mental arithmetic.
    A lot of languages have specific words not only for the singular digits 1-10, but also for some numbers into the teens. English has "Twelve", for example, instead of "Twoteen". French has a single digit words for eleven, twelve, thirteen, fifteen, and sixteen. And I think there's also some linguistic benefit to having words for numbers like twelve rather than "ten two" than just a historical linguistic artifact--small integers are just the numbers we will use the most, being able to express them quickly and unambiguously is inherently valuable, even if it makes the language harder to learn than Toki Pona. It's also worth noting that languages tend to have specific words for 20, 30, 40, 50, etc. In English: twenty, not "two ten"--now there's no syllable advantage here (although in some languages the word for 20 is one syllable) but there may still be a linguistic advantage to having a separate word--even if hearing is an issue, you'll never mistake "twenty" for "ten" or "two".
    Rather than express number words in base 4, I think it would probably be advisable to have language work in...probably hexadecimal honestly? Either that or Octal, but I would lean hexidecimal for two reasons. First because it's 2^4, and 4 is a power of 2, so it'd be easier to deconstruct if you were already thinking in binary. Second having number names for numbers higher than 10 is fairly reasonable, cause a lot of languages already have that (1-12 in English and German, 1-16 in French and Spanish).
    But honestly, this is all hypothetical, really. People are never going to switch number bases unless governments force it by changing money to a different number base. As long as people have 10s, 20s, and 50s in their wallet, they're going to think in decimal.

    • @Yasser-444
      @Yasser-444 11 місяців тому +5

      you have got to make a video for the better way to say numbers

  • @4thalt
    @4thalt 8 місяців тому +25

    i fully support the use of "stack" as an official name for 2^6

  • @epicman590
    @epicman590 2 місяці тому +19

    "Alright buddy, you've pissed me off."
    *counts to 20 in binary using my hands*

    • @HelPfeffer
      @HelPfeffer 2 місяці тому +2

      counts to I .I.. using my hands*

    • @isavenewspapers8890
      @isavenewspapers8890 2 години тому

      You extend your pinky and middle finger?

  • @tristanridley1601
    @tristanridley1601 11 місяців тому +13

    As someone who played with numerals a lot as a teen, and who's done a lot of programming, I find it VERY telling that we programmers who work with it often will ALWAYS display it as hexadecimal.
    The 'best base' is really about what is the best base for humans, and minimizing how it pushes against our mental limits.
    I really liked your new binary-based symbols for hexadecimal numbers. I wonder if a society based on binary math and those symbols would work better and learn math easier.
    I think the binary naming in this video got really awkward and long to speak. Instead, use the groupings and name those. I think a society would need to use octal or hexadecimal for communication, while doing arithmetic in binary.

    • @tristanridley1601
      @tristanridley1601 11 місяців тому

      I'm entirely convinced about the mathematic side. But I think that goes without saying as the arguments were quite conclusive.

    • @Balakin2
      @Balakin2 11 місяців тому +1

      As a programmer myself, during my education (specifically when learning assembly), I always found working with the binary numbers far more intuitive / less cumbersome than working with the hex numbers. Like, at all points, I would think about it in the binary expansion, but then every time I had to actually write the number in the program I would have to group the binary by 4s and convert to hex, its just a mess.
      This is not to say hex is bad per se, but that it is necessarily just a layer of translation/abstraction over the actual numbers, which are binary. "x5555" is obscure, needs translation. "101 101 101 101" is the real number, the thing you actually need to work with. Anyways..

    • @05degrees
      @05degrees 10 місяців тому

      Well let’s see. The majority of programming is done staring at a text rendered with a monospace font. Why of course it would be quite a nightmate to juggle literals 32+ characters wide. There’s no real compressibility unless the programming language allows macros or something to use a custom number literal format (or the IDE used allows to work with proportional fonts in comfortably).
      I suspect there can be more mundane reasons other than this one.

    • @ShuAbLe
      @ShuAbLe 10 місяців тому +1

      @@05degrees Yeah, suppose we start with a system like the proposed. I think it wouldn't take much for people to start comming up with symbols and meanings that more readly represents the common quantities and groupings.

  • @Camilo-ne1sx
    @Camilo-ne1sx 11 місяців тому +15

    1:07:16 That Toki Pona fact at the end... This man doesn't know mercy

  • @matthewe3813
    @matthewe3813 11 місяців тому +8

    16:14 this is exactly what floating point does. It doesnt store the leading one to save a bit, which allows the number to have a bit more precision

  • @LeavingGoose046
    @LeavingGoose046 9 місяців тому +9

    I have no idea why youtube didn't recommend this to me sooner this is the rabbithole I live for

  • @lostGash
    @lostGash 11 місяців тому +16

    I want to point out that another word, while less common, for 2^4 is "nibble" if we're using "byte" for 2^8. Hex is fine, but I want more excuses to use "nibble", thanks.

    • @ThatRobHuman
      @ThatRobHuman 11 місяців тому +2

      came here to point out "Nybble" as well :)

    • @minerscale
      @minerscale 11 місяців тому +1

      I think 'word' instead of short is better too.

    • @xmcacutt4525
      @xmcacutt4525 11 місяців тому

      @@minerscale personally I'd have to disagree here. Word only exists for its counterparts Dword and Qword. It would perhaps be better to either go with short, int, long or switch all of them to Word Dword Qword

  • @ARockRaider
    @ARockRaider 10 місяців тому +19

    i would love to see some examples of this binary notation used in some common settings.
    some examples
    >in a car for speed and distance.
    >prices and measurements in a grocery store.
    >numbers in a video game.
    >a deck of playing cards.
    that batch of 4 trick seems like it would be very readable.
    i would also like to see something like "babies first numbers video", that would really show how easy binary actually is.
    a webpage for "try math in a new base" could be a nifty demonstrator for it's usability.
    i think the symbols themselves need a direction notation, the underline may be enough but I'd like it more obvious.

    • @nickm3694
      @nickm3694 9 місяців тому

      I made a userscript that you can find on greasy fork called "convert to binary" that attempts to convert numbers on webpages to their binary representation. The only pitfall of it is that it doesn't accurately convert non-integer numbers (like it'll turn 10.32 into lılı.lııııı)

    • @jibbjabb43
      @jibbjabb43 9 місяців тому

      First speed limit sign you see that says 10110 is basically the end of the emperiment.

    • @ARockRaider
      @ARockRaider 9 місяців тому

      @@jibbjabb43 well you wouldn't be using Arabic numerals for the task, you would use binary combs like the ones showed in the video.

    • @jibbjabb43
      @jibbjabb43 9 місяців тому

      @@ARockRaider It doesn't look any better. The issue here is both conversion and size. It's pretty silly to suggest that using rather indistinguishable characters is somehow better here. There is *some* ability to parse a misread sign simply becuase of possible interpretation, but that's because we're operating within a presumed 'field' of possible speeds.
      It's also more important that I used a number like 22, which I can defend, and you instead focused on what the digits look like. Which tells me you either didn't take my critique seriously or you are too predisposed to the idea of it working without considering it's real-world applications.

    • @ARockRaider
      @ARockRaider 9 місяців тому

      @@jibbjabb43 I had assumed that you picked a number to look the most outlandish, i was pointing out that you wouldn't use actual 1s and 0s and that you would be using a notation that makes the numbers every bit as clear.
      that you picked 22 makes my assumption of an intentionally outlandish number very clear, on top of that the exact speed would be adapted to the number system 20 for example would be i .i.. and as a group with proper underlines would be very different from 40 or i. i...
      neither look anything like 30 or i iii.
      but i expect that you wouldn't be using multiples of 5 for speed-limits, rather you would pick a new batch that always stays neat and round.

  • @SirFranex
    @SirFranex 11 місяців тому +12

    I really loved the video, but I think, as many commenters have pointed out, that the legibiliy of your line system could be improved. Some might even compare it to a certain Minecraft optimised number notation system.
    My suggestion would be to change out the short line for a small circle. This not only de-clutters the lines by separating them more cleary, but also prestents a great opportunity for ligatrues utilising the existing latin alphabet and also reducucing stroke number. or for l. and and for .l maybe for l.l, and maybe for .l. Keep in mind the arcs would be proportionally smaller in written notation
    I'll flesh this out further and come back to this comment later, I'm expecting some grouping and priority conflicts, but there might be a nice way to deal with them.

  • @gebrem
    @gebrem 10 місяців тому +9

    My first reaction was "wait, binary??", especially as i watched the jan Misali's videos before, but then it turned into "oooh, thats how we can do it", and then "it's beautiful as heck"

  • @jonasgajdosikas1125
    @jonasgajdosikas1125 11 місяців тому +18

    16:00 I thought I'd heard that somewhere; it's a "trick" used to store floating point numbers in the IEEE standard; the leading 1 in the mantissa is implied

    • @proloycodes
      @proloycodes 11 місяців тому +1

      i dont think so. they have to represent 0 too

    • @mathcookie8224
      @mathcookie8224 11 місяців тому +7

      They represent 0 by setting the exponent to its lowest possible value, at which point that leading 1 is treated as a leading 0 instead.

    • @w1keee
      @w1keee 11 місяців тому

      jan Misali said this in his floating point number video iirc

  • @diegonals
    @diegonals 11 місяців тому +8

    Great video! I wasn't even half way through and you had me convinced. After watching the procedure for the square root, I managed to find a way to get any integer root! It works in every base, but its way simpler in binary.
    Basically instead of separating the original number in pairs, you separate it in base-of-the-root groups, and then instead of checking if its larger than or equal to the number above with a 01, you check if its larger than or equal to the following sum:
    sum from k=1 to q of (q choose k)*(2p)^(q-k)
    with q being the base of the root and p being the number above.

    • @diegonals
      @diegonals 11 місяців тому +6

      I think I might be the first person to discover this method, the method for square roots obviously already existed but I couldn't find anything about cubic or any other roots using this digit-by-digit method.

  • @DaBeast893
    @DaBeast893 10 місяців тому +10

    Felt compelled to decipher the text at 8:20.
    It reads:
    "You have got to be about the most superficial
    commentator on con-langues since the idiotic
    B. Gilson.
    Did I miss the one where you said which conlang
    you're fluent in and read at least three times a
    week and can read new books in every week of
    even one year or listen to radio shows in every
    week? New radio shows?"
    Was a fun challenge, thanks!

  • @charleskolozsvary8714
    @charleskolozsvary8714 11 місяців тому +10

    What a high quality video! I wonder if I’m really slow or most could keep up without extensive pausing and replaying. Congratulations on such a well made video regardless.

    • @mortismain6719
      @mortismain6719 11 місяців тому

      Not just you, lots of parts seemed a little confusing

  • @Blocka025
    @Blocka025 11 місяців тому +12

    This really is exceptional content. As a nerd I really appreciate the work that was put into this video. Great work. My only note is the pacing was too fast for me to grasp some of the details that were claimed to be “immediately obvious”.

    • @thebestwaytocount
      @thebestwaytocount  11 місяців тому +7

      that's what the footnotes are for! this video would've been astronomically long otherwise :)

    • @theramendutchman
      @theramendutchman 11 місяців тому

      @@thebestwaytocount Says the uploader of an over I hour long video responding to an I ..I. minute long one

    • @matheuscabral9618
      @matheuscabral9618 10 місяців тому

      ​@@theramendutchman Dude an hour and a half is very short, stop watching tiktok

    • @theramendutchman
      @theramendutchman 10 місяців тому +1

      @@matheuscabral9618 First, there's no need to make assumptions and attack people. Please refrain from it and maintain a civil discussion.
      Secondly, my point is that they said their video would've been longer, which is unexpected to me seeing how it responds to a 10 minute video; this video is already so much longer than the video it responds to!

    • @matheuscabral9618
      @matheuscabral9618 10 місяців тому

      @@theramendutchman eh

  • @sinom
    @sinom 11 місяців тому +9

    "just use only three fingers on each hand" leads to communication issues. The great thing about addition only decimal finger counting is no matter how you count you always get the same result. It is unambiguous and inclusive to everyone who has any fingers. But yes it also means that you can only communicate very few numbers at one time. Basically decimal counting is TCP (sacrificing speed and efficiency for making sure it is as unambiguous as possible within the system) while binary counting is UDP (so prioritizing speed and data density while risking the wrong message being sent)

  • @uigrad
    @uigrad 9 місяців тому +5

    Congratulations! You have been given the award for the most uses of "Fermat's Little Theorem" in a video that is not about Fermat's Little Theorem or about modular arithmetic!

  • @zombieslayer1468
    @zombieslayer1468 11 місяців тому +34

    did you literally create a channel just for this video

    • @theramendutchman
      @theramendutchman 11 місяців тому +11

      And made the video an hour long chaptered documentary? They did and I appreciate them for it.

  • @considerthehumbleworm
    @considerthehumbleworm 11 місяців тому +16

    I take some umbrage with the “efficient finger counting” argument, because finger counting is primarily a tool for teaching children. Binary finger counting (and even seximal finger counting) is more complex than simply counting the number of fingers raised. Bases are an arbitrary construct and humans don’t think in terms of them, so a child will never intuitively understand binary finger counting the way they understand “base 10” finger counting (though i would argue it’s more accurately described as base 1 finger counting)

    • @willguggn2
      @willguggn2 11 місяців тому +6

      Many cultures have counted in dozenal or hexadecimal on one hand. Many Asian cultures to this day count to ten on one hand and find the western way to count on fingers jarring. Your argument is eurocentric.

    • @considerthehumbleworm
      @considerthehumbleworm 10 місяців тому

      I’d argue the mentioned systems are still ultimately base-1 counting systems. They use 12 or 16 naturally ordered positions of the hand. Counting up to 12 with the dozenal thumb-thing is still just moving your thumb through a “number line” of hand positions. It still retains the simple linearity of western counting that’s lost with binary counting.

    • @considerthehumbleworm
      @considerthehumbleworm 10 місяців тому

      well actually maybe base infinity would be more accurate but my point is that neither 10 finger counting nor 12/16 one-hand counting have to actually deal with the things that make bases complicated (i.e. multiplying by powers of the base according to the position of the digit)

    • @willguggn2
      @willguggn2 10 місяців тому

      @@considerthehumbleworm During the Middle Ages doing arithmetics with your fingers was common enough that almost every book on mathematics had a chapter on it. For example in _'Liber Abaci'_ by _Leonardo Fibonacci_ finger counting is the first chapter. Systems to count up to 100.000 were around for quite some time.
      Conflating finger counting to what _we_ today in the west teach to toddlers is a mistake. Drawing conclusions from oneself about others rarely works out.

    • @considerthehumbleworm
      @considerthehumbleworm 10 місяців тому

      Finger counting is what we teach to toddlers tho. I think it’s a bad idea to offer binary finger counting as a replacement in those contexts. It’s useful to be able to count higher than only 10 in other contexts but it only muddies the water for learning basic arithmetic. Honestly, teaching toddlers systems that go up to 8 or 16 is probably preferable to 10 to ease the transition from “number line counting” to using actual positional binary (even binary finger counting, eh?). That transition’s a bit of a given with 10 finger counting and base 10, so it’s worth considering how that works with binary. Also we don’t have to hate each other because we disagree about numbers lol

  • @Riya-ho5zv
    @Riya-ho5zv 11 місяців тому +8

    Man really about to convince me the invention of every number after 1 was a mistake

  • @adjoint_functor
    @adjoint_functor 11 місяців тому +9

    i love the binary multiplication table because it's also the logical AND gate

  • @justineberlein5916
    @justineberlein5916 11 місяців тому +13

    Actually, I have a more general counterargument:
    Redundancy is good, actually. All of these arguments demonstrate that binary is the most efficient base in a similar way to how Ithkuil is the most efficient language. Sure, that might be true on a technical level, but if you miss more or less any information, it's harder to recover. For example, something weird happens with the HDMI on my TV, so the edges of the screen get cut off when I try playing a Switch game on it. But because all of the Hindu-Arabic numerals are fairly distinct, I was still able to follow the timer in the Star raids in pokémon, despite the top half of the number being cut off. Meanwhile, if the top half of your binary numbers got cut off, that'd be it. There would be no way to distinguish numbers anymore. Or similarly, consider seven-segment displays. They're actually *horribly* inefficient, since you can display 128 distinct figures with them, and we only use 10. But because we use so few, depending on which segment goes out, you can still distinguish most numbers. And even in a case like the middle segment going out and making 8 and 0 indistinguishable, context clues help. If you see 1-"thing that looks like it's supposed to be a 9" change to 10, you can infer that it's probably counting down and is probably supposed to be 18. But if it changes to "thing that's probably a 2"-0, you can infer that it's counting up and that it *is* supposed to be a 0.
    Or similarly, finger counting. Functionally, "binary" finger counting is actually duotrigesimal. No one's going to actually think of each finger as its own digit, so you're effectively expecting people to learn 32 different hand shapes. So if you're just using hand counting to show someone a number, like a kid going "I'm this many", it's going to be less efficient compared to just holding up a number of fingers and subitizing. Or similarly, if you're actually counting up or down, with both seximal and jisanbeop, you only ever need to change either 1 finger at a time or all 5 fingers. (And with all 5 fingers, it's also always either resetting the hand or changing 4 fingers to a thumb) Meanwhile, with binary finger counting, you might have to change any number or combination of fingers. And that's actually so well known of a problem that Frank Gray came up with the idea of reordering binary numbers so you only ever have to change 1 bit at once all the way back in 1947. (With the idea itself going back to at least the 1870s)

    • @impishlyit9780
      @impishlyit9780 11 місяців тому +1

      I actually agree with most of your points, but have a few nuanced points to make.
      1) This one's simple, actually using binary doesn't mean blocking out half the digit would leave it unreadable. Binary is actually pretty good about that, you can *always* tell if you can see part of the digit.
      2) I use decimal for readability purposes, but I find binary a better system for doing simple counting tasks. Remember that you could use different systems for different purposes, it's done in some cultures in other areas, such as speaking one language and writing another. (Looking at you, Switzerland...)
      3) While your argument about finger counting has some merit, I actually think that's only a problem for children. Since we're actually using a *unary* system for that task, binary finger counting is strictly better but also more complex. (Seeing each finger as a digit with two states, the *number of digits* doesn't have anything to do with the counting system - that's just a physical limitation.) It's too complicated to teach to children without a whole course around counting systems, which doesn't make sense at that stage of life. For adults in the mathematics or comp sci sphere though, it's easy enough to adopt and therefore we probably should do so on an individual basis.
      Not sure what the video itself seeks to argue, as I'm not about to watch someone try to convince me of the merits of a counting system I already use, so don't take any of this as an argument toward the creator's points. I'm simply arguing for what I believe to be best in my own experience.

    • @justineberlein5916
      @justineberlein5916 11 місяців тому +3

      @@impishlyit9780
      1. Eh, not necessarily. One of the video's weaker arguments has to do with number length. It basically makes a *font* based argument, where if you change binary numbers to tall (1) and short (0) lines, the horizontal width of numerals becomes comparable to other bases. And that really *does* run into that issue. Or more broadly, I forgot to include this bit for contrast, but imagine a binary display. If any one segment goes out, you cease to be able to distinguish anything in that place. At a minimum, you'd need to do something like pairs of dots, where only one can be on, for you to be able to lose a segment and still be able to distinguish numbers. Meanwhile, even though only the top left and bottom right segments lack minimal pairs, you can still generally make things out on a 7-segment display, even if one of the segments goes out. You'd need 2-3 to go out before it starts really impacting your ability to read things.
      2. No counterargument here.
      3. It's also more than just kids. For example, how often do you *actually* need to count on your hands? It's typically smaller things, like how you might silently count down from 5. And while I'll grant that people probably count down specifically from 5, in part because we have 5 fingers on each hand, unary feels a lot easier for that. In a way, it's sort of like sorting algorithms. Merge sort is more effective for really big lists, but it also requires a lot of overhead. So for shorter lists, the less asymptotically efficient insertion sort winds up running faster overall. The main time I can think of that it's potentially useful to display bigger numbers would be something like days, but there are also systems like the Medieval Arabic hand numbering system that do it more easily than finger binary. It's actually even more efficient than finger binary. It encodes one digit on your thumb and index finger and one digit on your other three fingers, so it can go up to 9999 on two hands, as opposed to 1024.
      But overall, my main criticism of the video really is that it successfully argues that binary is the least redundant numbering system possible, but not that redundancy is something we need to be avoiding

    • @typecasto
      @typecasto 11 місяців тому +1

      You should into your TV's settings and turn on either "overscan" or "just scan", or set the aspect ratio to "full" or "just scan". Turning on "game mode" might also fix this.

  • @vorquel
    @vorquel 10 місяців тому +18

    Me at the beginning:
    Worth watching, but unlikely.
    Me at the middle:
    Fantastic arithmetic, but I mostly say rather than play, and binary is long.
    Me at the end:
    I'm convinced.

  • @ShuAbLe
    @ShuAbLe 10 місяців тому +4

    I love how the sounds are so entangled with the meanings, impressive.

  • @shrodinger3844
    @shrodinger3844 10 місяців тому +13

    after much deliberation i've decided to use base 10

  • @eldabys
    @eldabys 11 місяців тому +9

    this is remarkably well-researched and thought out. just gotta show this to my mathematician friends to explain to me the bits i dont understand

  • @keiyakins
    @keiyakins 11 місяців тому +39

    Some notes as I go:
    - I see you don't want to be able to write the numbers 0 and 1, if the leading digit doesn't matter for information.
    - You seem to be neglecting the human tendency to ossify details. A binary system wouldn't stay a binary system for long. Within a few generations, eople would start writing shorthand octal or hex with a couple strokes rathet than four or five, and those would become the basic unit. That grouping trick is actually a negative when you look at language evolution.
    - "What's the Most Commonly Used Prime Which is Incompatible with This Particular Base?" got a laugh out of me, good work on that one!
    - Your repeating symbol and your grouping marks would be super easily confused in hasty handwriting. That's not an inherent binary problem though, just one with your notation.
    - 2⁴ should be called nybble or nyb. It's cuter and sounds better in practice.
    - ... I both love and hate you for pointing out to me that stack is a number name. It is though, saying something like "three stacks twelve" is perfectly normal in minecraft contexts.
    - I think seximal is still more aesthetically pleasing, to be honest. And that matters because the only context switching away from decimal will ever happen is art. ... though balanced ternary might win there, it's just the right amount of weird to be really fun.

    • @ThiagoGlady
      @ThiagoGlady 11 місяців тому +3

      i love this comment so much. Agreed with everthing you said 😂

    • @jarlsparkley
      @jarlsparkley 11 місяців тому +2

      For your first point: I do agree that they handled this poorly. But I think all is not lost. Instead, you can think of what they are talking about as a consequence of the fact that simply knowing the bit length of a number tells you the value of its most significant bit (which has to be 1). The “length” of the number does not give you so much information in other bases, this is definitely true.
      As for your second point, so long as people don’t forget where these ossified forms come from and they are visually similar to unossified forms and can be easily decomposed into them, then I don’t think this is actually an issue.

    • @keldwikchaldain9545
      @keldwikchaldain9545 11 місяців тому +1

      Since the measure of information per digit is considering all infinitely many numbers and the number of single digit numbers is finite, the amount of extra information carried by that first digit tends towards zero in the limit of considering all numbers since a finite portion of an infinite space is always 0% of the total space.
      I think this means that when considering information on the long scale this simplification is fine, since the context of the discussion was already the long term efficiency of a base and not its efficiency writing small numbers.

    • @keiyakins
      @keiyakins 11 місяців тому

      @@keldwikchaldain9545 1 and 0 are kind of important numbers though.

  • @CoolCatDoingAKickflip
    @CoolCatDoingAKickflip 11 місяців тому +17

    Base 4 + 3i is the optimal base.

    • @plopgoot5458
      @plopgoot5458 10 місяців тому

      i don't know aabout that, but base -1+i is buded the most beutiful base.

    • @TheBananaman-sg4xd
      @TheBananaman-sg4xd 9 місяців тому

      I personally prefer base 2pi-i*sqrt(97) because I hate rational numbers (especially integers), but this is an interesting choice as well

  • @bucktootha
    @bucktootha 9 місяців тому +6

    I LOVE how you play the corresponding musical interval whenever you mention a fraction

  • @Tomatenmark13579
    @Tomatenmark13579 3 місяці тому +10

    I feel like this system could be improved by using unique labels in spoken language for every permutation of 4 bits, effectively treating it like hexadecimal when talking. You already concede that spoken binary would create some very long number labels and offer quartery as a compromise, so you might aswell embrace the pseudo-hexadecimal nature of grouping 4 bits together by adding a horizontal line at the bottom by covering these groupings with a single label each.

    • @ceresgc
      @ceresgc 2 місяці тому +1

      Exactly! And since lower numbers don't have decimal based names (compare "eleven" to "twenty-one") we can start by borrowing those. In spanish we have unique names up to 15 (it's "quince" as opposed to "diecicinco") so we already have the firt 4 digits covered. From that point, I'd say the next 4 digits should have a prefix (so, I.II. would be something like hexasix), but we would need to find something that rolls of the tongue (I love stack for 64, but it sounds clunky as a prefix)

  • @minimo3631
    @minimo3631 6 місяців тому +10

    Grouping "bits" by up to for 4 is also pretty practical in a human sense, since around 4 is the natural range of human "subitizing" i.e telling how many of a thing there are at just a glance

  • @artemisSystem
    @artemisSystem 11 місяців тому +11

    holy shit, *holy shit*, i think this might be my favourite video. so so so many cool points brought up. so many new ways of thinking that were a delight to be introduced to. it has like, all my favourite things. this video is a masterpiece

  • @yoneda-emma
    @yoneda-emma 3 місяці тому +6

    by far the best of these videos on alternative bases that I've seen so far, incredible work!

    • @yoneda-emma
      @yoneda-emma 3 місяці тому +2

      one small sour point was the credits sequence just being a bunch of "point and laugh at these people" images but that feels like a small blemish on this otherwise amazing video

  • @imthecryptic
    @imthecryptic 11 місяців тому +17

    Babe wake up found new banger channel

  • @helleye311
    @helleye311 11 місяців тому +8

    Honestly the only reason why I never considered binary in this nerd debate of "best counting system" was the number length. With tally-mark-like digits this already makes so much more sense, and that's just chapter . in the video.
    we even have ascii characters for binary numbers: |.|. looks basically like the marks.
    regardless of what you think remember, every base is base 10 :3

  • @ChillGoblin
    @ChillGoblin 10 місяців тому +11

    I'm half convinced to switch to binary and the other 110010% supicious this is a prank

  • @livingpicture
    @livingpicture 10 місяців тому +8

    Having been in computer science, I and all the computers in the world agree with you, because it can also be used to represent pretty much any concept that can be stored or represented digitally ... until it comes time for a human to interpret what's being said, because it's horribly inefficient! This is why we compromised and use 4-bit and 8-bit, which transfer nicely to hexadecimal, and lead to more efficient ways to represent extremely large numbers, which has become necessary in the age of the gigabyte, terabyte, petabyte, and beyond.

  • @ctrlaltmilk
    @ctrlaltmilk 10 місяців тому +17

    no matter what you think, base 10 is always the best (as long as you read it in your base of choice, of course)

  • @ODR96
    @ODR96 3 місяці тому +23

    Hi, the best way to count is like this: 1, 2, 3, 4, 5, 6... Hope this helps.

    • @sighrelief
      @sighrelief 3 місяці тому

      you're arguing for base 10, which is arbitrarily based on the number of fingers we have (speculation)
      this video is an argument for base 2. You misunderstand the premise, and are blind to the implications of using a different base.
      Your computer thinks in binary. Hope this helps.

    • @ODR96
      @ODR96 3 місяці тому +15

      @@sighrelief this was a joke. Hope this helps

    • @sighrelief
      @sighrelief 3 місяці тому +1

      @@ODR96 actually its rude nonconstructive "criticism", if it were a joke it'd be funny

    • @weichang9693
      @weichang9693 3 місяці тому +6

      @@sighrelief they only went to 6 so it could be an argument for base 6 or 7 or 8 or 9 or 11 or 12 or 13...
      also jokes dont have to amuse you personally to be considered a joke

    • @sighrelief
      @sighrelief 3 місяці тому

      @@weichang9693 no, its pretty clear to me they're a schrodinger's asshole and that the "joke" is a post-hoc justification for being annoying about their preference for base 10

  • @bob36097
    @bob36097 11 місяців тому +8

    This makes my brain feel just like after the hackenbush video essay. Masterpiece

  • @Mr.Nichan
    @Mr.Nichan 10 місяців тому +13

    43:29 "Traditionally, to notate a recurring fraction, the entire recurring segment is marked, but that doesn't make a lot of sense: It's simpler to just mark where it starts."
    I think your opinion comes from the age of typing and digital text representations. In hand-writing, marking the recurring segment makes more sense for the following reasons:
    (1) Often, you will get this repeating decimal from just long division until you enter a cycle, and adding a line of the repeating part is something you can do after you've written the number, which doesn't require you to erase anything or rewrite the number, and also separates the repeating segment from any digits of the next repetition you may have written before realizing it was repeating. This doesn't apply if you're rewriting the number somewhere else, but if you're copying a hand-calculated quotient with a long repeating decimal, you'll want to use some mark like the over-bar to mark the repeating segment of the decimal anyway, so any other notation like the "r" you're using will just be another notation to learn IN ADDITION to something like the over-bar. Thus, I think this is the most important reason.
    (2) In hand writing, writing a line over several numbers is not significantly harder or more time consuming than writing an r before them. It's actually a slightly simpler shape than an "r", though the length and precision required mean I'll just say it's about as hard overall.
    This is different from typing or digital text, where putting bars over numbers requires special characters or text formatting, both things that are much more of a pain to deal with than just typing "r", both just in typing it, and in the sneaky problem that things like this sometimes won't render properly on other people's computers or on printers. (With typewriters, it usually requires some kind of tricks involving typing over the same text I suspect.)
    That being said, one downside of the over-bars specific to hand-writing is that, due to the imprecision of handwriting, it can often be unclear to readers exactly which numbers the over-bar is over. In typing, this would only really be a problem if your method of creating over-bars was bad, and using preceding "r" would get rid of this issue in handwriting (as would using parentheses or circling, although those aren't quite as convenient to add on to an already written sequence of digits as an over-bar is).

    • @hello-lv1qv
      @hello-lv1qv 10 місяців тому +1

      In my school they taught us to write repeating digits usung brackets:
      1/7 = 0.(142857)
      This eliminates the precision problem as brackets are easier to write and mark exactly where the repetition begins and ends

  • @danielmccann2979
    @danielmccann2979 11 місяців тому +12

    Personally as programer I chose binary with hexadecimal compression because it is the best of both worlds. Your number to long, just start compressing into hexadecimal, need to do math decompress it. It just allows better writing efficacy and in low level programming you just do base two operations on hex nums anyways.

    • @Tarou9000
      @Tarou9000 11 місяців тому +4

      I am also a programmer, I love the idea of having two different ways of writing numbers, I previously only thought about hexadecimal and even made my own writing system for it wich also uses a sub-base of 4, 2*2 = 4, and 4*4=16, I love the symmetry
      Binary for math operations and hexadecimal for showing numbers!

  • @_wetmath_
    @_wetmath_ 10 місяців тому +10

    oh my god this is the first math video in a long time that has made me feel like this

  • @MariuszWoloszyn
    @MariuszWoloszyn 9 місяців тому +11

    "Single hand is chiral". My favorite sentence that says so much while just saying that hand is a hand :)

  • @PrinceOfKenya
    @PrinceOfKenya 3 місяці тому +4

    Was so skeptical of the premise in the beginning that I almost closed the video when you said it was about binary, but came out the other side completely convinced. The advantages for addition, and especially multiplication, are really something. Very interesting and well made video.

  • @triplebog
    @triplebog 11 місяців тому +15

    I think the whole argument that non-binary systems are "more wasteful" because they might have an extra leading zero is pretty enormously flawed and relies on the assumptions that A) pattern recognition and readability isn't a thing, and a series of two symbols that repeat over and over is at all functional.
    By this argument, and the whole ""efficiency"" radix argument, you could also make the same deduction, that all language should just be written in binary strings. After all, what is the English alphabet but a series of base 26 numbers?

    • @mmlgamer
      @mmlgamer 10 місяців тому

      Good point, except the alphabet isn’t for numbers, but for words and/or sounds. You’re not performing arithmetic with words. Also, no one is ignoring pattern recognition. The video simply argues that it can, in fact, apply to binary, especially with the right notation and proper parsing methods for the bits.

  • @Inspirator_AG112
    @Inspirator_AG112 11 місяців тому +11

    My favorite numerical base is centovigesimal, or base-120, because it is really good for divisibility tests and representation of fractions... not only because 120 is very composite, but its neighbors are also composite (119 = 7 • 17 and 121 = 11²).