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.

drama in the counting community

I'm a bit excited

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.

"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.

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

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

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

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.

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?

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.

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.

+1 for playing overtones behind fractions

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.

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

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

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

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.

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

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.

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

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

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

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

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

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

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.

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.

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

This video is exactly 200 minutes in seximal. Cheeky.

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? "

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.

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".

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

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.

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"

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

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

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

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

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

Babe wake up found new banger channel

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.

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.

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

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!!

"What an awful dream, one's and zero's everywhere, and I thought I saw a two" "It was just a dream, Bender. There's no such thing as two"

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

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.

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

I propose a much worse way to count, base -29

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

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

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".

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

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

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.

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

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)

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"

“We are mathematical heretics” is such a raw line, I absolutely love it

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

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.

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

let's just go to base infinity, every number has its own unique symbol or something like that i guess or maybe instead of base 2 let's go with base 1 so every number you just have to count out like tally marks

Base 4 + 3i is the optimal base.

after much deliberation i've decided to use base 10

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.

did you literally create a channel just for this video

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

1, 2, many. There has never been a better system.

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

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

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.

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”.

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

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!

I tried the sqrt algorithm with 225 and I feel like a forbidden secret has been unlocked to me

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)

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.

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

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

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.

"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)

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).

Is this Loss? 1 2 3 4 (explanation) | |. || |..

Putting this video at 1.5x speed gets the pace near Jan Misali's speaking speed!

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.

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

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

Binary is truly one of the numbering systems.

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.

8:19 as a Chinese speaker, this took me a while to decode lol idk if anyone else has done it translated text: "you have got to be about the most superficial commenter 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 ever one year or listen to radio shows in every week? new radio shows?" of course, the creator of the video might have made mistakes when writing this, so here's a readable version: "You have got to be about the most superficial commenter on conlangs 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 every one year or listen to the radio shows in every week? New radio shows?" ...wait, I just realized what it says

i think my love for binary just doubled

The "best" base is the one which lies at the intersection between maximal efficiency (cramming in as much info as possible), maximal legibility (being able to get that info back out), and maximum versatility (being useful in multiple numerical arenas). While binary is objectively the most efficient way of storing data, it isn't the most legible or versatile, so that's just the starting point for finding our magic intersection. Legibility peaks around the concept of subitization, the ability for the brain to quickly count numbers, which begins to decrease after 4 and is gone for most people by 8. This means that any number longer than 4 digits is going to be harder to read, objectively, with separators as a bandaid patch. Thus we definitely don't want any common numbers to exceed 4 digits, so binary isn't necessarily the best choice on this front. The last point is versatility: can it express simple fractions simply, how easily does it convert to binary, can you count on your fingers with it simply, etc. At a guess based (heh) on all this, the intersection is probably around base-4, which means no one gets to be happy and DNA actually got the right answer somehow.

This is the best video I saw this week, by a long shot. Although I am now convinced that binary is the most efficient number system for any arithmetic, your didn't adequately adress compactness. There are three ways to convey information: 1. Speaking 2. Typing 3. Writing Writing binary, even in your notation, is still way slower than decimal. You should probably make a follow-up video, trying to invent the most efficient way to write down, speak, and type binary. For writing down, the most efficient notation I could come up with is something like /\\//, but I think this isn't optimal. For speaking, the fastest way to convey two symbols is by clicking with your tongue (requires some training), but you don't want to constantly indicate your position. Typing with your thumbs goes a lot faster, because your thumbs don't have to switch position. This is so fast that there is no advantage of setting up complicated multi-finger systems, when you can apply faster clicking techniques, because would finish your numbers quick enough.

I love that every time you write a number you play its corresponding overtone!

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.

binary finger counting is good for every number aside from 4 and 132.

59:00 4 bits is sometimes called a "nibble" (in addition to being the amount of information in a hexadecimal digit, which is why you called it "hex").