the best way to count
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- Опубліковано 16 чер 2024
- an introduction to a numbering system that's objectively better than seximal
- external links -
footnotes, script, other readables: github.com/lucillablessing/th...
soundtrack on UA-cam: • the best way to count ...
soundtrack on Bandcamp: lucilla.bandcamp.com/album/th...
source code: github.com/lucillablessing/bi...
discord: / discord
- credits -
Lucilla ( @lucillablessing ): concept, script, programming, visuals, animations, music, etc.
kepe ( @kepe__ ): narration
Addy ( @AddyLovestar ): additional narration
- chapters -
0:00 introduction
7:16 chapter zero
11:41 chapter one
17:25 chapter two
22:32 chapter three
31:46 chapter four
42:16 chapter five
55:25 chapter six
1:02:23 chapter seven - Фільми й анімація
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.
please do a responde video! not only. for exposing more of your points but also for giving this guy more attention here on youtube
I think the answer then would be some more usable power of two such as 8 or 16
+
@@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
@@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.
drama in the counting community
lol
When are the diss dropping?
I'm a bit excited
a
Because Vötgil has so many vowels
I am waiting for a formal debate
vötgil :3
Because this episode is a first in a few ways
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.
Wouldn't they also be expressing the numbers 128 and 132?
@@mehulpandya4761 The most avid mathematicians on the back seat usually flaunt their counting skills in this way.
"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.
i'm not sure you understand how a response works
youre missing the point but its still funny
Guys it's a joke, don't take it as him being serious
kekw
@@katie-ampersand
short vid = sprint
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.
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 ^^
@@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
we're honored to be compared to videos like these! glad you enjoyed
59:03 Excuse me, but four bits is a *nibble* (half a byte!). I will not drop the cute name. I love it.
fr agree, how wouldnt you wanna say 8DEC as "a nibble"
"gimme a nibble burgers"
"i would like a nibble kilo of ice cream"
"give me nibble apples"
@@im-radio "Can I just have a nibble of your sandwiches?"
"NO!"
If you wanted to keep it monosyllabic you could shorten it to "nib" :P
@@im-radio36332 right?
I just appreciate how unnecessarily hostile the video is. It's honestly hilarious.
Yes, and it makes the thesis so much more compelling
One cute fraud.
yooo wikipedia bisexual lighting skeleton
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.
There are 10 types of people, those who understand binary, and those who don't
Underrated comment
And those who weren't expecting a ternary joke
There are 10 types of people, those who understand the hexadecimal system, and F the rest.
@@MuzikBikethats still 2 #binaryandseximalareslaynumbersystems
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.
My phone did arithmetic to like ur comment
+1 for playing overtones behind fractions
i loved that
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?
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
2 months ago
@@LucasFerreira-gx9yh he may end it up studying Gaussian integers. Hahahahaha.
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.
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.
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.
@@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).
I also think it would pay to write numbers little-endian.
@@duncanw9901 Exactly what I had in mind!
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.
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 shared your astonishment when I realized there's an algorithm for that. It just shows how the compactness of binary makes it so versatile.
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
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.
@@Salsmachevthis video's been out for like 3 days
it's just too bad they're completely unreadable at a glance
@@mrosskne I'm curious if you're saying this having used that notation for a while or not
@@starstufs I literally just said "at a glance"
I got converted to binary after seeing the square root algorithm, knowing how complex it is in base 10
gd guy
its funny cuz the main narrator kepe also made yBot, small world huh
@@arf101088 WHAT
missed opportunity to title it "The best way two count"
smart!
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
no way its the crystal garden golden person
i frogelined and peacelined
oh hey it's the |..|eg guy
The fact that the little sound effects match with the number on screen and the harmonic series is a very nice touch
Some fingers are significantly harder to extend individually than others. This applies both physiologically and culturally.
Ah yes, the four (l..) finger ;)
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
@@OMGYavanithree fingers per hand still means you can flip someone off, and arbitrarily skipping the middle finger would introduce ambiguity.
finger counting 19+113 💀💀
Back for a rewatch. This is levels of autism I strive for
fr lol
yess
She truly made a channel and a dedicated trailer for the counting video essay. Dedication like that deserves my full attention and like!
Check the credits! The writer/editor has a feminine name and isn't the narrator
@@timperkin9 thanks! I fixed it in the original comment :) I never check the description or anything so I missed that one :(
1:07:16 That Toki Pona fact at the end... This man doesn't know mercy
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.
This video is exactly 200 minutes in seximal. Cheeky.
Are minutes a seximal unit?
@@Arbarano(kinda sexagesimal)
I like how we all do this research but will still all ever only use decimal casually
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.
"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".
@@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.
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.
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.
@@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.
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.
npc ahh comment
@@mikechad27npc reply
As a programmer seeing hex byte short int used as power names is both horrifying and amazing
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 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 love the binary multiplication table because it's also the logical AND gate
"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"
My jaw dropped when I saw that square root algorithm. Fuckin’ black magic 👍
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
IKR?
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!!
Summary: binary > every other base because binary < every other base
unary.
Man really about to convince me the invention of every number after 1 was a mistake
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
MINECRAF???!?!??!!
wow I didn't get it on the spot that's just super funny x'D
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"
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? "
this is gold. thank you.
interestingly the characters pronounced in chinese are close to the sound of their corresponding letters
amazing dedication
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".
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.
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.
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
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.
@@thebestwaytocount These issues are much more significant in binary since they show up much earlier on than in something like decimal
Recursive algorithms are simple algorithms. No one that has any experience reasoning about procedures thinks any different.
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.
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
It's my favourite feeling tbh
> that one really strong that
I think the noun is missing.
Regardless, yes.
@@zairaner1489 oops
I propose a much worse way to count, base -29
Great idea, but I prefer base 2.5 myself
i fully support the use of "stack" as an official name for 2^6
10^110
and i use nibble for 16
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
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
i dont think so. they have to represent 0 too
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.
jan Misali said this in his floating point number video iirc
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"
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. 🙂
@@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 :)
someone please like this comment later today so I remember to come back to this amazing comment
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"?
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.
you have got to make a video for the better way to say numbers
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
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.
This comment is pure perfection.
@@lemoneer7474 Wouldn't nonabinary be base 18?
I'm non-decimal. It's a shame no-one supports me! /jk
@@lemoneer7474base √-1 -1 (called i-1) works well too
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
I have no idea why youtube didn't recommend this to me sooner this is the rabbithole I live for
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".
Devastatingly nerdy comment, love it
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
@@rubixtheslime after qword is either oword (octa) or xmmword (128 bit simd register)
after oword is xword (hexadeca) or ymmword (256 bit simd register)
Based and Embeddedpilled
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".
"Single hand is chiral". My favorite sentence that says so much while just saying that hand is a hand :)
after much deliberation i've decided to use base 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
oh my god this is the first math video in a long time that has made me feel like this
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
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.
This makes my brain feel just like after the hackenbush video essay. 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.
don't explain the joke
explain the joke
@@mrosskne 10 is 2 in binary
@@mrosskne 10 is 6 in base 6
@@mrosskne10 is 10 in base 10
1, 2, many. There has never been a better system.
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 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)
First speed limit sign you see that says 10110 is basically the end of the emperiment.
@@jibbjabb43 well you wouldn't be using Arabic numerals for the task, you would use binary combs like the ones showed in the video.
@@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.
@@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.
I tried the sqrt algorithm with 225 and I feel like a forbidden secret has been unlocked to me
though I do have one question, how would this algorithm work with non-perfect squares and would it work with complex numbers as well?
@@nukollodda For non-perfect squares, the algorithm continues past the decimal point to whatever degree of accuracy is required. As for how to adapt it to accept complex inputs and outputs, that's above my current level of understanding.
Doing multiplication in binary always makes me feel like a robot.
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.
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!
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 infinity truly is the chaotic neutral of bases
base -1
Base -1-i
did you literally create a channel just for this video
And made the video an hour long chaptered documentary? They did and I appreciate them for it.
"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)
Binary is truly one of the numbering systems.
I LOVE how you play the corresponding musical interval whenever you mention a fraction
Base 4 + 3i is the optimal base.
i don't know aabout that, but base -1+i is buded the most beutiful base.
I personally prefer base 2pi-i*sqrt(97) because I hate rational numbers (especially integers), but this is an interesting choice as well
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 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.
The number of strokes I have while writing simple words Is one major factor,
I love how the sounds are so entangled with the meanings, impressive.
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.
came here to point out "Nybble" as well :)
I think 'word' instead of short is better too.
@@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
I'm half convinced to switch to binary and the other 110010% supicious this is a prank
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).
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
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.
I'm entirely convinced about the mathematic side. But I think that goes without saying as the arguments were quite conclusive.
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..
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.
@@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.
Putting this video at 1.5x speed gets the pace near Jan Misali's speaking speed!
And at 1/2 speed it matches the pace of W and C
I love that every time you write a number you play its corresponding overtone!
You can't stop here. Please make more videos. Thanks.
14:49 I can't speak for jan Misali, but I think he probably just meant that if you write binary with Hindu-Arabic numerals, the numbers get unwieldy in size, and base 4 in Hindu-Arabic numerals is a good way to compress it.
15:36 This fact isn't what makes binary the most efficient, it just makes it the most efficient by a long shot. Even if we didn't consider the fact that the leading digit can't be 0, by replacing b-1 with b in the formula, binary would still be more efficient than base 3.
side note: I don't know how we're measuring which is better rigorously, even though it's clear intuitively. Because the graph for base 3 does sometimes dip below the graph for base 2, like for example between 8 and 9. Is it the one which is the lowest for the most numbers, which has the lowest average, or what?
16:27 I wouldn't be so hard on seximal. jan Misali admits that in seximal, numbers are written longer, and the justification isn't radix economy, it's that the square base is small enough to be used for compression, it's only too large to do basic arithmetic.
In fact, I think it doesn't make all that much sense to use radix economy as an argument at all, our brains don't simply look at the representation of a number and take a specific amount of time to process each digit based on the log of what they expect the digit to be. Although it would be fun to see a study comparing each base in its own writing system and the speed of writing or reading numbers.
jan misali's worst enemy
Allow me to introduce, base 7
You are the worst kind of person.
1:49 very good drawing, Da Vinci is jelaous of you.
26:58 I was skeptical, but this completely bought me oh my
But I think you over complicated square root, it's much easier to visualize using factorization, although I don't know how it would work out with binary
Take 36 as an example. To factorize, you have to divide it by the smallest possible number multiple times until it hits 1 and group the answers in pairs, like this:
36 | 2
18 | 2
9 | 3
3 | 3
1 |
As you can see it has one pair of twos and one pair of threes, so the answer to the square root of 36 is 2x3 = 6
It works for any "n" sized root, intead of taking pairs you take a group of size n
@@cuboembaralhado8294 not quite. What you are suggesting only works if the number is the *perfect* square. If it isn't, say you're trying to calculate √2 or √11, then you need the root algorithm from the video (which in Eastern Europe is taught in middle school, and yes, it's a tad horrific)
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").
Hmm, yes very informative. (Goes home and proceeds to only count in tally marks)
When I taught middle school math, I went down to the elementary to know how the teachers there were teaching numbers, and they taught 4-digit binary, shuffling coins around place mats to derive additions and times tables, then translated the results into base ten to be able to write and speak the numbers as society does.
It was fast, intuitive, efficient.
Imagine how much better it would be if we just stayed in binary at the end?
what they're teaching binary in elementary school that's cool ig
this video gave me a flashback to highschool omg. i remember some stupid nerd and I were having a heated discussion about different bases and he was praising base 12 while I defended binary. We went back and forth for maybe a week and a half and even asked the algebra, geometry, and computer teachers to chime in to mediate. In the end we were both unconvinced and very angry at each other. I hope that guy is doing well these days, i heard he's studying at embry riddle. This video gave me a chuckle
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
“We are mathematical heretics” is such a raw line, I absolutely love it
29:16 This is so ingeneniously simple that I had to pause the video due to how awed I was.