a base-neutral system for naming numbering systems

a description of the Misalian base-naming system, as previously described at www.seximal.net/names-of-othe...
article about the system on the Googology Wiki: googology.wikia.org/wiki/Misa...
download link for BASE OFF: www.seximal.net/s/BASEOFF.zip
poll for which of my current video projects you want me to finish first: forms.gle/A52qfrxHvhUFHLNr7
/ hbmmaster
conlangcritic.bandcamp.com
seximal.net
/ hbmmaster
/ janmisali

[@kate-os5ww]

the baker's dozenal thing comes from a joke base 13 proposal i made a few years back, youtube won't let me post links but its linked from the original base name page which is in the video description

[@felipevasconcelos6736]

You’re their friend Kate? Would love to also see that English Cyrillic page that has been down for years. Does it still exist somewhere?

[@KelniusTV]

Have you considered "pandozenal", Since panem means bread in Latin (and pan is bread in Spanish [and maybe some other Romance languages, but I don't speak Spanish I just use Duolingo, don't at me])?

[@thezipcreator]

@@KelniusTV pan also means grain in Toki Pona

[@weirdlanguageguy]

@@KelniusTV panem is the accusative case of panis, btw

[@h-Films]

hinal

[@defenestrated23]

I love how this constantly pings between "wow that's super intuitive and well-thought-out, I can see papers written with these terms" and "I'm pretty sure Jan Misali is shitposting right now".

[@blablabla4513]

Aka the feeling you should get from every Jan Misali video should be somewhere between academic paper and shitpost.

I just want to see baker's dozenal in an academic paper

[@PROPLAYEN]

@ bikers dozenal

[@nycki93]

if you enjoy academic shitposting, also check out Tom7.

[@tilde7220]

"seximal is used instead of senary because senary isn't reminiscent of six"
ok that makes sense
"thirty-six is niftimal"
???

[@Ruminations09]

I thought "Baker's dozenal" was peak comedy, but I was a fool who who had yet to see the truth of "Biker's dozenal".

[@theapexsurvivor9538]

Followed by the beauty of sexer's dozenal.

[@felipevasconcelos6736]

@@theapexsurvivor9538 there’s no sexer’s dozenal. It’s hexaker’s dozenal.

[@yaitz3313]

Triker's dozenal. Which I suppose is a baby biker's dozenal.

[@mozarteanchaos]

@@felipevasconcelos6736 :(

[@ValkyRiver]

For counting in baker's dozenal, the words instead of "eleven", "twelve", and "thirteen", can be "jack", "queen", and "king".

[@MACIEJ454545]

This is so delightfully organic that I can imagine someone complaining about learning all of it's rules in school

[@ledocteur7701]

yeah, that my problem with this system, okay, having to know base 10 to understand what another base means is silly, but if I was an alien that didn't knew base 10 I'll much rather learn base 10 to understand another base name, than remember all those semi-random rules.

[@Luigicat11]

@@ledocteur7701
Which 10 are you talking about? Every base is base 10. That's literally the entire point of the video. Were you even listening?

[@ledocteur7701]

@@Luigicat11 base 10 as in base decimal, or base gesimal if you are using his system.
and yes, I was listening, thank you for asking.

[@Luigicat11]

@@ledocteur7701
You're welcome, self-liker.

[@rainbowkittycat627]

@@Luigicat11they brought up a valid criticism of the video, you didn’t have to insult them 😭

[@noemiej.marquis732]

"Every base is base 10, one zero"
Unary: "Am I a joke to you?"

[@EnriqueLaberintico]

Prisoners' system.

[@zombiekiller7101]

@@EnriqueLaberintico lmao

[@chrisg3030]

@Unknowable One way of making sense of 00 could be to argue that if unary is a tallying system, that is the number of digits you write equals the number of things counted, then 0 is one, 00 is two, 000 three and so on.

[@i_am_anxious0247]

@@chrisg3030 that might make it the most intuitive number system asides base 10 for those already accustomed to base 10

[@tomasbeltran04050]

@@RTDelete i hate that word

[@robbiecoombes1649]

when you trick yourself into liking maths by treating it like linguistics

[@crumble2000]

When you trick yourself into liking linguistics by applying it to maths

[@Somber_Knight]

when you trick yourself into liking maths and linguistics by watching jan misali

[@failedsocialexperiment2382]

@@Somber_Knightl̥̝̟̹̚ĩ̪n̯̈ɡ̰̪̰̬̥̩̤̬̥̪̃̃̃̃̃̃̃̃̃̃̈̚ʷ̰̃˞u̪̰̚˞̃sti͜͜͜͜͡͡͡c˞s̬̆ hosted by t̪θ ŋɔʃθɑʎɣɪɑ çritiɕ

[@ObsessionistVideos]

This is bonkers and I really want an undergrad professor to gaslight their students into thinking it's accepted practice

[@ookazi1000]

It's not gaslighting if getting enough people to believe you actually makes it true /j.

[@normanclatcher]

It's not gaslighting if you're paying obscene amounts of money (and/or going into debt) to learn it as truth, no matter how suspect said knowledge could be in real-world contexts.

[@normanclatcher]

TL;DR gaslighting != gaslighting.
Ignorance is strength, war is peace, freedom is slavery.
Big Brother is watching me.

[@defenestrated23]

How do you think things actually *become* standard practice? In 50 years, this *will* be the canonical naming scheme for base notation, simply because one didn't exist, and this filled the void.
Which means that math papers on fractional radix will contain a ridiculously obscure in-joke.

[@ookazi1000]

@@normanclatcher "/j" stands for /joke.

[@WhirligigGirl]

I hope it's not lost on you that this naming system is effectively a generalized baseless counting system. And that is way cooler than just the fact that it is a way of describing bases.

[@samellis1055]

Good point!

[@richardpike8748]

Great catch

[@beanbagburrito]

Fr

[@timewave02012]

I was hoping that was going to be some sort of punch line, where instead of the thumbnail "every base is base 10", the conclusion is that "every number is 10".

[@BigGovernment1984]

wouldn't it be base-infinity as every base has its own unique name?

[@cbling1422]

The effort you put into this is pretty unbelievenary.

[@kayakMike1000]

Hahaahahahaha

[@_fedmar_]

GAWD DAMMIT THAT'S SOME GOOD ASS SHIT RIGHT THERE RIGHT THERE 👌👌👌

[@wilyriley_]

it’s pretty DEC23? what’s so DEC23 about it? /j

[@deet0109mapping]

“fortunately, the name ‘seximal’ is completely clear, and nobody would ever misinterpret it as referring to anything other than base six”
- jan Misali, 2021

[@General12th]

"siximal" :)

[@felipevasconcelos6736]

Actually, the “jan” is lowercase, because it’s not part of their name. It’s a honorific for humans.

[@Salsmachev]

​@@felipevasconcelos6736 I'd capitalise Mr./Ms./Mx. so I'd capitalise Jan too. Toki Pona doesn't even have capitalisation in its proper script, the Toki Pona syllabary, so we should just apply the rules of Latin script.

[@felipevasconcelos6736]

@@TheZenytram “toki” is just “language”, “speech”, or “talk” in toki pona, so it sounds like you’re saying “we’re talking in English not a language”.
Back to the argument, Misali writes their own name as “jan Misali”, sometimes omitting the jan. When used in English, “jan” may be considered part of their name, but it’s still written in lowercase. If Apple can get away with iPhone, Mitch can get away with “jan Misali”.

[@felipevasconcelos6736]

@@Salsmachev in toki pona, proper names (and only proper names) are usually capitalized. Capitalizing “jan” would look weird, like if I said Gary Oldman, referring to any old man named Gary.

[@talideon]

This is only slightly less complicated than counting in Danish.

[@LFSDK]

-sure danske lyde-

[@emdivine]

I hope whoever let Danes and French near numbers got thoroughly spanked :P

[@zackchristvevo]

@@emdivine Okay the french might say ""four twenties and thirteen", but confusing so "four-twenty-thirteen"" but the danes say ""half-five (that's four and a half lol) twenties and three" - and wait, let's make that an abbreviation, like "half-five-s and three (the -s means twenty lol)", but that's not convoluted enough, so we say "three and half-five...-s" i gUeSs tHaT'LL d0 LoL xD"

[@emdivine]

@@zackchristvevo Well described! I'm quite aware of the silliness present in both languages, and I know Danish is very much the most chaotic one :P But I also like to take the opportunity to laugh at French which half-way gave up when making up the names for numbers above 60

[@gergelygalvacsy2251]

@@zackchristvevo Half five meaning four-and-a-half actually makes sense to me lol. In my language, Hungarian, when talking about time, “4:30” (as in half past four o’clock) is referred to as “half five”, and so on. It is a weird coincidence.

[@Zi7ar21]

"the last thing I want is for people to hear me talking about base six and think I'm actually talking about something completely unrelated"
*proceeds to name base six "seximal"*

[@22tfortnitevevo]

lmao sex

[@Anonymous-df8it]

***imal should be base-(68+1) instead!

[@AuraSight]

Yes
That's the joke

[@oyungogdfrust4136]

@@AuraSight there is a joke?

[@hardcorshik31]

biseximal

[@MateusSFigueiredo]

"having spoken parentheses like this is a kinda unnatural thing to do"
Chemists naming molecules are like "what do you mean unnatural"?

[@disgustof-riley8338]

If it's scientific, it's natural /j

[@DeJay7]

@@disgustof-riley8338 if /s is for sarcasm, what is /j for? just kidding? /j

[@nate_storm]

@@DeJay7 joking. afaik there’s really no difference between /s and /j idk when or why people started using the latter

[@MarxismLilyism]

@@nate_storm hi im a month late but typically sarcasm denotes a more condescending or potentially rude tone, while “joking” is more light hearted

[@nate_storm]

@@MarxismLilyism if joking is light hearted then what’s /lh

[@JacksonBockus]

I’m going to call base 18 “nonbinary” and you can’t stop me.

[@godminnette2]

Technically every base after base two is nonbinary

[@CasualMitosisCollective]

Damnit, man. You got me roflmao-ing.

[@theapexsurvivor9538]

I won't try and stop you, I'm too busy calling base 12 biseximal.

[@JacksonBockus]

@@godminnette2 You’re not wrong, but I don’t like it.

[@camwoodstock]

wha??? No biney??? Hardly any biney??? Thatse so cool...

[@MissPoplarLeaf]

I laughed out loud at 17 being "suboptimal". Brilliant

[@1224chrisng]

Gauss is rolling in his grave

[@aaronnichols4120]

Also both bielevenary and unbielevenary, pronouncing it like "believe"

[@aaronnichols4120]

And bikers dozenal 😂

[@Aquadolphin314]

I swear I did too, for several seconds!

[@colerougas5137]

Literally had to pause the video, was not expecting that

[@erik.isomer]

This man solved a problem nobody had, in a way nobody wanted, simply because he could. And for that, we commend him
Thank you

[@norude]

You've just described math

[@user-rg7uz8of9r]

He has solved basism

[@yuvalne]

*they

[@myotiswii]

Me and a friend of mine were working on base infinity system. Basically every number only has one symbol and unique, and we had a spreadsheet that went into the (decimal)thousands.
It still was somewhat systemised, meaning that numbers that are close use similar symbols and sounds.
It was absolutely ridiculous but actually more usable then you would think. We both remembered the symbols until like (decimal)2000, and you rarely need anything above that.
I know that an infinitesimal system is absolutely insane.
But really big systems would actually be ok, I think.

[@chrisg3030]

Great experiment! I've often thought along the same lines, how would it be if you always come up with a new symbol for every new quantity counted. After running out of the familiar Indo-Arabic numerals maybe you go on to uppercase letters, then lower case, then other keyboard symbols, maybe other alphabets like Hebrew, then emojis (enormous number of them these days), then flags of all nations? However similar any symbol might be to another, there could be no rule for deriving it, its use would always be arbitrary. Then one day you'd crack and say to hell with this, I'm going to express the next numbers by recycling symbols already used. At that point and only then you have a base.
At the other end of the scale if you were for ever using one and the same symbol to count with, say #, just adding it to the string of #s already there (unary or tallying), your "to hell with this" moment would arrive when
you do come up with a new single symbol to express and replace that long string, and again only then would you have a base.

[@myotiswii]

@@chrisg3030 Oh emojis are so smart. We just made squiggels and shapes. Some system was in there. I remember from like 223 - 4** was very flowy and after that for a few hundret was very straight lines. But emoyis would have made it typable.

[@torreywhiting5402]

#s

[@thatoneguy9582]

-bro show us the spreadsheet-

[@melitopiia4730]

*SHOW US THE SPREADSHEET*

[@DarkShadows713]

When I was a preteen, I watched an episode of iCarly where the main character pranked an unruly child by convincing him the math board had created a new number between 5 and 6 called "dorf," convincing him to do his entire math test in an elevenary system. That was my first exposure to the concept of a non-decimal number system, and ever since then I have been obsessed with number systems.

[@MrCrashDavi]

i need to watch iCarly

[@rauhamanilainen6271]

After all these years since watching that episode, derf always lay at the back of my mind, waiting for someone to mention it once again.

[@lewislockwood9402]

that episode always annoyed me because he (at like age 12) is clever enough to immediately perform calculations in base 11 in his head but apparently he needed carly as a tutor !

[@DarkShadows713]

Lewis Lockwood It's been a while since I've seen the episode, but I thought he pretended to need help in math to have an opportunity to bully Spencer?

[@lewislockwood9402]

@@DarkShadows713 My memory was that he just bullied Spencer to pass the time in between tutoring but it's also been ages since I last watched the episode

[@tokiWren]

"The names of base-x number systems are confusing. This is why I will be constructing an entire language to name them."

[@RichConnerGMN]

nice pfp

[@chrisg3030]

I've been arguing we don't need new names, we could simply name any base after its top single digit, the symbol conventionally used to designate the maximum quantity before we start carrying or doubling up. So what we currently call decimal or denary or whatever is now base 9, seximal or whatever is base 5, duodecimal base B, hex base F.

[@weir9996]

@@chrisg3030 But I don't think there is a standard for representing the highest digits for an arbitrary base, is there? So we would need to create a standard for that anyways, plus then decimal becomes base ten and binary becomes base one, which is a tad confusing to people used to the old way

[@chrisg3030]

@@weir9996 I don't see the problem. The standard for the highest digit in any base is simply whatever is in some kind of generally recognized use as such. F for example is the top digit for hex as far as my Casio calculator is concerned, which is good enough for me, though doubtless there are people who prefer other characters. We know it's the top digit because when you enter F + 1 you get as an answer not another single digit but the recycled pair 10.
This brings me to the main point of my suggestion. It's meant as a third alternative to calling it a verbal name like, say, hexadecimal, or favoring decimal as a standard by calling it base 16.
I think you meant decimal becomes base 9, like binary becomes base 1. Yes that's confusing, so I'm not seriously challenging the "old way". Mind you my suggestion would mean what is often understood as unary or base 1, or a tallying system, would now become base 0. But that's kind of appropriate, since the position of a tally digit in the string doesn't affect its value. Or the number of things counted minus the number of digits equals zero, unlike higher bases.

[@arcynic-education3221]

I agree with every thing except for the baker’s dozenal. Calling it Undozenal is so much better: it demonstrates the un- suffix in the case of prime numbers, you don’t have to use the awkward -ker, and you don’t need to know special pastry knowledge to decypher it. It also goes well with your generally philosophy of not wanting to cause confusion.

[@blablabla4513]

I think you missed the joke.

[@arcynic-education3221]

​@@blablabla4513 Seems like I did now that I read the newly pinned comment

[@IloveRumania]

Thirteen is called a baker's dozen, so it makes sense.

[@kindlin]

@@arcynic-education3221 I'm not privy to the joke, myself, but I could tell, after having watched 10+ jan videos, that his dry humor was coming through.

[@nouche]

@@kindlin: His username is Misali!

[@Anonymous-df8it]

Jan Misali: This algorithm can't be done by hand
Also him: Explains the algorithm in full detail allowing people to work out abbreviations by hand

[@poudink5791]

not really. it's not an algorithm that's practical to do by hand at all.

[@amythistfire7]

Jan: Senery is bad because it sounds like a different, unrelated word
Also Jan: Niftimal is good because it sounds like nifty

[@annyone3293]

Oh yeah, and “seximal” definitely doesn’t sound like some other unrelated word. :D

[@byronlopezellington8839]

Their name is not Jan, "jan" is just the prefixal noun used for names in the conlang Toki Pona.
Great comment though, you are very right xD

[@pentelegomenon1175]

@@byronlopezellington8839 also "jan misali" rhymes with "ron weasley"

[@theapexsurvivor9538]

@@annyone3293 nor doze dozenal. Especially not in baker's dozenal, biker's dozenal, triker's dozenal, and sexer's dozenal.

[@j3011]

But they're not unrelated

[@tomc.5704]

The fact that terrible bases have names like suboptimal, unbielevenary, and baker's dozenal is just SO GOOD

[@635574]

Your likes are bakersdozenal, perfectly balanced as all things should be

[@PibbDFanta]

Cannot like, likes are a prime number (which would have a name like this)

[@KaosFireMaker]

Your current number of likes is 10 in unbielevsnatetraseximal

[@CarMedicine]

@@KaosFireMaker it would actually be unbi *leva* snatetraseximal
(the prefix of elevenary is -leva-)

[@upseguest]

Why are they terrible?

[@webx135]

Unary, base 1, would be an interesting one. Basically it has one value, and that value doesn't increase with the number of digits since each place is only multiplying by one.
So it's basically tally marks.
12 in Decimal would be 111111111111 in unary.

[@SreenikethanI]

how do you do padding tho? like how in decimal we can write 23 = 023 = 0023 = 00023 = 0000...
but this wouldn't be possible in unary... right?

[@sirk603]

No it would be 000000000000

[@Tuberex]

@@SreenikethanI That wouldn't be possible since unary is not really a number system it's more like the length function

[@quinn7894]

That's bijective unary. Normal unary just involves the digit 0 and it's impossible to write any number that isn't zero.

[@JonathanMandrake]

Unary has a number of big problems.
0 can't be written unless by using empty space, which is problematic for a huge number of reasons.
Fractions can't be written as floating point numbers, since I.I= 1 × 1^0 +1 × 1 ^ -1 = 2 = II where you can see that all floating point numbers are whole numbers in unary. This is pretty horrific for dealing with irrational numbers, like Sqareroots, but even worse for unalgebraic numbers like e and pi.
Last, it is pretty bad visually. Unless you connect each five with the fifth tick, it is pretty horrendous to count which number it is, and if you use tick marks, it is a worse version of Base 5

[@MrSafeTCam]

A lot of systems in language have exceptions to rules.
Base Nif Dozen Four is called Tetraker's Dozenal, which fits the rules. But we might use the Latin quad- prefix rather than the Greek tetra-, just this once, because then when we also abbreviate it wrong, we can call it "Quaker's Dozenal" which is funnier because of some aspect of US history that I do not understand because I'm from Australia.

[@thewanderingmistnull2451]

It boils down to "Quakers are different, can't have that in America". Also, they take swearing vows extremely seriously.

[@ZBisson]

They make oatmeal too I think.

[@lunkel8108]

I like the incredibly long base names tbh, they have the same vibe as IUPAC names for large organic compounds

[@qwertyTRiG]

They put me in mind of that too. But at least these don't have embedded digits and commas.

[@iuscactus]

Honestly when he showed the three-letter abbreviations, I couldn't help but think of amino acids

[@warbler4954]

The abbreviation system looks like something railways and aviation use to shortern their station/airport names. Maybe his code can help next time?

[@tyler1107]

Ill have you know that (6E,13E)-18-bromo-12-butyl-11-chloro-4,8-diethyl-5-hydroxy-15-methoxytricosa-6,13-dien-19-yne-3,9-dione is a perfectly natural way to phrase a chemical name (C32 H52 BrClO4)

[@qwertyTRiG]

@@tyler1107 I used to understand IUPAC organic chemistry names. I actually have a degree in chemistry, but it's been almost a decade since I graduated.

[@meowtherainbowx4163]

Everyone’s laughing at “baker’s dozenal,” but here I am with my mind blown at how he could not only reference Vötgil but find a practical use for the clumsy “vöt-“ prefix.

[@jivejunior8753]

11:30 ...do I need the n-word pass to talk about negative bases?

[@theletteralpha]

hopefully not

[@manioqqqq]

Yes, you niggabinary.

[@AlbertTheGamer-gk7sn]

No. Nega- is not racist, but another word is.

[@LaugeHeiberg]

​@@AlbertTheGamer-gk7snyou mean nigga? 😊

[@ActingNT]

If we ran with the idea of unique names for common bases, emphasizing their strengths, the Decimal System could become the Dactyl System

[@wildstarfish3786]

i think dactyl would be better for seximal considering you can very easily count to 36 by hand counting in seximal

[@Designed1]

decimal would be bihandal in that case

[@heck_n_degenerate940]

I must now make it my quest to learn the sacred mathematics of *suboptimal.*

[@MCredstoningnstuff]

In the same way that decimal has properties relating to 3 and 9, I'll bet that suboptimal has properties with all powers of 2 up to 16 which would be pretty cool.

[@meta04]

@@MCredstoningnstuff yeah, every base has properties similar to decimal 9 for the base minus one, which I've seen called the "omega" in some circles with the "alpha" being the base plus one
so suboptimal's omega is 16, which has similar properties to decimal 9
alpha is 18, which behaves like decimal 11
and the *square* alpha is 290, which has the same alternating-sum properties as decimal 101 (oh right you literally can't get worse than square-alpha for fives)

[@boldCactuslad]

why learn everything in 27 when you can learn -1/27

[@anxez]

@@MCredstoningnstuff Not very suboptimal of it, now is it?

[@ferociousfeind8538]

Representing 1/2 in suboptimal (assuming 0-9 + A-G for numbers) would look something like 0.8888888...
1/3 in suboptimal would be... 0.5B5B5B...
1/4 in suboptimal would be 0.4444444...
1/8 would be 0.22222222...
1/16 would be 0.11111111...
So, yeah, has some of the properties of hex, but kind of in a useless infinitely-repeating form, the way 1/9 is 0.111111 in decimal.

[@Aquadolphin314]

No one has yet mentioned the sheer genius of "unbielevenary", so I will.

[@validpostage]

I lost my marbles at that one

[@tanyaomrit1616]

Not to mention that it's for "base 23" lol

[@driveasandwich6734]

@@tanyaomrit1616 Why is that funny?

[@tanyaomrit1616]

@@driveasandwich6734 The whole 23 conspiracy theory thing

[@driveasandwich6734]

@@tanyaomrit1616 Oh, I didn't know about that one

[@ParadoxProblems]

Amazing, I love clever ideas like this that just say "no, that way is dumb" and makes something brand new and awesome. I've been putting off watching this for a while because I knew I was going to love it (if that makes sense) but I also love your style of humor.

[@PeoplesTaste]

The New Numeral System -- a new way to calculate and express numbers.
th-cam.com/video/GWX-TBijClc/w-d-xo.html

[@themathmoth7393]

Fun fact!
Centesimal is very large, so you would want to break up the digits in the same way you would hexagesimal.
However when you do this, you notice that the middle factors of 100 are both 10, because it is a square base.
This means that both sub-digits of a single centesimal digit would be in decimal.
Thus, when you convert a base 10 number to a base 100 number, you just get back that base 10 number with a few colons mixed in.
For example: 123456 in decimal, is just 12:34:56 in centesimal!

[@willsterjohnson]

so mixed radix centesimal is just paired decimal, that makes conversions really easy, and I assume it works for any base which is a power of 0o12?

[@themathmoth7393]

@@willsterjohnson It specifically works this way for any and all square bases (or at least those square bases greater than 36, because those bases can just be written digit-wise normally.)

[@egon3705]

same applies to tessahex, 123456789ABCDEF0 in hex is 12:34:56:78:9A:BC:DE:F0 in tessahex

[@angeldude101]

Given that many places prefer to put spaces between certain digits for large enough numbers, you could argue that a lot of the time we use decacentesimal (base one-thousand). In fact, SI is more decacentesimal than it is decimal, even though _Metric is_ decimal. Rather than a square-base, this is a cube-base used less for compression and more for mental chunking.

[@sponge1234ify]

TIL French phone numbers are Base-Centessimal

[@andzagorulko]

To summarise the video:
- In what base are you counting.
- Base 10.
- Do you have the slightest idea, how little that narrows it down?

[@chrisg3030]

- In what base are you counting?
- I call it base 9
- How does that narrow things down?
- 9 is the top or max digit in what we currently call decimal, denary or whatever, using the conventional symbols 0 1 2 3 4 5 6 7 8 9. Duodecimal is now base B, hex is base F, as these too are widely recognized single symbols which can precisely specify top digits, enough to uniquely designate a base without using any other base.

[@eomoran]

@@chrisg3030 hex uses lowercase letters so someone might think you’re talking about base 42

[@chrisg3030]

@@eomoran It's not so much that hex uses certain letters as we humans use them, but by no means universally or consistently. I just said "widely" in my comment.
Having said that, on my Casio calculator when using the hex function you have no alternative but to enter uppercase into the register top left in the display, say 5Bx1, but you always get an answer back in lowercase, 5b. I don't know why.

[@antonliakhovitch8306]

While impractical in real life (as literally all of this is), another proposal is to always default to binary for base names. Binary is the smallest base and therefore is inherently special. Plus, you could arguably call it the most used number system on the planet.

[@lu_ck]

@@antonliakhovitch8306 base 1?
0 = 0
00 = 1
000 = 10
0000 = 11
00000 = 100
...

[@Dooge]

I saw the hexadecimal issue a mile away. However, I was pleasantly surprised by biker's dozenal.

[@gisopolis77]

dooge

[@goopy2585]

dooge

[@Mx_M29]

dooge

[@PokeNebula]

dooge

[@xf3s_]

dooge

[@LaurieKoudstaal]

You could also call bakers dozenal “witchinal” since 13th hour is sometimes considered the witching hour.

[@AlbertTheGamer-gk7sn]

And base-14 as the poulter's dozenal as well.

[@Hans-jc1ju]

jan Misali: “Dozenal users don’t like it if it is called duodecimal because this is defined via 10 and does not give them their own identity.”
also jan Misali: “base 17 is suboptimal or mal-“

[@felipevasconcelos6736]

I’m pretty sure all zero of suboptimal users are very happy with that name.

[@IONATVS]

since the only people who suggest using base seventeen are doing so as a joke, I don’t think there’ll be many complaints.

[@FinetalPies]

It is morally correct to bully people who prefer suboptimal

[@darcieeastham9347]

@@IONATVS I guess it's used for coinage in Harry Potter? But even then that's an indirect parody of predecimalised currency (and is also fiction).

[@meta04]

@@darcieeastham9347 Most of the ways suboptimal is worse than elevenary or baker's dozenal only start if you use it for all the place values and not just one-all of the first five primes have maximal-length repeating periods and 13 has half of the maximum
actually I wasn't expecting the other one to be untetraseptimal but still that at least has a two-digit fifth and a one-digit seventh

[@Natibe_]

“Binbinbinbinbinbinoctelevenary”
This system is perfect

[@soumen_pradhan]

Organic Chem welcomes you.

[@freyalalumiere4664]

TELL ME WHAT BASE THIS IS FOR.

[@harrygenderson6847]

@@freyalalumiere4664 5758 in decimal (12:51).
Or base 10 in binbinbinbinbinbinoctelevenary.

[@freyalalumiere4664]

@@harrygenderson6847 hank you :)

[@disfordumboo4411]

“the last thing i want is for people to hear me talking about base six and think im actually talking about something completely unrelated. so that’s why i call it seximal”
i adore jokes like this delivered the way misali does and sometimes with little things like that i just can’t help but be in awe of how the ridiculous amount of content on the internet leaves each of us with that handful of creators who make the exact style of content that just makes us happy it exists. what a cool world

[@edwardbarton1680]

We actually do use 60 different symbols when working in hexagesimal for time. Each symbol just happens to be a composite of two decimal symbols. Hence the need for ":" to separate the places.

[@jarlfenrir]

Mayan base 20 system also used similar system, but in a slighlty better way. You have only dashes and dots. Dot is 1 dash is 5. You stack those symbols vertically to create a digit (up to 19 - 3 dashes 4 dots) and those digits are placed horizontally to create numbers. Up to debate whether you want to call dash and dot a unique symbol, or every combination of them is a unique symbol to you.

[@willsterjohnson]

we technically don't need the ":" in digital time, just like we don't technically need the "," in "1,000,000".
235959, 050239, 165243, these all contain all the information needed to convey time.
23:59:59, 05:02:39, 16:52:43 are just easier to read.
same as 1000000 vs 1,000,000, not necessary to separate but it helps a lot

[@lusciouslocks8790]

Isn’t this like calling English a logographic language where each logograph just happens to be a composite of multiple Latin logographs…

[@FeedsNoSliesMusic]

You forgot to mention that eleven's etymological root is literally "one left over", making it effectively a base ten name in the same way dozenal is.

[@22tfortnitevevo]

shhhh

[@GuiSmith]

It’s factorisation makes that work, though, as elevenary and its multiplicative bases are influenced by ten, much like how larger prime bases are influenced (and named after) the bases below them.

[@samellis1055]

But also hardly anyone knows that. But I guess it's a small number of people that would spot duo decimal referring to 2 and 10

[@claytoncoe838]

One addition to recommend: base (1+√5)/2 should be called phinary

[@Anonymous-df8it]

Ahhhh, phinary, pinary, binary. I always get those mixed up!

[@AlbertTheGamer-gk7sn]

With ф as the prefix.

[@dilgeatakan9366]

unarootpentavötbinary
/junəɹutpæntʌvɒtbaɪnɛɹi/

[@josephcoon5809]

First impression:
I would have went with a naming convention that incorporated full factorization coupled with addition, exponentiation, and tetration.
Base 12 = 2^2*3
Bipbip-Trinary
BpT
Base 18 = 2*3^2
Bi-Tripbipary
BTpB
Base 19 = 2*3^2+1
Bi-Tripbipnary
BTpbn
Base 27 = 3^3
Exponentiation: Triptripary
Tpt
Tetration: Tritbitary
Ttb
Base 24 (my favorite number) = 2^3*3
Biptrip-Trinary
BptT
Base 72 = 2^3*3^2
Biptrip-Tripbip
BptTpb
Base 210 = 2*3*5*7
Bi-Tri-Quin-Heptary
BTQH
Base 216 = 2^3*3^3
Exponentiation: Biptrip-Triptripary
BptTpt
Base 65,536 = 2^16 = 2^2^4 = 2^2^2^2
Exponentiation: Bipbipbipbipary
Bpbpbpb
Tetration: Bitquatary
Btq
My second iteration:
Use the Latin roots to symbolize the position of the prime factor base.
Un: 2
Bi: 3
Tri: 5
Qua:7
Pen: 11
Sex: 13
Hep: 17
Oct: 23
Non: 29
Dec: 31
Numerals designate tetration level.
PT where P is a prime factor and T is the tetration level
U1 = 2
B1 = 3
U2 = 2^2 = 4
T1 = 5
Q1 = 7
U3 = 2^2^2 = 16
B2 = 3^3 = 27
T2 = 5^5 = 3,125
U4 = 2^2^2^2 = 65,536
B3 = 3^3^3 = 7,625,597,484,987
Tetration levels are applied directly to the Latin initial directly preceding the level designation.
Tetration Level 1 is designated only for prime numbers.
Tetration levels for prime factors are designated only for levels greater than 1.
Upper case Latin initials designate prime factors.
Lower case Latin initials designate prime factor powers.
Uu3b2 = 2^(2^2^2*3^3) = 2^432 = 1.109e130
Ununtritbibitpary
Uu3B2 = 2^(2^2^2)*3^3 = 1,769,472
U4B2 = 2^2^2^2*3^3 = 1,769,472
Base: Name
2: Ununtary { U1
3: Biuntary { B1
4: Unbitary { U2
5: Triuntary { T1
6: Un-Biary { UB
7: Quauntary { Q1
8: Unbipary {Ub
9: Bibipary { Tt
10: Un-Triary { UT
11: Penuntary { P1
12: Unbit-Biary { U2B
13: Sexuntary { S1
14: Un-Quaary { UQ
15: Bi-Triary { BT
16: Untritary { U3
17: Hepuntary { H1
18: Un-Biunpary { UBu
20: Unbit-Triary { U2T
23: Octuntary { O1
25: Triunpary { Tu
27: Bibitary { B2
30: Un-Bi-Triary { UBT
36: Unbit-Biunpary { U2Bu
48: Untrit-Biary {U3B
72: Unbip-Biunpary { UbBu
81: Biununtary { Bu2
210: Un-Bi-Tri-Quaary { UBTQ
216: Unbip-Bibitary { UbB2
2310: Un-Bi-Tri-Qua-Penary { UBTQP
3,125: Tribitary { T2
65,536: Unquatary { U4
823,543: Quabitary { Q2
285,311,670,611: Penbitary { P2
7,625,597,484,987: Bitritary { B3

[@ConnorMcCormick]

> Latin roots to symbolize the position of the prime factor base
I love this. And it's clear which bases are useful because they'll tend to have lots of 'un': 60 is Ununbiuntriun
I think that this makes for an argument to write the 'un' part as something much shorter since it will be used a lot in useful places. Perhaps a single vowel like 'e' or 'o' since it's essentially never used.
Also, I think I get a bit confused with your use of 'un'. Even in base 2 it's written as 'Ununtary' but without a base 1 symbol, there's no way to specify that it's 2^1, 'ununtary' looks like 2^2 and 'biuntary' looks like 3^2, but is actually 3^1. This means we need a base 1 symbol.
We could just move your system back 1. So now it would be:
Un: 1
Bi: 2
Tri: 3
Qua:5
Pen: 7
Sex: 11
Hep: 13
Oct: 17
Non: 23
But in my head I can't escape my tendency to associate Qua with 4 instead of 5 or Sex with 6 instead of 11 (not sex, obviously, that would be inappropriate)
So I would argue that we should instead reuse the existing associations (at least until they run out) Eg:
Un: 1
Bi: 2
Tri: 3
Pen:5
Sept: 7
Once?: 11
Trit?: 13
???: 17
???: 23
But now we find that we need a base name generation system for our base name generation system. Because what happens if we want to talk about 463, the 90th prime? Do you know the Latin base for 90? I don't
So it's as though we can't escape the need to have a base. In your case by going to Dec you chose base ten as the base of your base system. But It could as easily be six or seventy, it's just controlled by the number of symbols we've previously come up with. Which is hugely dissatisfying.
Unless... if we had a base agnostic way to generate base names we'd be set. So, what's an approach we could take? Well our real constraint isn't letters or symbols, it's phonemes. Well I can only use 44 of them (because I speak English). And of those 44 (www.dyslexia-reading-well.com/44-phonemes-in-english.html) I can only easily distinguish some of them. The difference between the 'th' in thong and the 'th' in leather is hard to tell apart. And of the ones I can distinguish, I can only write a subset of those in a way that's unambiguous when read by a standard english speaker.
That really only leaves us with:
f, v, p, b, t, d, k, g, s, z, th, h, j, l, m, n, r, sh, ch, ue, ae, ee, aiy, oa, e, u, oy
It's actually pretty difficult to figure out how to write the vowels because the 'a' should be read as the a in 'bait' not 'cat', but if you generate a word with this system that looks like "bat" you should actually read it like "bait". That's not nice. So let's choose only the unambiguous letterings.
We start with all possible vowel expressions:
[['a', 'ai', 'au'],
['a', 'ai', 'eigh', 'aigh', 'ay', 'er', 'et', 'ei', 'au', 'a_e', 'ea', 'ey'],
['e', 'ea', 'u', 'ie', 'ai', 'a', 'eo', 'ei', 'ae'],
['e', 'ee', 'ea', 'y', 'ey', 'oe', 'ie', 'i', 'ei', 'eo', 'ay'],
['i', 'e', 'o', 'u', 'ui', 'y', 'ie'],
['i', 'y', 'igh', 'ie', 'uy', 'ye', 'ai', 'is', 'eigh', 'i_e'],
['a', 'ho', 'au', 'aw', 'ough'],
['o', 'oa', 'o_e', 'oe', 'ow', 'ough', 'eau', 'oo', 'ew'],
['o', 'oo', 'u', 'ou'],
['u', 'o', 'oo', 'ou'],
['o', 'oo', 'ew', 'ue', 'u_e', 'oe', 'ough', 'ui', 'oew', 'ou'],
['oi', 'oy', 'uoy'],
['ow', 'ou', 'ough'],
['a', 'er', 'i', 'ar', 'our', 'ur'],
['air', 'are', 'ear', 'ere', 'eir', 'ayer'],
['a'],
['ir', 'er', 'ur', 'ear', 'or', 'our', 'yr'],
['aw', 'a', 'or', 'oor', 'ore', 'oar', 'our', 'augh', 'ar', 'ough', 'au'],
['ear', 'eer', 'ere', 'ier'],
['ure', 'our']]
But then we drop all consonants because we're already using them elsewhere:
[['a_e'],
['ae'],
['ee'],
['uy', 'ye', 'i_e'],
['oa', 'o_e', 'eau'],
['ue', 'u_e'],
['oi', 'oy', 'uoy']]
Of all those we don't want to use a_e (nor o_e or u_e) because we want to append letters, not have a bunch of 'ate' 'ape' 'ake' etc. plus it would be ambiguous to read with 'are' and 'age'. That gets us to
[['ae'],
['ee'],
['uy', 'ye'], as in 'guy' or 'stye' chose 'ai'
['oa', 'eau'], like 'beau' or 'moat' chose 'oo'
['ue'],
['oi', 'oy', 'uoy']], like join, boy, buoy
Arbitrarily I decided that from between ['oa', 'eau'] we should go with 'oa'.
From among ['uy', 'ye'], as in 'guy' or 'stye' we go with 'aiy' (in other words: naiyther). Look, you can read all of these: spaiyder, skaiy, naiyt, paiy, gaiy, staiy, aiysle, aiysland, haiyt, kaiyt
That just leaves us with ['oi', 'oy', 'uoy']], like join, boy, buoy. 'oi' looks like Ron greeting Harry. 'ouy' looks like french, gross. And since it's so close to french let's just choose the french word for yes which sounds exactly the same 'oui' (this means you should forevermore write 'join' as 'jwin' ).
Just kidding. 'oy' it is.
Now we're done, that's how we get these vowels:
vowels = [
'ae', as in bay, maid, weigh, straight, pay, foyer, filet
'ee', as in be, bee, meat, lady, key, phoenix, grief, ski, deceive
'aiy', spider, sky, night, pie, guy, stye, aisle, island
'oa', open, moat, bone, toe, sow, dough
'oo', who, loon, dew, blue, flute, shoe, through
'e', as in end, bread, bury, friend, said
'oy', as in join, boy, buoy
'u' as in lug, monkey, blood, double
]
"Wait," you might say, "isn't that more than the options we started with?" Yes. I don't want to explain, it took forever.
Now we could just naively combine these, but 'uoyoaaeee' would be problematic. So perhaps we implement a rule that there should always be a consonant between vowels so that we can tell them apart.
But I'm still not done, because if we just combine the words in any way we'll get strings like 'fuk' and 'shit' and 'dik' which will bum you out if they happen to land on your favorite base. Or maybe you'll love it. Nevermind, you'll love it. Ok, so we now just pick a canonical ordering for our phonemes.
I'll start with the consonants, let's use a custom alphabetical order:
consonants = ['z', 'b', 'ch', 'd', 'f', 'g', 'j', 'k', 'l', 'm', 'n', 'p', 'r', 's', 'sh', 't', 'th', 'v']
Then let's define the canonical ordering of the vowels:
vowels = ['oo', 'ae', 'ee', 'aiy', 'oa', 'e', 'u', 'oy']
'oo' is up front so that it can be 0 in this system. 01 is one just like any system, but in this one you can't have one singular digit (because 'b', 'j','k' etc sounds bad without vowels, but 'oob' 'ooj' and 'ook' are phenomenal)
Now we can construct arbitrary numbers, let's do up to 5:
0. ooz
1. oob
2. ooch
3. ood
4. oof
5. oog
most importantly, Jan can now easily talk about their favorite base 10, base ooj.
I tried to write a python function to return the full list of numbers, but honestly I found it really difficult.
It's hard to work with mixed bases, I guess.
Can you write a function to return each successive number?
Ok here are the first 501:
0: ooz
1: oob
2: ooch
3: ood
4: oof
5: oog
6: ooj
7: ook
8: ool
9: oom
10: oon
11: oop
12: oor
13: oos
14: oosh
15: oot
16: ooth
17: oov
18: aez
19: aeb
20: aech
21: aed
22: aef
23: aeg
24: aej
25: aek
26: ael
27: aem
28: aen
29: aep
30: aer
31: aes
32: aesh
33: aet
34: aeth
35: aev
36: eez
37: eeb
38: eech
39: eed
40: eef
41: eeg
42: eej
43: eek
44: eel
45: eem
46: een
47: eep
48: eer
49: ees
50: eesh
51: eet
52: eeth
53: eev
54: aiyz
55: aiyb
56: aiych
57: aiyd
58: aiyf
59: aiyg
60: aiyj
61: aiyk
62: aiyl
63: aiym
64: aiyn
65: aiyp
66: aiyr
67: aiys
68: aiysh
69: aiyt
70: aiyth
71: aiyv
72: oaz
73: oab
74: oach
75: oad
76: oaf
77: oag
78: oaj
79: oak
80: oal
81: oam
82: oan
83: oap
84: oar
85: oas
86: oash
87: oat
88: oath
89: oav
90: ez
91: eb
92: ech
93: ed
94: ef
95: eg
96: ej
97: ek
98: el
99: em
100: en
101: ep
102: er
103: es
104: esh
105: et
106: eth
107: ev
108: uz
109: ub
110: uch
111: ud
112: uf
113: ug
114: uj
115: uk
116: ul
117: um
118: un
119: up
120: ur
121: us
122: ush
123: ut
124: uth
125: uv
126: oyz
127: oyb
128: oych
129: oyd
130: oyf
131: oyg
132: oyj
133: oyk
134: oyl
135: oym
136: oyn
137: oyp
138: oyr
139: oys
140: oysh
141: oyt
142: oyth
143: oyv
144: booz
145: boob
146: booch
147: bood
148: boof
149: boog
150: booj
151: book
152: bool
153: boom
154: boon
155: boop
156: boor
157: boos
158: boosh
159: boot
160: booth
161: boov
162: baez
163: baeb
164: baech
165: baed
166: baef
167: baeg
168: baej
169: baek
170: bael
171: baem
172: baen
173: baep
174: baer
175: baes
176: baesh
177: baet
178: baeth
179: baev
180: beez
181: beeb
182: beech
183: beed
184: beef
185: beeg
186: beej
187: beek
188: beel
189: beem
190: been
191: beep
192: beer
193: bees
194: beesh
195: beet
196: beeth
197: beev
198: baiyz
199: baiyb
200: baiych
201: baiyd
202: baiyf
203: baiyg
204: baiyj
205: baiyk
206: baiyl
207: baiym
208: baiyn
209: baiyp
210: baiyr
211: baiys
212: baiysh
213: baiyt
214: baiyth
215: baiyv
216: boaz
217: boab
218: boach
219: boad
220: boaf
221: boag
222: boaj
223: boak
224: boal
225: boam
226: boan
227: boap
228: boar
229: boas
230: boash
231: boat
232: boath
233: boav
234: bez
235: beb
236: bech
237: bed
238: bef
239: beg
240: bej
241: bek
242: bel
243: bem
244: ben
245: bep
246: ber
247: bes
248: besh
249: bet
250: beth
251: bev
252: buz
253: bub
254: buch
255: bud
256: buf
257: bug
258: buj
259: buk
260: bul
261: bum
262: bun
263: bup
264: bur
265: bus
266: bush
267: but
268: buth
269: buv
270: boyz
271: boyb
272: boych
273: boyd
274: boyf
275: boyg
276: boyj
277: boyk

[@josephcoon5809]

@@ConnorMcCormick I also considered using a different set of initialisms, and I was a bit put off with using the Latin roots in two different ways that created a confusing application depending on usage as a prime factorization versus exponentiation or tetration.
As for the Prime numbers, the suffix actually denotes tetration (hence the ‘t’ instead of ‘p’). The tetration symbolism denotes the tetration level. In other words how many levels of exponentiation.
Base 2
Ununtary breaks down into:
Un { first prime: 2
-unt { one level of tetration; or just 2
Base 4
Unbitary breaks down into:
Un { first prime: 2
-bit { two levels of tetration; or 2^2
Base 16
Untritary breaks down into:
Un { first prime: 2
-trit { three levels of tetration; or 2^2^2
Base 65,536
Unquatary breaks down into:
Un { first prime: 2
-quat { four levels of tetration; or 2^2^2^2
Using a ‘p’ for power instead of ‘t’ for tetration, you get different bases.
Base 2 (redundant with Ununtary)
Ununpary breaks down into:
Un { first prime: 2
-unp { raised to the first power; or 2^1
Base 2 (redundant with Unbitary)
Unbipary breaks down into:
Un { first prime: 2
-bip { raised to the second power; or 2^2
Base 8 (first nontrivial exponentiated factor)
Untripary breaks down into:
Un { first prime: 2
-trip { raised to the third power; or 2^3
Base 16 (redundant with Untritary)
Unquapary breaks down into:
Un { first prime: 2
-quap { raised to the fourth power; or 2^4
My original post took me about an hour of developing, so I was too burned out to tighten up the tetration. Eyes get kinda crossed typing on a mobile phone for that long while dragging your mind though concepts it doesn’t swim in often. 😂
I’m a bit burned out now, so I’ll have to go through your response a couple more times to get it settled in my mind better.

[@josephcoon5809]

@@ConnorMcCormick “But in my head I can’t escape my tendency to associate Qua with 4…”
You can. It was difficult at first for me as well, but pouring over the nomenclatures for an hour helped solidify that the first root denotes the nth Prime. I did it this way, partially, to make it an exercise in remembering the cardinal value of each prime number
Un is the first prime: Psub1 = 2
Bi is the second prime: Psub2 = 3
Tri is the third prime: Psub3 = 5
As for really large primes…I feel like throwing in the towel and just going base ten, like you said, and just cycle back through with superscripted numerals
The Psub90 (90th prime) would be Dec^9
The Psub90 (80th prime) would be Dec^8
The Psub90 (70th prime) would be Dec^7
The Psub90 (60th prime) would be Dec^6
.
.
.
The Psub10 (10th prime) would be Dec.
I’ll think on it some more tomorrow night.
Cheers 🍻

[@ConnorMcCormick]

@@josephcoon5809 Would love to hear your thoughts!

[@lucyc5844]

@@ConnorMcCormick damn, that's perfect

[@miniman3112]

There is a chemistry joke hiding in "base-neutral"

[@tracerbullet1741]

plot twist: the real chemistry joke was the IUPACnomenclature parody

[@erik.isomer]

@@tracerbullet1741 lol this system is magnitudes less complicated than iupac

[@iantaakalla8180]

Then what is the equivalent language equivalent for something “acid-neutral”?

[@polifemo3967]

this is one of those videos where I start out thinking "oh yeah, I've tried something like that before, wonder how he did it" and then three minutes in its gone waaaaay past anything you could have imagined.

[@palladianaltruist8047]

"Naming a base after the one right below it is okay"
*changes base 11's "undecimal"*

[@Zachyshows]

At some point, every base would be made up of exclusively un-,hen- and -sna-s.

[@WhizzKid2012]

snasnasnasnasnasnasnasnasnasnasnasnasnasnasna

[@docopoper]

I love how you went through this whole process to name bases in a way that doesn't assume a base. Then you assigned them short sets of letters to distinguish them... Thus labelling them in base 26.

[@eklectic497]

I almost screamed when you got to the vöt bases. Absolutely brilliant

[@Thatwasademo]

I was a bit excited

[@kornsuwin]

holy shit your'e here

[@MonkOrMan]

Wait it's that person who did the thing and he's here now wow

[@oliwyrm]

is this a fucking crossover episode?

[@jmanabc]

Requiring knowledge of base 10 to understand the justification behind other numbering systems’ names: ❌
Requiring knowledge of multiple obscure conlangs and English wordplay to understand the justification behind other numbering systems’ names: 👍

[@thewanderingmistnull2451]

Ndom is a natural language. So is Komnzo.

[@unknown-mg6rv]

@@thewanderingmistnull2451 ah yes google is so smart, cause ndom is definitely translated to English.

[@corlinfardal9246]

@@thewanderingmistnull2451 There are, technically, multiple conlangs involved: Esperanto for the mal- prefix, and Vötgil for the vot- prefix. Of those two, I'd only really consider Vötgil to be particularly obscure - Esperanto at least shows up in things like Google Translate, and I feel like most people who can name more than, like, three languages will have at least heard of Esperanto, even if they couldn't tell you anything about it.

[@_yalov]

if he doesn't want to use base 10 positional notation, easier compromise is to use non-positional notation, for example roman numerals.

[@tochoXK3]

Roman numerals are also kinda base 10

[@BearOverlord]

So glad that this channel exists to provide me with videos about the history of stuff like caramelldansen and ALSO human language, while ALSO delving into some math theory. It's a baffling combination of content, but it's also a very specific demographic that I just happen to be a part of.

[@mihailmilev9909]

Ikr

[@mihailmilev9909]

that's what I was thinking, and I didn't even know he did the carmelldansen one. Or didn't remember ig.

[@mihailmilev9909]

I was thinking from the beginning of the video he should collab with Oliver Lugg. Same sort of seemingly random or diverse but yet -(still?)- beautiful set/collection of topics. That also all seemingly match my interests...... WHAT FIELD ARE YALL IN AND HOW I GET IN?!!!

[@dangerouspie0319]

I didn't expect this to be so fleshed out. I wonder how much of this is his homebrew and how much is already established. It's a really intellectual thing to just try make a universal mathematical system out of the barely standardized topics of math.

[@jackeea_]

this is the most useless, useful, weird yet oddly practical thing I can see approximately zero people using. great video

[@SteveBakerIsHere]

It's not remotely "practical" - or "useful". Anything that requires a complex piece of software to encode and decode (and worse - one with S-L-O-W runtime because it's not an O(N) algorithm) is horribly IMPRACTICAL - it obfuscates unnecessarily. "Practical" is what we actually do: Use "base N" (where N is, by convention, decimal)...and use nicknames for the handful of bases that are actually used in common practice...so we can say "hex" rather than "base sixteen" if we're computer programmers. As I explained in my earlier comment, this entire system (as complex as it is) is missing a whole lot of things that number bases can do - signed digits, for example - and it doesn't tell you what set of symbols to use for digits in bases 11 and above...so you go to all of this trouble to NAME the base of the number - but provides no means to actually write the number down.

[@coreblaster6809]

@@SteveBakerIsHere hey steve baker, I think it's pretty impressive you were able to write that whole comment with a stick up your ass, pretty cool👍

[@cobalius]

I bet my brother will use that xD

[@driveasandwich6734]

@@SteveBakerIsHere If you want/need a pronounceable, base-neutral system, this is very useful. You would only need the software if the nomenclature has to be standardized, otherwise, using any combinations of factors wouldn't really be a problem.

[@SteveBakerIsHere]

​@@driveasandwich6734 But the whole premise of that is that it presupposes some dire need for a "base-neutral system". But why do we need that? What's wrong with using base 10 as the default - and calling every base by the simplest, most easily understood system..."base N" (where N is a number that's expressed in base 10 by default).
That *tiny* piece of convention - has to be weighed against a system so baroque that it needs a complex algorithm to decode it - and a dog-slow algorithm at that.
Where is this all-important "use case" for an utterly base-neutral system? If it's to somehow eradicate the cultural basis upon which we use base 10 by default - then it fails *HORRIBLY* because it just uses more obscure base10 words. For example, using "sex" or "hex" as a way to say "six" makes no sense if you're trying to work in a base 4 society that has no word for six. This is a solution in need of a problem...and not a particularly good solution at that.

[@andrewlonghofer]

“untriseximal” is no more confusing than “quatre vignts dix-neuf” so I’m on board

[@Salsmachev]

Have you ever tried singing 100 bottles of beer on the wall (or alternatively cent bouteilles de vin sur le mur) in French? It's significantly funnier.

[@cursedmailman3999]

quatre vingt dix neuf is probably the least confusing name ever, so you're wrong on that. In fact, the reason why it's dunked on so hard is because of precisely that, because it's so simple that it's literally just addition/multiplications.

[@Salsmachev]

@@cursedmailman3999 Ninety-nine is literally just multiplication and addition too (nine tens and nine). The difference is that ninety nine fits the same basic logic as the rest of the number system to which it belongs. French counts in decimal through 79 and then inexplicably switches to vigesimal. That's why quatre-vingt dix-neuf doesn't make any sense. It's also not very succinct. Neufant neuf is three syllables. Quatre-vingt dix-neuf is almost twice as long without any improvement in clarity. Now if it was just pure multiplication (eg. quatre-vingt for eighty) I feel like that's helpful because it shows you something different about the divisibility, but eighty is basically the only French number that actually takes advantage of that.

[@mbgdemon]

The use of quatre-vingts is a remnant of an ancient tradition of using base 20 numbering systems, not joking

[@browncoat697]

@@Salsmachev Also worth remembering that French spoken outside France itself often uses different numbers. Walloon/Belgian French uses "nonante" instead.

[@kingturboturtlednoc5722]

15:29 regardless if it's intentional or not, I think it's a good rule
The last letter is almost always going to be L or Y so they're going to be pretty unusefull in feeling like a good, intuitive abbreviation since it would sound like all the others

[@WetRatGaming]

Niftimal sounds like a portmanteau of nifty and optimal, and I think that's really fitting for the term itself!

[@Bootleg_Jones]

I think I'm going to unironically start using "biker's dozen" to mean 26 from now on.

[@CasualMitosisCollective]

I was about to write something here, but you... You just cracked me up.

[@theapexsurvivor9538]

I also think I'll be using this naming system system for referring to base 78.

[@CasualMitosisCollective]

@@theapexsurvivor9538 ??? What do you mean? (Also, REMEMBER ME???? I'M THE POULTER'S DOZENAL GUY FROM THAT OTHER COMMENT'S REPLIES!!!!)

[@theapexsurvivor9538]

@@CasualMitosisCollective sorry, meant 78, not 72. 78 is 6*13.

[@CasualMitosisCollective]

@@theapexsurvivor9538 oh. Ok.

[@darrend.4835]

I think it would be absolutely hilarious to call base-18 nonbinary and I am so sad you didn’t give that name as an option

[@mel-burnes]

you. i like you

[@skyscall]

oh boy

[@seanwaddell2659]

Binonary sounds a lot like binary too

[@frimi8593]

Thank you for improving my enjoyment of this video even more

[@PhoenixClank]

I was absolutely certain that joke would happen and waited the whole video for it and it never dropped and I'm so confused

[@kevinscott7292]

"I don't want the name to make people think about something so distractingly unrelated to math like "scenery""
Proceeds to put "sex" in the name
"There! Nothing distracting about that!"
A true mathematician

[@CheesySpeakeasy]

This is absolutely insane and I'm 100% on board for it. Please explain how a negative base system works

[@RyanTosh]

It's a lot like a normal base system, but since you have a built-in way of representing negative numbers, no negative sign is necessary. Somehow it just ends up working, like normal bases. E.g., positive numbers up to 9 would be the same in negadecimal, but ten would be 190, representing +100 - 90 + 0, since every other digit is negative

[@phroggu]

"a quick little video"
The video: longer than most conlang critics, his main series

[@ookazi1000]

Yes, but see: this video didn't come with /reading and research/.

[@Duiker36]

@@ookazi1000 I mean, it did. It's just that it was reading one page and then one algorithm. Both of which he wrote. I've gone back and re-read stuff I wrote a long time ago and it totally counts as research.

[@ookazi1000]

@@Duiker36 A fair point for a reasonable definition of research. I don't consider browsing one's own work research, but if you do, that's fair.

[@unlurkingsentinel6872]

_Nobody:_
_Misali, figuring out how to name rational base systems:_ I'm a bit excited.

[@EnriqueLaberintico]

They were the first ~in a few ways~.

[@pacotaco1246]

I cant wait for the sequel where he figures out how to name irrational base systems

[@grish6313]

Another great video! Your ability to continuously make interesting and fun content is truly unbielevenary.

[@Zachyshows]

Suggestions:
Base-64 is Stackimal. You get it or you don't.
The prefix for Stackimal (64*65) should be Blocka or Stacka, so 64*65 is Stackapentaker's Dozenal
Should base-32 be called Tetroctal or Semistackimal?

[@EnriqueLaberintico]

Just stack, like hex it doesn't rhyme.

[@dilgeatakan9366]

Tetroctal can stay. If you want to describe 32 as 64/2, you could use stackavötbinary

[@ookazi1000]

biker's dozenal: The optimal number of bikers in a gang.

[@davidgustavsson4000]

If anyone thinks "hexagesimal" sounded arbitrary, it's actually not just a replacement consonant, -gesima is latin for -ty. Cf. Quinquagesima, the 50th day before Easter.

[@lawrencecalablaster568]

booyah

[@zeeperry1576]

indeed, this is why base-sixty, outside of JM's naming system, is often called sexagesimal

[@FeedsNoSliesMusic]

I never thought I'd ever read a word beginning with "quinquag".

[@PMA65537]

Isn't that negative pentecost?

[@Ratchet4647]

Well, you can see it in the name in this system for twenty as well, Vigesimal.
The word for 20th in Spanish uses that term too, Vigésimo.

[@brendansmith7703]

I love that you tried to explain a linguistic theoretical system using programming, like the linguistic nerds understand it. I love it more that it helped me understand what you were saying

[@KaosFireMaker]

So, as a fun tidbit, when I was designing a magic system, I actually decided to go for a prime factorization representation of numbers, where each prime has its own glyph/rune, or by a geometric shape. There was the fun point that humans in setting didn't know all of them(as there are infinite primes) so past a certain point there are gaps in the available values for spell construction without the use of multiple calculation steps.
I might actually nab the, (number bellow it plus 1) notation so that the large primes are represented with (n-1) with a circle around it.

[@RyanTosh]

It would be really cool if like, spells were tied to numbers, and you'd learn new spells by discovering new prime numbers

[@chloeeeeeeeeeeeeeeeeee]

“i can’t comprehend that you use base 23
unbieleveable”

[@cobalius]

Just saying that to someone using base 23 would be epic

[@jisaswarm5218]

Yeah, base thirty-one IS unconventional thank you for pointing this out.

[@angelodc1652]

@@cobalius Is that a motherfucking SCP reference?!

[@whatyoulookinfor]

“I figured I would make a quick little video”
*17 minutes long*
Classic jan Misali

[@ookazi1000]

A 10(sub) minute video, for which he had to do no additional research.

[@tomc.5704]

@@ookazi1000 ‍I'm so mad at you, but so proud.
An actual use of suboptimal in the wild

[@intellectualInsectoid]

this is unironically my new favorite video on this platform

[@HungerGamesFan88]

dozenary is the absolute gigachad of numbering systems, i have no other internet-argument hills NEARLY as satisfying to die on

[@letMeSayThatInIrish]

I can't believe 10[dislikes] people disliked this.

[@bacicinvatteneaca]

I GOT THE JØKE

[@arska-pelejavlogejajaautoj5030]

It is baker's dozenal right now

[@Salsmachev]

@@arska-pelejavlogejajaautoj5030 Now it's bilevenary

[@nope69q]

it's trinonary now

[@LlamasOnJUPITER]

underrated comment

[@worriedpikachu174]

I love how all your stuff is so genuine but also just insincere enough to be funny

[@mbgdemon]

Consider this alternative and simpler system which implicates absolutely no decimal-bias introduced by traditional prefixes: Let the consonants of the alphabet, in order, represent the first 21 prime numbers. b=2, c=3, d=5 and so on for the rest of: bcdfghjklmnpqrstvwxyz. The first prime we can't cover is 79, so probably any base we actually want to use can be covered in this manner. One could extend this system by using extra phonemes like "th" and so on, or consonant pairs. And let the vowels simply represent the numbers 1 to 5: a=1, e=2, i=3, o=4, u=5. Again if we really need to we could make the long vowels or dipthongs 6,7,8,9,10. Use the suffix "-mal" at the end to show it's a base number.
Now since any number has a unique prime factorization, we can create a prefix by writing the primes in ascending order and using vowels for exponents. This is a simple phonetic transcription of the ordered prime factorization with no ambiguity. So in your example base 6254 is written henbihentetraheptasnasnabintetraker's dozenal. 6254 = 2*53*59, giving the word "batavamal" in my system. Base 600 is tetrahexapentaquinary in your system, but since 600= 2^3*3*5^2 is my system it is "bicademal".
If we really wanted to you can of course make it fully complete by adding systems for parens and rules for making sequences for higher primes. However I would point out that when it comes to choosing base systems for counting, what we are generally looking for is factorization by a lot of small numbers, because this makes the base highly composite and therefore convenient, while large primes tend to make for "suboptimal" base systems, so not including primes higher than 73 is not a huge issue in my opinion. Babylonian-style base 360 is 2^3 * 3^2 * 5 encoding as "bicedamal" for example, and in fact most bases you'd ever use can be encoded using only a fraction of the available consonants. Pretty much everything you'd ever want can be encoded this way in short and easy to pronounce words, which I find superior both for its simplicity and because it does not imply the various base-10 infiltrations caused by using traditional number root systems.
Here are the first 20 base systems encoded this way:
2 = bamal
3 = camal
4 = bemal
5 = damal
6 = bacamal
7 = famal
8 = bimal
9 = cemal
10 = badamal
11 = gamal
12 = becamal
13 = hamal
14 = bafamal
15 = cadamal
16 = bomal
17 = jamal
18 = bacemal
19 = kamal
20 = bedamal
Of course it really shines when you want to have it scale to large numbers. Base 18,617,307,318,176 for example is 2^5*7*19^3*59^4, encoding as "bufakivomal" which is not substantially longer than most of the other relatively small bases.

[@hesseceja2830]

goddamn i love this good job

[@ConcreteAfterRain]

but, this system is harder to implement in real life. misali's system makes use of already existing names for bases, so that, when used in the real world, unless useing extremely uncommon cases, someone doesn't have to learn a whole new system, but merely be familiar with common conventions

[@mbgdemon]

@@ConcreteAfterRain Maybe true, but this is only the case because of our pre-existing base-10 intuition for dealing with numerical word roots. So if the goal is to extirpate decimal bias you're going to need something contrived.

[@ConcreteAfterRain]

also, base 64 has no name

[@fireflash6012]

When you said "hentri" I was waiting for some sort of rule that changes it in specific scenarios to "hentai"

[@sylviewrath2199]

it makes sense not to include the final letter as part of the abbreviation for the simple fact that all of these base names have only a few options for the final letter.
Whether that logic is sound for saying they're worth excluding is a different question, but i think the logic of why makes some sense.

[@taimunozhan]

"Senary" looks like something related to old people (senex, senile, senator).

[@WodkaEclair]

coz cognate. when yr 60 yr old

[@MrCrashDavi]

@@WodkaEclair ohhhhhh

[@morbidi]

sena means six.. that's the name of the card numbered six

[@bobus_mogus]

To me senary sounds more like a name of a building

[@leirbag75]

@@WodkaEclair Nope, it's just a coincidence. If that were the case, then the first e in senex would be long (like sēnus), but it's short

[@tamaramacadam8650]

"Just looking at the thumbnail makes my head hurt" - my friend

[@lukec1471]

Makes your friend hurt?

[@tamaramacadam8650]

@@lukec1471 oops fixed shhh

[@lukec1471]

@@tamaramacadam8650 lol nice

[@Xnoob545]

100th like

[@jimshepherd6500]

I'm an engineer and I'm officially going to use this base numbering system from now on.

[@eskewroberts7663]

I'm so happy I happened to stumble upon this. This exact thing is something I've been thinking about alot

[@janmelantu7490]

“Baker’s Dozenal” MY SIDES

[@kate-os5ww]

hey i came up with that one

[@sanscipher9166]

Wait until biker's dozenal

[@samstephens7388]

@@sanscipher9166 wouldnt that make base 78 (6*13) sexer's dozenal?

[@CasualMitosisCollective]

BASE DEC14 SHOULD THEN BE CALLED POULTER'S DOZENAL. I CAME UP WITH THAT NAME (cause I'm actually making a base DEC14 counting system called Poulter's Dozenal) AND I'M GONNA FORCE EVERYONE TO USE THAT NAME FOR BASE DEC14!!!!

[@theapexsurvivor9538]

@@samstephens7388 that sounds like something that would be enjoyed by biseximals...

[@josefruiz3435]

Jan Misali renames "senary" to "seximal" so he can get away with saying the naughty word: June 2021 (colorized)

[@belcavendishny]

the renaming happened several years ago, keep up lol

[@ookazi1000]

@@belcavendishny jan Misali doubles down on saying the naughty word, circa June 2021 (colorized)

[@josefruiz3435]

@@belcavendishny the date is when the footage was released

[@AlbertTheGamer-gk7sn]

There are no naughty words in any of this.

[@AlbertTheGamer-gk7sn]

@@piethedye3948 Which is not a profanity.

[@gunnervi]

Biker's Dozenal is great but I'm really excited for pinary and Grahamimal. also for further named bases might i suggest "natural" for base e and "finary" for base 1/127

[@meissmart6678]

TREEnary
Rayonary
Negavötdozenal

[@Sylocat]

"Negavötdozenal" sounds cool, but I think -1/12 deserves a special name. Perhaps "Infintesimal," since it's the sum of infinite integers?

[@TheRenegade...]

@@Sylocat I know 1/12 should be Uncial but idk about -1/12

[@thewanderingmistnull2451]

@@Sylocat That's not actually true. That's what happens when you do the math incorrectly since summations aren't commutative.

[@Sylocat]

@@thewanderingmistnull2451 Yes, I know, I saw that Mathologer video too. I was making a funny.

[@feta_cheesecake]

I was thinking about this exact topic the other day while waiting for the bus and this video help clean up the mess a little bit

[@sigstackfault]

"Excel column numbering system" I died

[@alexanderjoseph5380]

what? that's what it actually is.

[@huhneat1076]

Man, I can't believe your name for base 23.
22 was more realistic.

[@LFSDK]

Unbelievable

[@CasualMitosisCollective]

Get out

[@bandie9101]

Unbelievery

[@felipevasconcelos6736]

I was trying to figure out why the name “triquinary” was bad, and “biseptimal” good. Then I remember decimal.

[@CasualMitosisCollective]

@@felipevasconcelos6736 YOU CALL BASE DEC14 "BISEPTIMAL"?????? CALL IT "POULTER'S DOZENAL"!!!!!!!! (the joke is that "Poulter's Dozen is an actual term used to refer to the number DEC14)

[@haniamritdas4725]

"And that's...almost everything." 😂
At some point watching this I just began to laugh, a long and pleasant laugh at how ridiculous we are. Thanks for the details!

[@papawheely3627]

This has woken me up to my new favourite counting system: Decadozenal, or DED. I will be therefore spending my time choosing the appropriate symbols to make writing in DED easier, as computing already is.

[@coryellsworth9705]

Misali, you're probably the only person in the world that can keep me interested in the nuances of number system nomenclature for 17 minutes. Thanks for your interesting content as always!

[@arska-pelejavlogejajaautoj5030]

10 minutes in suboptimal

[@MagicGonads]

10 likes in suboptimal

[@titanichydra8094]

bard

[@ear212]

I do like the "just add -nary" solution for irrational numbers less than 6, but I was really hoping for a "base e is known as natural" line in there.

[@DarkPortall]

wait that was for irrational numbers

[@smeevca]

I've been working on a number system for a conlang for a while that's triquinary, so I'm unreasonably happy to hear that it actually got a good sounding and didn't end up being named suboptimal

[@SilverSerpent705]

"look dorward for at least one of those" is SUCH a content creator-mathematician way to end the video. I love it.

[@SJrad]

Although unwieldy, hexagestimal is my favorite non-practical base system due to 60 being a Superior highly composite number

[@conmattang8492]

Dozenal gets the job done just as well without being unwieldy

[@DeJay7]

We literally don't have 60 symbols even if we use all numbers and letters

[@klobiforpresident2254]

@@DeJay7
1. Then don't demand one symbol per position.
2. Base64 would like to have a word with you.

[@darmorel549]

@@DeJay7 We have way more then 60 symbols. Upper and lowercase give you 52 , and that just with English. Add that to the 0-9 we normally use, and we up to 62. We can add another 38 (If not more) if you count any symbol on the United states keyboard keyboard (like ~). So even without making anything new, we can get to base 100.

[@sortagoodish8491]

1:00 yeah I do like hexadecimal -- they binary/byte/hex conversion is just so clean!

[@jarrod752]

When you write a thesis nobody asked for.
As somebody who recently implemented an bivegisamal (Quadra-heximal? octo-octimal?) numbering system in code, I really appreciate your video.

[@JesseKawell]

This whole video is just 18 minutes of the "can't tell if serious" meme. Love it. It's also 18 minutes of my brain.

[@narwhals6465]

Much easier solution: use base one while talking about other bases.
Binary = base II
Decimal = base IIIIIIIIII
Hex = base IIIIIIIIIIIIIIII
This won’t be annoying at all and it works with basically everything.

[@Quesbe]

Ah yes, I do love using base IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
(there's 256 I in here)

[@YellowBunny]

That way you're just choosing unary to represent your base, which is almost as bad as choosing decimal except for the fact that unary is in a way the simplest and smallest (integer) base.

[@sand747]

@@YellowBunny at least it's not just an arbitrary choice

[@KaneYork]

@@YellowBunny It's exactly as bad as using unary for any practical purpose.

[@diegobrand6970]

But how would you extend this system beyond the natural numbers?

[@raf74hawk12]

This feels like math meets organic chemistry

[@cesaresaladandthespicycrou4080]

God i love that you made this. Amazing

[@gracewenzel]

“There’s a couple more minor rules for optimizing stuff..”
... with 8 more minutes to go