time for your local conlang channel to make another math video at the whims of the youtube recommendation algorithm seximal.net / hbmmaster / hbmmaster
For ratios, you could create a new system. I'm not even remotely an expert, so I'm gonna coin this (most likely already named) system "Nested dots" (since calling them decimal points is like calling Dozenal "Duodecimal"): For DEC1/4th, you write ".IIII". DEC3.25 would be "III.IIII". So what about three fourths? DEC3.75 would be "III.IIII.IIII.IIII", so literally three fourths. Just don't try to write IP adresses in this notation, you'll run into issues.
Mine is more like llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll
@@rateeightx I know it's a joke but you can't have a base i, but I don't know if it's possible to have an usable imaginary base at all ? interesting idea
No the fair enough was regarding the important of fourths. Quarters isn't more or less proper than fourths; one is used in the US and one is used in the UK. jan Misali is clearly from the US and thus says fourths
@@disgustof-riley8338 we use quarters for some things in the US. Most notably for our money (25¢ piece is a quarter). But also quarter gallon (though this is shortened to "quart"), or in divisions of a year (Q1 2023 = Jan-Mar 2023). -If I had to guess as to why we use fourth when talking about fractions in math in the US, I would say that it has to do with keeping them lined up with how we enumerate lists in writing (first, second, third, fourth) - using quarter in that context would make no sense.- EDIT: I just thought about it for a bit and realize we don't use "second" for fractions either, we use half. So I retract my guess. I mean, fourth clearly comes from enumeration terms, but that doesn't answer the "why". It honestly might just be to avoid confusion with money. Or perhaps something to do with how we measure things in inches/feet.
Here's a really stupid reason that's convinced me to switch to seximal: It's pretty easy to count to yourself. For example, if you're sorting out objects or doing pushups, it's easier to do them in groups of six than in groups of ten--I tend to get lost around the 7 or 8 mark.
I'm a cashier so I'm always counting coins in decimal for obvious reasons, but I always have to double check to make sure I actually have a pile of 10 before moving on. I might start using Quinary for everything except Quarters from now on just to make sorting coins go faster.
Working out, if the number of my repetitions is divisible by 5, I tend to count in groups of 5. Otherwise, groups of 4, which I find the easiest to keep track (dedicating almost no brain power to it at all); probably because of listening/making music, and playing drums.
@SQ38 But there could be 3 forms of threeven-ness, just like there's 2 forms of even-ness (I know the actual word is parity but who cares). There's numbers that are divisible by 3, numbers that are just above a multiple of 3, and numbers that are just below a multiple of 3. In addition to threeven (3n), I'll call these morven (3n+1) and lessven (3n-1) because I'm coming up with these names on the spot and I lack imagination. Anyways, another cool thing about seximal is that the 6 digits correspond with all possible combinations of evenness and threevenness, so you an easily tell both by the last digit of any number 0=even & threeven 1=odd & morven 2=even & lessven 3=odd & threeven 4=even & morven 5=odd & lessven
But the imperial system, even in base 12 or 6, is still wack. We can still use the metric system, but replace all the 10-powers to 6-powers. A kilo isn't 10³ but instead 6³, and so on.
The imperial system is too irregular. If you're changing to a dozenal system anyway, you might as well introduce a new metric that uses the dozenal system like the current metric system uses decimal. All you have to change is the constants that appear in various places in formulas, as well as our mental associations with what size of number is about right in a certain situation. The second one is automatic for a new generation that grows up with the new base 12 and new constants.
I am really starting to like seximal, it's weird I never considered it. Some of my reasons are: - I liked binary and balanced ternary as bases from a fundamental standpoint, and 2*3 = 6. - Standard dice are 6 sided, which reflects the fact that there are 6 directions in 3D space. - 1+2+3 = 6, so my only reason for liking decimal (1+2+3+4=10) works for seximal too.
@@gamerrfm9478 That would be unary, which was mentioned in the video, actually! Tally marks are a unary counting method. Unfortunately, it can't really represent anything but nonzero integers, making it almost completely impractical.
TheGreenNinja Sorry! I must’ve gotten it wrong! I was simply making a joke on its uselessness and I fully acknowledge how terrible of a system it would be.
being a dozenal advocate be like: >says dozenal to avoid decimal centrism >doesn't realize "dozen" comes from French "douze" which comes from Latin "duodecim" meaning "two and ten"
plus the dec-el-do-gro-mo nonsense and the HUGE variety of digits you need to learn for ten and eleven, not to mention 1/5 = 0.24972497249724972497 recurring
@@MCLooyverse I’m panseximal. The amount of sixes required to add an extra digit to my numerical representation doesn’t have a meaningful representation.
@@HenriqueErzinger yeah but that's the basic main ones and all , I forgot where I got this number , but I think it was like the 900 kanji people learn in japan at young age + a few other important ones or something like that , I think it has to do with how many they learn at school or something I'm not sure , whatever it's just for a stupid joke about unpractical huge base nothing more really , didn't put a lot of thought into it
Honestly, my understanding of binary is the only reason I passed high school math. Being able to count to 1024 on my fingers and actually understanding the concept of powers made it seem like I was smarter than I was. Because 2^2 is 100 in binary, and somehow that made math work for me.
Same for me!! I didn't know how to multiply or divide until binary. I put powers of 2 to egyptian hieroglyphs, and used egyptian multiplication/division. Without that I wouldn't have passed highschool algebra!! (Recently passed college calculus)
@Gurnaj Virk if you assign each finger to a power of two, increasing from 1, then, assuming you have ten fingers, you could count from zero to 1023 using your fingers.
If you use a positional base, like this video is all about. Base 1 has 1 digit: 0, and it has only one number: 0. - The "unary" base is not a positional base, but a bijective base. A bijective base doesn't have 0, so bijective base 10 is 1-2-3-4-5-6-7-8-9-A. In positional base 1; 00 isn't a different number from 0, just like in any other positional base. So you can only write 0.
There are versions of Unary that are usable and historically used, but it does not work with positional systems AT ALL. They're basically just tally marks: position and order doesn't matter, just count the number of "1"s to get the number. Most that were actually used, like roman numerals, had special symbols for large groups of tally marks to make counting faster, and once you do that you can add special rules based on the order in which they appear, but fundamentally a "pure" usable unary system would only care about the number of 'ticks' and nothing else. Also can only represent ratios as ratios, since using a normal positional radix point anything on the other side of the radix point would just be more 1s--though cultures that used such systems usually had pretty simple notation for writing ratios, like |||:||||| for decimal 0.6 so just a different way of thinking about it and still perfectly usable as long as the numbers are small...which they never do.
If you want less jokey (and more universal!) measures, try powers of the Planck units. For example, six to the niftieighth¹ power Planck lengths is _shockingly_ close to foursy-four² centimeters! Give it some fitting name and base units around it. ¹ forty-fourth ² twenty-eight It's also about nine tenths of a foot.
You have no idea how much I want to see Planck units adapted to a reasonable set for everyday usage. For example, 1 nano-c is a little under 1 foot/second, and surprisingly close to 1 km/h. For a seximal alternative, 1/6^10 (one nif-biexianth) c is 4.958m/s. Combining these two units as they are isn't great since the only give about nif thirsy two (56.47) milliseconds. Some fine tuning will be necessary to find powers that work for all the main units.
I'm a personal fan of doing something similar to the way the Babylonians did base-60, but with twelve digits repeated five times instead of ten repeated six times. The *entire* problem with base-12 is how it handles 5 and fifths, so making the five very explicit and integral helps a lot.
Welcome to numbering system critic! The show that gets facts wrong about your favourite numbering system! I'm jan Miseli and in this episode I will be reviewing base-59
Something that would be nearly painless to convert: book page numbers, where the order of the numbers is important, but the quantity isn't as much. Someone who has no idea that 150 is almost 200 will still know that 150 is less than 200, so they need to flip forward a bit. It'll take them a little bit longer to find their page since they'll initially over shoot, but that's easy enough to overcome. (It'll be easier than finding a word in the dictionary where the number of pages between letters is arbitrary.) If they are paying attention, they'll pick up on the number pattern and adjust, learning written seximal as they do. Also, unlike most uses of numbers, individual books can convert to seximal page numbers independently, so it can happen over time without a big change over all at once.
I was already planning to do this, yes. I'm making a ttrpg with my friend and we're going to do that for the rulebook. I even designed new digits from zero to five, making it look like runes.
I use a weird shorthand based on seximal as shorthand for times of day. A day has exactly 400 (aka 240) 14 (aka 10) minute chunks. 0xx is some time in the first 6 hours 3xx is some time in the final 6 hours. The 2nd digit specifies which of the 6 hours, the final digit specifies which increment of 14 (10) minutes it is. 3:40 in the morning is 034. 13:50 in the afternoon is 215. 18:20 is 302. 23:40 is 354. I do this so nobody else can understand my notes when I die. Using dozenal would be so much more effective.
Hi! These are the (extremely weird) bases you did't talk about. -Golden ratio base (having the golden ratio as base) en.wikipedia.org/wiki/Golden_ratio_base -Factorial base (impratical since the base will change according to position. also needs infinitely many symbols) en.wikipedia.org/wiki/Factorial_number_system -Base with sign digit (Balanced Ternary is the well-known example of these bases) en.wikipedia.org/wiki/Signed-digit_representation -Negative bases (base -2,-3,-10 etc.) en.wikipedia.org/wiki/Negative_base -Quater-imaginary base (base 2i when i² is -1) en.wikipedia.org/wiki/Quater-imaginary_base P.S. I'm not a native English speaker. So apologies for any grammartical error in advance.
It's ok, dude..... Some ( times) people just can't keep up with the sexually seximal nerdiness of it all. It's alright, I haven't mastered chemistry.... Yet. Lol
"Senary" is what that one person who desperately avoids suggestive language uses, but when you realize it puts more focus on the suggestion they're trying to get away from.
@@Anonymous-df8it Because as a listener you're going to think "Why that obscure term? Is this person really trying this hard not to say 'sex'?" I grew up in a country with a language where "six" and "sex" are commonly pronounced the same. A few rare people try to pronounce "six" in a different way which doesn't at all fit with the region, so it's artificial and forced, and everyone can immediately tell. But as for "senary" and "seximal", at least most people in the real world will think one is a nerd no matter what one calls it.
I feel like Hexal would be the best alternative for seximal or heximal. Short enough not to be abbreviated and conforms both to "decimal" and "dozenal" naming schemes. :)
Since you decided to argue with fraction lengths, I wrote a program to add up the lengths of the periods of all unit fractions from 1/2 to 1/144 for the bases in question (2-20). Result: The best base by far is 16, followed by 4 and 9. When going higher, 36 and 25 take second and third place. Then I decided to test convenience by removing multiples of all primes > 11. Now the best base becomes 15, followed by 10, 6 and 9. Considering more fractions, base 18 here pulls ahead and gets second place. Just for fun removing multiples of 11 too, the best now are 15 and 6. Interestingly, with other variations of the parameters, 55 got first place twice. Dunno what's up with that.
It's cool that you wrote a program to check it. Fraction lengths isn't the key thing that matters for divisibility tests, though. What makes for easy divisibility testing: - If the number is not a prime power, all its prime power factors should have easy divisibility tests. - If the number is a prime power and its prime factor is shared by the base, it's always easy test divisibility. - If the number is a prime power and it is coprime to the base, then check the period length. If the period is length 1, the divisibility test is easy. Otherwise, the divisibility test is hard, with maybe 11 as a special exception. Also, going up to 1/144 seems way too high. Even 1/19 is getting pretty high.
@@blueblimp The things you name are closely related to fraction period lengths though. In base b, the fraction 1/n has period length ord_m(b) (order of b modulo m -> why worst-case period is phi(n) ) with n=g*m where g is the greatest divisor of n containing only prime factors of b. - Your first point is basically the fact that gcd(p,q)=1 implies ord_(p*q)(b) | ord_p(b)*ord_q(b) - The second point is equivalent to ord_1(b) = 0 (no period) - The last point just simplifies matters to ord_m(b) easy, else hard I agree that 144 may be too high. On the other hand, the ranking is not stable when going too low. There is definitely a mistake I made: I basically weighted all the lengths equally. The result become much better for 6, 12 and 10 when weighing the periods (of the fractions 1/n) inversely proportional to n or n^2.
Great idea! Though you should adjust the scoring of your program to weigh the lengths of a certain fraction by its value (i.e. the reciprocal of the denominator), instead of uniform weights. After all, that's the probability that a given random integer contains the considered factor, so a good measure for the relevance of divisibility by that factor. It's intuitively obvious that the further you move out to larger denominators, the less important they get. I'd be interested in the updated result!
It matters whether they are reccurring or not. Also, the higher you go, the more decimals there will be after the period, but the LESS weight it should have, because you are less likely to see it in math. So the weighting system should actually be reversed somehow. I think the lower bases would perform better when this is done.
I think a good metric would be to look at all the primes p_1, p_2, ... up to some stopping point. There's no need to test non-primes since everything is governed by the primes anyway. If l_n is the length of the period of the base expansion of 1/p_n, then calculate Σ (l_n/p_n)^2 and see which base minimizes this value. On a side note, there's a chance that this sum would converge if taken over all primes. I would be curious to know if it does and what that means.
I personally find it interesting how, at least in the examples you gave, all of the composite numbers that look prime in any given base are the squares of the first not easy to write reciprocal expansion
That's definitely not a coincidence; the numbers that are easy in fractions are the same numbers that are easy for divisibility rules (factors of the base, one less than the base, and one more than the base)
If anyone wants to build a silly comunity that uses seximal, a regularised calendar, esperanto, Dvorak-style keyboards, and all the improved systems we can think of, let me know! I'd love to meet other utopists :)
In my fictional universe there's a colony on Mars which uses Esperanto, with the Shavian/Sxava writing system, on a Darian calendar. The first two are the result of a political decision to "fix our mistakes and build a better world together".
2:11 SI isn't entirely incompatible with other bases because it's a coherent unit system, so you just need new prefixes. And unless you want to add prefixes to the already prefixed kilogram, you'd have to replace it for the grave. So, what he said at 3:04.
@@pixiepandaplush I'm not disputing the origin. I'm simply pointing out that, if you care at all about adoption, you will be fighting an uphill battle.
hexadecimal remains my favourite simply because it's SO useful in computing, and having everyone learn it since birth would make it easier for people to grasp how code works.
I'm a computer science student. I mentally convert every mention of binary numbers into decimal numbers, pretending that computers work in decimal. It works almost every time. Here is an example using the floating-point number system: A float has 1 sign bit: 0 for + and 1 for −. Lets convert that to decimal: 1 digit: 0 for +, 1 to 9 for −. The exponent is a binary number using 8 bits. It has a bias of 127, meaning you subtract 127 from it to get the actual value of the exponent. This is used to create a number of the form 2^(exponent), ranging from 2^-127 to 2^128. And now in decimal: 3 digits, with a bias of 499. This creates a number of the form 10^(exponent), ranging from 10^-499 to 10^500. The mantissa has 23 bits. It is almost allows preceeded by an implicit 1, to create a number of the form "1.(mantissa)". In decimal we have to make one small adjustment: The only thing we can guarantee in bases other than binary, is that there is a 0 to the left of it. This does not really allow for an implicit extra digit, but that has exceptions anyways. So, in decimal, the mantissa is just a 17 digit number between 1 (inclusive) and 10 (exclusive). Using this system, I can perfectly understand every topic like "precision problems with floats" or "subnormal numbers" or "how to represent NaNs", without actually having to ever think about binary. Binary just isn't ACTUALLY as useful to the average programmer as people say. Its infinitely more important to somebody who designs computer hardware. A coder just needs to know what the limits are, like "a byte is 8 bits and goes from 0 to 255", which are just regular numbers that I literally just wrote in decimal. "What's the decimal value of DEADBEEF" is a question that nobody has ever actually needed the answere to.
Someone: Quarters would be the more proper terminology Mitch: Resolutely continues to use the term fourths because the interval has claimed dominion over his brain.
Thank you for introducing me to quaternary counting! It’s how I do things intuitively anyway and seems pretty useful. You could make a system where 0, 1, 2, and 3 are represented as A, C, G, and T, for example, to mirror nucleotide sequences. (Someone probably already has.)
You really are one of the best cgannels on youtube, you cover most of your bases on things that could be questions and you encourage critical thinking instead of accepting what anyone (including yourself which you state clearly) says.
You've convinced me, seximal is awesome. It's great for both large integers and fractions. It seems like people often forget one of them when promoting bases
3:594:20 That's an excellent point, it guarantees any even base to have a quarter that at most has only one more digit than a half, so might as well optimize a different fraction like a third or fifth.
Base 30 is the smallest base that gives you a nice way of representing halves, thirds, and fifths. That is pretty good and thankfully fewer symbols to remember than base 60.
I was working on some program to get primes (I forget how it worked), but I started caring about 1, 2, 6, 30, etc., and they're called "primorial numbers". Factorial, but you multiply primes.
@@MCLooyverse But to derive the nth prime with your program, you need to know the nth primorial number, and to derive that, you need to know the first n primes, which includes the nth 🤦♂
@@Anonymous-df8it no. You know how you can ignore any even number greater than 2 when looking for primes? You can also ignore any number that isn't 1 or 5 modulo 6 that's greater than 3, or any number that isn't 1, 7, 11, 13, 17, 19, 23, or 29 modulo 30 that's greater than 5, etc.
i have a plan to gradually shift everything into seximal. the secret weapon is the mindset that we don't need to change everything at once. i begin with just one step: using seximal in my next videogame, most notably its scoring system.
Same thing happened to me when I searched "is 65 prime or composite?", and while a lot of sources said 65 is composite (since the factors are 1, 5, 13, and 65...), ONE, which was Angel Number, said that 65 is prime, which it isn't because of 5 and 13, so I had to check other websites to see if this was incorrect (which it is) and yes it was incorrect, so 65 is composite.
@@toters2724 If you want to know if a number is prime or not (or, really, anything about the number), ask wolfram alpha, or write your own program for it. Also, for other interesting facts about an integer, chuck it into the [Online Encyclopedia of Integer Sequences](oeis.net).
8:23 So like how octal and hexadecimal is used to compress binary. If we need to compress our human, non-computer base in the first place, we should probably just use a larger base.
That's pretty much advanced tallying. Each symbol represents a specific number, meaning you will need a new symbol to count higher than M (1000?) or whatever the highest numeral is. In our system, each symbol represents a multiple of a power of ten, depending on where it is. (325 = 3*10^2 + 2*10^1 + 5*10^0) You can just add digits to the end to make the number bigger, instead of inventing a new numeral if you want to represent any large number (n>10000), as needed for roman numerals. If M is the largest roman numeral, I believe the only way to represent 50000 (50 thousand) would be this, MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM, 50 Ms. I hope you see why using a Roman Numeral style system is far worse than our current system.
@@greyduck4965 If that's the case then most measurement systems would also suffer from the same problem but they don't because there is a certain point were counting or measuring that distance or number would be impractical for most people. The romans were able to build truly massive buildings, aqueducts, and roads across their empire with their system because you only need to be able to count to certain number to do most things. edit; you could also write the number as a word rather than a numeral
The roman numeral system works great in base 1000 and simplifies some early digits of decimal. But Infact lacks easy usage of anything above M. Want to write out 75? LXXV. Simple. But want to write out 2476? MMCDLXXVI(in simpliefied roman numerals) or MMCCCCLXXVI(in old roman numerals.) But the numbers 10, 50, 100, 500 and 1000 are the only really simple numbers in roman numerals. X, L, C, D, M. And anything directly below those numbers like IV or VC etc.
wait, what if we used N (for nihil) as zero, and grouped numbers in hundreds, so 7,280 would be VII,CCLXXX. and 500,000,000 would be D,N,N Then you could do decimals the same way, 3.141,592,653 would be III.CXXXXI,DLXXXXII,DCII That way the numbers would be infinitely expandable if you didn't use the subtraction system and wrote 4 as IIII and 9 as VIIII there would be no need for M
A variation on Quaternary I started using when counting measures of rest in music: Since so much of music is based on 4/4 time, and so many musical phrases are based on groupings of 4 measures or other multiples of 4 such as 8-bar periods, 12-bar blues, etc. I started counting base 4 on my hands a lot when performing music. I usually start with my left hand: 1 = left index finger, 2 = left index & middle fingers, 3 = left index through ring, 4 = left index through pinkie. Then I start using my right hand for the next place: 5 = right index & left index, 6 = right index & left middle, 7 = right index & left ring, 8 = right index & left pinkie And I continue using combinations like that: 9 = right middle & left index, ten = right middle & left middle, eleven = right middle & left ring, dozen = right middle & left pinkie and so on. It's a different way of doing it, like the base itself wouldn't be written as 10, it's still 4. But the number one after the base is 11. Counting looks like 1, 2, 3, 4, 11, 12, 13, 14, 21, 22, 23, 24, 31, and so on. There is no 0 in this system, because beat numbers and measure numbers in music use one-based-indexing and not zero-based-indexing.
Base 118 because I've almost memorised the periodic table. This is very crude because ASCII 1: H, Its the letter h | | |---| | | 2: He, No space between letters | |--- |---|--- | |--- 3: Li, Merged into 1 letter here . | | |_ 4: Be, This one has been mangled by ASCII. The letters are also merged btw |---\--- |----|--- |---/--- 5: B, It's the letter B |---\ |----| |---/ 6: C, It's the letter C |------- | |------- 7: N, It's the letter N |\ | | \ | | \| 8: O, It's the letter O |-------| | | |-------| 9: F, It's the letter F |--- |--- | 10: Ne, not much to say |\ |--- | \ |--- | \|--- 11: Na, another mangled one |\ |---| | \ | | | \|---|_ 12: Mg, Has a tail and is hard to draw |\ |---| | \ |---| | \| | __| 13: Al, not much to say again /\ | /----\ | / | 14: Si, it's a dotted S and mangled again ___; |----| ___| 15: P, It's the letter P |----\ |----/ | 16: S, It's the letter S and mangled again ___ |----| ___| 17: Cl, it's almost but not exactly an O |-------|-- | | |-------|-- 18: Ar, not much to say again /\ |--- /----\ | / | I could keep going probably
Respect to you for doing this. Seximal is one of the best bases out there. Double props for mentioning balanced ternary. You skipped over bases 14,15,21,34, 666 and 714 which are all good for finding prime factors. My favorite is base 21 which covers the primes up to 11. Also 101 in base 21 is equal to 2 times 13 times 17.
Prime numbers ending in either 5 or 1 is interesting. I have noticed that numbers divisible 6 tend to be near prime numbers and like to hang out in the middle of double primes :)
I would like to say that hex has one advantage that really makes it stands out: specifically for the case of counting, it is by far easier than any other base. It's 4 4's. With surprisingly little training, one can listen to a fast burst of clicks and, without even counting, know exactly when it reaches 16₁₀. That being said, beyond counting and computer science, it sucks.
@@rubixtheslime No. I'm referring to this: With surprisingly little training, one can listen to a fast burst of clicks and, without even counting, know exactly when it reaches 16₁₀.
@@Anonymous-df8it I figured that's what you were referring to. But I guess that answer doesn't work for you. So like, it just works? Is that the answer you're looking for? Like I don't know of anyone having specifically studied whether people do things with music... Maybe I was just biased because I've studied music to a small extent, so it wasn't difficult for me? I really don't know what you're wanting here.
jan Misali o, sina wile e nanpa mute a. jan li wile kepeken e nanpa wan, e nanpa tu taso. jan li wile ala e nanpa unpa ni, a a. mi toki musi. sina toki e ijo pona.
While before you had convinced my seximal was bestimal, the "primes end with 1 or 5" bit is like THE COOLEST PART!!! I was literally just watching a video about how prime numbers act that way the other day!
I'd like to point out at here (2:40) that we in the UK still predominantly use our own (the original!) version of Imperial, with metric only being used for scientific purposes (most of the time - railways are measured in chains (!), but motorways are in kilometres - and all other roads are in miles).
I'm still in school at England and we have been taught completely in metric. Anything that needs measuring is done in metric. At this point the only people I know that still use imperial are my grandparents
@@equaius893 You are still allowed to use imperial units in expressions; we do that in Swedish, even though we are using only metric nowadays. By switching to metric doesn't mean you have to give up on expressions. You can still say "inches forward" for something slow.
Not hard-wired, just trained for very nearly your entire life. If you actually try to use a different base for a long enough time, you will find it natural. It is incredible how quickly your brain can gain intuition for something if you let it. Just a few weeks ago, I was struggling to remember to use my Caps Lock key for Escape (I recently changed it to do that), and then a few days ago, I found myself doing it automatically on a machine that didn't have that set up. Similarly, when I get into (left-to-right) seximal for a bit (which I do every once in a while), I get pretty good at not messing it up. Also, verbal anything is weird and hard. 43 makes a lot more sense than the spoken "thirsy-four", especially when he still calls 41 "ten".
@@angel-ig Because writing numbers left-to-right is more consistent with how we write everything else, and you get to add, subtract, and multiply from left-to-right, instead of having to teach kids to do it in reverse.
@Ángel I.G. What do you mean backwards? No one writes numbers from the right to left. Maybe the Japanese. Or are you really telling me that Americans are taught to do this and this has been true for decades? That's inhumane honestly
@@TheAlison1456 I wrote "43" (4 and 3 sixes) in left-to-right seximal, as opposed to the normal right-to-left way everyone does in English. That's the backwards number he was talking about. Also "41" (4 and six).
I used to use a modified base 19 for writing dates, since a year of 365 (or 366) days is only 4 (or 5) more than 19 squared, or 361. The digits are 0..9 a..i, with j for the extra days at the end of the year. And the fact that it's a really awkward prime just makes it more fun.
My favorite is Base 60, it easily beats decimal, dozenal and seximal in terms of fractions because it is divisible by all numbers 1 to 6. You can avoid having to use 60 digits by writing each digit as two decimal digits like on clocks.
Always been a huge fan of base 6, great video! Btw have you ever considered how the numerical system affects the way time periods are perceived? In base six we wouldn't think in centuries or millennia, but the six-equivalents (whatever quirky name you want to call them). For example we would be in year 13203, we would consider year 10000 (1296) a big deal, and we would experience a millennium fear every 216 years. Also the stages of human life would be perceived differently (or would they): 0-6 (infancy) 6-12 (pre-adolescence) 13-18 (~teens), 18-24 (~college years) 24-30 (young adulthood) 30-36 (100 years landmark) Pretty neat!
Now we just have to hope my great grandma lives to 108 instead of the 106 she already has. Three nif is another form of "centenarian" that makes sense in seximal.
on the topic of finger counting, your solution for seximal finger counting isn't much better than that of dozenal. hypothetically, if everyone in the world were to switch to seximal, and i were to hold up both my hands, one of them with one finger raised, and one of them with five fingers raised to communicate to someone who isn't within speaking distance, but you can still see each other clearly, how would a viewer know whether i meant eleven or fifsy-one? unless there were some very specific decisions made on how one should interpret hand counting, there's no real way for someone to know, mainly because the viewer doesn't know relative to whom the signaler decided to show the numbers. as well, would the entire system flip dependent on a language's reading direction? on the surface level, that would seem to make sense, but if you were to have members of an exchange who spoke languages whose writing directions differ trying to communicate through finger counting, what would happen? obviously someone would have to switch reading direction. although, in my opinion, it would seem a bit unfair to force only one member of the exchange to change direction. same thing for a standardised direction, one group of language speakers would have to adapt to a new system while another would not. all of these problems are avoided by the standard decimal finger counting system. the standard decimal finger counting system has no parity or directionality and is recognisable by both signalers and viewers regardless of their native language's reading direction. the only real way to solve all of these issues for either dozenal or seximal, at least in my mind, is to create another distinct hand shape, because you yourself noted that values in decimal finger counting are distinct and those in dozenal aren't, which is more or less impossible, due to various counting standards throughout the world. for example, some groups start counting with their thumb as one, and others start counting with their index finger as one. these standards don't get in the way of decimal finger counting, because one must simply count the number of fingers raised. in both the dozenal and seximal systems, there is more complex meanings embedded in the system, which can easily cause ambiguity and confusion between members of an exchange due to differing finger counting standards.
Just a thought, but I learned a method of counting with one hand (based on decimal because of most common use) that goes to 20 on one hand that uses a combination of hand position and orientation (either towards or away from the intended recipient) to make them readily distinguishable even from a distance, then dropped back to using only the configurations for 0-9 with lateral movement from proximal to distal to indicate place, which worked just fine mirrored as well. Obviously it'd need some adaptation, but it doesn't seem particularly difficult to implement something similar for other number bases. Edited in a link to it here: th-cam.com/video/ic-_UW-_rnE/w-d-xo.html
The Sumerian counting system is great for when you need to tally large numbers. It requires slightly more paper, and is honestly the most useful when you're actually organizing physical objects. My modified version uses standard tallies, but when you have two tally groupings, you cross that out, and then go one line below and make the line with a triangle on top system for a ten, and then continue. The physical variation is really just you create a pile of five with the objects you're counting, and then when you get two piles of five, you create one pile and move it to the side. I created it to help me check the card count for MTG and Pokemon TCG decks, so basically by accident, it is also base 60. I developed the written version after what I think was a 39 clues browser game where you had to use the Sumerian counting system for something.
As a Metricman, I find it extremely uncomfortable counting time- one of the most fundamental elements of life -using a base-60/base-12 system. As much as I know it'd be inconvenient having one quarter of a day not being a whole number, I'd appreciate a metric time system where there's 100 seconds in a minute, 100 minutes in an hour, and 10 hours in a day.
The only problem this would create is with the names, because 10,000 (a metric hour) doesn’t have a name in the metric system, unless you want a “decakilo” second. You could still refer to them as metric hours, though.
The thing about binary and hexadecimal is that where they are used, at least at a level humans interpret, ratios don't matter. They are used cardinally. Oh and binary can be used to represent a string of Boolean statements and the hand counting thing is awesome and I have found it practical at times. The more I use those 10 bases, the more beautiful I find them and the more I hate base A.
@@vsl5455 The ONLY one I have EVER heard *IN COMMON USE of that was Binary. Never the others you have mentioned. *had to edit in because sleep deprived me is an idiot.
I’m so sad that no one mentioned the better way to finger count! You can use your thumb as a representation of 5, so 1-4 are counted normally, 5 is just the thumb, and then 6-9 are the positions for 1-4 paired with the thumb. I was taught this method in elementary school and it’s so useful, because it allows you to could to 99, if you use your left hand as the tens digit.
Hi there! I really enjoyed both this video and it's first part. If you're interested in exploring other numeral systems, I would like to suggest that of Kizh, (formerly referred to as "Garbieleño Chumash") the language indigenous to where I am from. It is a quinary system, and I understand that such a prime-based system makes representing fractions more difficult, but there are very interesting other features in Kizh's numeral system, including "kavyaa’" which operates as "X almost twice", or "X + (X-1)" (ex: wachaa’ kavyaa’ is "four almost twice" or "4 + (4-1)", which is 7. In a quinary system, this would be written as "12", of course.) I would be happy to link you to the resources through which I learned of Kizh's numeral system, as well as a document I made exploring and explaining this system to those who are familiar with base 10. (I am by no means an expert in mathematics, numeral systems, or Kizh itself, but this explanation was part of my final project for a course I took titled "North American Indigenous Languages", instructed by Dr. Marriane Mithun, in the Linguistics department at UCSB.) Thank you for your time and labor, and I hope you have a great day!
Base 64 in TH-cam is: A-Z a-z 0-9 - _ and you can type many more letters on a keyboard: . , : ; + ? = \ / ( ) [ ] { } ! $ € § % & and depending on language, you might also be able to type Á È Ǫ Ű Ī Đ Ə Ʒ so you can reach much higher bases than just 64 with a keyboard.
@@poudink5791 yes, but the point is that as a power of 2, its very easy to encode data in base64. you can perfectly fit any 3 bytes in 6 digits of base64
(2:40) Why create a completely new system when you still can use metric? You just need new prefixes. so deca-, hecto-, kilo-, which are 10¹×, 10²×, 10³×, would instead be: 6¹×, 6²×, 6³× the same with deci-, centi-, mili-, currently being 10⁻¹×, 10⁻²×, 10⁻³×, would be 6⁻¹×, 6⁻²×, 6⁻³× new names and letters can be used, to avoid any confusion. Using the prefixes from Conlang Critic; nifti- is 6⁻²×, so a niftimeter (nm) is 0.01₆ meters. unti- is 6⁻⁴×, so an untimeter (um) is 0.0001₆ meters. biti- is 6⁻⁸×, so a bitimeter (bm) is 0.00000001₆ meters. feta- is 6²×, so a fetameter (Fm) is 100₆ meters. grand- is 6⁴×, so a grandmeter (Gm) is 10000₆ meters. - Additional prefixes would still be needed, as you do have GW (gigawatt), GB (gigabyte). But this is a good start. So in computing, you have byte (B), fetabyte (FB), grandbyte (GB) ≈ 1.30 KB or 1.27 KiB, so you need larger prefixes.
@@diribigal Kilogram should rather be renamed to gram if we switch base; so if the kilo- prefix isn't used, just dropping it altogether works. Another option is to make up a new name and define it the same as 1 kg.
alright, if you want to get silly with it, base -1.5 is pretty fun to play around with, i spent a half hour or so trying to do working out to figure out the pattern for counting, along with how you have to do the basic four math operators
i love how you constantly switch between base 10, base 10 and base 10
@ainielyabut6191true, needs more comments
HEY
I use base 36,
@@Thiegocolla77you mean base 10?
Yeah- "all bases are base 1-0." ("Base Neutral method for base names")
OK here me out
Unary
1 = |
2 = ||
3 = |||
4 = ||||
5 = |||||
All fractions are equally unimportant
also zero apparently lol
r/woooosh
Huh, this only has two likes!
columbus8myhw yea the guy speaking about base IIIIIIIIIIII is very stupid
For ratios, you could create a new system. I'm not even remotely an expert, so I'm gonna coin this (most likely already named) system "Nested dots" (since calling them decimal points is like calling Dozenal "Duodecimal"):
For DEC1/4th, you write ".IIII".
DEC3.25 would be "III.IIII".
So what about three fourths? DEC3.75 would be "III.IIII.IIII.IIII", so literally three fourths.
Just don't try to write IP adresses in this notation, you'll run into issues.
I finally get it, all those "IlIlIlIlIlIl" gamertags are just their IQ in unary
lol
An IQ measurement would have to be much less precise if it was unary-based, so maybe that's good.
Mine is more like llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll
I have an iq of 99, I only missed one question on the test
Its the internet equivalent of those "1I1I111II1" license plates.
"After all, that's what really counts." The pun is appreciated.
No it's not. It caused me physical pain.
It's appreciated by other people.
I would.
I KNOW ITS GREAT
@Fihlippe Luhis Maybe.
Base-5040 is clearly the best.
SO MANY FACTOOOORS
Base infinity is far better.
Base i Is Best!
@@rateeightx I know it's a joke but you can't have a base i, but I don't know if it's possible to have an usable imaginary base at all ? interesting idea
@@lpu_n.4926 So... Base Pi?
"(also you should say quarters it's more proper)"
"Fair enough."
_proceeds to call it fourths_
There's only one logical name for the thing between thirds and fifths.
@@TheEvilCheesecake
You make a good point: wholes, halves, thirds, half halves, fifths, third halves, septenths, half halve halves... Etc
No the fair enough was regarding the important of fourths. Quarters isn't more or less proper than fourths; one is used in the US and one is used in the UK. jan Misali is clearly from the US and thus says fourths
@@disgustof-riley8338 we use quarters for some things in the US. Most notably for our money (25¢ piece is a quarter). But also quarter gallon (though this is shortened to "quart"), or in divisions of a year (Q1 2023 = Jan-Mar 2023).
-If I had to guess as to why we use fourth when talking about fractions in math in the US, I would say that it has to do with keeping them lined up with how we enumerate lists in writing (first, second, third, fourth) - using quarter in that context would make no sense.-
EDIT: I just thought about it for a bit and realize we don't use "second" for fractions either, we use half. So I retract my guess. I mean, fourth clearly comes from enumeration terms, but that doesn't answer the "why". It honestly might just be to avoid confusion with money. Or perhaps something to do with how we measure things in inches/feet.
@Ethan Matzdorf I'm from the US and I've never heard people use Q1 for jan-mar like that
"A base one hundred system is inconvenient"
Ithkuil: Hold my beer
"A base 100 system is inconvenient"
Ithkuil: *ôdhwawe*
... i think. I have no idea if that's right, Ithkuil is fuckin impossible to understand
so count from 1 to 99 in ithkuil
@@Blue-Maned_Hawk Iţkuîl ňal
@@BetaDude40 that does seem like it'd be a fun word to loudly declare before doing something dumb
Here's a really stupid reason that's convinced me to switch to seximal: It's pretty easy to count to yourself. For example, if you're sorting out objects or doing pushups, it's easier to do them in groups of six than in groups of ten--I tend to get lost around the 7 or 8 mark.
I do that too sometimes. Counting by myself is pretty nifty in seximal.
I'm a cashier so I'm always counting coins in decimal for obvious reasons, but I always have to double check to make sure I actually have a pile of 10 before moving on. I might start using Quinary for everything except Quarters from now on just to make sorting coins go faster.
Working out, if the number of my repetitions is divisible by 5, I tend to count in groups of 5. Otherwise, groups of 4, which I find the easiest to keep track (dedicating almost no brain power to it at all); probably because of listening/making music, and playing drums.
@@LaPingvino
Haha _nif_ ty
I never get to the 7 or 8 mark
I love the term "threeven" so much
@SQ38 Probably
@@Miju001 But what if the number can be written as 3k+2?(k is a natural number) throden?
@@EsperantistoVolulo I think it'd still be throdd
@SQ38 But there could be 3 forms of threeven-ness, just like there's 2 forms of even-ness (I know the actual word is parity but who cares). There's numbers that are divisible by 3, numbers that are just above a multiple of 3, and numbers that are just below a multiple of 3. In addition to threeven (3n), I'll call these morven (3n+1) and lessven (3n-1) because I'm coming up with these names on the spot and I lack imagination.
Anyways, another cool thing about seximal is that the 6 digits correspond with all possible combinations of evenness and threevenness, so you an easily tell both by the last digit of any number
0=even & threeven
1=odd & morven
2=even & lessven
3=odd & threeven
4=even & morven
5=odd & lessven
It'd make a good character name
broke: changing the imperial system to metric
woke: changing the decimal system to base 12 or 6 so the units fit
But the imperial system, even in base 12 or 6, is still wack. We can still use the metric system, but replace all the 10-powers to 6-powers. A kilo isn't 10³ but instead 6³, and so on.
@@Liggliluff we could just use any base then...just change the powers...
The imperial system is too irregular. If you're changing to a dozenal system anyway, you might as well introduce a new metric that uses the dozenal system like the current metric system uses decimal. All you have to change is the constants that appear in various places in formulas, as well as our mental associations with what size of number is about right in a certain situation. The second one is automatic for a new generation that grows up with the new base 12 and new constants.
@@Leyrann it's either that or change the imperial system
Liggliluff
The *_s t i c k_*
Definitely call it seximal. The snickering in math class every time the teacher mentions it makes it worthwhile.
Yeah, astronomy teachers can't be the only ones to suffer.
Also, I saw someone else in this comment section saying to call "dozenal" "biseximal", which I enjoyed.
@@MCLooyverse As a bisexual, I would love this
I call it Base Six
Or bitrinary if you're a teacher tired of your student's shit. Just saying.
I am really starting to like seximal, it's weird I never considered it. Some of my reasons are:
- I liked binary and balanced ternary as bases from a fundamental standpoint, and 2*3 = 6.
- Standard dice are 6 sided, which reflects the fact that there are 6 directions in 3D space.
- 1+2+3 = 6, so my only reason for liking decimal (1+2+3+4=10) works for seximal too.
On the other hand, every even base cannot be balanced : (
Base 15 (1+2+3+4+5) here I come
Primary base (1=1)
@@gamerrfm9478 That would be unary, which was mentioned in the video, actually! Tally marks are a unary counting method.
Unfortunately, it can't really represent anything but nonzero integers, making it almost completely impractical.
TheGreenNinja Sorry! I must’ve gotten it wrong! I was simply making a joke on its uselessness and I fully acknowledge how terrible of a system it would be.
I love the word "threeven" it's a little silly but also simple and intuitive and useful
Combo Class fan?
@@wyattstevens8574I got that term from that guy
Integer, even, threeven, fourven, fiffven, sixven, sevven, eighven, nineven, tingven.
"I've been jan Misali before, and someday I will be jan Misali again." Why does that sound vaguely threatening?
To me, it sounds like he's on a quest.
It sounds like he is taking a break.
I was sold when you said "niftimeter" tbh
Its so nifty!
Its so nifty!
Its so nifty!
It’s so nifty!
Nif tens. It's so nifty!
being a dozenal advocate be like:
>says dozenal to avoid decimal centrism
>doesn't realize "dozen" comes from French "douze" which comes from Latin "duodecim" meaning "two and ten"
plus the dec-el-do-gro-mo nonsense and the HUGE variety of digits you need to learn for ten and eleven, not to mention 1/5 = 0.24972497249724972497 recurring
The decimal roots are obfuscated in “dozenal”, though, but they’re practically neon billboards in “duodecimal”.
Alternative name: biseximal. Base 2*6
@@DragonWinter36 That's great. Yeah, I'm biseximal.
@@MCLooyverse I’m panseximal. The amount of sixes required to add an extra digit to my numerical representation doesn’t have a meaningful representation.
what about base-1296 , great for remembering your kanji's !
I just wonder what a chinese base would look like
why? what does this number have to to with kanji? There are a lot more than this.
@@HenriqueErzinger yeah but that's the basic main ones and all , I forgot where I got this number , but I think it was like the 900 kanji people learn in japan at young age + a few other important ones or something like that , I think it has to do with how many they learn at school or something I'm not sure , whatever it's just for a stupid joke about unpractical huge base nothing more really , didn't put a lot of thought into it
1296 = (6^4)
@@keonscorner516 oh yeah I remember now
Honestly, my understanding of binary is the only reason I passed high school math. Being able to count to 1024 on my fingers and actually understanding the concept of powers made it seem like I was smarter than I was.
Because 2^2 is 100 in binary, and somehow that made math work for me.
Same for me!! I didn't know how to multiply or divide until binary. I put powers of 2 to egyptian hieroglyphs, and used egyptian multiplication/division. Without that I wouldn't have passed highschool algebra!! (Recently passed college calculus)
@Gurnaj Virk if you assign each finger to a power of two, increasing from 1, then, assuming you have ten fingers, you could count from zero to 1023 using your fingers.
Just don't let anybody catch you counting to 132. It's 128+4, which would be both middle fingers by the way I can think of to do it.
@@orion6able 132
@@DigitalJedi Oh, I most certainly had people catch me counting to 132.
Bacteria be out here counting in base 1.
If you use a positional base, like this video is all about. Base 1 has 1 digit: 0, and it has only one number: 0. - The "unary" base is not a positional base, but a bijective base. A bijective base doesn't have 0, so bijective base 10 is 1-2-3-4-5-6-7-8-9-A.
In positional base 1; 00 isn't a different number from 0, just like in any other positional base. So you can only write 0.
So 1 in base 1 is just repeating 0, except instead of repeating off to the right, it repeats to the left...
Actually, no, that's still dumb.
@@Liggliluff you can also write -0 which can be a different thing in some contexts
There are versions of Unary that are usable and historically used, but it does not work with positional systems AT ALL. They're basically just tally marks: position and order doesn't matter, just count the number of "1"s to get the number. Most that were actually used, like roman numerals, had special symbols for large groups of tally marks to make counting faster, and once you do that you can add special rules based on the order in which they appear, but fundamentally a "pure" usable unary system would only care about the number of 'ticks' and nothing else. Also can only represent ratios as ratios, since using a normal positional radix point anything on the other side of the radix point would just be more 1s--though cultures that used such systems usually had pretty simple notation for writing ratios, like |||:||||| for decimal 0.6 so just a different way of thinking about it and still perfectly usable as long as the numbers are small...which they never do.
If you want less jokey (and more universal!) measures, try powers of the Planck units. For example, six to the niftieighth¹ power Planck lengths is _shockingly_ close to foursy-four² centimeters! Give it some fitting name and base units around it.
¹ forty-fourth
² twenty-eight
It's also about nine tenths of a foot.
I totally had the same idea! I might still have my notes somewhere.
"and *base* units around it"
Was that intentional?
it's just nif eight, not niftieight
@@torreywhiting5402 probably not actually, but hilarious once you pointed it out
You have no idea how much I want to see Planck units adapted to a reasonable set for everyday usage. For example, 1 nano-c is a little under 1 foot/second, and surprisingly close to 1 km/h. For a seximal alternative, 1/6^10 (one nif-biexianth) c is 4.958m/s. Combining these two units as they are isn't great since the only give about nif thirsy two (56.47) milliseconds. Some fine tuning will be necessary to find powers that work for all the main units.
I'm a personal fan of doing something similar to the way the Babylonians did base-60, but with twelve digits repeated five times instead of ten repeated six times. The *entire* problem with base-12 is how it handles 5 and fifths, so making the five very explicit and integral helps a lot.
7: Am I a joke to you?
As a science nerd, I have lost track of counting numbers since learning algebra.
Welcome to numbering system critic! The show that gets facts wrong about your favourite numbering system! I'm jan Miseli and in this episode I will be reviewing base-59
In an alternate universe... he starts out as Conlang Critic and becomes Jan Misali, as opposed to reality
@@serglian8558 that's this universe
*69
@@serglian8558 ???
Something that would be nearly painless to convert: book page numbers, where the order of the numbers is important, but the quantity isn't as much. Someone who has no idea that 150 is almost 200 will still know that 150 is less than 200, so they need to flip forward a bit. It'll take them a little bit longer to find their page since they'll initially over shoot, but that's easy enough to overcome. (It'll be easier than finding a word in the dictionary where the number of pages between letters is arbitrary.) If they are paying attention, they'll pick up on the number pattern and adjust, learning written seximal as they do.
Also, unlike most uses of numbers, individual books can convert to seximal page numbers independently, so it can happen over time without a big change over all at once.
Writing my next book with seximal page numbers. Thanks.
this sounds like a horrible idea. i will do it
I was already planning to do this, yes. I'm making a ttrpg with my friend and we're going to do that for the rulebook. I even designed new digits from zero to five, making it look like runes.
@@ezdispenser Why horrible?
Flipping pages is so trivial that I can't believe you thought this comment was worth posting
0:57 jan misali calls me out 😳😳😳
tbf you did a lol. Just to point it out. Others were more.. well..
Lol
Can we just take a second and a half to appreciate the name "suboptimal"?
6 seconds
@@norude I think you mean '10'
@@leave-a-comment-at-the-door 0b110
17* seconds
You definitely don't talk too fast, you're one of the few youtubers I dont have to put on 1.25x or 1.5x speed lol
Ikr
I thought I was on 1.5 lmao
Wait a second... if you put a fast youtuber on 1.5x speed then won't it get even faster?
Still waiting for base-5040, or as I like to call it platimal.
We just need to come up with all those symbols and number names is all.
Platimal, brought to you by the power of cheating: each digit is a decimal number 0 through 5039 with a - between digits for easier reading.
1,000,000,000,000 = 7-4087-3018-2080
1,000,000,000 = 39-1852-3520
1,000,000 = 198-2080
1,000 = 1000
100 = 100
10 = 10
1 = 1
1/2 = 0.2520
1/3 = 0.1680
1/4 = 0.1260
1/5 = 0.1008
1/6 = 0.840
1/7 = 0.720
1/8 = 0.630
1/9 = 0.560
1/10 = 0.504
1/11 = 0.458-916-1832-3665-2290-4581-4123-3207-1374-2749 recurring
1/12 = 0.420
1/13 = 0.387-3489-1163 recurring
1/14 = 0.360
1/15 = 0.336
@@bernhardschmidt9844 You have done gods work
@@Gareon155 Does DEC5040 = a plat?
@@shadowyzephyr no, but it was Plato's favorite number. Fetaheptavigesimal is fun.
Misali: 14:14
Google software engineer: **cries in base64**
I use a weird shorthand based on seximal as shorthand for times of day. A day has exactly 400 (aka 240) 14 (aka 10) minute chunks. 0xx is some time in the first 6 hours 3xx is some time in the final 6 hours. The 2nd digit specifies which of the 6 hours, the final digit specifies which increment of 14 (10) minutes it is. 3:40 in the morning is 034. 13:50 in the afternoon is 215. 18:20 is 302. 23:40 is 354.
I do this so nobody else can understand my notes when I die. Using dozenal would be so much more effective.
how does this comment only have 5 likes after 3 yrs(i actually understood how it works and can use it slowly)
This is fucking cool as hell
Hi! These are the (extremely weird) bases you did't talk about.
-Golden ratio base (having the golden ratio as base) en.wikipedia.org/wiki/Golden_ratio_base
-Factorial base (impratical since the base will change according to position. also needs infinitely many symbols) en.wikipedia.org/wiki/Factorial_number_system
-Base with sign digit (Balanced Ternary is the well-known example of these bases) en.wikipedia.org/wiki/Signed-digit_representation
-Negative bases (base -2,-3,-10 etc.) en.wikipedia.org/wiki/Negative_base
-Quater-imaginary base (base 2i when i² is -1) en.wikipedia.org/wiki/Quater-imaginary_base
P.S. I'm not a native English speaker. So apologies for any grammartical error in advance.
Where's base pi?
@@zyaicob pi is so close to 3 it whould be the ternary system with very slight changes
Oh god the quater imaginary bases are killing me.
But now i want to use one, fuck.
Are you okay?
It’s funny how people who say English isn’t their first language have better grammar than native English speakers
Friendship ended with DOZENAL, now SEXIMAL is my best friend (dead meme I know)
It's an old meme, sir, but it checks out.
@@Vizaru All your base are belong to us would be the oldest relevant meme here.
_gumball_
Excellent. Rewatched recently. I felt your sincerity. Beautiful. I feel you dude, really.
Seximal!!!!!!! Hell Yeh. I love sex, and I LOVE seximal!!!!
It's ok, dude..... Some ( times) people just can't keep up with the sexually seximal nerdiness of it all. It's alright, I haven't mastered chemistry.... Yet. Lol
It Took Me A Good 7 Seconds To Realise The Replies Were From The Original Commentor.
@@rateeightx *11 seconds
"Senary" is what that one person who desperately avoids suggestive language uses, but when you realize it puts more focus on the suggestion they're trying to get away from.
???
@4ourevermore Why does it put more focus on that word?
Well, if you search up that base, people will think you have misspelled "scenery".
@@Anonymous-df8it Because as a listener you're going to think "Why that obscure term? Is this person really trying this hard not to say 'sex'?"
I grew up in a country with a language where "six" and "sex" are commonly pronounced the same. A few rare people try to pronounce "six" in a different way which doesn't at all fit with the region, so it's artificial and forced, and everyone can immediately tell.
But as for "senary" and "seximal", at least most people in the real world will think one is a nerd no matter what one calls it.
@@waluigi-time But senary is the normal name, is it not?
By the way, qwaternary is the base of life (TGAC in DNA).
You're not wrong and I don't know how to feel about that.
this means you are approximately SEX10^155350 or DEC10^12041.2 or DOZ10^6559.8 or HEX10^2710 or NIF10^5YX
I feel like Hexal would be the best alternative for seximal or heximal. Short enough not to be abbreviated and conforms both to "decimal" and "dozenal" naming schemes. :)
Minor drawback: Hexal AG is a German pharma corporation.
@@SugarBeetMC *Major
Since you decided to argue with fraction lengths, I wrote a program to add up the lengths of the periods of all unit fractions from 1/2 to 1/144 for the bases in question (2-20). Result:
The best base by far is 16, followed by 4 and 9. When going higher, 36 and 25 take second and third place.
Then I decided to test convenience by removing multiples of all primes > 11. Now the best base becomes 15, followed by 10, 6 and 9. Considering more fractions, base 18 here pulls ahead and gets second place.
Just for fun removing multiples of 11 too, the best now are 15 and 6.
Interestingly, with other variations of the parameters, 55 got first place twice. Dunno what's up with that.
It's cool that you wrote a program to check it. Fraction lengths isn't the key thing that matters for divisibility tests, though.
What makes for easy divisibility testing:
- If the number is not a prime power, all its prime power factors should have easy divisibility tests.
- If the number is a prime power and its prime factor is shared by the base, it's always easy test divisibility.
- If the number is a prime power and it is coprime to the base, then check the period length. If the period is length 1, the divisibility test is easy. Otherwise, the divisibility test is hard, with maybe 11 as a special exception.
Also, going up to 1/144 seems way too high. Even 1/19 is getting pretty high.
@@blueblimp The things you name are closely related to fraction period lengths though.
In base b, the fraction 1/n has period length ord_m(b) (order of b modulo m -> why worst-case period is phi(n) ) with n=g*m where g is the greatest divisor of n containing only prime factors of b.
- Your first point is basically the fact that gcd(p,q)=1 implies ord_(p*q)(b) | ord_p(b)*ord_q(b)
- The second point is equivalent to ord_1(b) = 0 (no period)
- The last point just simplifies matters to ord_m(b) easy, else hard
I agree that 144 may be too high. On the other hand, the ranking is not stable when going too low.
There is definitely a mistake I made: I basically weighted all the lengths equally. The result become much better for 6, 12 and 10 when weighing the periods (of the fractions 1/n) inversely proportional to n or n^2.
Great idea! Though you should adjust the scoring of your program to weigh the lengths of a certain fraction by its value (i.e. the reciprocal of the denominator), instead of uniform weights. After all, that's the probability that a given random integer contains the considered factor, so a good measure for the relevance of divisibility by that factor. It's intuitively obvious that the further you move out to larger denominators, the less important they get.
I'd be interested in the updated result!
It matters whether they are reccurring or not. Also, the higher you go, the more decimals there will be after the period, but the LESS weight it should have, because you are less likely to see it in math. So the weighting system should actually be reversed somehow. I think the lower bases would perform better when this is done.
I think a good metric would be to look at all the primes p_1, p_2, ... up to some stopping point. There's no need to test non-primes since everything is governed by the primes anyway. If l_n is the length of the period of the base expansion of 1/p_n, then calculate
Σ (l_n/p_n)^2
and see which base minimizes this value.
On a side note, there's a chance that this sum would converge if taken over all primes. I would be curious to know if it does and what that means.
No matter your favorite base, at least we can all agree the best one is base-10.
I personally find it interesting how, at least in the examples you gave, all of the composite numbers that look prime in any given base are the squares of the first not easy to write reciprocal expansion
i wonder what the results would be if squares weren't counted
That's definitely not a coincidence; the numbers that are easy in fractions are the same numbers that are easy for divisibility rules (factors of the base, one less than the base, and one more than the base)
"it's fun to get silly sometimes" is a motto i wanna live my whole life by
15:43
Proverbs 22 : 07
The rich rule poor, and the borrower is a slave to the lender.
Proverbs 15 : 43
(not found)
Driving to de Dearest Dealers
If anyone wants to build a silly comunity that uses seximal, a regularised calendar, esperanto, Dvorak-style keyboards, and all the improved systems we can think of, let me know! I'd love to meet other utopists :)
A seximal keyboard does free up 4 digits for other symbols :)
@@misotanniold787 esperanto is more edgy
In my fictional universe there's a colony on Mars which uses Esperanto, with the Shavian/Sxava writing system, on a Darian calendar. The first two are the result of a political decision to "fix our mistakes and build a better world together".
Nah toki pona
And our circle constant, Tau, is close to 10
2:11 SI isn't entirely incompatible with other bases because it's a coherent unit system, so you just need new prefixes. And unless you want to add prefixes to the already prefixed kilogram, you'd have to replace it for the grave. So, what he said at 3:04.
You should review esolangs! Like conlangs, but with more math. Also you can actually learn and get familiar with one in a reasonable amount of time.
Imagine thinking esolangs are good
ugh Most are pretty crap. There are a few good ones. And they're only slightly more useless than conlangs.
if our reason for doing conlanging stuff was because they were useful we would have stopped by now lol
Starry Sunrose or we would’ve actually made a useful conlang
@@Blue-Maned_Hawk and he is cool
Or call it heximal anyway, as hex is just short for hexadecimal.
edit: spelling
I will say, as a programmer, this is unappealing to me. We call hexadecimal "hex." It would be inconvenient to make that common term ambiguous.
It's a matter of abbreviation. In the programming world, we use he this way, as six was never a thought.
@@pixiepandaplush I'm not disputing the origin. I'm simply pointing out that, if you care at all about adoption, you will be fighting an uphill battle.
@@pixiepandaplush Hex is the common abbreviation of hexadecimal.
I'll clarify my original comment. I don't see a situation where people would confuse "heximal" and "hex"
I'm going into computer science, but if you'd asked me before, I would've already said that I favor base 16. IT'S SO GOOD
hexadecimal remains my favourite simply because it's SO useful in computing, and having everyone learn it since birth would make it easier for people to grasp how code works.
Exactly. Would also help people understand how powers work, making higher level mandatory math easier to adjust to
I'm a computer science student. I mentally convert every mention of binary numbers into decimal numbers, pretending that computers work in decimal. It works almost every time. Here is an example using the floating-point number system:
A float has 1 sign bit: 0 for + and 1 for −. Lets convert that to decimal: 1 digit: 0 for +, 1 to 9 for −.
The exponent is a binary number using 8 bits. It has a bias of 127, meaning you subtract 127 from it to get the actual value of the exponent. This is used to create a number of the form 2^(exponent), ranging from 2^-127 to 2^128. And now in decimal: 3 digits, with a bias of 499. This creates a number of the form 10^(exponent), ranging from 10^-499 to 10^500.
The mantissa has 23 bits. It is almost allows preceeded by an implicit 1, to create a number of the form "1.(mantissa)". In decimal we have to make one small adjustment: The only thing we can guarantee in bases other than binary, is that there is a 0 to the left of it. This does not really allow for an implicit extra digit, but that has exceptions anyways. So, in decimal, the mantissa is just a 17 digit number between 1 (inclusive) and 10 (exclusive).
Using this system, I can perfectly understand every topic like "precision problems with floats" or "subnormal numbers" or "how to represent NaNs", without actually having to ever think about binary.
Binary just isn't ACTUALLY as useful to the average programmer as people say. Its infinitely more important to somebody who designs computer hardware. A coder just needs to know what the limits are, like "a byte is 8 bits and goes from 0 to 255", which are just regular numbers that I literally just wrote in decimal. "What's the decimal value of DEADBEEF" is a question that nobody has ever actually needed the answere to.
Well, this fits my theory of why people prefer certain number systems. "This system is the best because it's so much easier for me personally!"
@@BaldorfBreakdowns when did i say that this is easier for me?
@@swedneck You said it makes it easier for coding, which I presume is something you do, based off of your comment.
I will now only count in suboptimal. You've convinced me.
Suboptimal is base-17 right?
Smug Dragon That’s correct.
Someone: Quarters would be the more proper terminology
Mitch: Resolutely continues to use the term fourths because the interval has claimed dominion over his brain.
Quarter is the word for fourth in the UK. In the US it's correct to say fourth
@@disgustof-riley8338 jan misali is American
@@disgustof-riley8338 Never in my life have I heard a person say "It's a fourth mile from here". Lets go over coins: penny, nickel, dime and fourths!
Thank you for introducing me to quaternary counting! It’s how I do things intuitively anyway and seems pretty useful. You could make a system where 0, 1, 2, and 3 are represented as A, C, G, and T, for example, to mirror nucleotide sequences. (Someone probably already has.)
Also base 1 is basically how we do finger counting anyway
Yes, representing numbers with arbitrary letters will make my life easier for sure.
@@BaldorfBreakdowns It's in your genes!
6:50 ...prevents even and THREEEVEN numbers from looking like prime... Omg I love you. By the way how many E's does threeven have?
I counted, threeven has three Es.
Why am I Dead in Discord A threeven number of Es
You really are one of the best cgannels on youtube, you cover most of your bases on things that could be questions and you encourage critical thinking instead of accepting what anyone (including yourself which you state clearly) says.
Compression binary is an interesting concept I will explore. Really cool how you can do that with base 4 and Base 9.
You've convinced me, seximal is awesome. It's great for both large integers and fractions. It seems like people often forget one of them when promoting bases
Your closing statement was hilarious! I've never heard that one before 🤣
3:59 4:20 That's an excellent point, it guarantees any even base to have a quarter that at most has only one more digit than a half, so might as well optimize a different fraction like a third or fifth.
Base 30 is the smallest base that gives you a nice way of representing halves, thirds, and fifths. That is pretty good and thankfully fewer symbols to remember than base 60.
I was working on some program to get primes (I forget how it worked), but I started caring about 1, 2, 6, 30, etc., and they're called "primorial numbers". Factorial, but you multiply primes.
@@MCLooyverse But to derive the nth prime with your program, you need to know the nth primorial number, and to derive that, you need to know the first n primes, which includes the nth 🤦♂
@@Anonymous-df8it no. You know how you can ignore any even number greater than 2 when looking for primes? You can also ignore any number that isn't 1 or 5 modulo 6 that's greater than 3, or any number that isn't 1, 7, 11, 13, 17, 19, 23, or 29 modulo 30 that's greater than 5, etc.
@@MCLooyverse Why primorial numbers in particular, though?
49 has 0 prime numbers, finally proof! I keep telling this to my fam but they keep repeating 7 squared, Im like, squared up against who tho
i have a plan to gradually shift everything into seximal. the secret weapon is the mindset that we don't need to change everything at once.
i begin with just one step:
using seximal in my next videogame, most notably its scoring system.
Balanced ternary is my favourite, I love the way it handles negative numbers without any special cases
Fun Useless Fact: when i was in 6th grade, i asked my mom if 39 was prime and she said yes! everyone forgets school someday!
13x3=39.
What is school, and what is prime? Sorry I am grade of the 6xt
@@loop5720 prime numbers are numbers that can only be divided by one or themselves.
Example: 2.
2 can only be divided by either 2 or 1.
You mean that you asked is 103 was prime, but it obviously isn't as 21x3=103.
Same thing happened to me when I searched "is 65 prime or composite?", and while a lot of sources said 65 is composite (since the factors are 1, 5, 13, and 65...), ONE, which was Angel Number, said that 65 is prime, which it isn't because of 5 and 13, so I had to check other websites to see if this was incorrect (which it is) and yes it was incorrect, so 65 is composite.
@@toters2724 If you want to know if a number is prime or not (or, really, anything about the number), ask wolfram alpha, or write your own program for it. Also, for other interesting facts about an integer, chuck it into the [Online Encyclopedia of Integer Sequences](oeis.net).
It ain’t conlangs... but it’ll do
For now
Then I’ll need sacrifices
@@pqbdwmnu the reverse card from UNO
i love listening to your video essays which are very similar to infodumps
i don't remember writing this
8:23 So like how octal and hexadecimal is used to compress binary. If we need to compress our human, non-computer base in the first place, we should probably just use a larger base.
what if you use a roman numeral style system instead of an arabic numeral system
I Once Made A Numeral System. It's Very Simple, And Very Difficult To Tell What A Number Is Just By Looking At It, As All Symbols Look Pretty Similar!
That's pretty much advanced tallying. Each symbol represents a specific number, meaning you will need a new symbol to count higher than M (1000?) or whatever the highest numeral is.
In our system, each symbol represents a multiple of a power of ten, depending on where it is.
(325 = 3*10^2 + 2*10^1 + 5*10^0) You can just add digits to the end to make the number bigger, instead of inventing a new numeral if you want to represent any large number (n>10000), as needed for roman numerals.
If M is the largest roman numeral, I believe the only way to represent 50000 (50 thousand) would be this, MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM, 50 Ms.
I hope you see why using a Roman Numeral style system is far worse than our current system.
@@greyduck4965 If that's the case then most measurement systems would also suffer from the same problem but they don't because there is a certain point were counting or measuring that distance or number would be impractical for most people. The romans were able to build truly massive buildings, aqueducts, and roads across their empire with their system because you only need to be able to count to certain number to do most things.
edit; you could also write the number as a word rather than a numeral
The roman numeral system works great in base 1000 and simplifies some early digits of decimal. But Infact lacks easy usage of anything above M. Want to write out 75? LXXV. Simple. But want to write out 2476? MMCDLXXVI(in simpliefied roman numerals) or MMCCCCLXXVI(in old roman numerals.) But the numbers 10, 50, 100, 500 and 1000 are the only really simple numbers in roman numerals. X, L, C, D, M. And anything directly below those numbers like IV or VC etc.
wait, what if we used N (for nihil) as zero, and grouped numbers in hundreds, so 7,280 would be VII,CCLXXX. and 500,000,000 would be D,N,N
Then you could do decimals the same way, 3.141,592,653 would be III.CXXXXI,DLXXXXII,DCII
That way the numbers would be infinitely expandable
if you didn't use the subtraction system and wrote 4 as IIII and 9 as VIIII there would be no need for M
Suboptimal is the counting system for me. I love long recurring division and nesting fractions
A variation on Quaternary I started using when counting measures of rest in music:
Since so much of music is based on 4/4 time, and so many musical phrases are based on groupings of 4 measures or other multiples of 4 such as 8-bar periods, 12-bar blues, etc. I started counting base 4 on my hands a lot when performing music.
I usually start with my left hand: 1 = left index finger, 2 = left index & middle fingers, 3 = left index through ring, 4 = left index through pinkie.
Then I start using my right hand for the next place: 5 = right index & left index, 6 = right index & left middle, 7 = right index & left ring, 8 = right index & left pinkie
And I continue using combinations like that: 9 = right middle & left index, ten = right middle & left middle, eleven = right middle & left ring, dozen = right middle & left pinkie
and so on.
It's a different way of doing it, like the base itself wouldn't be written as 10, it's still 4. But the number one after the base is 11. Counting looks like 1, 2, 3, 4, 11, 12, 13, 14, 21, 22, 23, 24, 31, and so on. There is no 0 in this system, because beat numbers and measure numbers in music use one-based-indexing and not zero-based-indexing.
Base 118 because I've almost memorised the periodic table. This is very crude because ASCII
1: H, Its the letter h
| |
|---|
| |
2: He, No space between letters
| |---
|---|---
| |---
3: Li, Merged into 1 letter here
.
|
|
|_
4: Be, This one has been mangled by ASCII. The letters are also merged btw
|---\---
|----|---
|---/---
5: B, It's the letter B
|---\
|----|
|---/
6: C, It's the letter C
|-------
|
|-------
7: N, It's the letter N
|\ |
| \ |
| \|
8: O, It's the letter O
|-------|
| |
|-------|
9: F, It's the letter F
|---
|---
|
10: Ne, not much to say
|\ |---
| \ |---
| \|---
11: Na, another mangled one
|\ |---|
| \ | |
| \|---|_
12: Mg, Has a tail and is hard to draw
|\ |---|
| \ |---|
| \| |
__|
13: Al, not much to say again
/\ |
/----\ |
/ |
14: Si, it's a dotted S and mangled again
___;
|----|
___|
15: P, It's the letter P
|----\
|----/
|
16: S, It's the letter S and mangled again
___
|----|
___|
17: Cl, it's almost but not exactly an O
|-------|--
| |
|-------|--
18: Ar, not much to say again
/\ |---
/----\ |
/ |
I could keep going probably
Respect to you for doing this. Seximal is one of the best bases out there. Double props for mentioning balanced ternary.
You skipped over bases 14,15,21,34, 666 and 714 which are all good for finding prime factors. My favorite is base 21 which covers the primes up to 11. Also 101 in base 21 is equal to 2 times 13 times 17.
6 * 9 in base 13 is 42.
Prime numbers ending in either 5 or 1 is interesting. I have noticed that numbers divisible 6 tend to be near prime numbers and like to hang out in the middle of double primes :)
"(also you should say quarters it's more proper)"
"yeah fair enough. So fourths-"
This is all excellent and I'm down for the revolution but I nearly collapsed when you said "threeven." It all makes sense now.
I would like to say that hex has one advantage that really makes it stands out: specifically for the case of counting, it is by far easier than any other base. It's 4 4's. With surprisingly little training, one can listen to a fast burst of clicks and, without even counting, know exactly when it reaches 16₁₀. That being said, beyond counting and computer science, it sucks.
Source?
@@Anonymous-df8it in music, 4 beats in a measure and 4 measures in a phrase is extremely common. Or it's 16 sixteenth notes in a measure.
@@rubixtheslime No. I'm referring to this: With surprisingly little training, one can listen to a fast burst of clicks and, without even counting, know exactly when it reaches 16₁₀.
@@Anonymous-df8it I figured that's what you were referring to. But I guess that answer doesn't work for you. So like, it just works? Is that the answer you're looking for? Like I don't know of anyone having specifically studied whether people do things with music... Maybe I was just biased because I've studied music to a small extent, so it wasn't difficult for me? I really don't know what you're wanting here.
@@rubixtheslime Can 5/4 time be used for decimal?
jan Misali o, sina wile e nanpa mute a. jan li wile kepeken e nanpa wan, e nanpa tu taso. jan li wile ala e nanpa unpa ni, a a. mi toki musi. sina toki e ijo pona.
nanpa unpa, a a a!
I just learned the about Toki Pona language today, pretty nice...
While before you had convinced my seximal was bestimal, the "primes end with 1 or 5" bit is like THE COOLEST PART!!! I was literally just watching a video about how prime numbers act that way the other day!
“That’s what really counts!” Ough! Good one. I see my comment from a year ago that it got me back then also.
yay another video!
I'd like to point out at here (2:40) that we in the UK still predominantly use our own (the original!) version of Imperial, with metric only being used for scientific purposes (most of the time - railways are measured in chains (!), but motorways are in kilometres - and all other roads are in miles).
and miles are better for literary purposes. would you rather hear in a song "I will walk 500 kilometers" or "I will walk 500 miles"
@@equaius893 That's what "klicks" is for.
@@ivanlovell1195 Still doesn't sound as good as miles.
I'm still in school at England and we have been taught completely in metric. Anything that needs measuring is done in metric. At this point the only people I know that still use imperial are my grandparents
@@equaius893 You are still allowed to use imperial units in expressions; we do that in Swedish, even though we are using only metric nowadays. By switching to metric doesn't mean you have to give up on expressions. You can still say "inches forward" for something slow.
you should create an entire channel on seximal. I would love to see that.
The measurement arguments are my favourite.
WHAT-IMAL RESPONCES??? 😳😳😳😳😳
Sus-imal
I think my brain is hard-wired in decimal, because once you start using terminology for a different base, I have a stroke
Not hard-wired, just trained for very nearly your entire life. If you actually try to use a different base for a long enough time, you will find it natural. It is incredible how quickly your brain can gain intuition for something if you let it. Just a few weeks ago, I was struggling to remember to use my Caps Lock key for Escape (I recently changed it to do that), and then a few days ago, I found myself doing it automatically on a machine that didn't have that set up. Similarly, when I get into (left-to-right) seximal for a bit (which I do every once in a while), I get pretty good at not messing it up. Also, verbal anything is weird and hard. 43 makes a lot more sense than the spoken "thirsy-four", especially when he still calls 41 "ten".
@@MCLooyverse Why do you write numbers backwards?
@@angel-ig Because writing numbers left-to-right is more consistent with how we write everything else, and you get to add, subtract, and multiply from left-to-right, instead of having to teach kids to do it in reverse.
@Ángel I.G. What do you mean backwards? No one writes numbers from the right to left. Maybe the Japanese.
Or are you really telling me that Americans are taught to do this and this has been true for decades?
That's inhumane honestly
@@TheAlison1456 I wrote "43" (4 and 3 sixes) in left-to-right seximal, as opposed to the normal right-to-left way everyone does in English. That's the backwards number he was talking about. Also "41" (4 and six).
I used to use a modified base 19 for writing dates, since a year of 365 (or 366) days is only 4 (or 5) more than 19 squared, or 361. The digits are 0..9 a..i, with j for the extra days at the end of the year. And the fact that it's a really awkward prime just makes it more fun.
My favorite is Base 60, it easily beats decimal, dozenal and seximal in terms of fractions because it is divisible by all numbers 1 to 6. You can avoid having to use 60 digits by writing each digit as two decimal digits like on clocks.
Base 30 does the same thing.
Always been a huge fan of base 6, great video!
Btw have you ever considered how the numerical system affects the way time periods are perceived? In base six we wouldn't think in centuries or millennia, but the six-equivalents (whatever quirky name you want to call them). For example we would be in year 13203, we would consider year 10000 (1296) a big deal, and we would experience a millennium fear every 216 years.
Also the stages of human life would be perceived differently (or would they):
0-6 (infancy)
6-12 (pre-adolescence)
13-18 (~teens),
18-24 (~college years)
24-30 (young adulthood)
30-36 (100 years landmark)
Pretty neat!
Now we just have to hope my great grandma lives to 108 instead of the 106 she already has.
Three nif is another form of "centenarian" that makes sense in seximal.
@@meta04 I hope she does too! My best wishes
on the topic of finger counting, your solution for seximal finger counting isn't much better than that of dozenal.
hypothetically, if everyone in the world were to switch to seximal, and i were to hold up both my hands, one of them with one finger raised, and one of them with five fingers raised to communicate to someone who isn't within speaking distance, but you can still see each other clearly, how would a viewer know whether i meant eleven or fifsy-one?
unless there were some very specific decisions made on how one should interpret hand counting, there's no real way for someone to know, mainly because the viewer doesn't know relative to whom the signaler decided to show the numbers.
as well, would the entire system flip dependent on a language's reading direction?
on the surface level, that would seem to make sense, but if you were to have members of an exchange who spoke languages whose writing directions differ trying to communicate through finger counting, what would happen? obviously someone would have to switch reading direction. although, in my opinion, it would seem a bit unfair to force only one member of the exchange to change direction. same thing for a standardised direction, one group of language speakers would have to adapt to a new system while another would not.
all of these problems are avoided by the standard decimal finger counting system. the standard decimal finger counting system has no parity or directionality and is recognisable by both signalers and viewers regardless of their native language's reading direction.
the only real way to solve all of these issues for either dozenal or seximal, at least in my mind, is to create another distinct hand shape, because you yourself noted that values in decimal finger counting are distinct and those in dozenal aren't, which is more or less impossible, due to various counting standards throughout the world. for example, some groups start counting with their thumb as one, and others start counting with their index finger as one. these standards don't get in the way of decimal finger counting, because one must simply count the number of fingers raised. in both the dozenal and seximal systems, there is more complex meanings embedded in the system, which can easily cause ambiguity and confusion between members of an exchange due to differing finger counting standards.
Just a thought, but I learned a method of counting with one hand (based on decimal because of most common use) that goes to 20 on one hand that uses a combination of hand position and orientation (either towards or away from the intended recipient) to make them readily distinguishable even from a distance, then dropped back to using only the configurations for 0-9 with lateral movement from proximal to distal to indicate place, which worked just fine mirrored as well.
Obviously it'd need some adaptation, but it doesn't seem particularly difficult to implement something similar for other number bases.
Edited in a link to it here: th-cam.com/video/ic-_UW-_rnE/w-d-xo.html
finally, I have an inspiration
im gonna use seximal for my conlang :D thx for the idea and free info
The Sumerian counting system is great for when you need to tally large numbers. It requires slightly more paper, and is honestly the most useful when you're actually organizing physical objects. My modified version uses standard tallies, but when you have two tally groupings, you cross that out, and then go one line below and make the line with a triangle on top system for a ten, and then continue. The physical variation is really just you create a pile of five with the objects you're counting, and then when you get two piles of five, you create one pile and move it to the side. I created it to help me check the card count for MTG and Pokemon TCG decks, so basically by accident, it is also base 60. I developed the written version after what I think was a 39 clues browser game where you had to use the Sumerian counting system for something.
As a Metricman, I find it extremely uncomfortable counting time- one of the most fundamental elements of life -using a base-60/base-12 system. As much as I know it'd be inconvenient having one quarter of a day not being a whole number, I'd appreciate a metric time system where there's 100 seconds in a minute, 100 minutes in an hour, and 10 hours in a day.
The only problem this would create is with the names, because 10,000 (a metric hour) doesn’t have a name in the metric system, unless you want a “decakilo” second. You could still refer to them as metric hours, though.
@@derBrezelmann You could call it a deci-day
@@Anonymous-df8it fair
@@derBrezelmann It's worth mentioning though that the second fails (centi-milli-day)
Forget, hours, minutes and seconds, just have everything measured as decimal fractions of a day (eg. 0.1 days instead of a "metric hour")
The thing about binary and hexadecimal is that where they are used, at least at a level humans interpret, ratios don't matter. They are used cardinally. Oh and binary can be used to represent a string of Boolean statements and the hand counting thing is awesome and I have found it practical at times. The more I use those 10 bases, the more beautiful I find them and the more I hate base A.
Base C is better
*@[**12:41**]:*
Base-21, unvigesimal, is decent at fractions for an odd base as well... which is also mostly because it is a threeven base.
I absolutely love hexadecimal.
Base16 is awesome when writing big numbers. Also, 1024 rounding error makes justice.
Senary sounds like a WHOLE other word and made no sense to me so I agree with Seximal. :/
Binary, trinay, quartanary, quinary.. Just saying, seeing these senary Kind of does make sense
Tbh senary sounds like it should be for base 7
@@vsl5455
The ONLY one I have EVER heard *IN COMMON USE of that was Binary. Never the others you have mentioned.
*had to edit in because sleep deprived me is an idiot.
@@Mical2001 yeah.
@@cameoshadowness7757 He mentioned them in the video
I’m so sad that no one mentioned the better way to finger count! You can use your thumb as a representation of 5, so 1-4 are counted normally, 5 is just the thumb, and then 6-9 are the positions for 1-4 paired with the thumb. I was taught this method in elementary school and it’s so useful, because it allows you to could to 99, if you use your left hand as the tens digit.
chisanbop
Hi there! I really enjoyed both this video and it's first part. If you're interested in exploring other numeral systems, I would like to suggest that of Kizh, (formerly referred to as "Garbieleño Chumash") the language indigenous to where I am from. It is a quinary system, and I understand that such a prime-based system makes representing fractions more difficult, but there are very interesting other features in Kizh's numeral system, including "kavyaa’" which operates as "X almost twice", or "X + (X-1)" (ex: wachaa’ kavyaa’ is "four almost twice" or "4 + (4-1)", which is 7. In a quinary system, this would be written as "12", of course.) I would be happy to link you to the resources through which I learned of Kizh's numeral system, as well as a document I made exploring and explaining this system to those who are familiar with base 10. (I am by no means an expert in mathematics, numeral systems, or Kizh itself, but this explanation was part of my final project for a course I took titled "North American Indigenous Languages", instructed by Dr. Marriane Mithun, in the Linguistics department at UCSB.) Thank you for your time and labor, and I hope you have a great day!
Thank you HBM, very nifty!
ba dum ts
Base 64 is used often to incode things, and it has good origins by using every possible character on a keyboard.
Base 64 in TH-cam is: A-Z a-z 0-9 - _
and you can type many more letters on a keyboard: . , : ; + ? = \ / ( ) [ ] { } ! $ € § % &
and depending on language, you might also be able to type Á È Ǫ Ű Ī Đ Ə Ʒ
so you can reach much higher bases than just 64 with a keyboard.
I'm pretty sure almost every keyboard layout is capable of more than 64 characters
@@poudink5791 yes, but the point is that as a power of 2, its very easy to encode data in base64. you can perfectly fit any 3 bytes in 6 digits of base64
(2:40) Why create a completely new system when you still can use metric? You just need new prefixes.
so deca-, hecto-, kilo-, which are 10¹×, 10²×, 10³×, would instead be: 6¹×, 6²×, 6³×
the same with deci-, centi-, mili-, currently being 10⁻¹×, 10⁻²×, 10⁻³×, would be 6⁻¹×, 6⁻²×, 6⁻³×
new names and letters can be used, to avoid any confusion.
Using the prefixes from Conlang Critic; nifti- is 6⁻²×, so a niftimeter (nm) is 0.01₆ meters. unti- is 6⁻⁴×, so an untimeter (um) is 0.0001₆ meters. biti- is 6⁻⁸×, so a bitimeter (bm) is 0.00000001₆ meters. feta- is 6²×, so a fetameter (Fm) is 100₆ meters. grand- is 6⁴×, so a grandmeter (Gm) is 10000₆ meters. - Additional prefixes would still be needed, as you do have GW (gigawatt), GB (gigabyte). But this is a good start. So in computing, you have byte (B), fetabyte (FB), grandbyte (GB) ≈ 1.30 KB or 1.27 KiB, so you need larger prefixes.
A wrinkle is that the kilogram is the standard SI unit of mass, so do we have niftikilograms, niftigrams, or both? If both that's an imperial pain.
@@diribigal Kilogram should rather be renamed to gram if we switch base; so if the kilo- prefix isn't used, just dropping it altogether works. Another option is to make up a new name and define it the same as 1 kg.
alright, if you want to get silly with it, base -1.5 is pretty fun to play around with, i spent a half hour or so trying to do working out to figure out the pattern for counting, along with how you have to do the basic four math operators
I love the new, nonsensical vocabulary I'm learning from these videos that I can also safely say I'll never use in my life, but wish I would ❤❤