Every Weird Number System Explained

[@ThoughtThrill365]

We have a great topic lined up for our next video! Let me know if there's a topic you'd like me to cover next. 😊

[@mentalist0808]

how am i the first person to see this video wtf

[@indartaaji8651]

You forget dozenal (base 12)

[@Thirtyninefan]

@@indartaaji8651 and ternary (base 3)

[@AB-Prince]

if you assume that the pattern must be consistent; that IV is 4, XL is 40 and CD, is 400. seeinng as there's no symbol past M it must stop at 3999 however in practice there were two solutions in common use, allow for more Ms, or do V, X, L, C, D, M again but with a bar above them. and although not seen, you could absoluely keep reusing the sybmols with more bars over them. I remember seeing a video going ove obsurdly large numbers in roman numerals, where after 3 bars, you write a roman numeral on it's side above the ordinary numerals, and continue to count up from there as a sort of pseudo exponent.

[@ktgeofficial]

That is the most common extension of roman numerals today! It's called vinculum, and the video where they extend vinculum to it's absolute limits is "Expanding the Roman Numerals" by sys128.

[@Tile10Oc]

_ IV

[@Yehor-v7y]

​@@Tile10Oc ĪV̄

[@Yehor-v7y]

​@@Tile10OcI͞V͞

[@ondrejkrech9892]

Lukewarm take: base golden ration is the only system from this video I would consider "weird"

[@DAngelo-cy4xo]

Yeah, roman numerals is juat complex, not weird

[@mummyhugo]

@@DAngelo-cy4xobinary too

[@bitonic589]

​@@DAngelo-cy4xoroman numerals are literally not even a proper base-N system so they shouldn't even belong here

[@cubefromblender]

​​@@mummyhugobinary is the most simple base Not necessarily best (although it is imo), but the most simple one

[@cinnamoncat8950]

​@@bitonic589the video is titled with number systems not based

[@pollywatson8099]

> claims to explain 'every weird number system' > doesn't even mention balanced ternary, my beloved

[@huzzah_2763]

How does it work tho

[@pollywatson8099]

@huzzah_2763 it's base 3, but instead of 0, 1, 2 the digits are -1, 0, 1. place value is still based on powers of 3 but now it includes subtraction. for example 2[base ten] in balanced ternary would be represented as 1(-1), ie 1*3^1+(-1)*3^0 (or 3-1). its wildly impractical for almost every purpose and I love it So Much. it is great for old-school balancing scales though.

[@LaugeHeiberg]

​@@pollywatson8099I have no idea what that means keep it up 👏👏👏

[@Wither_AnimationsTCO]

​@pollywatson8099 I re-invented it not knowing it already existed 😭

[@pollywatson8099]

@Wither_AnimationsTCO congratulations on being the coolest person on the planet (I'm not joking or being sarcastic btw) (I genuinely think that's awesome)

[@ktgeofficial]

Base-10 is too inefficient.

[@tbird2013]

Just get over it bro

[@JR13751]

Base(10) or base(-10)?

[@dankboi42069]

Bro imagine trying to do any field of maths without base 10 your brain will hit the rope bro l. Istg if i did calculus with base 6 numbers i think i would want to jump in a volcano

[@chrisuko7928]

Base 12 is better

[@ktgeofficial]

@@chrisuko7928 True

[@themsdosnerd]

My favorite Number system is Zero-indexed Big-Endian Balanced-ternary or Zibebt for short. It has many advantages over decimal: - It has just 3 digits and no minus sign. - It has no weird exceptions such as the digit 3 being larger than the digit 4 for negative numbers. - When adding numbers, you can just add. You don't have to negate and subtract if a number happens to be negative. - When adding numbers, you can just write left to right, rather than having to add digits right to left. - When adding digits, the chance you'll get a carry, is halved compared to decimal. - In zibebt, the carry is a zibebt digit, while in decimal, it is a binary digit. - Subtraction can simply be done by adding with the negative. - When multiplying single digits, the result is a single digit. - When multiplying single digits, the result can be negative. This can cancel out positive numbers, making multiplication faster. - The fast algorithm to check whether A is divisible by B that is used in binary, also works in zibebt, and is even faster there. (It doesn't work in other bases) - Being zero-indexed, a number with zero characters always means zero, while in decimal it could mean 1 (For example "PS" means "PS1" in the sentence "I bought the PS weeks before the PS2 came out.") - Being zero-indexed, modulo calculations are easier. - Having a negative digit allows you to express that something belongs to a group but is not finished yet. This avoids the annoying "version 3.0 alpha" that decimal has. - The result of comparing two numbers is a single digit: . Computers using zibebt rather than binary would therefore be able to traverse binary trees faster. - Zibebt computers would also have faster data transfers since a wire can have a negative, a zero or a positive current. (some old Soviet computers used this) - Zibebt allows you to count from decimal -121 to decimal 121 on just 1 hand. - On 2 hands you can count from decimal -29524 to 29524. You'll never be short of fingers. - Being big endian, the first digit is always the units digit. This means that if you write numbers below each other, you can left align them. - When reading a number, you read zibebt left to right to count the digits, and than right to left a few significant digits. In decimal, you need to read from left to right to count the digits, jump back to the beginning, read a few significant digits and jump to the end. - Rounding a number can simply be done by removing the last digits (or setting them to zero)

[@Koko-knot]

cool

[@squishy024]

cool

[@cinnamoncat8950]

cool (genuinely)

[@GameDesignerJDG]

I'm surprised you didn't go into base 12, base -2, or the French number system (base 60)

[@FebruaryHas30Days]

Remember that base 12 is LIKE HEXADECIMAL, but without C, D, E and F.

[@SigmaGamerProzst]

this is like the 5 postulates, the first 4 makes sense and are easy to grasp. The last one is total chaos

[@juniotongol2392]

1th 2th 3th 1:26

[@Yellow434]

I see that too

[@DrAmanpreetSingh-tt7ef]

I also saw that That's actually hilarious

[@Kguy-r6e]

Doman numerals I, II, III, IIII, IV, V, VI, VII, VIII, VIIII, IX, X

[@HhgreggMerge]

YOU HAVE MY PROFILE PICTURE❤❤❤

[@ZG900alt]

It's just the colour wheel it's just a small coincidence and I don't think anyone will give a frock

[@sugurcat]

nice❤❤❤

[@kaiserwhence2468]

3:34 why can't we represent 4000 as MMMM? Why is 3999 the largest possible?

[@idonothavealife]

according to new rules we can only use 3 of the same digits in a row and 4 in the entire number (except for D, L and V, which have a limit of 1) with old rules, the largest number possible is 4999, as MMMMDCCCCLXXXXVIIII this is not including extensions

[@ThoughtThrill365]

3999 is the largest possible with the Standard Form of Roman numerals. Since 1,000 is the largest number that a single ordinary numeral "M" can represent, for large numbers such a system rapidly becomes unwieldy. There are, however, notational extensions to provide for addressing such numbers. Most notably, a vinculum, overline bar, is used to multiply by one thousand. So IV with vinculum is 4,000. The largest Roman number we have a visual inscription for is 2,100,000.

[@kaiserwhence2468]

Thanks all!

[@DarrenDeSilva-j2y]

MMMCMXCIXI =4000 ?

[@skanderbeg152]

​@DarrenDeSilva-j2y you can't just add another I onto the end, thats not how roman numerals work. Like the video says, you have to separate every place first, then represent each digit with the numerals. The I you tack on the end does not represent any part of the number. In 3999, you need to represent the '3', then each '9' separately. In other words, numbers are not represented by roman numerals as a whole, they are separated into their own digits and represented individually, so you can't just add more numerals to the end of it to make it larger.

[@GiyeokFan1997]

N = 5,000 P = 10,000 S = 20,000 T = 50,000 W = 100,000 Z = 200,000 Y = 500,000 A = 1,000,000

[@GiyeokFan1997]

Example: NI Means 5001

[@GiyeokFan1997]

Example: TSPN: 50,000 + 20,000 + 10,000 + 5,000 85,000

[@Yehor-v7y]

4:25 as a fan of computer science, i can indeed confirm i am familiar with base 2 / binary

[@FebruaryHas30Days]

Converting binary, quaternary and hexadecimal shouldn't be that hard. Try it: - 0b1100011001010 to hexadecimal - 0q310212 to binary - 0x69EFA to quaternary - 0q102131322 to hexadecimal - 0b110111110011 to quaternary - 0xA23C to binary

[@toby6180]

Corrections: At 8:23, 9:14, and 9:30, "1 0" and "1 1" should be referred to as one-zero and one-one, not "ten" and "eleven", since they do not represent ten and eleven times either one or phi. Similarly, at 8:07, it should say one-zero (base 2) = two (base ten) At 9:04, + 1 was dropped from the right-hand side of the equation, but magically appeared in the next step as the leading 1 in 1.11. (The latter being correct). At 7:55, you probably meant to write 16 instead of 6, since the rest of it refers to the previous discussion. 6 is, of course, also valid as a number base. The base of a number system refers to the powers in the various positions, and it is secondary that the same number is the number of digits needed.

[@BOT_CORP]

3:02 Well yeah, size 49 shoes would count as being very big, so yeah

[@Jj82op]

There is also the base 20 system made by the Mayans. Numbers are represented by dots and dashes from 0 to 19 and add up in orders of base 20. They combine the symbols vertically, bottom to top.

[@lubomirkubasdQw4w9WgXcQ]

1:45 oh so that's why they're called digits

[@belchgod]

decimal, binary and hexadecimal aren't weird, and neither is roman numerals. Also base phi is just... a different base.

[@hamedajab2483]

8:53 the first line of the algebriac manipulation should be a/a + b/a = a /b. The first term on the left-hand side should be a/a not a/b.

[@HaramGuys]

This should be called numerical system. Number system should be used to refer to sets and their algebraic structure, like integers, reals, complex, p-adics

[@merlon8599]

8:52 I think there is an error in the algebra. In the video is: phi = a/b + b/a = a/b But correct would be: phi = a/a + b/a = a/b

[@alesiggy2711]

Nothing: Me using base-9,223,372,036,854,775,807: -----

[@demoknightmain22]

64 bit integer limit?

[@demoknightmain22]

But negative?

[@marcelob.5300]

Excellent, thanks very much!

[@alesiggy2711]

Me with base-16: 1234567890ABCDEF Base-10: "Nobody likes you. Womp womp."

[@JR13751]

Negative bases, balanced bases, NAF binary?

[@gigadog2247]

I lost at golden ratio 😫😫😫

[@Dan1shPro_X2025]

3:37 4000 is literally just M(V+)

[@RICHROBLOX-r6z]

Gyro, Gyro, Gyro Zeppeli.

[@Thirtyninefan]

3:34 bro add and underscore to the IV and you get 4000

[@SeriousApache]

Roman Empire fell because the number system was too inefficient.

[@wkromhout8532]

So, this video had you thinking about the fall of the Roman Empire?

[@AutisticAnn]

Where’s P-Adic?

[@leafofkael5924]

I loved this video I hope it gets the attention it deserves

[@Bolpat]

3:25 What!? Even the Romans used IL and IC (=99) and even more wild notations such as XIIX for 18.

[@jaykay8426]

I heard of base-60 numbers

[@doreenellul]

In roman numerals there were also fractions A dot represented 1/12 2 dots represented 2/12 And so on And then 6/12 was 'S'

[@JacePlaysRoblox274]

So XS is just 10½

[@ceilebear]

1:45 Why are the hands backwards 😭

[@crabobserver]

8:52 i dont understand the third step

[@pudgesnextturnaround3112]

Me: (learning about the golden ratio) My brain: (perplex zendaya meme) My other classmates: (wat)

[@AutisticAnn]

I thought 49 in Roman numerals would be IL

[@eberhardt9602]

Technically, shouldn't we rather say "The binary number fourteen is the decimal number fourteen" while showing onscreen 1110base2 and 14base10 ? Saying one-one-one-zero is very pictographic, yes, but you wouldn't say the base10 number 14 as "one-four", would you? 🤔

[@Vers1.0]

Sometimes you gotta wonder what internet rabbit holes this guy has to go on when he's bored or needs cash.

[@marcelob.5300]

I don't know if this suggestion would be useful or doable or if you have already done it as topic for a video but, for example, misconceptions or common mistakes, example: confusing the root function with the roots of a positive number.

[@infostutorialsbyannie7008]

the largest number in roman numerals is infinity 5000 is v with a dash on the top

[@MichaelDarrow-tr1mn]

so what's 10¹⁰⁰ written as? X with 33 bars on top? Or are multiple bars abbreviated as a sideways Roman numeral?

[@beauwilliamson3628]

@MichaelDarrow-tr1mn like, X with horns (sideways C on top). That would look pretty cool actually.

[@Quartz512_]

Base 2, my beloved

[@Porto5452]

You should have at least talked about an additional integer base like senary or dozenal as that is way more important than base phi. Also phi isn't the only irrational number where every integer can be represented with finitely many digits. In every metalic ratio base you can always represent every digit with finitely many digits and these are not even all the bases. The cubic counterparts of the metalic ratios like the plastic ratio and supergolden ratio. There are also quartic, quintic, sextic... counterparts, so no reason to highlight golden ratio, this is more of a property of Pisot numbers which are the algebraic numbers that converge to integers in an exponential rate.

[@jevilscythe]

Jaiden should totally play hollow knight

[@RoyFrancisco-b9e]

Now i understand why high school students cry at math

[@Administration-w6m]

Since 4000 is MMMM or ? Its a line on a IV

[@jakeg3126]

3 is only one that makes sense and is why the metric system is screwed up. A circle is 360 degrees, that is divisible by 3. Time is divisible by 3, if distance/speed is not divisible by 3 you can’t do simple mental math to convert distances or anything. Non metric everything is 3. Even things like acres are measured in square feet. How do you make a metric acre?

[@Quartz512_]

"Non-metric everything is 3" Except the number system we use. Base 2 is plain better than base 3. If you want something along the lines of an acre in metric, you can use hectares. Metric is standard, and so is base 10.

[@jakeg3126]

@@Quartz512_ True, although as a PITA, I have to say they do go to 12 until the numbers get repetitive. twelve then everything with teens. I know its that way in German too. I'm not sure about the Romance lanuages.

[@mrhangertv1829]

How about base -10

[@Microwame]

Syntax error

[@PlanisGR]

You didn't mention the greek numeral system...

[@Explanatorius]

Everything in this world is 0 or 1, true or false, correct or wrong, good or bad... computers is a good representation of that.

[@andrewharris4268]

They’re not weird. They’re just number systems.

[@captainpolar2343]

i refuse to believe that IL is not canon

[@beauwilliamson3628]

historical examples show people using Roman numerals in messy, but easy to understand, ways. but like today, there were prescriptive types who insisted on **proper** rules. also, a lot of the extensions that today are dismissed as **later** developments happened in the first few centuries CE, which seems pretty historical to me. So I say, have fun with your IL, people who want to pretend they don't understand can lump it

[@fredbearnf6818]

Golden ratio metioned jjba reference?

[@sapiate971]

3:19 Ma molto più semplicemente 49 si scrive IL!

[@thedeveloloper]

Didn't even hit duodecimal, Babylonian, or base 64.

[@SomeBritishBanana]

my guy forgot tally marks 😭😭😭🙏🙏🙏

[@bitonic589]

That's base-5 😂

[@Potatoinatree]

Base 64>>>>>>

[@Quartz512_]

Give me 64 symbols which are easily distinguishable and simple to remember and write

[@Potatoinatree]

@ bruh i was making a joke about minecraft 😭😭😭

[@bitonic589]

​@@Quartz512_ Dude base64 is literally the most significant number system in all of technology Without base64 you literally would not be watching this video, sending messages, or using technology at all. It is abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789+/

[@Simonthesprunki273]

2024: MMXXIV 2025: MMXXV

[@Hjahaiainai]

Digital Genius covered this once

[@swayambhoir9740]

Well π is just 10 in π base system

[@iamapersonnamedme]

Positive integers* /j

[@lucas.-en8dx]

-2

[@totally_not_theo]

2:17 so Roman numerals are basically base 7?

[@azraet2331]

An explanation is in order.

[@Yehor-v7y]

​@@azraet2331waiting

[@Yehor-v7y]

NO because roman numerals are a sign-value system while base 7 is a place-value system

[@alibowman862]

2=phi

[@MyMohanta]

Phi is a much more complicated topic

[@patrickgambill9326]

Surreal Numbers?

[@thecoolestanimator]

Lost me at base phi

[@Arisilva0213]

Base 300

[@unknown0607]

binary is "thrill" at thumbnail

[@JohnnyOttosson85]

Ehm... Tatvic system?

[@noahwaaga5079]

IEEE 754

[@bitonic589]

That's just a way to represent other number systems

[@alisu-x6630]

not arabian mathematician ,iranian mathematician

[@CuppzGeo]

WRONG.

[@MyMohanta]

Lol

[@foo0815]

*Every* number system is base 10

[@kingpeanut7273]

What?

[@foo0815]

@kingpeanut7273 When you write the base in the number system itself.

[@this_commenter_had_a_stroke]

​@kingpeanut7273 This is a joke on how if you were to represent the base in any system, you'd get the number representation "10" ("one zero") for example, in binary 2 would be represented as (2^1)*1+(2^0)*0, which is written as "10"

[@Bonnie_2.0]

⁠​⁠@kingpeanut7273base 2 is considered base 10 in binary, because 2 is represented by 10. This the case for pretty much all number systems

[@A_literal_cube]

@kingpeanut7273I see that you don't understand.

[@нет-в1ш]

not your idea

[@Hnxzxvr]

Well did you think of it

[@нет-в1ш]

@Hnxzxvr nah, another youtuber

[@Hnxzxvr]

@@нет-в1ш who

[@нет-в1ш]

@@Hnxzxvr idk, dont wanna try to find him