Expanding the Roman Numerals 

Fun fact: sometimes, the romans just added 4 together, so stuff like 14 was written as XIIII instead of XIV, but not always. If you bend this a little you could go slightly higher.

This felt like a downward spiral and I love it

While it is normal nowadays to hear “you can only string a max of 3 Ms, Cs, Xs, or Is together” when discussing Roman Numerals, this is a modern *convention* that exists purely to give each number a “canonical” form like Hindu-Arabic numerals do. When they were actually used regularly in daily life, no such convention existed, IIII and IV were just as valid ways to “spell” the number 4, and IM was just as valid as CMXCIX, the current “standard” way to spell 999 in Roman Numerals. Thus, even sticking purely to the seven universally accepted characters, you can *technically* write any positive whole number, no matter how large, by simply using Ms as tally marks. It’s a brute-force method, but would be allowed. Of course, real people needed to use Roman numerals for real things back in the day, and even back then they had strategies to extend the numbers in a more…useable way for larger whole numbers and simple fractions. The most common being adding S for 1/2 and • for 1/12 fractions (which covers the most common fractions people use in daily life, though 1/5 and 1/7 still had to use another strategy, usually stating the fraction as a ratio) and the two different strategies for extending the system upwards to easier to write multiple thousands (and no, you’re not the first person to come up with using multiple lines to extend it to millions and billions, just by the time regular people were working with numbers above a few million, Hindu-Arabic numerals had firmly replaced Roman ones in most fields, so it was a nonissue. And fields that had used those kinds of numbers for a long time (government accounting, grain shipments, and military inventories being the main ones), they just worked in accounting units that were large in-and-of-themselves to avoid using such large numbers (eg “V Legions of MMMMMM men each” instead of “30000 men” or “M pounds of sterling silver” instead of “240,000 pence,” where pence were a currency seen in daily life, but pounds sterling, while eventually being debased to the point the modern British Pound is comparable to a dollar, was originally worth exactly what it says on the tin, a pound of silver, which would be over $300 today, and basically only existed in noble account books as a way to deal with large numbers).

I absolutely love your videos, it's always so interesting! From Vibri to anything math. Keep it up!

I am absolutely smitten with both the adorably unique animation style and the sheer aura of smugness that this video emanates instant sub love the glace

8:57 That looks nothing like fractions. In Roman numerals, fractions are represented much like integers, with their own symbols, though only additively without the 3-symbol limit. The symbol for a twelfth is · (a dot) and for half its S. These are the main ones, but there’s also Σ or Є for half a twelfth, and a few obscure ones that don’t even show up on my device. I don’t think most Romans were very concerned with small or precise fractions, as the other fractions appear to be only used by apothecaries. Edit: timestamp

The art you've created is super cute and cool, also this was a really good video for a first impression on me. You've gained another subscriber!

Your videos are always interesting and entertaining

sick video, and criminally underrated channel!

Yo? Okay, I'm going to be completely real with you here, I am probably the biggest nerd when it comes to large numbers, even if I don't really delve to much into the true abyss of large numbers. And, this idea is just, simply beautiful. I love every single bit about it. If we could, d'you mind if we could have a chat, and maybe extend this entire system? I already know of a couple ways this system could be made even better, and to- Well, make it easier to write out. If we could, my robotic heart would be more than happy. Anyways, lovely video my dude, I hope to see more!

that intro is god damn awesome, and the rest of the video was very good too

This is honestly a really cool concept! It's reminiscent of the exponent system in Arabic numerals, but it actually takes us further since each line is one thousand instead of just ten. Anyways, I really like this, and I am tempted to turn in actual homework using entirely extended roman numerals.

The Romans actually came up with a system for fraction and it did not look like arabic numeral fractions but instead s for 1/2 or 6/12 and a dot was 1/12

This is amazing. Roman numerals are so impractical, but I kinda of loved the chaotic nature of them, but this just takes it to a new level. Great video, I'd love to even extend it further, which should be easily possible.

Looks pretty nice.

I actually like this system, Thanks mate!

I had an idea similar to this. Start with X, X line, X line line, X line line line, then what's next? X. LINE. >. that's right, we're going meta. 😎 you can take that sideways number and put more sideways numbers on top of that, until you've gone all the way around the circle 360°, and eventually you get this crazy quadruple-X throwing star lookin' thing.

I absolutely love this concept~

Another application of Roman numerals is labeling chords in western music theory! Capital letters are major, while lower case are minor, and each chord has functional significance.

Underrated channel

This video is very well made

This is so weird and i love it

bruh this is the best crossover in history

"yea i'm going there" i love that you know that you are insane and need help. this is my favorite video

I like how he says that he can't stack 50 lines on top of each other because vertical space and then he proceeds to stack 50 fractions on top of each other

amazing video, subscribed

Very good idea I really approve and appreciate it!

You are going to become big one day, I just know it

The recursive stacking of number bar number bar number etc brings up the same problem mentioned earlier in the video: lack of vertical space. Is there some way to solve this, too?

What a beautiful video!

This system you are hinting at was actually in use : what motivated the use of roman numerals was the use of the abacus. Slices of three digits were covered with vertical numerals.

Interesting idea, I also have the same thought as you while I’m looking for number that exceed 4e+06 (4 million) in Roman numerals. Since we are writing bunch of bars, I’ll shorten down the bars count into exponential places, such as: V^2 = V with 2 bars = 5 million X^3 = X with 3 bars = 10 billion And so on

This is absurd and I love it

Im so glad i was on youtube in 2:48 am. on the 25.05.2023 ,Thursday Amidiatly subbed

im loving this

Great video!

A googol is equal to: Scientific: 1.00e100 Engineering: 10.00e99 Letters: 10.00ag Standard: 10.00 DTg Emoji: 10.00😠🌈 Mixed scientific: 1.00e100 Mixed engineering: 10.00e99 Logarithm: e100.00 Mixed Logarithm (Sci): e100.00 Brackets: e]]{.]) Infinity: 0.3244∞ Roman: ⅠⅩ∷↑ⅩⅤ· Dots: ⠨⣿⠚⠹⣲⡎ Zalgo: 1̶̍.̚̚5̶͓ Hex: FD11C3A9 Imperial: 19 small minims Clock: 🕕🕖🕓 Prime: (2⁴×5⁴)^(5²) Bar:  Shi: 侍施逝 Blobs:  Blind: ALL: 1̶̍.̚̚5̶͓ Community notations: Greek Letters: 10.00 Ι Omega: ω[25](β₂₆₅) Omega (Short): ω[25](β₂₆₅) Precise Prime: (2×31×3114028594973)⁷ Japanese: 1.00×10の100乗 Tritetrated: 3.8305↑↑3 Flags: 10.00🇧🇸 YesNo: YES Evil: 1.00e100 Emojier: 1.0🎃e💯🎄🎃 Chinese: 一點〇〇〇万极极 Elemental: 3.55 × 48 H Binary: 1.01e101001100 Hexadecimal: 1.25e53 Haha Funny: 242755 Nice: 54.38 Long scale: 10000,00 SxDc Infix engineering: 10₉₉0 Reverse infix engineering: ₁₀99₀ Infix short scale: ₁₀DTg₀ Infix long scale: ₁₀.₀₀₀SxDc₀ English: ten duotrigintillion Fours: 4^(4!÷4+4×4×(4!÷4+4)) Blobs (Text): :bigblobsleep-154: Blobs (Short Text): :blobsleep-1685:

I like how we can understand even tho even tho it’s some lines

Excellent.

Amazing

heyyyy this is pretty goood

i like your white lines on grey background style! it reminds me of Vib-Ribbon

8:57 "YoU lOoNeY! tHaT iS wHaT a FrAcTiOn LoOkS lIkE!"

At the point 6:22, the 2 lines or the *1000000, can be also represented as the letter but it has a line on top and 2 vertical lines at sides, like a draw of a house without the roof. Anyways really interesting

HERNN is an awesome acronym, I'm considering using it for that alone

I LOVE NUMBERS!!! (cute art too :3)

Amazing video

I coincidentally invented the same system not too long ago. I did however extend it further Having 2 lines with a numeral above it signifies that there is a "numeral-line-numeral" stack that many numerals high. this can be done with 3 lines where it is a stack of "numeral - 2 lines - numeral" and so on and then you get to having too many lines again

Roman numeral power towers, awesome!

Nice!

Might I suggest changing things slightly, by making the upper numerals be on a separate plain attached with an underline to an overline. That way, and stacking of numerals can be moved to horizontal space or vertical space

i like how it ends up mapping into decimal because its based on thousands, neat

You could represent the amount of numbers in the tower with another roman numeral like you did with the lines, that would give you an equivalent of exponentiation for roman numerals. Then comes tetration, which is the same thing for towers of powers.

On the topic of numbers in different languages: I’m currently studying Japanese, and while more common to just use the Arabic numeral symbols, there is a set of symbols corresponding to numbers in Japanese. 一 = 1 ニ = 2 三 = 3 四 = 4 五 = 5 六 = 6 七 = 7 八 = 8 九 = 9 十 = 10 百 = 100 千 = 1,000 一万 = 10,000 Now, 一万 is interesting because it has the 一 (1) symbol in it; that’s because the 万 symbol is odd as it doesn’t _really_ represent 10,000, but rather more of a vague idea of multiplying something by 10,000. In order to get numbers outside these, you just arrange the symbols of the digits next to the appropriate power of 10. So… 五千百二 = 5,102 四百七十一 = 471 九千一 = 9,001 Very interesting to see how other cultures’ number systems work. Some are quite similar to what’s most common while others are quite disconnected.

this is very similar to certain versions of myriad notation in Greek numerals.

That feels like base 1000positional system with extra steps

he inveted roman numeral powers

OBJECTION!!! that tower at the end has the same problem as having multiple lines. it requires you to write vertically. best way could be to use conway chained arrow notation. or some sort of variation. that allows you to reach numbers so big you can't call them big.

How about adding a line below (let's agree to not add lines above and below simultaneously, shall we?) to represent division by 1000? Another oddball effect is with the small numbers above the line, you have an instant rudimentary path to log base 10, except for the large roman numeral beneath the lines.

I extended it to my version expanded hyper extended Roman numeral notation, (E.H.E.R.N.N). Note: not to be confused with extended Roman numeral notation. Basically instead of writing a large stack of Roman expansion, you can put 2 lines on top of each other and put the Roman numeral on top, that Roman numeral shows how many layers there are. If you want it more precise then put a comma in front of that and write the Roman numeral on the layers. Then the Roman numeral on the bottom can be put in parentheses to indicate that it is a regular Roman numeral that is not in extended Roman numeral notation. For example, X|X|X|X|C can be written as IV,X||C). And don’t ask me why it is horizontal

There was proto writing, like the hieroglyphs and other ancient scripts, long ago.

great video

If I remember correctly, there was a QI episode which showed that several units of (I)(I)(I)(I)(I)... chained together and written on a gravestone represented several million victims of a war.

since a bar on top means x1000 and a bar is just a sideways I; you can put a sideways V to signify x5000 (or any numeral to signify it times 1000 times the entire number) and since that bar on top is a numeral in of itself you can add a bar to itself, or more precisely to its right (or left depending on which way the V points towards) and have _it_ be multiplied by a factor of a thousand and since that is a numeral in of itself you can repeat this cycle again, and have an ever growing spiral of multiplication

if extended further could make a decent googological notation

interesting to say the least, very interesting, very very

as with all math beyond what they teach you in algebra 2, i can feel the insanity begin to come forth as the explanation continues

You are the best content creator i've ever seen! Your editing skill is awesome and i love the quality of your videos, you will have a lot of subscribers in a short time and you have potential! also, your character is cute

expanding more roman numerals please

11:11 one hundred and sixty four 31414-illion

i appreciate the effort you went through to visualize this nonsense

we have successfully avoided the year 4K bug, as well as the 4M, 4B, and so on

How to create the worlds biggest roman number in HERNN In Psudocode: While(true): print(X) print(--) run until it's big enough

I thought of my own similar expansion for Roman numerals when typing them. What I do is put any Roman numeral from 1 to 3,999 between parentheses. For example, (CXXV)=125,000. For larger numbers, I would simply put a Roman numeral in between two opening parentheses and again in between two closing parentheses. For example, (IX(M)IX)=one nonillion.

neat

11:15 3.1415 are the digits of piπ 31415927 (the 5 would be 6 though because of averaging)

I think we can use - like we you , for numbers for example 10,001 can be X-I but we might need a letter for 0 but it can be either O, N, Z or just a space

Near the end, you rediscovered "hereditary base notation" for base 1000. Hereditary base-n notation is where you write a number m = a_k*n^k + a_{k-1}*n^(k-1) + ... + a_0*n^0 (just like you normally would in base-n), remove the 0 coefficients, and repeat the same process on the exponents, recursively, until all exponents become 0. In your case, the Roman numeral under each bar is a value of a_k, and the exponent k is above the bar. In fact, hereditary base-n notation is related to Goodstein sequences, which are mathematical sequences whose length grows *way* faster than exponential, even faster than tetrational or other hyper-operators. In fact, Goodstein sequences grow so fast that the "standard" axioms of arithmetic can't prove that the process to generate them always works; you need stronger axioms. en.wikipedia.org/wiki/Goodstein%27s_theorem#Hereditary_base-n_notation

It looks like Newton's notation for calculus, quite often used in Physics to denote time derivatives but not often larger than 2.

i'm watching this in MMXXIV and i extended this

Tetration in Roman numerals. How practical.

You just unlocked... The Scientific Notation!!!

Moly holy...

Exponential Towers... hmm. You could very much well expand this further making something similar to Knuth's up-arrow notation.

In Roblox slap battles : combat there’s Roman numerals for certain gloves such as reaper (combat) and reaper: pure darkness such as rpd going to 665 (DCLXV) and then 666 is just run in a bunch of different fonts and then reaper (combat) upto 16,666 but 6666 says “how did i reach this far?” Allowing you to walk on water.

nice

8:57 You looney! That’s what a fraction looks like! *makes the numeral on top on the line smaller*

6:15 I already knew what was gonna happen

if we're using the same ? over base over and over we could represent it as ? line, line base number. but after this rule runs into the same problem as before. I say we just introduce conway chains if you wanna go even higher.

Honestly, might be useful for having large numbers that are precise, without taking up too much space

This video already has XVI thousand views? Not enough, deserves more.

Just saying, numerals beyond M probably had existed, since units over 1,000 were used somewhat regularly in Roman society, for example military divisions. It's just likely that the common man wouldn't need such high numerals regularly, given that modern uses of big numbers either didn't exist back then, or existed but only a small fraction of Romans would need them, so they were never standardized, hence why there aren't any in the "modern" Roman system, since they're based on whatever got standardized. Also, IX is more common than IV (IV often got represented as IIII), so if we take that into consideration even vanilla Roman numerals can reach a little higher (MMMMCMXCIX, 4,999) without breaking the system. But, with this hyperextended variant, M is only ever needed to be subtracted from or to end a number anyway, so not a huge deal.

I was expecting that after stacking a bunch of horizontal lines, you would interpret the lines as the letter I rotated by 90 degrees, so I was thinking you'd be ending up having one roman numeral rotated by 90 degrees on top of another, and then if you repeat this process, you end up with some kind of spiral xD

If there is a number "n" above the number "a", then the formula is a•10³ⁿ. Easy.

8:58 “THAT'S WHAT A FRACTION LOOKS LIKE”

8:58 U Suni!Thats what a fraction looks like

IV was historically written as IIII

Fun Fact: There's An Extension Of Vinculum That Uses Two Vertical Lines And An Overline (Or Just A Box), Which Multiplies A Number By One Hundred Thousand. There's Also A Way To Write Fractions In Roman Numerals. A Dot Is 1/12, Two Dots Are 2/12, Three Dots Are 3/12, Etc. S Was Used To Symbolize 6/12, Or 1/2. Then It Continues. S And One Dot Is 7/12, S And Two Dots Are. 8/12, And Finally 12/12, Or 1/1 Is I, Because 12/12 Is Equal To 1. So You Could Theoretically Add S⁙ To The End If The Whole Equation To Make It Even Bigger!

NUMBER DOUBLE LINE NUMBER

If we were to just put numbers on top of another and needed to distinguish it from fractions, would putting two lines or even just ditching the line altogether be more efficient or easier to do?