Expanding the Roman Numerals

I like numbers! Do you...? Gee, tough crowd.

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Graff - Rain Eater

[kephrekhtheunbroken]

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.

[IONATVS]

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 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).

[psimaster]

This felt like a downward spiral and I love it

[stephenweigel]

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.

[tripleoof]

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

[Xcyiterr]

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 <3

[felipevasconcelos]

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

[cheeseburgermonkey]

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!

[KarlsGB]

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

[slushiiwoman]

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! <3

[amojc]

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.

[vii-ka]

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?

[EdOne]

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

[Moralsiz]

Your videos are always interesting and entertaining

[-Lexi_Bexi-]

In fact very practible. I started it as a joke, taking a whole notebook and saying I'll "go to infinity with roman numerals". I've been writing in my boredom at school in it for 6 years already. I could reach 1 million even if I'm only at 14623 and filled 106 pages made 564 Collums (I arranged the numbers vertically in Collums each of 26 rows.)

Thanks for giving me a few more quattrovingentdecillion eternities to work on my neverending progress.. (filled up 1.5 thick notebooks btw)

[stardy]

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

[cjrmmacpherson]

bro invented tetration using roman numerals

[soapycanthandle]

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.

[WilliamWizer]

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.

[the_vine_queen]

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.