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How Did Anyone Do Math in Roman Numerals?

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Re: How Did Anyone Do Math in Roman Numerals?

#11

Post by jaymzcampbell »

WalterBright wrote: post #6

It's interesting how the notation used can encourage or retard progress. For example, Leibniz's calculus notation was vastly superior to Newton's, and calculus theory advanced much more quickly where Leibniz's notation was used. https://en.wikipedia.org/wiki/Leibniz%27s_notation

Another excellent example of the power of good notation to aid understanding and increase efficiency is Dirac, or Bra-Ket notation[1] used in Quantum Mechanics.

This allows you to do all sort of calculations with wave functions without constantly grinding to a halt bogged down by integrals and conjugates all over the place.

The ladder operators (aka raising & lowering), really put this notation to good use[2]. It would be tremendously tedious to manipulate such expressions repeatedly without the simplifying properties of Bra-Kets. Once you are done manipulating them you then use the rules of the bra-kets to transform it back into a plain old integral, evaluate, and you're done.

I used to think they were very mysterious until I realised they were (essentially) notational convenience.

[1]: https://en.wikipedia.org/wiki/Bra%E2%80%93ket_notation

[2]: http://www.tcm.phy.cam.ac.uk/~bds10/aqp/lec3_compressed.pdf

Re: How Did Anyone Do Math in Roman Numerals?

#12

Post by blattimwind »

WalterBright wrote: post #6

It's interesting how the notation used can encourage or retard progress. For example, Leibniz's calculus notation was vastly superior to Newton's, and calculus theory advanced much more quickly where Leibniz's notation was used. https://en.wikipedia.org/wiki/Leibniz%27s_notation

An important facet to mathematics in general, that most are unaware of before studying it, is that the majority of proofs, especially those done in bachelor university courses, are purely notation. Other problems often become trivial to solve by using a different notation (e.g. polar form vs. points on the complex plane) as well.

Re: How Did Anyone Do Math in Roman Numerals?

#13

Post by amelius »

WalterBright wrote: post #6

It's interesting how the notation used can encourage or retard progress. For example, Leibniz's calculus notation was vastly superior to Newton's, and calculus theory advanced much more quickly where Leibniz's notation was used. https://en.wikipedia.org/wiki/Leibniz%27s_notation

I prefer Mathematica's notation over Leibniz's, because it is not as ambiguous (dx can also mean d TIMES x, as a simple example, but also dy^2 can mean d(y^2) and (dy)^2)

Re: How Did Anyone Do Math in Roman Numerals?

#14

Post by isolli »

blattimwind wrote: post #12
WalterBright wrote: post #6

It's interesting how the notation used can encourage or retard progress. For example, Leibniz's calculus notation was vastly superior to Newton's, and calculus theory advanced much more quickly where Leibniz's notation was used. https://en.wikipedia.org/wiki/Leibniz%27s_notation

An important facet to mathematics in general, that most are unaware of before studying it, is that the majority of proofs, especially those done in bachelor university courses, are purely notation. Other problems often become trivial to solve by using a different notation (e.g. polar form vs. points on the complex plane) as well.

What do you mean by that?

Re: How Did Anyone Do Math in Roman Numerals?

#16

Post by sideshowb »

thunderbong wrote: post #2

I had, for some reason, never thought of that directly. Although I do remember some joke on arithmetics in one of the Asterix comic books. But reading this article and trying out a few things, I found it was great fun!

...which is funny (the Asterix thing), because spoken French isn't exactly brilliant with numbers either: 99 for example is expressed as "eighty nineteen", 70 as "sixty ten".

My friends lived in France a while and said their landlady could never count their rent (paid in cash) correctly first time. Always stumbled somewhere between 100x+60 and 100x+100 for integer values of x.

The Swiss have corrected this in Swiss French.

Re: How Did Anyone Do Math in Roman Numerals?

#19

Post by IshKebab »

MayeulC wrote: post #15

The article is wrong on a couple of counts (for multiplication and division). Here is a more complete one: https://thonyc.wordpress.com/2017/02/10/the-widespread-and-p... (Surfaced on HN with https://news.ycombinator.com/item?id=13636277 )

Huh so I've wondered how the Babylonian "base 60" system worked. Looking at the image in that article it's not base 60 at all! It's more like a mix of base 6 and base 10. The factor increase for the columns are not:

60x 60x 60x 60

The are

6x 10x 6x 10

Much simpler than it sounds from "base 60".

Re: How Did Anyone Do Math in Roman Numerals?

#20

Post by mseebach »

sideshowb wrote: post #16
thunderbong wrote: post #2

I had, for some reason, never thought of that directly. Although I do remember some joke on arithmetics in one of the Asterix comic books. But reading this article and trying out a few things, I found it was great fun!

...which is funny (the Asterix thing), because spoken French isn't exactly brilliant with numbers either: 99 for example is expressed as "eighty nineteen", 70 as "sixty ten". My friends lived in France a while and said their landlady could never count their rent (paid in cash) correctly first time. Always stumbled somewhere between 100x+60 and 100x+100 for integer values of x. The Swiss have corrected this in Swiss F…

> 99 for example is expressed as "eighty nineteen"

Actually it's four-twenty-ten-nine (quatre vingt dix neuf) -- -- which is perfectly logical on a twenty-based numbering system. Of course it's not very helpful that they switched to ten-based, but only up to 60.

http://www.woodwardfrench.com/lesson/numbers-from-1-to-100-i...

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