How important is our number system for science?

[omie]

I know that our laws are as far as the logic goes Universal? Now, can we use other ancient number systems and come up with the same results, or is the success of all the recent science dependent on the efficiency of Hindu Numerals ? Is the logic of all mathematics based on Hindu numerals , and might we have a new number system in the future that is more efficient ?

 

[mfb]

How we write numbers has no deeper relevance for mathematics. It would be the same if we would use Greek letters, Hindu numerals, or anything else. Using something like the decimal system is convenient because you can write down any (rational) number with a fixed number of symbols (here: 10) but any system that has an unambiguous way to do so works.

 

[Vanadium 50]

Mathematically, it doesn't matter. Practically, try and multiply MMMDCCCLXXXVII and MMMMCDLXXIII in Roman numerals. See you tomorrow.

 

[FactChecker]

Any math that is beyond arithmetic does not care about the number system representation used. That being said, it is hard to imagine a person learning advanced mathematics if he can not do arithmetic. But it could also be said that science depended on the invention of the pencil and paper.

 

[jedishrfu]

The number system notation we use today is a much cleaner scheme than what was used in the past. Some early number systems had no notion of negative numbers, zero or fractions. Our decimal based system combines these ideas together into a concise operational system that allows us to do math with less effort. Imagine trying to do what we do now with Roman numerals or Egyptian fractional math.

The number base chosen determines how much one has to memorize for addition or multiplication. If you consider binary numbers the tables (2x2) are quite small versus base 10 (10x10)or consider base 60 (60x60) and how big the tables would be. I suppose we could have used base 12 as it has more factors (2,3,4,6) than 10 (2,5) but convention chose the decimal system.

This process repeats itself in abstract math notation as well where Newton’s Calculus notation was superseded by Liebnitz notation which is arguably cleaner and more flexible. Math notation is a tool that make it easier to do the math and that desire drives us to discard some notation and choose others.

 

[fresh_42]

Any math that is beyond arithmetic does not care about the number system representation used.

Yes. With a little exaggeration one could say: we only use $\pm 2, \pm 1 , 0$ anyway.