Number systems and their effect on physics

[Cody Richeson]

The Egyptians were known for using base 6 while base 10 is more popular presumably because of the number of fingers we have. How much does the value of the base number of a mathematical system affect the underlying math used to describe physics? Would we still be able to arrive at the same conclusions if we say, used base 11 or base 23? Is it possible that physics would have progressed faster or even slower, if we had used a different number base than 10, or is it all interchangeable?

 

[jbriggs444]

It's all interchangeable.

Base 6, base 10, base 11, Roman numerals or other systems are simply notations used to write down "numerals", i.e. convenient labels that refer to the underlying numbers. The numbers themselves are the same regardless of what system of numerals is used to refer to them.

Though there could be some computational inefficiency if we tried to do arithmetic on, for instance, Avogadro's number expressed in Roman numerals.

 

[sophiecentaur]

It's not just the numbers; it's how you can manipulate them that counts. You could say that moving to a decimal system (or at least a system with a consistent base - unlike yards, feet and inches or Tons, cwt, lbs and oz) was a big help with calculations. The worst example that comes to mind is the Roman system. No wonder they didn't make much headway with quantitative Science. The 'Arabic' system allowed (as it does today) seriously complex arithmetic to be done very easily.
I don't think the actual number base would make a lot of difference except when you need to do calculations with a machine, in which case, binary, octal or Hex becomes more convenient - but not necessarily for ever. It depends on future computer architecture.