Maths in 1M Years: Can We Improve?

[mr-tom]

Assuming we're not extinct, what will maths be like in one million years. Can the language be improved in any way? Would we be more efficient with fewer/more digits than 9.

Imagine if we we're using roman numerals how crap everything would be...

 

[tgt]

I think they'll use completely new notations for everything which would make everything so much more easier and hence teach the equivalent of abstract algebra in primary school.

 

[humanino]

We probably haven't the slightest idea. Look back ten thousand years ago, then one thousand, then one hundred, it seems that mathematical speed of progress accelerates ever more. So, one million years, we can even assume that our body shape will have evolved, not even to mention knowledge...

 

[Moridin]

At that point in time, we have killed ourself long ago.

 

[Jimmy Snyder]

In the future everything will commute.

 

[BobG]

Assuming we're not extinct, what will maths be like in one million years. Can the language be improved in any way? Would we be more efficient with fewer/more digits than 9.

Imagine if we we're using roman numerals how crap everything would be...

What's wrong with Roman numerals?

It's a pretty lousy way to write numbers, but a very efficient way to think about numbers. If there's a problem with the system, it's that it is taught in elementary school by liberal arts majors that lack any understanding of the system other than how to write it.

It's no coincidence that it pops up in so many ways, such as money ($1, 5$, and $10 bills).

Also, we use 10 digits in a base 10 system, including 0.

Elementary schools could probably do a better job teaching kids how to count on their fingers and toes, too. (Couldn't resist)

 

[Daiquiri]

I think (actually, I hope) it will follow the evoluton of our brains - which will (probably) be routinely upgraded with various microelectronic devices.

Maybe one day we will have the capacity to perform FFTs, triple integrals and differentials etc. mentaly just like today we add or multiply numbers when we go shopping.

That would be a basis for a much more complex multi-dimensional math, but written in apparently simple way.
Say, A + B = C (mentally), where A, B and C are things we resolve today (in a painstaking manner) with tools like Matlab, Mathematica and similar, without even really understanding their intimate meaning.

 

[Schrodinger's Dog]

The same as it is now but with more dimensions probably. Mathematicians like dimensions. Probably have some advanced probability maths that allow us to predict economics or sports with much greater precision. And physics will finally explain using an advanced mathematical model well beyond our ability to comprehend (God knows how!) How the humble bumble bee can fly.

 

[humanino]

What's wrong with Roman numerals?

Base six (or twelve) might be more efficient, since division (multplication) by 2 and 3 become trivial. By extension, base 30 also includes 5, and base 210 includes 7... and base \Pi p_n with n up to N will include the N fisrt prime numbers. This (modular) way of thinking about integers numbers is very powerful, leads to the continuous fraction n=a+\frac{1}{b+\frac{1}{c+\frac{1}{\cdots}}} form which is sometimes claimed to describe how Ramanujan conceived numbers. That starting point would constitute a significant leap leading to a genuinely different construction of mathematics altogether.

Disclaimer : writing those lines, I was just listening to myself and have no intention to justify those claims unless under the theat of face fish-slapping [/size]

 

[humanino]

In the future everything will commute.

I was exactly thinking the opposite

 

[Math Jeans]

Fortunately I love the current way we do math in this time.

Specifically, I love how there is not yet an equation that allows computers to find crazy high prime numbers very fast. Mainly, the current equations require lots of computation rather than large numbers coming from few computations.

Case in point. Working on those numbers is probably the best way to get rich in this day in age because companies will pay you crazy amounts of money to 1) keep quiet and 2) make encoding for them.

 

[binzing]

At that point in time, we have killed ourself long ago.

Can you read? He said assuming we don't kill ourselves. Now, for fun, look up "End of Ze World" on Youtube.