Sunday, December 04, 2016

When simplicity bemuses

One problem I have had for two decades now is when I look at something that seems too simple to me that I discovered. Which is not just a problem I have as get a weird pleasure out of noting that my first paper sent off to a math journal was covering packing of spheres and was rejected as too simple. Here's a link to a post I finally put on the blog in 2008 discussing, and yeah I lost the paper. So I had to recollect the argument.

Far as I know the original paper which was on paper is gone. Probably tossed it into the trash or something, which doesn't matter. My problem with it was, how could there be this simple approach to a problem that was over two thousand years old?

I'm just not able to maintain confidence on that one as I tell myself, but Sir Isaac Newton worked on this problem, how could he not have noticed this simple approach? Then am like, but I don't need it anyway. I say that about lots of things. Is like, who cares, and I look at something else I have. And now? Have TONS.

Like take a look at this one. Copying over from a post on my Beyond Mundane blog though LOTS of posts about it on this one:

With natural numbers--means use ints or longs--where pj is the jth prime:

P(x,n) = x - 1 - sum for j=1 to n of {P(x/pj,j-1) - (j-1)}

It counts primes when n equals the count of primes up to sqrt(x), so if n is greater than the count of primes up to and including sqrt(x) then n is reset to that count.

There is nothing simpler which is as fast for counting prime numbers in ALL of mathematics. And nothing faster for its size. But is SO simple. For years will admit bugged myself by wondering why Archimedes doesn't have it, and how would human history have changed if he had?

And that's not even expressing it pretty as Blogger doesn't make that easy far as I know. If it IS doable without a bunch of extras would like to know! Would switch to showing that way. Is MUCH prettier with the summation sign used.

These days am not as bemused about it as in the past, but still am to an extent I rarely admit. It uses mathematics that is easy, as you really only need division. And in a more general form you don't even have to know what a prime is, as it will select them out.

The math knows what a prime number is. There is nothing else like it in all of mathematics and it even leads to a partial differential equation.

That the math does know what a prime number is without some human guiding it used to mess with my mind massively. And I realized, the math does not need us.

So why is such a simple discovery mine? I could go on. I could fill this post with simple results that bemuse me. I even improved upon work by Gauss. Found results in areas where Euler and Ramanujan both considered something. And what of it?

When I need a pick me up though can just do Google searches. And even at times will make myself look for math things done by others related to my results. I wish they were as interesting though. That's better for the human species.

One thing will admit, I don't know how anyone who knows mathematical history thinks a person has just one result. Or even a couple and is a big deal. You want to compete in mathematical discovery? Start talking with at least half a dozen major results, maybe. It's an incredibly competitive arena. Maybe most competitive of all human intellectual endeavors.

I shrug at people claiming a single result. Am like, maybe you're getting started? But probably not or you'd know better. Come back when you have a dozen.

And have thought now for years about how these are mine, but reality is I'm just some guy who figured out some math.

Maybe the reality is we really will never know why about some thing.

But how do you know?

James Harris