Monday, February 19, 2018

Some surprising finding about prime numbers

I don't write here a lot about science or math, even though I am a theoretical (mathematical) physicist by training. But this is not really a science or mathematics blog. I thought of launching something like that many times now, but have decided against it. At this point, it would be just too much of a distraction from my business and other things in my life. I have been distracted too much over the last two years by things I really could not control, so to cut down on distraction I have to limit things I can control.

Still, I have been dabbling in mathematics for the past 3 years or so using Mathematica and PARI/GP for my mathematical explorations, focusing mainly on discrete mathematics and number theory.

That might have paid off. Perhaps even "bigly," but that's subjective.

Namely, I have recently uncovered something quite interesting in the distribution of prime numbers. Primes are a very fundamental class of numbers whose history of research spans over 2000 years and still attracts attention of the best mathematical minds.

I must say that I am still quite unsettled by this finding. It happened around February 4th. By February 11th, I had the first draft of a paper documenting it and now I am wondering what to do next. I am unsettled because what I have discovered, an anomaly of sorts (or bias), could have been discovered even 40-50 years ago by professional mathematicians with access to state of the art computing facilities and 20 years ago even by amateurs with the help of Mathematica, Maple, or a similar piece of software.

The fact that this effect has been overlooked makes me wonder if I am right. I think I am. The whole thing was rather simple to uncover, and perhaps the main reason it took so long for it to happen is because no one was really expecting it. The discovery was a bit accidental, as they sometimes are, but not entirely, because it was also driven by elementary curiosity helped by an attitude of not taking things for granted. Hence, an amateur may have had a better chance at it.

A paper on a similar thing (when it comes to the class of effects rather than their nature) made quite a splash when it was published recently in one of the most prestigious research journals. Its finding was reported on quite widely in popular science and mathematics media as very surprising, though superficially it did not look like that. Or, at least that's the impression you might have gotten from those popular outlets that often simplify things a bit.

When looked at deeper (or if you consulted more serious outlets, such as blogs of professional mathematicians) its surprising aspect became clearer. The moral: yes, there is a difference in how experts and journalists approach things, which may also mean that fake news are not necessarily deliberate but sometimes an outcome of someone's limited competence (see also this Wikipedia article on Hanlon's razor).

This moral has ramifications also when it comes to trading. Trading newbies often try learning from other newbies on trading forums. That's like learning from journalists (and often poor at that) versus learning from experts. There may be a price to pay for that down the road, often steep. Professionals are more likely to recognize this problem, that's probably why my educational business tends to attract them.

Well, we'll see. I should probably be more excited than I am. I was quite a bit when doing my research, but now the whole oomph  is gone and I have a few other things to keep me busy, some definitely unwanted, such as dealing with a psycho neighbor. Yes, psychos are still tougher to handle (and much less pleasant) than math. At least, for me.

I have lived in Hollywood for over 18 years now. Perhaps it's time to move out. I actually wanted to do this last year (and even earlier). The only thing that has really kept me in Southern California for so long is its great weather. But that's not enough in a grander scheme of things. If you take into account earthquakes and wildfires (and, occasionally, psychos), the place can be as dangerous as it is gorgeous.

6/05/2018: See also this post for an update.