Category: Uncategorized


Still Alive…

… for now. My diagnosis was updated a few years ago to Friedreich’s Ataxia. A different name, slightly different symptoms, but everything else is basically the same. It’s not even confirmed: that requires a genetic test costing approximately what I make in a year and not covered at all by any insurance.

Not that it matters. My life is a Choose Your Own Adventure story with one ending. Come to think of it, so is everyone’s. Mine’s just half as long.

My current goal is to get my Ph.D. before I need a wheelchair. It’s going to be close.

xckd hovertext

There is an excellent webcomic called xkcd. By excellent, I mean it is primarily for very nerdy math and science oriented people. It has the tendency to make very good points.

In addition to three new comics every week, if you hover your mouse over each one, a piece of text appears (much as when you hover over a file or folder, the name tends to appear). The hovertext is generally another joke, or an addition to the comic which makes it funnier, or makes another point. Something like that.

The most recent comic makes an astounding point about homeopathy. It reads:

“I just noticed CVS has started stocking homeopathic pills on the same shelves with–and labeled similarly to–their actual medicine. Telling someone who trusts you that you’re giving them medicine, when you know you’re not, because you want their money, isn’t just lying–it’s like an example you’d make up if you had to illustrate for a child why lying is wrong.”

Loathe as I am to say it, I hope someone dies while taking homeopathic medicine from CVS when actual medicine could have helped them, just so their blood will be on the hands of whoever thought this was ok.

Tau Day

Anyone, I repeat, ANYONE, who thinks we should use Tau instead of Pi is an imbecile. It isn’t a matter of tradition, or stubbornness. It has nothing to do with rewriting results, or reteaching anything whatsoever.

The most elegant formula in the history of mathematics would be ruined by it. Any argument (or number of arguments) lose to this one.

Tau is idiotic. If you like it, so are you.

Depression

It’s not a rational thing. I’m sitting in my car, listening to emo music, lights off, and have been for at least ten minutes. Well aware that it is dumb. Can’t motivate myself to go inside and go to bed. Sleep is an escape from the problems of the awake. I don’t really want to sleep problems off. Or be awake. I just want to not have problems. That last bit’s probably common.

My next post will be about math. Promise. Oh, 6/2*(1+2)=9. Learn what the order of operations means, don’t just memorize a mnemonic.

Ketchup

Still alive… for now. It’s been a while, but writing a thesis will do that to you. It’s almost done. I’ll post it (or excerpts, or something) when it is.

Still not sure where I’ll be next year. Fate, it seems, is not without a sense of irony.

A puzzle, then I’m off to teach. Using two 3s, two 8’s and elementary operations (+,-,*,/, and parentheses), write an expression equal to 24. There is a non-silly solution (ex. (3 over a sideways 8)+(3*8) is a silly solution)

Ta-ta.

Partition Numbers

This is amazing. Rather than write on it (hey, class in 40 minutes), I’m going to link to the blog of a really cool physicist/mathematician that I read from time to time. Trust me, you’ll want to read up on this:

Finite Formula Found For Partition Numbers.

New Year’s

It’s been a while. I wish I had more time to write. I certainly could, it just isn’t currently prioritized high enough.

2010 was certainly one for the books. Unfortunately, one of the only reasons why is that I found out I’m terminally ill. Other things happened, for sure, but hopefully you understand that this news makes everything else difficult to consider important.

The good news? Every year I live after this will be great, if for no other reason than the fact that I’m still alive.

It’s funny how the biggest things in your life make you appreciate the littlest things.

Non-Transitive Dice 3

For background (if you care), see this post (which links to the first one as well).

I have proven that balanced, non-transitive n-sided dice exist for every n>2 (and the proof is quite slick, I think). The trick to this is a particular kind of labeling followed by concatenation. I have also proven several nice things (if a set is balanced, all 3 dice add to the same total!) on top of my original thoughts. My task now is attempting to find an upper bound for the victorious probability. My conjecture is 2/3. I also conjecture this is unattainable, that is, it is asymptotic.

I’m going to be writing a lengthy paper on this topic, so it’ll be easier to link to that once it’s done (in April or so).

That’s enough on dice. Back to your regularly scheduled blogramming.

Thanks for reading.

Non-Transitive Dice 2

You’ll want to read the first post to catch up.

So, I’ve decided to call these scenarios “balanced non-transitive dice”. I’ve yet to prove that balanced non-transitive n-sided dice exist for n>2. It should be straightforward, but a simple construction would be nice. At any rate, I’m convinced of this.

The issue beyond is the following: Most solutions so far have a victorious probability of: (floor((n^2)/2)+1)/(n^2). This is fancy language for “as close to half as possible”. The first post mentions this. I have no doubt that this is a sharp bound for n=3. This means that a set of balanced non-transitive 3-sided dice exist with victorious probability 5/9 (it’s written in the first post), but that a set does not exist with victorious probability 6/9.

A professor of mine ran a program for n=4, with interesting results. The only balanced sets he found had victorious probability 9/16. Unless his code has an error, the bound is sharp for n=4.

I then did some diagram chasing by hand, and found, for n=5:

A: 15, 9, 8, 7, 1

B: 14, 13, 6, 5, 2

C: 12, 11, 10, 4, 3

A beats B beats C beats A 14/25 of the time. The bound is broken! Then, just now:

A: 15, 14, 5, 4, 2

B: 13, 12, 11, 3, 1

C: 10, 9, 8, 7, 6

A beats B beats C beats A 15/25 of the time! Now this is cool.

More to come.

Thanks for reading.