Monday, January 19, 2015

Mushroom Life

Here is a fun game to keep you a little occupied.

A mushroom spaceship, or "a weekender"
Maybe if you are one of the ten people who follow my facebook page, or google+, or any of my social media accounts, you might come to the conclusion that I'm obsessed with this game this morning. Which is very true, and it's one of the few math games I can get away with playing at work and claim that I'm being productive.

John Conway's Game of Life is a zero player game where the initial state is chosen by a person and then AI is allowed to take over and create many patterns. Someone modified the game a bit, so that pins would become mushrooms in a couple generations. I really want to find the person who made this game, and failing in that I want to steal this code. Is it still wrong if your honest about your intentions to do wrong?

The final stages of an exploder
I introduced a coworker to the original game this morning, and he came back to me with this version. The both of us being mushroom dorks, this was a fun version to use. At first it was disappointing because it was too small and can't handle a small glider gun. As I sat and watch the patterns evolve across the screen, I started to recognize some of the patterns. This is what happens when you spend three years watching mushrooms grow. Mushroom farming is a zero player game in which the outcome is controlled by the initial state.

It's still a complex system, and the rules are different. But if the super complexity is ignored for a moment, stuff like nutrition in the soil and the presence of predators, then outcome of setting up the original box is something amazing to watch. The health of the mycelicum, where water collects in a bed, all of that and more create the patterns that occur.

Thursday, January 8, 2015

ISWG a day late, and horns with no volume

A day late for ISWG, so I'll give you two posts in one! The first one is my insecurities, and my second one is being too smart for my own good.

New years resolutions, amiright?  I stopped setting them a while ago, but I still try to improve myself. I stopped setting them because of that god awful trap that I tended to fall into where I miss the goal and I think "Oh, damn it I failed! No I'll never be able to do it!" and then I would give up until next year.

Now, I've got stuff I do and I feel about when I can't do it as well as I can. It's a journey. Write when I can, try to improve my organizational skill, get better faster harder stronger. You know the whole drill.

How are you guys doing on your resolutions?

This month the Minions of Math are going to start talking about infinity. Not to ruin the surprise, but we'll talk more about infinity next month too. This is a video month, and I watched this video by Numberphile this morning before running 2 miles in 3o Fahrenheit weather. That combination has proven time and time again to kick my mind into overdrive, so if figured I would take the time to address one of the paradoxes here: Gabriel's Horn.

There is a soft spot in my heart for Numberphile and Vihart because those two along with Gödel,Esher, Bach and the great Lewis Carrol did more for my interest in mathematics than 13 years of schooling. With that said, I've noticed that the deeper and deeper I get into math the Numberphile videos are a bit harder to watch since a majority of them seem to be aimed at I Fucking Love Science crowd. Instead of complaining about this, here are some more thoughts about Gabriel's Horn.

He points out that what makes it a paradox is the fact that it's a horn that tapers into infinity, and as such it has infinite surface area, BUT it has a finite volume. It seems paradoxical, until calculus is involved.

WAIT! Come back! I promise it's simple calculus! It needs to be, since I have yet to take an honest to god calculus class. First things first, I don't know much about the average reader's childhood, but a few of you must of noticed something about thirds at some point in your life. Namely this: 1 divided by 3 is equal to 0.3333 where the three just goes off into the distance. Multiply that number by 2 and you get 0.66666 repeating. So far so good, but if you multiply that first number by 3, depending on your calculator you won't get 1, you'll get 0.99999 repeating. That's a paradox, honestly, because you already divided 1 by 3 to get 0.333333, but multiplying 0.333333 by 3 doesn't give an answer of 1. This is simply because god hates math.

OK not true. The truth is 0.999999 repeating is so close to 1 that it's 1. That answer always struck me as unsatisfying when I was younger, but if we except that axiom we can do something more amazing with Gabriel's horn. More amazing than what the guy in video says with the whole "You couldn't paint the surface, but you could fill it with a finite amount of paint."

If there is a number that is so close to 1 that it's 1, then a number like 0.000 . . . 001 can be so close to zero that it's 0. Why Gabriel's Horn works is it's an infinite series, which can be best explained by a joke:
There's a math conference in town, and all the mathematicians walk into a bar. The first mathematician orders a beer. The second orders half a beer. The third orders a quarter. The forth orders an eight. The bartender stops them at this point and hands them two beers.
 It works for 2: 1 + 1/2 + 1/4 + 1/8 + 1/16 . . . to infinity. It works for 1: 1/2 + 1/4 + 1/8 + 1/16 . . . to infinity. In fact, it works with zero if ou work with small enough numbers. In a sense, the volume kind of works the same way for the horn, it's an infinite series. Less cool when you know how it works. What I've been working up to this whole time is that IF this is the case, AND a the sum of an infinite series can equal zero, THEN a Gabriel's trumpet exists that not only has infinite surface area, but also has a volume equal to zero. I'll leave it as an exercise to the reader.