The Ultimate Baseball Game

Math fascination snuck up on me by way of baseball. Addition, subtraction, division, multiplication, percentages, averages, angles, distances, probabilities, speed, projections, time, all of it within the context of a baseball game. Baseball was my personal gateway drug to mathematics. Baseball counts everything! 

Then, before I knew what was happening to me, I learned that mathematics was really a language. The language of music.  

Music is math. Each sound is called a note. Each note is given a name and assigned a number. Beats are measured in time and expressed in numbers. Pitch is assigned a mathematical frequency by way of a number. Timbre is given depth.  Octave a range. Tempos, fractions, and volumes are all assigned mathematical expressions, and when all of this is put to paper, bingo-bango, magically a   language appears that sounds amazing.

Math is the language of the universe. Everything that can be quantified, everything that exists, is observed, or measured, can be represented by math. Math is a kind of not-so-secret decoder, a universal language translator that represents everything, like a Dick Tracy decoder ring or a Star Trek universal translator.

As time passed (more math) I discovered pi. Pi blew me away. Take a circle, any size circle. Divide the circumference by the diameter and you get this number, it’s called pi (3.14159…). 

Here is an easy example. Let’s say you walk around a circle that has a diameter of 100m. How far did you walk?

100m X pi (3.14159…m) = 314m. 

Now in and of itself, that is fascinating (because the circle’s size doesn’t matter, the number will always be pi) BUT the real mind-bender of it is that pi can be calculated forever. There is no end to it, there is no pattern to it, EVER. Pi has been calculated to over 100 trillion decimal places and still, there is no pattern to the digits. Pi is famous. Pi is a celebrity. Pi is a rock star. 

Heck, there is even a pi song

and a pi day, March 14th, (3/14). I hope that on pi day on March 14th, in 1592 at 6:53 a.m. and 59 seconds that there was a big party.

Well then, with this mathematical magic, one must certainly come to the understanding, (as I did), that the universe, and our collective conscious understanding of it, like pi, must be a never-ending string of expressions without interruption, pattern, or conclusion. Thank you pi. Thank you math. Case closed! 

Not so fast there Mr. Poindexter, math boy.

About the time I got my addled brain wrapped around the “eternity” of math, by way of pi, along came what is known as the “Collatz Conjecture”.

The Collatz Conjecture has been labeled the most dangerous problem that young math students are warned NOT to research. It is a simple problem that the best mathematicians in the world are unable to solve.

Paul Erdos, a famous mathematician, said that modern math understanding is not yet ripe enough for such a question.

Here it is:

Pick a number, any number. (Saying that in my head, I heard W.C. Field’s voice, my little chickadees) It can be a single digit or any integer of numbers, it doesn’t matter, pick one. Let’s pick the number 7 just for fun.

Now that we have our number selected (7) there are only two simple rules.

Rule 1 – if the number you selected is an odd number then you multiply it by 3 and add 1.

Using our selected number (7).  3 x 7 = 21, + 1 = 22.

Rule 2 – If the number is an even number then you just divide it by 2.

So, our 7, being odd, became 22, which is now even, so we divide it by 2 and now our number is 11.

Eleven is an odd number, so keep applying the correct rule, on and on. 

Eventually, no matter whether you picked a single digit to start or 9,999, or any positive integer, eventually if you keep applying the correct rule to your new number, you will come to a loop. An unbreakable, constant, never changing loop.  4 then 2 then 1. 

The first time you get to the number 1, being an odd number, if you are still following the rules, you will then get 4 (1×3+1).  Keep following the rules, then 4 becomes 2 which becomes 1 and you are right back to 4. Forever. Endlessly caught in the loop, which has been given a math name of course (the 3n+1 problem).

In case you are wondering, no one has proved the conjecture (broken the loop), it has been verified for every number up to 2 to the 68th power. So if you want to work on this you can start with a base number of 300 quintillion. In about three years, if you obey the two simple rules, you will be caught in the 4-2-1- loop.

It seems that numbers are not infinite after all. I guess somebody ought to tell pi that, ya know since it has its own song and day. 

How can both of these concepts be correct? 

Maybe the Zen masters are correct. Both yin and yang have to exist together in balance. It takes both a closed loop and an infinite string to play baseball or life.

All I know for sure is that in just a few short weeks it will be time (math) for baseball Spring training to begin here in Florida and that’s all the math I need.

Pitching for the Loopers, with an undefeated record, number 4-2-1 Colletz.

Pitching for the Infinities, with an undefeated record, number 3.14159265359… Pi. 

The umpire for today’s game, behind home plate, is You the reader, and would you look at that, up there, in the stands, selling peanuts, popcorn, and Cracker Jacks, is Poindexter math boy.

Today’s game is brought to you by none other than Mathematics.

Play Ball!