Recently Roy Halladay pitched a no hitter in the NLDS playoffs. Those friends of mine who are Yankees fans will quickly point out that some old dude who played for them did better by pitching a perfect game in the post season...yadda yadda yadda. Well my apologies go out to Doc, as I am the single reason he walked Jay Bruce. Now I've never personally interacted with Roy Halladay or even attended a Phillies game since he joined the team. Yet, midway through the 5th inning, I irreverently switched positions from the couch to a chair while watching the game. The baseball gods did not miss this transgression: Roy missed on a full count ruining the perfect game.
In essence, the principle is simple (atleast it should be considering Ashton Kutcher made a movie about it), one small change in one part of the world can cause a huge change elsewhere. So I began to think about whether or not simple chair switch could have done anything in respect to what I know about physics (don't get your hopes up, it isn't much).
First, I'm going to ignore any possible electromagnetic and gravitational field effects because those any such field I could create would quickly radiate in all directions and the amount of power that would eventually reach the playing field is too small to be calculated much less affect the movement of a baseball. This is a reasonable assumption because of Lentz's Law. So instead, I'm going to imagine that "bad luck" exists in the form of an imaginary particle (like an evil electron if you will)
Now imagine this "bad luck particle." My act of changing seats creates this particle and it begins travelling around.
The first major obstacle is that the "bad luck particle" from my location would have to reach the playing field.
I'm approximately 30 miles or roughly 50,000 meters from Citizens Bank Park. There is a hyperbole often used to describe fast things: the speed of light. Well most people know that this is a theoretical "speed limit" of the universe. Nothing moves faster than the speed of light. So let's assume that any change that my shift in seats would cause could only travel at this speed: 300 million m/s. This means that travelling at the speed of light, it would take my "signal" 0.00016 seconds to reach the playing field. To put that into context, that's about an eigth as long as your camera flash...So it seems very likely that I could have ruined a perfect game.
BUT that assumes that my signal travels directly from my chair to the playing field, taking the shortest possible route. Well this of course is physically possible, but the probability of such a perfect journey is next to nothing. So we assume that the trajectory of my particle, like other particles is random. By this I mean that at any given instant, it has much of a chance travelling East as West, North as South, Up as Down, etc. The analogy is best described by the walk of a drunk sailor staggering around in a strange town. He's just as likely to stumble backwards as forward, side step, etc. (Let's ignore the irony that my bad luck particle is, for all intents and purposes, drunk). So it turns out in all likelyhood that the total distance my signal will travel will be far far greater than the simple 30 miles.
So let's try to calculate the number of steps required for my signal to get from my chair to the ball park (a process which I'm not so sure of myself and will make many, many assumptions which simplify matters). Its important to first describe the distance of each "step." That is, the length my signal will travel in one direction before being able to switch to another direction. If we go back to the analogy of the drunken sailor the size of each "step" is simply the length of the sailor's stride (before he pauses, collects himself and attempts to step again). Let's just say the step size of my "bad luck particle" is 1000m. (A astronomical size when you consider that most elementry particles are over 100,000,000,000,000 times smaller. Well shut up, and don't ruin my moment). This also means that we can only define the position of the particle to 1000 m by 1000m by 1000m grids. So we're just going to try to go for the 1000 m^3 grid that contains the ball park and not a more precise location, like Roy Halladay himself.
That means in the best case scenario there are (50,000m/1000m) or 50 steps required for the particle to get there.
Now it takes the particle 3 milliseconds to travel one step.
Let's also assume that there are only 6 directions to choose from: Up, Down, Left, Right, Forward, Reverse (not to be confused with Up, Up, Down, Down, Left, Right, Left, Right, B, A).
So that means each step there is a 1/6 chance that the particle goes in the right direction at each step.
So simple probability means that the chance the particle passes within the 1000m cube of the playing field in the most direct route is one sixth (based on the number of choices for direction) to the 50th power (minimum number of steps). An incredibly small number. However, with every "step" (actually every other step to be precise) there is another chance the particle passes our target grid containing the field.
Now what is the probability that the "bad luck particle" could have reached the field within the 5 minutes from my change in seats at the start of the half inning and the walk? Well there are 90 million steps in 5 minutes. The chance that in those 5 minutes the particle will at some time pass within the 1000m cube containing the playing field is less than 1 in 1,000,000,000,000,000,000,000,000,000,000,000,000.
The chance that in my lifetime, I could have done anything at home to affect this game is only negligibly better.
In fact, if you include even more possible direction for the particle to travel (like diagonally) or a smaller step size (like say 1m), the probability is even more ridiculous.
So basically, Roy Halladay's perfect game was not broken up by my bad luck. And I'm a huge nerd.
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