Just got this in an email from Stephen: Recently, a Philosophy student posed me the age old question if a tree falls in the forest and no-one is around to hear it, does it make a sound? As a Philosophical Science student, I like to think I can answer philosophical questions with science. Also, because Im kind of an asshole, and like to frustrate Philosophy students. But thats besides the point. The point is more the answer that I gave. There are two possible answers to this question, a classical, Newtonian answer, and a more modern Quantum Mechanics answer. The classical answer is the easiest to fathom; Conservation of Energy means that, when a tree falls, air particles are moved and this creates a sound. Nice and simple, the answer is always yes. In Quantum Mechanics, however, we have a principle most commonly recognised as the Schrodingers Cat Paradox. Im sure youre either aware of this, or can look it up on your own, so I wont bore you with the details. The concise version, however, is that an unobserved system is simultaneously in all possible states until observed (in physics, we call this collapsing the wave function). Im not the first person to link this theory to this statement, and its fairly common to come to the conclusion that the tree simultaneously makes a noise and doesnt make a noise. So lets take this a step further. If there is no observer, then does the tree even fall in the first place? The answer is both yes and no. In fact, this is true of every tree in the forest. So, lets do some mathematics. Currently, the smallest recorded forest is Adak National Park, a forest comprising of (at its lowest count) thirty-three trees. Each tree has three possible states which we are interested in; Not Falling, Falling Silently and Falling Noisily. At this point, we could make a tree diagram to work out all the possible combinations, but let me save you the time and effort. After all, there are 3^33 possible combinations (approximately 5.55906057X10^15, or 5,559,060,570,000,000, for those less mathematically inclined), and I dont wish to be the cause of a biro drought from people trying to draw this out. The probability of never having a tree Falling Noisily is (2/3)^33 (since we are calculating the probability of one of three options not happening in thirty three instances). This comes out as 1.54521335X10^(-4)% (or 0.000154521335%). So what does this face full of numbers allow us to conclude? Well, simply put, even in the smallest of forests, when not being observed, there is only the minutest chance (approximately one in a million) of a tree falling and not making a sound. So to conclude, if a tree falls in the forest, and no-one is around to hear it? Regardless of your physical interpretation of the system, Id put my money on the tree making a sound. Hope you enjoyed my bizarre physics ramblings. Feel free to pass this on to anyone who may be interested (Im sure several of them will gladly pick apart the mathematics on this subject. Its an incredibly simplified model of the system where theres a 1/3 chance of no trees falling, amongst other simplifications I made to not go into a number coma. If anyone gives a more accurate model of the probability, Id love to see it).
Posted on: Mon, 03 Feb 2014 12:43:44 +0000