![]() ![]() One can't explain it to others – listening about force, torque, aiming and balance doesn't help in learning but one can learn it by exercise. Professional knife throwers do that with astonishing certainity and unbelivable precision! Man can do that with the same knife, the same eye, the same arm and the same brain, which initially seemed to get unpredictable, random results only. However, as we try over and over again, we learn how to feel the balance of the knife in our hand, how to adjust the force, rotation and direction, and gradually we manage to stick the knife into a board again and again. That's because we seem to have no control over it. The angle, at which the knife hits the board, as well as the point of collision, seem pretty random initially. Have you ever tried to throw a knife at a wooden board so as the knife sticks into it? I'm sure you didn't even get the knife to hit the board with its blade at start, let alone to stick in it. Deterministic doesn't mean you personally can be certain of the answer ) How much do you know about the coin? Do you have a 3D profile of its mass distribution? Do you know how much air resistance its materials create? The air currents in the room? How precise is the flipping mechanism? How does the landing surface interact with the coin? How much time, capability and inclination do you have to actually use all that information if you had it? The less you know and the less you care, the closer you are to p=0.5. In Jaynes' approach these questions never really stop, the only question is when you get to the point where it's not practically worth while incorporating more information.īack to your question. Iii) Are they independent? If flipped by a machine loaded the same way will they be biased? Sound like a stupid concern? Go search for batch effects in GWAS. Ii) Are there really only two possible outcomes? Could the coin land on its side? Could the experiment be disrupted? Sound like a stupid concern? Go search for censored data in survival analysis. I) Are the flips really symmetric? Do we have a high speed camera capable of capturing the initial conditions? Or, more likely does the flipper have an incentive to produce biased coin flips? Now (i - iii) denote points where other information could easily enter in: ![]() So you will likely answer 1/2 and your teacher 1/4 because your probability is conditional on a different set of information. Conditional on one H, we're back to a single coin toss.The coin flips are independent (iii), so HH, HT, TH, TT are equally likely giving 1/4 a priori probability to HH.There are two possible outcomes per toss (ii), giving probability 1/2 each.Coin flipping is roughly symmetric (i), so H/T on a single coin toss is equally likely. ![]() I show one to you, but not your teacher it's a head.Ī first Jaynesian analysis proceeds like so: Before you answer I flip two coins, hiding the results with my hands. I explain that I will flip two coins, and will want to know the probability of two heads. Ponder this: I get you and your teacher together. This is a Bayesian idea, and receives a book length treatment in Jaynes's Probability Theory: The Logic of Science. Uncertainty is a statement about our ignorance of the true facts, rather than a property of the facts themselves. Keep asking these questions, but don't expect your teachers to always get you ) He managed to flip the coin about 10 times and got a head every time. In my class, I point out that it is only random because of our inability to exactly replicate the experiment.Īs a fun aside, a colleague in graduate school, who also happened to be a magician, told us that he could toss a coin with a much higher than 50% chance of getting a head. Now, when most people talk about "tossing a coin" they don't stipulate that all these experimental conditions have to be the same and thus there is a random experiment. Since quantum effects are negligible, the coin should end up with the same side up, i.e.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |