The World is Built On Probability
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The book beautifully illustrates the probabilistic nature of our world through a dialogue between the author and an imaginary reader.
Randomness desired inside diameter of the nuts, while the variance characterizes the scatter of the obtained diameters around the desired value. The three-sigma rule . A normal distribution is shown in Fig. 1.16. It has a maximum at the expected value E (x). The curve (the Gaussian curve) is bell-shaped and is symmetric about E (x). The area under the entire curve, i. e. for the interval (- 00 < x < + (0), is given by the 00 integral J j(x) dx. Substituting (1.19) here, it can be shown that
probability of generating the word from "letter noise". The generation of a sentence, let alone a line from a well-known work, is less probable. Nonetheless, the probability of doing is nonzero, and so there is the possibility of any information being generated randomly from noise. Thus, we can say (although this sounds strange) that chance generates information by chance. The greater the information, the smaller the probability of its random generation. That random information can be generated
halves (A and B) by a partition with a trapdoor over a microscopic hole in it. And suppose, Maxwell continued, a "being" (Maxwell called it a "demon") controls the trapdoor causing it to close and open the hole so as to let the fastest molecules from the A half .of the vessel enter the B half and to let the slowest molecules from the B half into the A half. Thus, the demon would increase the temperature in the B half and decrease it in the A half without doing any work, which evidently _ _ _ _
Similar relations can be written down for other components of the coordinates and the momentum of the microbody: liy lip, ~ Ii and liz Sp, ~ h, These are Heisenberg's famous uncertainty relations. We shall limit ourselves to a discussion of the coordinate-momentum uncertainty relations. However, there are similar relations for some other pairs of variables, for instance, for energy and time, and angle and the moment of momentum. Heisenberg wrote that we cannot interpret the processes on the
believed that the environment can directly induce changes in the shape of living being's organs. For instance, there was a time when giraffes with short necks existed. For some reason, their habitat changed and their food rose high above the ground (the leaves of high trees). In order to reach the food, giraffes had to extend their - -- . -- . ..robability in Biology Mutations that bring about changes seem to be a random phenomenon at first glance, but they have regularity in the long run.