The Hamilton-Jacobi Equation A Global Approach by Benton

By Benton

Hamilton-Jacobi Equation: an international method

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The greater the absolute value of the physical quantity S or I becomes, the coarser becomes the scale that allows us to distinguish differences in the received physical quantity. Moreover, all separate perceptions contain the same amount of information. Because of the logarithmic relation between the perception and the physical quantity, we establish that our subjective perceptions are appropriate measures for the information content ofthe physical quantities that we observe. Nature obviously equipped our senses with a scale adapted to the information content.

When we now observe an experiment once without conditions and another time with certain conditions, then the preliminaries of the experiment change if the conditions and the events of our experiment are not independent. For example, if we take a look at the throwing of a die, we have six elementary events. We combine them into the two events: 'even numbers' and 'odd numbers'. These are the events we are interested in and they form the basis elements of our sigma-algebra. Our sigma-algebra thus contains all intersections, all union sets and the complementary events of the interesting events {Q, 0, 'even numbers', and 'odd numbers'}.

However, as this machine is only able to type the characters and not to create sense, it will never be able to understand the sense of the books that it is writing in this senseless way. It can produce all possible books with a very simple instruction for their construction, but it will not be able to understand them, because it only follows the given instructions in a senseless way. This points out another problem of information. It is very easy to create a lot of information, but the use of this information, and especially the meaningful use of this information, depends on the recipient.

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