{Hawking [(...)][(3)]}[22nd July 1988]

[Redbook5:217-218][19880722:1150]{Hawking [(...)][(3)]}[22nd July 1988]

19880722.1150

*'Rather similar, seemingly absurd infinities occur in the other partial theories, but in all these cases the infinities can be canceled out by a process called renormalization. This involves canceling the infinities by introducing other infinities. Although this technique is rather dubious mathematically, it does seem to work in practice, and has been used with these theories to make predictions that agree with observations to an extraordinary degree of accuracy. Renormalization, however, does have a serious drawback from the point of view of trying to find a complete theory, because it means that the actual values of the masses and the strengths of the forces cannot be predicted from the theory, but have to be chosen to fit the observations.'**

***'Even if we do discover a complete unified theory, it would not mean that we would be able to predict events in general, for two reasons. The first is the limitation that the uncertainty principle of quantum mechanics sets on our powers of prediction. There is nothing we can do to get around that. In practice, however, this first limitation is less restrictive than the second one. It**** arises from the fact that we could not solve the equations of the theory exactly, except in very simple situations. (We cannot even solve exactly for the motion of three bodies in Newton’s theory of gravity, and the difficulty increases with the number of bodies and the complexity of the theory.)'#

*Hawking, ['A Brief history of Time', Bantam, 1988], p157

**(ref, above [e.g. [Redbook5:214-215][19880719:0000e]{Hawking [(1)][continued (5)]}[19th July 1988]&2ff;

& last previous entry but one, [Redbook5:216-217][19880719:0000j]{Hawking [(...)][(2)]}[19th July 1988]])

***Ibid, 168

****The 2^nd one, presumably.

#[Hawking's paragraph continues as follows: 'We already know the laws that govern the behavior of matter under all but the most extreme conditions. In particular, we know the basic laws that underlie all of chemistry and biology. Yet we have certainly not reduced these subjects to the status of solved problems: we have, as yet, had little success in predicting human behavior from mathematical equations! So even if we do find a complete set of basic laws, there will still be in the years ahead the intellectually challenging task of developing better approximation methods, so that we can make useful predictions of the probable outcomes in complicated and realistic situations. A complete, consistent, unified theory is only the first step: our goal is a complete understanding of the events around us, and of our own existence.']

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