Here it is, our regular Friday diet of suggested readings for the weekend:
Which is more fundamental? Processes, or things? On the metaphysics of both.
What music would you like to hear on your deathbed?
The strange story of Julian Jaynes and his strange book, The Origin of consciousness in the Breakdown of the Bicameral Mind.
Lab grown mini-brains may teach us something about what makes humans special.
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Footnotes to Plato 
Robin,
I stand corrected. Should go to bed.
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No. The problem is practical, not theoretical. If you put in any number whats so every you can calucalte exactly what will happen. The fact that you can’t place a ball on a dome exactly is a practical.
You can make up a dome and all it’s properties exactly and the results are completely determined. If you ‘put it’ on the exactly on the top, and ‘turn the crank’ the prediction will be that it stays on top indefinitely.
If you start it on the side with just enough energy to reach the stop and do the math it will end up balanced (on a knifes edge) on the top and stay there.
In a theoretical example you can specify all the numbers and do the math.
In the real world besides the impossible precision, there are all kinds of thermal motions and breaths of air that make the experiment impossible to do. And the real world is quantum too.
It’s not the same as the intrinsic indeterminacy of QM. Even in ‘many worlds’ you don’t know what world you will find yourselves in (though some of the ‘yous’ will end up in unpleasant worlds).
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Again the solutions to the equations of motion need not be reversible. Reversible only means that the same equations apply either way. Norton’s dome is a nice example of such a case. Most classical solutions are reversible — even quite complex cones like 6×10^23 particles in a box.
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Again, the reason that the particle cannot be at a computable location is purely mathematical.
The theory is defined on real numbers and so all mathematical facts about real numbers must be part of the theory.
The theoretical probability of a particle being at a computable location is zero. In a theoretical example you can specify a theoretically impossible impossible location for the particle if you like, but it is mathematically incompatible with the theory.
It is not intrinsically indeterrministic for the reasons that QM is intrinsically deterministic, it is intrinsically deterministic for completely different reasons.
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A (sitting on the top of the Dome) does not imply B (rolling down the side of the box). If sitting still at the top is your initial condition, by Newton;s 1st law, B will never occur. It explicitly ways that without a force, the ball will just sit there.
Starting out at a point on the side of the box with just the right speed up will yield A (sitting) on the top. It’s not a logic problem, but physics (of though experiment type). Many points on the side going up will yield the state A. This is built in to symmetry of the dome. The symmetry is broken by the initial conditions, i.e., where you place the ball, so each solution violates the symmetry and by the symmetry each solution (the particular trajectory) leads to the same result.
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It’s probably best to say that our descriptions of classical physics allow for source of indeterminacy. Despite the example of Norton’s Dome, a more famous example is that of a triple collision. Newton’s laws are not enough to figure out what happens next. In fact, gravitational problems are replete with issues like this. It’s possible for a body to escape to infinity in a finite time in celestial mechanics. This source of indeterminacy, where the solutions become singular, affects all our classical descriptions, and we have no general treatment of it. Relativity doesn’t help as the theorems of Hawking and Penrose show, in fact it seems that singular solutions are guaranteed in any non static spacetime.
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There is also that energy and information can arrive from any direction at the speed of light, so that there is no frame in which all possible input into any situation can be known prior to its occurrence. It is the occurrence of an event which does the calculation of its inputs.
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