4 ms·

Probability, seems to me, cannot be fundamental, because, a machine built to flip a coin with always the same pressure, can be adjusted to always give heads, or

by nyc111 4y ago

Probability, seems to me, cannot be fundamental, because, a machine built to flip a coin with always the same pressure, can be adjusted to always give heads, or tails. In such a setup there won't be probability. From George Boole's The Laws of Thought, p.244: "Probability is expectation founded upon partial knowledge. A perfect acquaintance with _all_ the circumstances affecting the occurence of an event would change expectation into certainty, and leave neither room nor demand for a theory of probabilities." Can we deduce from this that nature is not probabilistic?

likeabbas 4y ago
What if the machine was built with 99% precision?
notafraudster 4y ago
It is true that (at least above the level of quantum physics) we tend to believe that reality is deterministic. When the meteorologist gives a chance of rain, in truth if they had perfect forward information on all of the clouds and pressure systems, they would simply declare whether or not there was future rain. In cases like physical phenomenon, you can think of observed uncertainty or chance as being a product of the exact settings of the unmodeled but deterministic factors underlying a particular outcome, or else errors in the functional form of the model with respect to the measure. We tend to assume that unmodeled factors are as-if orthogonal to the causes we are interested in modelling, and thus zero-centered, and our models minimize error predicated on this assumption. In your proposed flipping model, there are likely to be very small physical imprecisions (vibrations in the flipper, say, drifting tension of some kind of spring or actuator, or small amounts of circulating air, or perhaps tiny imprecisions in the way the coin is loaded into a slot). The machine might always flip heads, but it's still possible to say that whatever arbitrary degree of certainty you need to model the coin's behaviour in the air to achieve 100% accuracy, there could still be arbitrarily smaller error below that threshold, and we'd view this as "randomness" even if it isn't by the laws of physics.
empyrrhicist 4y ago
Not a physicist, but your argument is pretty unconvincing in that it relies entirely on intuition about classical physics, ignoring quantum phenomena entirely. If one were to argue that probability were fundamental, they'd very likely start by describing wave functions, which are probabilistic and seem pretty close to fundamental to observable reality.
dariosalvi78 4y ago
unfortunately nature IS, most likely, probabilistic: https://en.wikipedia.org/wiki/Hidden-variable_theory https://en.wikipedia.org/wiki/Hidden-variable_theory
deltasevennine 4y ago
If it is not fundamental then it must be derivable from other things. From what can you derive probability from?

by nyc111 4y ago

likeabbas 4y ago

What if the machine was built with 99% precision?

notafraudster 4y ago

It is true that (at least above the level of quantum physics) we tend to believe that reality is deterministic. When the meteorologist gives a chance of rain, in truth if they had perfect forward information on all of the clouds and pressure systems, they would simply declare whether or not there was future rain. In cases like physical phenomenon, you can think of observed uncertainty or chance as being a product of the exact settings of the unmodeled but deterministic factors underlying a particular outcome, or else errors in the functional form of the model with respect to the measure. We tend to assume that unmodeled factors are as-if orthogonal to the causes we are interested in modelling, and thus zero-centered, and our models minimize error predicated on this assumption. In your proposed flipping model, there are likely to be very small physical imprecisions (vibrations in the flipper, say, drifting tension of some kind of spring or actuator, or small amounts of circulating air, or perhaps tiny imprecisions in the way the coin is loaded into a slot). The machine might always flip heads, but it's still possible to say that whatever arbitrary degree of certainty you need to model the coin's behaviour in the air to achieve 100% accuracy, there could still be arbitrarily smaller error below that threshold, and we'd view this as "randomness" even if it isn't by the laws of physics.

empyrrhicist 4y ago

Not a physicist, but your argument is pretty unconvincing in that it relies entirely on intuition about classical physics, ignoring quantum phenomena entirely. If one were to argue that probability were fundamental, they'd very likely start by describing wave functions, which are probabilistic and seem pretty close to fundamental to observable reality.

dariosalvi78 4y ago

unfortunately nature IS, most likely, probabilistic: https://en.wikipedia.org/wiki/Hidden-variable_theory https://en.wikipedia.org/wiki/Hidden-variable_theory

deltasevennine 4y ago

If it is not fundamental then it must be derivable from other things. From what can you derive probability from?