Randomness in causality physics only exists when we have a lack of ability to measure all possible parameters. — Christoffer

That is what is questioned by the Del Santo article.

That is what is questioned by the Del Santo article. — Banno

It's also true that a fair dice has probability 1/6 of landing on each side. Randomness as a physical property of systems rather than an epistemic limitation on them is something people really resist. But I think this is tangential to the determinism spoken about in the OP article.

He makes the argument that classical physics are non derterministic in The Open Universe: An Argument for Indeterminism” (a compendium of articles written in the 70s)

The notion that the universe is determined fails. — Banno

I don't follow this conclusion from the Galton box example. The epistemological claim is obvious: I don't know where the ball will land. The metaphysical claim is not obvious: the ball's path is not predetermined.

With God like knowledge (even if we posit is impossible for any human to attain), we could know where the ball will land.

None of this is to suggest that metaphysical indeterminism doesn't exist at the quantum level. It's just to suggest the Galton box isn't an example of it.

I can predict with 100% accuracy the ball will land within the Galton box, and not, for example, on Mars. A newborn infant can make no such prediction. The point being that my ability to predict something about the ball, however limited, does speak to a metaphysical discovery about causation. I do recognize however that my limitations about what I might be able to predict about the ball are due to my infantile knowledge of the forces acting upon the ball.

"If the initial state within an arbitrary system was completely specified, it would evolve into a unique state at any given time point". — fdrake

One argument presented in the article (if I have understood it aright) is that a finite volume of space can only hold a finite quantity of information. But if a measurement within that volume were made to infinite precision, that measurement would consist in infinite information. Hence, infinite precision is not possible.

That is what is questioned by the Del Santo article. — Banno

Problem is that it's inaccessible to non-members. But I see your point. The abstract points to an attempt at solving the bridging problem.

But I was mainly objecting to the conclusion you made "The notion that the universe is determined fails."
Which only makes sense if there was a high probability of large consequences of random operation, which doesn't really exist in our reality. We only conclude something like that based on what we yet cannot measure or do with physics. So at best it's a low probability conclusion that it fails, but more likely that we can measure the existence of it, but not yet understand it.

Problem is that it's inaccessible to non-members. — Christoffer

https://arxiv.org/pdf/2003.07411.pdf

The standard philosophical prejudice is that given an accurate enough account of the position of the box and a given ball, a competent physicist will be able to tell us which of the bins across the bottom the ball will land in. — Banno

That's absurd... no competent physicist would even attempt such a thing. They would use a demon.

why assume that we could have infinite information about our measurement... — Banno

I'm more sympathetic to his alternative, operational definition of classical physics, not least because history has moved on and we understand how deterministic macroscopic behaviour emerges statistically from non-deterministic fundamental behaviour, and indeed exact values of e.g. momentum are, in the initial conditions of a quantum system, modified by complex numbers in weighted sums, i.e. are not real in phase space.

It was more the "Has physics ever been deterministic?" question I'm feeling isn't really addressed in his treatment. Redefining epistemological certainty in such a way that the answer to a question that was previously "Yes" is now by definition "No" isn't so profound.

The idea of a trajectory through phase space does not depend on infinite epistemological precision anyway, and I feel he equates two statements that aren't equivalent. I can define a trajectory z(t) = y(t) = x(t)=t for t>=0. I can't specify to infinite precision in decimal or rational format the position at t=pi, but I can specify it precisely at any t that is representable in decimal or rational format, so yes I can specify points in phase space to infinite precision. But it's not a real trajectory of a real object! he might say. No it's not: it's ideal. If his argument applies only to real trajectories, he cannot generalise to ideal ones as he does.

Real-valued epistemological uncertainty, rather than ontological uncertainty, is already incorporated into statistical physics, ensemble QM, and others. What he seems to be proposing is a different way of doing it, and the measure of that is in its usefulness I think.

They would use a demon. — InPitzotl

Of course; but which one: Maxwell's or Laplace's?

That determinism of implication doesn't hold for almost every phenomenon because we know it's practically impossible to completely specify the input state that lead to its emergence. — fdrake

Isn't that covered by 'if'? Laplacian determinism also tells you that if you cannot know the initial state to infinite precision, you aren't guaranteed to know the final state to infinite precision.

What remains of Laplace's demon as an ontological thesis when it's rendered merely a hypothetical? We can't feed almost every system into its defining implication. So what systems are left? — fdrake

But epistemology isn't everything. That we may never know the initial state of a system does not prevent it from having a well-defined value ontologically. The use, I think, is illustrated not by removing epistemological certainty but by removing ontological certainty. Laplace's demon still holds: it's just that the condition is always false. The extent to which QM predicts very different kinds of results to classical mechanics is the extent to which the ontological thesis seems substantiated to me.

But if the point is only that it was wrong in hindsight, well... yes! Or, at least, maybe. Ontological uncertainty isn't specifically anti-deterministic. The difference is that states corresponding to some measurement (e.g. momentum) are multi-valued, which means that trajectories through phase space are also multi-valued. So long as you don't then insist on a way of making it single-valued (e.g. wavefunction collapse), everything is deterministic (i.e. the Schrodinger equation is deterministic), and that seems to me the likely mistake.

This is different from the game illustrated in the OP. We cannot predict where the ball will go at any point if there is any epistemological uncertainty in the initial conditions. However we can visibly see that the actual trajectory is fairly well-defined as it falls. (Not infinitely precisely, but we can see the narrow range of possible trajectories consistent with the uncertain path.)

Of course; but which one: Maxwell's or Laplace's? — Banno

Depends on the discussion... the conversation about epistemic limits reminded me a lot about Maxwell's demon.

As he concludes, the value of the article is in showing that there is an alternative to determinism within classical physics; not in showing that it is true.

Could they be the same?

Could they be the same? — Banno

They're distinct... Laplace's demon has free omniscience... Maxwell's demon's knowledge has costs.

As he concludes, the value of the article is in showing that there is an alternative to determinism within classical physics; not in showing that it is true. — Banno

Yeah that's fine, and it's interesting from Sec. III onwards. I have no issue with it. I'll be mulling it over for a while, so thanks for bringing it to our attention.

Wrote a comment about randomness as internal to systems a long time ago here.

But epistemology isn't everything. — Kenosha Kid

Knowledge is everything to Laplace's demon. If such a state of knowledge is impossible in some circumstances, Laplace's demon couldn't function as described in those circumstances. We already know it is impossible in most circumstances.

The difference is that states corresponding to some measurement (e.g. momentum) are multi-valued, which means that trajectories through phase space are also multi-valued. — Kenosha Kid

Say we've got the following system:

(1) A time variable $t$ ranging from 0 to $\infty$.
(2) A normal distribution $N(0,(\sigma^2 /t))$
(3) A sampling operator; $N(0,(\sigma^2 /t)) \rightarrow \mathbb{R}$. What it will do is generate a sample from the distribution at $t$

If we were to observe that process, the measurements would come from the sampling operator, not from the deterministic evolution of the distribution. Even if the evolution of the probability over time is fully deterministic, that doesn't tell us the sample paths; which are the events which actually happen; arise from a deterministic law. It's a baby and bathwater thing - yes, the distributions of time varying random processes can evolve deterministically in time, but no, that does not entail the events which happen due to them are determined. It's more apt to weaken "determined" to "constrained" regarding the observed events of deterministically evolving probabilistic laws, I think. A deterministic time evolution of a probability function still only constrains its realised sample paths. Laplace's demon has absolutely nothing to say about the sampling operator, only the time evolution of the distribution it acts upon.

This user has been deleted and all their posts removed.

Knowledge is everything to Laplace's demon. If such a state of knowledge is impossible in some circumstances, Laplace's demon couldn't function as described in those circumstances. We already know it is impossible in most circumstances. — fdrake

True, but the whole point of Laplace's demon is that it knows what we cannot necessarily know. Our uncertainty doesn't imply its uncertainty. Ours is a technological limit. The demon is constrained by ontological. Otherwise there's no point considering it in the first place.

If we were to observe that process, the measurements would come from the sampling operator, not from the deterministic evolution of the distribution. — fdrake

Yes, the trajectory I was describing would be the trajectory of the distribution, not the line joining the measurements. This is akin to the Many World interpretation of QM, wherein a particular (non-deterministic) measurement does not change the (deterministic) trajectory of the body under consideration (minus the fact that the probability of a given future measurement does not depend on your measurement history, which is a statement about you rather than the trajectory).

The many-valued, deterministically-evolve state I had in mind was like the distribution, not the measurements which are discrete in time (I presume). however, we can be quite sure that physics isn't like that. If a body is falling from a tower of height T and we measure it first at height 0.9T then later at 0.5T, we can be quite sure that a third measurement won't be at 0.7T, for instance, unless something other than gravity was acting.

for instance, unless something other than gravity was acting. — Kenosha Kid

Exactly! The majority of the time something else is in play too. When we imagine a system, it's usually determinate - it has a system of equations that describe its evolution. Then you try and measure its parameters and that sneaky $\epsilon \sim N(0, \sigma^2)$ crops up at the end of the line. In the lab it's measurement error. Outside of controlled circumstances, it's pretty much everything. That epsilon is individual level variation.

With God like knowledge (even if we posit is impossible for any human to attain), we could know where the ball will land. — Hanover

If you assume that here is an actual physical value for each item in the Galton box; and that this value could be known.

One puts a kettle on a fire, and it does not heat up.

There is, as per Hume, no contradiction in this; the description is coherent; we know what has been said.

Causation is not logical necessity.

Here we might better follow Hume than Kant.

The standard philosophical prejudice is that given an accurate enough account of the position of the box and a given ball, a competent physicist will be able to tell us which of the bins across the bottom the ball will land in.

And in this sense the path of the ball is determined.

But of course no one could determine the final resting place of the ball. Even the smallest error in the initial positions will be magnified until it throws out the calculations.

Anscombe wrote this in a time of only nascent chaos theory, which could only serve to amplify her point.

The notion that the universe is determined fails. — Banno

Your assumption and the article's assumption is that the Universe is simple enough for extremely intelligent humans to predict an extremely complicated universe. This article was written by a simpleton. Much of quantum physics is disagreed upon by many physicists. Not all Quantum Physicists agree on Quantum Physics. People very often assume that Theoretical Physicists always make the right judgements.

If i or you don't 100% understand the math and the lab results behind a scientific theory, you and i (right/wrong/or indifferent) are putting our faith in scientists. Belief, Faith, and partial understanding of a concept are all forms of gambling.

All philosophers, of every school, imagine that causation is one of the fundamental axioms or postulates of science, yet, oddly enough, in advanced sciences such as gravitational astronomy, the word "cause" never occurs.

Russel, On the notion of Cause

He's got a point. A few times I've seen it written on these forums that Newtons first law is the law of causation. Of course, it isn't. But this is so hard to argue when those who advocate causation will not agree as to what it is.

This article was written by a simpleton — turkeyMan

You're new. You will need to present more than this barely articulate drivel should you wish to receive responses here.

This article was written by a simpleton — turkeyMan


You're new. You will need to present more than this barely articulate drivel should you wish to receive responses here. — Banno

How is it inarticulate? You know full well what is meant and most people can understand it. Why don't you want to understand what i wrote?

Are you honestly going to argue about what the definition of Causation? Do you believe in Objective truth?

Are you honestly going to argue about what the definition of Causation? — turkeyMan

Actually, yes, that's pretty much what this thread is about.

This, @Hanover, is the issue in Anscombe's article, so well articulated above by @tim wood.

I think you want to believe in free will. The only way free will exists is by some cosmic miracle. Free will is a desire of people who want pseudo-god hood and want to look down on people less fortunate than them.

I think you want to believe in free will. — turkeyMan

Why would you think that? What have I said that would lead to that conclusion? Or are you just making assumptions?

But of course no one could determine the final resting place of the ball. Even the smallest error in the initial positions will be magnified until it throws out the calculations. — Banno

That doesnt show that determinism fails, it shows the limits of the predictive method used. This is just increasing the complexity of the calculation to create the illusion that it isnt determined (cuz we cant show how, which is a fallacy).
A box of much simpler design would show determinism quite obviously. We could increase the complexity of the box and continue showing how the balls path is determined right up until the point where the complexity grows beyond our ability to predict but that doesnt show determinism failing, it would only show the ability to predict as failing.