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? — Banno

Ok. You might be playing games but as long as you claim not to believe in free will, i'll let it go. People should make good decisions because we are all animals, not because it will quickly propel them to some false god hood. Reality is extremely complex. I guess we do agree on some things.

That doesn't show that determinism fails, it shows the limits of the predictive method used. — DingoJones

On review, Anscombe seems to me not to be saying that even if we had perfect information we could not predict the landing place of the ball, but rather that since we do not have perfect information, we cannot do so.

Yet no one could have deduced the resting place of the ball – because of the indeterminateness that you get even in the Newtonian mechanics, arising from the finite accuracy of measurements. From exact figures for positions, velocities, directions, spins and masses you might be able to calculate the result as accurately as you chose. But the minutest inexactitudes will multiply up factor by factor, so that in a short time your information is gone. Assuming a given margin of error in your initial figure, you could assign an associated probability to that ball's falling into each of the pipes. If you want the highest probability you assign to be really high, so that you can take it as practical certainty, it will be a problem to reckon how tiny the permitted margins of inaccuracy must be – analogous to the problem: how small a fraction of a grain of millet must I demand is put on the first square of the chess board, if after doubling up at every square I end up having to pay out only a pound of millet? It would be a figure of such smallness as to have no meaning as a figure for a margin of error.

While a box of much simpler design would show determinism quite obviously, a box of more complicated design would foil our best efforts. Just as our poor physicists completes their calculations, we add an extra row of pegs...

That is, determinism ceases to be a physical Law so much as a metaphysical desire on the part of certain philosophers.

Add to this the Russel article and the physics posited by Del Santo, and laws of causation looks more like wishful thinking.

If nothing else, they ought not be taken as granted.

On review, Anscombe seems to me not to be saying that even if we had perfect information we could not predict the landing place of the ball, but rather that since we do not have perfect information, we cannot do so. — Banno

Ok, then I would only point out how little is actually being said there, seems pretty obvious at that point.

That is, determinism ceases to be a physical Law so much as a metaphysical desire on the part of certain philosophers — Banno

Well it could be both those things.
So there are 3 things at play, the knowledge of how something is determined to go(which we can do pretty well on pretty simple examples), the actual things that determine the way things go and the range of determinate factors we are actually able (and/or not able to) to track.
It seems to me only the middle one is what determinism is about. The others are so much more generic and tangental as to fall under different purview.

If nothing else, they ought not be taken as granted. — Banno

Agreed.

So there are 3 things at play, the knowledge of how something is determined to go(which we can do pretty well on pretty simple examples), the actual things that determine the way things go and the range of determinate factors we are actually able (and/or not able to) to track.
It seems to me only the middle one is what determinism is about. The others are so much more generic and tangental as to fall under different purview. — DingoJones

Hmm. The first and third concern epistemology. Del santo's Principle of Infinite Precision characterises it thus:

despite it might not be possible to know all the digits of a physical quantity (through mea- surements), it is possible to know an arbitrarily large number of digits.

The second concerns ontology:

there exists an actual value of every physical quantity, with its infinite determined digits (in any arbitrary numerical base).

Del Santo's reply to the ontological point is, in part,

...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. — Banno

Perhaps the state of a particle in phase space might be given not by a point but by a volume.

Del Santo's definition, all his own afaik, is that infinite epistemological precision means that the number of of decimal points has no finite lower bound, but may not be infinite. This is equivalent to saying that the error may be arbitrarily small, but not zero, which, to me, says it cannot be arbitrarily small. His infinite precision is that attained by infinite technological progress which always approaches, but never reaches zero uncertainty. It is in itself a reasonable definition, but he is using different language to cast doubt on determinism rather than using argumentation within the same language. — Kenosha Kid

If you read the ".999...=1" thread you'll see that Banno believes that a small nonzero quantity actually is zero, and considers the alternative as lunacy.

@Kenosha Kid, indeed, before you enter into a discussion with Meta, do take a look at the 0.999... = 1 thread.

Sure, but isnt 2 the only one determinism specifically entails? Thats not mutually exclusive to what you said.

If you like; There's a difference between a thing being at a particular position and a thing being measured to be at a particular position.

indeed, before you enter into a discussion with Meta, do take a look at the 0.999... = 1 thread. — Banno

Yeah I've read it. Del Santo's definition pertains to a finite number of decimal points, however large. 0.999... has an infinite number of decimal points, and so is identically 1.

One should not forget that even logical laws are doubtable whenever they are interpreted extensionally as referring to a collection of real-world objects, as opposed to when they are used intensionally as rules of production.

Most of the time logic is used and appealed to directly, without reference to extensions, because it is used for asserting normative statements. The logical description of an ideal electronic circuit is comparable to the expression "Tidy your room! because i said so!". This ideal use of logic is comparable to ethics and it makes no sense to speak of epistemic doubt here. In contrast, if a circuit description was thought to universally describe the operations of real world electronics, this is obviously a highly doubtable proposition.

Physical laws are the joint expression of normative sentiment and physical description and so they aren't pure propositions in the ideal philosophical sense. The normative part is expressed by the use of universal quantifiers that aren't falsifiable and which say "Every X is a Y". But they don't need to be falsifiable, for their purpose is political,namely to assert scientific and cultural policy in the same way as the electronic circuit design that implicitly asserts "Intel should make chips this way".

Getting back to the original discussion, consider how one determines measurement precision. Isn't it's very definition ultimately in terms of the reproducibility of experimental results? In which case, if repeated experiments fail to reproduce results, then by definition measurement precision is lacking.

Del Santo's definition pertains to a finite number of decimal points, however large. 0.999... has an infinite number of decimal points, and so is identically 1. — Kenosha Kid

The problem though, is this:

However, the principle of infinite precision is inconsistent
with any operational meaning, as already made evident by
Max Born. — https://fqxi.org/data/essay-contest-files/Del_Santo_FQXI_essay_indete.pdf

So Del Santo suggests that the tiny uncertainty hidden by a faulty application of the principle of infinite precision, in an instable system, would increase exponentially with time, allowing for the appearance of indeterminacy.

The idea is that any initial position (inertial frame of reference) cannot be represented with infinite precision, so the notion that it might be represented in this way ought to be dismissed. Therefore to have the most accurate representation, which is consistent with the real possibilities of representation, we ought not try to represent it with infinite precision.

As we will show in the next section, one can indeed envision
an alternative classical physics that maintains the same general laws (equations of motion) of the standard formalism, but
dismisses the physical relevance of real numbers, thereby assigning a fundamental indeterminacy to the values of physical
quantities, as wished by Born. In fact, “as soon as one realizes that the mathematical real numbers are not really real, i.e.
have no physical significance, then one concludes that classical physics is not deterministic.” [13]. — https://fqxi.org/data/essay-contest-files/Del_Santo_FQXI_essay_indete.pdf

I contend that hazard is no illusion, and that we all know this, intuitively. We often say things like"Shit happens", or "Nobody can know what the future will bring", etc.

Considerations of some mysterious "onthological certainty" are useless, because we humans will never be able to access this magic realm of "things in themselves". We're better off assuming hazard exist, because for all intent and purpose, it does exist for us. It's part of our condition.

If you really need to think in terms of what hypothetical demons and gods do, consider that if God exists, He could well have made his creation open, evolutive and able to surprise even Him. Otherwise what's the fun of creating anything?

Consider that any demon predicting the whole future would also need to predict what he himself will think in the future (assuming the demon is part of the universe)... and that if he does so, he will think it now and not in the future!

Anyone proposing that the whole history of the universe was exactly 'determined' at the time of the Big Bang + 1 second -- including me writing this sentence from a Roman bar today -- better try and prove it, because that's quite an extraordinary claim...

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. — Banno

More word games, Banno?

If it is a given that the account of the position of the box and a given ball are accurate, then why would there be errors? If it were accurate, then that means that there are no errors, so you're contradicting yourself.

And then you contradict yourself again by asserting that even "the smallest error" determines that the "calculations will be thrown out".

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

You actually showed that it doesn't because you used reasons to determine your conclusion.

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. . . . . The notion that the universe is determined fails. — Banno

Many years ago, I visited the Seattle World's Fair, and came across a large display of a Galton Box or Quincunx, [image below]. The adjacent sign says : "when the falling balls are observed one-by-one the path of each is unpredictable, but taken many by many they form an orderly predictable pattern". This is a graphic illustration of order within randomness. The overall bell-shaped pattern at the bottom is predictable, and seems to be predestined by statistical laws of Probability. However, one of the white ping-pong balls was painted red, and it landed in a different location after each randomized ball-drop. That exception to the rule seems to imply that there is Freedom Within Determinism.

Obviously, ping-pong balls have no freewill, but the Galton Machine reveals a tiny glitch in statistical determinism : there are exceptions to the Normal or Average pattern. Therefore, philosophers who interpret Physics as Fatalistic are wrong. Instead, I take this graphic illustration of Probability to mean that there is a possibility of Individual Freewill Within General Determinism. The future course of the physical universe was indeed fixed at the moment of the Big Bang, with all laws & constants established, and with an unbroken chain of cause & effect. And yet, self-conscious reasoning humans seem to be able to manipulate the laws of Nature to their own ends. Scientists call it "Technology", but I call it "Freewill" : the ability to deny Destiny. :nerd:

Rationalism vs Fatalism : http://bothandblog2.enformationism.info/page67.html

Determinsm : “Determinism is a long chain of cause & effect, with no missing links.
Freewill is when one of those links is smart enough to absorb a cause and modify it before passing it along. In other words, a self-conscious link is a causal agent---a transformer, not just a dumb transmitter. And each intentional causation changes the course of deterministic history to some small degree.” ___Yehya

Galton Quincunx Machine :


Galton Box in Motion : https://en.wikipedia.org/wiki/File:Galton_box.webm

we can be quite sure that a third measurement won't be at 0.7T, for instance, unless something other than gravity was acting. — Kenosha Kid

So regarding the measurement error thing. Wanted to make my argument more precise.

Two main points:
(1) Laplace's demon does not take error terms' interpretations' seriously.
(2) The existence of error terms in a model breaks the deterministic relationship between the observed values of measured quantities in those models.

Say you're testing a linear relationship, the theory says that the following relationship holds between two quantities:

$y = mx + c$

where $y$ and $x$ are both measurable in the lab. You do an experiment, and there's always individual level noise and measurement imprecision. In a situation like that, you modify the model to include an error term $\epsilon$:

$y = mx + c + \epsilon$

The relationship which is being studied is $y=mx+c$, the individual level errors are assumed not to be part of the causal structure being analyzed. Nevertheless, when you make the measurements, there is individual level variation. Its causal structure is unmodelled, it's assumed to be noise. But as part of the model that noise $\epsilon$ stands in for all other causal chains in the environment which influence the measurement.

Perhaps I'm wrong in this, but I think that from the perspective of Laplace's demon, it's imagined that Laplace's demon knows $y=mx+c$ holds, but must also know the entire causal structure that yields the $\epsilon$ to contribute to the measurements as they do. Laplace's demon knows why the $\epsilon$ that makes every measured $(y,x)$ pair deviate slightly from $(mx+c,x)$ takes the value that it does. But Laplace's demon knows with complete specificity the behaviour of unspecified, unknowable causal chains. Unspecified and unknowable regarding $\epsilon$ is part of the model structure. Such causal chains are not part of the causal relationship between $(y,x)$ being studied, but they're part of the causal chain in the experiment linking observed $x$ and $y$.

The status of that "unknowable, unstructured variation" is part of every model as soon as it ceases to be a theoretical idea and comes to obtain estimated parameters. What I'm trying to highlight is that the structure of interest - $y=mx+c$ loses its determinism (in the sense that $x$ intervention yields $y$ response) as soon as that $\epsilon$ gets involved. Even in the most precise measurements, it is possible that individual level variation explains the entire observed relationship, it can just be made vanishingly unlikely. That possibility mucks with characterising Laplace's demon's knowledge from how we use physical law, it's at best an unrealistic idealisation from it that forgets how the error term works. Every experimental model that involves an error term breaks the metaphysical necessity of the deterministic relationship contained within it insofar as it purports to explains the observed data.

https://fqxi.org/data/essay-contest-files/Del_Santo_FQXI_essay_indete.pdf — Metaphysician Undercover

Page not found. Wtf, MU?

Finally found:

"Bringing into play again Born’s operationalism, one ought to consider the following [9]:

'A statement like x = π cm would have a physical meaning only if one could distinguish between it and x = πn cm for every n, where πn is the approximation of π by the first n decimals. This, however, is impossible; and even if we suppose that the accuracy of measurement will be increased in the future, n can always be chosen so large that no experimental distinction is possible.Of course, I do not intend to banish from physics the idea of a real number. It is indispensable for the application of analysis. What I mean is that a physical situation must be described by means of real numbers in such a way that the natural uncertainty in all observations is taken into account.'

"As we will show in the next section, one can indeed envision an alternative classical physics that maintains the same general laws (equations of motion) of the standard formalism, but dismisses the physical relevance of real numbers, thereby assigning a fundamental indeterminacy to the values of physical quantities, as wished by Born. In fact “as soon as one realizes that the mathematical real numbers are not really real, i.e. have no physical significance, then one concludes that classical physics is not deterministic.” [13].
https://arxiv.org/pdf/2003.07411.pdf
Italics added.

Further:

"Principle of infinite precision
1. Ontological – there exists an actual value of every physical quantity, with its infinite determined digits (in any arbitrary numerical base).
2. Epistemological – despite it might not be possible to know all the digits of a physical quantity (through measurements), it is possible to know an arbitrarily large number of digits. It is only when its formalism is complemented with this principle that classical physics becomes deterministic.

"However, the principle of infinite precision is inconsistent with any operational meaning, as already made evident by Max Born. The latter gave pivotal contributions to the foundations of quantum formalism –introducing the fundamental rule that bears his name, which allows to assign probabilities to quantum measurements, and for which he was awarded the Nobel Prize– and became critical of classical determinism due to its “infinite precision”. Indeed, in his essay Is Classical Mechanics in fact
Deterministic? [9], he affirmed:

"It is usually asserted in this theory [classical physics] that the result is in principle determinate and that the introduction of statistical considerations is necessitated only by our ignorance of the exact initial state of a large number of molecules. I have long thought the first part of this assertion to be extremely suspect. [...] Statements like ’a quantity x has a completely definite value’ (expressed by a real number and represented by a point in the mathematical continuum) seem to me to have no physical meaning. [Because they] cannot in principle be observed.' " (Same source as above.)

--------------------------------

Reading this and the paper it came from, it's clear you did not take the time and effort to understand it, but instead quoted it out of context. And why would you do that, MU?

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

Determination and predictability aren’t the same thing. The whole point of chaos theory is that even a perfectly deterministic system can still be wildly unpredictable. But so long as the exact same starting conditions still give the exact same outcome always, it’s still deterministic.

My own addition to that topic: backward causation necessarily induces apparent randomness to a forward-looking observer. Prediction of the future approximates backward causation; it’s like getting imperfect information directly from the future. That is why predictive systems are inherently chaotic. So either the universe is random and so unpredictable, or else it’s deterministic and so predictable and so capable of containing predictors who would make it chaotic and so unpredictable.

Basically, so long as you have things like us who will do whatever prediction may be possible, the universe will be unpredictable, precisely because of those attempts at prediction. Even if it is fundamentally deterministic.

But so long as the exact same starting conditions still give the exact same outcome always, it’s still deterministic. — Pfhorrest

Unfortunately, this claim is not testable, and thus determinism is not a scientific theory.

..it's clear you did not take the time and effort to understand it... — tim wood

Now why would you say a thing like that?

The issue, as explained in the section following your quotes, is that in the application of real numbers, the infinite is represented as finite. (This is the point of the other thread, the infinite decimal extension of .999... is represented as 1).

Now, in philosophy we understand that what appears as infinite is really indefinite, or indeterminate, and this is a deficiency in our capacity to measure that thing. So when the application rules of the real numbers make what is really indefinite, or indeterminate, appear as definite or determinate, it is simply an illusion created by the customary use of that number system.

Now, in philosophy we understand that what appears as infinite is really indefinite, or indeterminate, — Metaphysician Undercover

Confusion on confusion. Do you understand the ratio between the circumference and diameter of a circle to be a number?

If it is a given that the account of the position of the box and a given ball are accurate, then why would there be errors? — Harry Hindu

Oh, Harry.

Do you understand the ratio between the circumference and diameter of a circle to be a number? — tim wood

No, it's an irrational ratio, that's the point. You might call it an irrational number, but representing it as "a number" is exactly where the problem lies. Making it "a number", is to make it something definite, determinate, when the essence of the irrational ratio is that it is indefinite, indeterminate.

So, according to the above described principle of infinite precision, this irrational ratio, the quotient which proves to have infinite decimal places, indicating a division problem which cannot be resolved, this thing which is by its very nature indefinite, is made to appear as finite and definite. Therefore that principle is faulty.

The point of that part of the article is that in using the real numbers this way, the indeterminateness which exists within the real world (reality), is made to appear determinate.

Del Santo's reply to the ontological point is, in part,

...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. — Banno

Given infinitesimals there seems to be no reason to conclude that an infinite amount of information could not be "held" within what we would think of as a finite volume of space. It seems to me the limitation on us is time not space, and that our consequent characterization of spaces as possessing finite volumes says more about us than it does about the spaces.

Given infinitesimals there seems to be no reason to conclude that an infinite amount of information could not be "held" within what we would think of as a finite volume of space. — Janus

Did you misword that? That an infinite amount of information could not be held in a finite volume is a result of Landauer’s principle, apparently; although that is not itself without objections.

I'll not argue the point here, but leave it to the physicist.

No, it's an irrational ratio, — Metaphysician Undercover

That is, π is not a number. Sorry, but your private understanding of the universe is going to have to remain all and only yours.

Apparently you missed this in what you quoted above, and what I requoted above in italics:

Of course, I do not intend to banish from physics the idea of a real number. It is indispensable for the application of analysis. What I mean is that a physical situation must be described by means of real numbers in such a way that the natural uncertainty in all observations is taken into account.'

See, your guy. He, your guy in your quote, does not have a problem with real numbers as numbers.

Did you misword that? — Banno

Thanks for pointing that out; it's now corrected.

and all:

Perhaps it might clarify things to return to the first example from the Del Santo article:

Referring to figure 1, consider a (classical) par- ticle that is bound to move in a one-dimensional cavity with perfectly elastic walls and total length l. If the particle has a perfectly determinate (i.e. with infinite precision) initial position x(t = 0) = x0 and velocity ⃗v(t = 0) = ⃗v0 , classical physics then allows to predict, also with infinite precision, the future positions x(t) and velocities ⃗v(t) for any time instant t.

We then introduce an error into the measurement of the initial velocity. Regardless of how small that error is, it will build over time until the error in predicted position is greater than the length of the cavity.

Now the default position adopted in my high school physics class was that the error was introduced by a lack of precision in the measurement. The assumption was that there is indeed some real number that gives the exact velocity to infinite precision, and that the error represented the degree to which one could operationally approximate the actual velocity. The alternative explanation being offered by Del Santo is that the initial velocity does not correspond to some real number, but instead to some region of the real numbers. The boundaries of this region are also indefinite, but lies within the bounds of our arbitrarily accurate measurement.

There's a certain intuitive appeal to this.

A further example. Suppose you are asked to measure a table's width. You use a tape to measure it to within a millimetre. You repeat this measurement a dozen times and calculate a value for the error.

Is it that the table has a specific width that would be given bu some real number, and your measurement approximates to that number; or is it that the width of the table is not definite, but is the range of numbers specified by the measurement and error?

It seems intuitively more difficult to see the width of a table as corresponding to some real number.

The alternative explanation being offered by Del Santo is that the initial velocity does not correspond to some real number, but instead to some region of the real numbers. — Banno

That is just quantum mechanics. Which appears to be how reality actually works, so no problem there.

My only point was that even if the universe was perfectly deterministic at its base and errors in measurement were just errors in measurement, a chaotic system still becomes impossible in practice to predict; and a system capable of predicting is inherently chaotic, so even if the universe was perfectly deterministic, our own ability to predict it (however imperfectly) would still undermine its predictability via chaos.

The whole of the Mandelbrot set is found in Z^2+C. The calculation is deterministic.

That is, a chaotic system is only unpredictable in practice - operationally. Given infinitely precise initial variables, there is only one outcome.

So I don't see a relevant difference in kind between the marble int he tube in my example and a chaotic system.

Show me if I'm wrong.

See, your guy. He, your guy in your quote, does not have a problem with real numbers as numbers. — tim wood

Why do you like to quibble tim? I could respond to your quote with the following quote:

In fact “as soon as one realizes that the mathematical real numbers are not really real, i.e. have no physical significance, then one concludes that classical physics is not deterministic.

But what's the point?

Whether or not a real number is or is not a "real" number is beside the point, and not at all relevant. What is relevant is the "natural uncertainty in all observations", which some use of real numbers tends to veil with the pretense of what he calls "infinite precision".

This natural uncertainty is true of all all descriptions of initial conditions, so it applies to all inertial reference frames. Since the uncertainty develops exponentially with the passage of time, we rapidly become deficient in the capacity to distinguish between an improperly represented inertial reference frame, and an external cause in the occurrence which follows. Determinism as an attitude, is dependent on the assumption of a reliable inertial reference. When uncertainty is apprehended as a feature of the initial conditions, (initial conditions being what limits future possibilities) rather than as a feature of the outcome of the activity, then determinism is vanquished. The certitude required to support determinism cannot be obtained.