And the math will set you free by Cristinel Stoica

Sorry for the ambiguity of some of my words that could be perceived more negatively than I meant. I did not mean that you had any intention to twist something. About this, I only meant I saw your interpretation of quantum physics as a sort of more complicated equivalent to other concepts I know. I am aware that when some ideas are discovered, they usually first appear in forms which are not the optimal way they can be expressed.

Of course I am aware that your idea of the line aimed to be interpreted mathematically only, so that physical interpretations of this idea were irrelevant. However, as long as it is about mathematical abstraction, I would consider it more relevant to stay in the vocabulary of abstractions, such as by the idea of encoding texts by numbers, and the idea that all natural numbers exist no matter how big they may be. So I just wanted to insist on the fact that a geometrical view adds strictly nothing to it, unless it gives a wrong intuition.

About NDEs, I think there are enough proofs, the only problem is that it is such a huge field that many people think there is no known proof yet just because they did not take enough time getting informed on what there is. I would just advise you to go explore the field without any preconception about what should a proof exactly look like to be conclusive, because many kinds of things can happen and form different sorts of proofs.

"Godel, what I said was in the context of Hawking's argument"

I did not check what Hawking's argument is, I just directly know what the incompleteness theorem says and how it can be proven :)

If you don't assume that the laws of physics should be able to address arithmetic then all comments on the consequences of the incompleteness theorem on the laws of physics should be dismissed as inapplicable: then physical laws cannot assert their own undecidability, simply because they are not even able to express the question of their own undecidability, no matter what Hawking might have suggested about it.

About branching time "in the context of indeterministic dynamical systems" : which indeterministic dynamical systems are you talking about, which can be found in known fundamental physics ? There is one established physical law, that is the unitary quantum evolution, which is deterministic. And there is the measurement problem, with disputed interpretations whether the collapse is due to conscious observation, or a spontaneous one, or none at all (MWI). I think, if you see a branching time somewhere, and you think that the choice operation retroactively modifies the state starting exactly from that branching time, then you make the behavior at that branching time discontinuous, since it does not conform to the unitary character of quantum evolution ; if you try to get a continuous indeterministic behavior from some non-linear differential equations with non-differentiable terms, I will dismiss such equations as having nothing to do with anything that could be scientifically verified about our universe.

I think you are over-interpreting my words. I do think your interpretation of quantum physics is more complicated than the Copenhagen interpretation. What I meant is that you tried to introduce the idea of restoring a continuity, since you criticize the Copenhagen interpretation as introducing a discontinuity. But I consider that we can reach the same "result" of looking at things in a physically continuous way, not by completely different ideas, but by re-interpreting the Copenhagen interpretation :) and more precisely considering the mind makes collapse interpretation as I described, which is not so different from Copenhagen.

I consider that your way of calling "anecdotal evidence" the whole body of existing observations which I guess you did not really care to study, is missing the point of the fact that even though "anecdotal" in some sense, some of these evidences (and even more: the accumulation of them) are nevertheless solid genuine evidence for your question of "distinguishing between remembering and imagination". Thus, I would dismiss the very categorization of evidences between "anecdotal" and some other, supposedly more solid kind of evidence, as meaningless : there is no such boundary. So, as soon as would be established that genuine out-of-body perceptions occurred during the experience (such as by the accurate report of information that could not be accessed by the body), it becomes logically necessary to reject any idea that such memory could be a fruit of the imagination by natural effects of neural activity, as an absolute impossibility, without any need of close examination of the brain activity.

" it doesn't make sense. It is like saying that if you don't assume the existence of tooth fairy it doesn't make sense to criticize a viewpoint which assumes the existence of tooth fairy."

It makes sense, and no it is not "like" what you say. Maybe you misinterpreted my words again, but for what I meant your comparison is just wrong, you are bringing up an example whose structure has nothing to do with the issue of the incompleteness theorem we were discussing. Let me be more precise to avoid any misunderstanding : I meant "Let us split possible cases: either the laws of physics are able to express arithmetic, or they are not. In the first case we can discuss the consequences of the incompleteness theorem on the laws of physics ; in the second case we can't, as it is not applicable". Any issue of personal belief is out of the question here.

" I addressed any possible indeterministic theory, to show that indeterminism doesn't guarantee free-will. Rejecting them because the only one you want to consider is quantum indeterminism is unjustified."

What is the point of discussing "any possible indeterministic theory" ? as if the probability for the mathematically expressible laws of physics of our universe to be as described by quantum physics, was close to zero; my view is to consider that this probability is close to 1. You seem to assume that some abstract general landscape of "all possible indeterministic laws" you nevertheless seem to have somewhat clear ideas of and that excludes quantum physics, should be admitted as much more likely to contain the correct picture instead. I think that my hypothesis has more scientific grounds than yours.

"branching in the space of states, the branching of the history into two possible histories", what the heck is that ? You mean the consistent histories interpretation ? Of course, except that quantum physics could never find anything to explain what may cause such branching, which has to be postulated from the outside of physics, and it makes the evolution clearly discontinuous, which you were claiming to avoid.

"You think one should discuss only what one believes". No I don't. Of course I don't !!!!! How can you imagine that nonsense ????? Again an absurd misunderstanding. What I meant is that any argument should clearly distinguish both cases. So the problem in your essay (or did I fail to read it correctly ?) is that you did not make it clear what are the assumptions under which your argument is written. And this matter of "the assumptions under which an argument is written" is a matter of text and clarified presentation. And this matter of text and clarified presentation, has nothing to do with any issue of personal belief of the author, which is obviously irrelevant. If my reply looks as if your personal belief was the matter, I am sorry I did not mean it. I thought it was your belief since you seemed to take for granted that the incompleteness theorem was applicable, which requires this assumption, but this is ultimately irrelevant. then if it is not your belief, the trouble I found is that your text did not seem to make the needed clarification of the distinction of cases.

I will reply in more details later.

Dear Christinel,

in your essay you outline clearly the 'isomorphism-paradigm' of the relation between physics and mathematics. I quote from you essay :1. 'If the universe is describable by a list of propositions, then there is a mathematical structure describable by the same propositions'.

And a bit later :2'....the unified theory must exists...because we can not live simultaneously in two disconnected worlds.'

I would like to point out that you make two strong metaphysical assumptions, based upon the ontology of classical mechanics :

1. That it is possible to come up with a complete list of properties of the entire! universe.

This assumption is clearly wrong!Why? Because you leave out the agent compiling the list.According to quantum mechanics it is simply not possible to auto-describe a state to a system.A quantum mechanical state ( even of the 'universe') is always assign by an observer outside the system. In other words, your 'complete' list always has a blind spot.

2.You make the assumption that there is only 'the-one-reality', with all of its parts in mutual 'connection'.

But it is again quantum mechanics which tells us otherwise. The parts of the reality 'to be connected' is not only a logical operation ( like the 'AND'-operator), but also a physical interaction between a system and an observer (another system).During the interaction the system will in general undergo a random change of state.

That means that your 'complete' list of properties not only has a blind spot, but it also undergoes random fluctuations.

As a conclusion, the notion of 'the-one-whole-reality' ( can be traced back to Parmenides) is exposed as a fairy tale.

We should learn to live and do physics without it.

In my essay I describe how physics is better understood as Darwinian process, instead of a static description of 'the -one-reality'.

regards

Frank

Dear Cristinel,

Lots of sweeping statements in this essay and many attempts to refute other arguments without sufficient logic or evidence and more of of attempts to persuade with a general sweeping comment (where is your evidence for "Even if we manage to extend the list with new truths about the universe, there is a mathematical structure which is isomorphic to the universe described by the extended list of propositions" or "Any phenomenon related to time, for example memory, can in principle be described mathemat- ically.").

The main issue I think you should consider is the evolutionary character of mathematics. Mathematics is not a constant where the universe could or could not be isomorphic to it. Mathematics and physics have grown together. For a couple millennia Euclid's fifth postulate was considered to be True, yet a little over 150 years ago it was shown to be one of a few options (it was only true in certain circumstances, so not all circumstances everywhere). Can we say that the universe was isomorphic to Euclildean geometry in 1800, but not now? Our current physics would not be possible without this fundamental change in mathematics beyond Euclid. Since we are all limited to our current time in history, we are limited in what we know of mathematics, which could be, even today, a very small amount.

You also seem to think mathematics is itself consistent and complete, which is impossible to prove (and Godel's proof indicates otherwise for completeness).

Finally, you appear to think that the universe does not have contradictions in it, something that defies all evidence we have at the moment (if reductionism is correct, why is an intelligent being at our scale needed to understand it and to affect the very small as part of the understanding process?) - so this must be an article of faith on your part, which extends as much to mathematics as to the known universe.

Thank you for your essay, but I an unconvinced by your arguments.

Donald

Now I more closely examined your article "Modern physics, Determinism and free-will", for properly replying to what you actually put there (sorry I was not careful enough last time). Indeed, I confused between your "interpretation" that you support, and your (incorrect) description of the wave function collapse with the role of free will in wavefunction collapse (that you criticize). I see now they were separate sets of concepts.

About your own "interpretation":

"even though the states |П€j0 вЊЄ were obtained by a unitary operator from the orthonormal states |П€j1 вЊЄ, they are not necessarily orthonormal, and may even become dependent. In fact, in our case they all become at t0 equal to |П€0 вЊЄ. The operator U is a unitary operator on the total space of |П€вЊЄ|О·вЊЄ, but not on the space of |П€вЊЄ. This shows that it is possible for |П€вЊЄ to satisfy the constraints of both observations, and still have unitary evolution"

Assuming for a moment that such ideas make sense, then why do you need the evolution to be unitary in the "total space" |П€вЊЄ|О·вЊЄ ? After all, this system is only a subsystem of the Earth. So, if all we need is that the evolution is unitary for the Earth system then the evolution of its subsystems do not need to be unitary. By the way, where is the assumption of unitarity in QM ?

Now seriously : according to the rules of established QM, what your claim rigorously means is that the first measurement device (that made the first measurement) keeps physically interacting with the system during the time between measurements, so as to progressively align it with the basis of the second observable. Such a claim of interaction is just plain wrong. In reality, after the first measurement, the system no more interacts with the first measurement device, and even if a little bit of influence might subsist, it would be ridiculous to assume that this interaction systematically manages to align the system to one eigenvector of the second observable. You seem to attribute this coincidence to final causes: you seem to argue that there should exist possible initial conditions that make the evolution fit this condition, so that the presence of the second measurement will retroactively arrange the initial conditions to make all things fit so as to achieve this evolution of the system from the eigenstate of the first observable to the eigenstate of the second observable. I consider this as a mere dream since anyway, in good approximation, there is not supposed to be any interaction between the first measurement device and the system after measurement, so that no fine-tuning of the apparatus can make its non-existing interaction with the system succeed to align it with eigenvectors of the second observable.

"In UIQM I acknowledge that the observed system is in fact entangled with all systems with which it interacted in the past."

Not entangled, but in continuous physical interaction. You are confusing between (the mathematical expressions of) entanglement and physical interaction.

In conclusion, your "interpretation" of QM is not an interpretation at all but some fantasy, another theory far from what QM actually says. Now since you did not explicitly claim to reject QM to develop your own theory, but kept giving the illusion that you respect it and only try to interpret it by keeping superficial similarities ("unitary evolution"...), it just shows that you have no serious understanding of quantum physics.

Now about your discussion of standard QM and the mind makes collapse interpretation:

"If humans base their choices on random inputs, then this by itself doesn't make them free."

Of course but only under the assumption that the inputs are actually random in the case under consideration. As I explained in my interpretation of QM, I consider that the same process of wave function collapse usually obeys randomness in non-living systems, but departs from it in the cases of brain processes where free will applies. And I explained in length why I see this sort of "discrepancy" between the kinds of outputs of the same physical process of wavefunction collapse (normal randomness in "purely physical systems", vs. free will in the brain), to be not a discrepancy at all but a very elegant, coherent solution. (I also like the explanation by the last reply of that thread).

"The configuration after the branching has to evolve, so that the agent can see where it is going"

Where does that idea come from ? I see no reason for it. My view is that the collapse occurs at some time after decoherence, when the different possibilities are meaningfully distinguished by the observer; there is no need to assume any branching to have occurred before that time, nor to assume that the observer has any explicitly conscious perception of the alternative possibilities among which he is actually (more or less) choosing.

"in the case of quantum mechanics, where the unitary evolution governed by Schrödinger's equation is interrupted from time to time by the wave function collapse. Assuming that an agent uses this randomness to perform free choices, she must act precisely at the appropriate moment and position where the branching appears."

"(The discontinuous jump) has never been directly observed. There is no known explicit process leading to the discontinuity. In fact, all interactions we know fit well in the Hamiltonian description, and the measurement devices are made of systems which obey it. So, where does the discontinuity come from?"

Indeed, if taken separately, these 2 issues would be problems. However, taken together they become zero problem as they resolve each other. Indeed, there is no definition of when the collapse occurs ? It looks like a mystery how the time of free choice may coincide with the time of collapse ? No problem : let the "time of collapse" be conventionally defined as given by the time of free choice. Then, there is no more mystery when and how the collapse occurs, and there is no mystery either how the time of choice may happen to coincide with it.

"It would violate the conservation laws". This is one of my objections against spontaneous collapse theories. But my interpretation of the collapse is different : I think it occurs not by projection but by selection of a world after decoherence (this is an emergent condition, that fits with my idea of collapse as a non-physical, non-local process) : it is still non-unitary but resolves some defects of the projection postulate. It does not satisfy the conservation laws if taken in a naive sense (expressed by averages) that you wrongly assume to be the necessary form of expression of the conservation laws, but does satisfy a more subtle understanding of the conservation laws that I explained there.

Generally, my page on the mind makes collapse interpretation replied to all of your objections in your "2.2. The internal tension of quantum mechanics".

"I find hard to believe that the environment is the cause of selecting the eigen-states, because these depend only on the measurement device. Change the measurement device, and leave the rest of the environment unchanged, and the eigen-states change too."

You missed that the role of the environment in decoherence happens by interaction with the measurement device. So, change the measurement device, leave the rest of the environment unchanged, then the environment will interact with the new measurement device to do the decoherence according to the new eigenstates given by the new measurement device.

You speak about the "decoherence interpretation" as if it was an option to accept or reject it. The reality, well-known by all serious participants in QM interpretation issues, is that decoherence is NOT an interpretation but a logically necessary consequence of established QM, completing the picture of what needs to be interpreted.

I stopped reading your article here. I consider that I found enough fatal flaws in it already. And I see it as a big bug in the academic system, to find such an incompetent "physicist" have any position as physicist there.

"to make a choice, you need to know what that choice means, some of its consequences. Otherwise what kind of a choice is that? The alternative is letting the randomness choose for you."

You are talking about fantasy, not about real facts. Of course it would be nice if we were always correctly informed about the consequences of our choices before making them, but this is not how things usually happen in the real world, or anyway the laws of physics do not provide this. I never claimed that freedom never turns out to be a poisoned gift by lack of proper available means to anticipate the consequences of choices (and personally I do feel it as a very absurd poisoned gift in many cases). To anticipate the consequences of our actions we only have our imagination, which is is fallible, and possibly diverse social structures, but such considerations lead us quite far away from physics.

I'm not sure what are all the exact details of your errors, since there are hundreds of possible ways to make mistakes, but I know that your interpretation is incoherent (and if I misinterpret things, then it seems at least that your presentation is very unclear). First, if there is entanglement between the first measurement apparatus and the system after measurement, i.e. the system after measurement is not clearly in one of the eigenstates of the first measurement, then it means that the first measurement never happened (in the sense of its given observable that must be defined independently of the second observation : this first measurement is classified as an interaction and not a measurement). Second, again if there is an entanglement, then the observed system does most surely not evolve into any unique eigenspace of the second observable, so that the second measurement gives random results according to some discontinuous projection. Indeed in the absence of physical interaction between subsystems (as is the case after the first measurement, between the measurement apparatus and the system), the evolution of an entangled state will always lead to another entangled state, i.e. its components cannot evolve into pure states (they keep their shape : dimension of the space of possible values, entropy...).

"Since you called me incompetent for not agreeing that decoherence solves the measurement problem"

Now you are obliging me to call you illiterate, because you could not even read correctly what I wrote : I never wrote that decoherence solves the measurement problem, only that it is part of the picture that needs to be interpreted. So now I'm done with you, I'll rather comment other essays. Bye.

Dear Cristinel,

I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher

Dear Cristi

I really enjoyed reading your beautiful essay.

Here some considerations.

(1)" A universe in a dot". This is a lovely peace of writing. It reinforces my conviction that the principle of finite information density must hold, as Feynman himself believed (see his 1982 Int. J. Th. Phys.) The continuum is paradoxical: you can write the whole history of the universe on a single atom. This is also related to the following point (3)

(2) I totally disagree with Smolin on many things, even if I enjoyed reading most of his books, in particular Time Reborn where he already expresses his new ideas that you can also find in his current essay taken from his last book. The two main things I disagree on are: (2a) the physical laws are not constant; (2b) mathematics cannot describe "particularities". I think that both assertions are unscientific according to Popper.

(2a) Imagine a physical law that changes every minute, and you don't know how it does. It is not a law anymore, right? What about if it is valid for a year, or a billion of year, or not valid e.g. two billions light-years from our planet. What should be the validity time (and space) of the law? If we state a law, it is supposedly eternal. This, however, does not protect the law from possible falsification, which will ask for another law, yet supposedly eternal. In particular, the new law maybe a "meta-law" which regulates the change of the falsified law.

(2b) A theory cannot describe "reality as it is". It can describe/predict only connections between known conditions/preparations/events and observed facts. Inferring initial conditions in the past needs an increasingly larger knowledge of the current state, the more distant is the past from the now. We can only connects known facts with known facts, or predict facts from known facts: the theory cannot provide the initial conditions. If we want to predict what will happen, we need information about the past. Accounting for the Smolin's "particularities" requires the knowledge of the initial conditions, otherwise it is not science: it is magic.

I love your ideas about "Is everything isomorphic to a mathematical structure?". I agree with you that the answer is positive, and I enjoyed very much this part of your essay. I think that the point, however, is another one, and again it is about "what is theory". A theory is a reduction of complexity of connections between events/observations. Transforming a set of observations (a peace of "reality") into a list of propositions does not necessarily entail a complexity compression, it is not a theory. Suppose I give you the observation made of the following digits:

3.1415926535897932384626433832795028841971693993751058209749445923078164062862...

A good theory would be the Plouffe formula that fits in few bits.

Also, as Poincaré says, the power of mathematics stays in the induction method, which produces an infinite compression of true statements. This is also the case of a physical law.

It would be too long to write everything I would like to say ..,

I hope to meet you again very soon and have a long discussion of philosophy of physics at a dinner table.

My best regards

and compliments again

Mauro