Seeking truth using different methods by Roger Schlafly

Dear Dr. Schlafly

First I have to present my apologies for my English. Being (i) French and (ii) under the pressure of time, my expression may be catastrophic.

I read with great interest your article, and I totally agree when you say that logical positivism is today seriously challenged. That being said, the virtual disappearance of this philosophical approach, not necessarily regrettable as such, leaves, in my opinion, a great void. It seems to me that great efforts should be made to fill it.

You rightly say that math and physics are essentially different things, working with different methods, based on different assumptions and pursuing different goals. This is incontestable. But the problem is precisely there, and the contest is about THIS PROBLEM. Despite these differences seeming insurmountable, there IS a kind collusion between math and the research field of physics.

You mention Kolmogorov and his axiomatization of probability. Such an axiomatization, by definition, does not found anything regarding physical reality. You are absolutely right to insist on it. HOWEVER, in physical world, there ARE events that comply with laws of probability.

In my own essay "A Defense of Scientific Platonism without Metaphysical Presuppositions" (Feb. 25, 2015, technical end note 2.) I try to show myself - by relying on Kolmogorov - that the law of large numbers has a significance in physical reality if and only if there are factual probability laws, knowing that, by definition, FACTUAL probability laws cannot be founded by the law of large numbers, nor by anything. (It would be my pleasure to know your opinion on this end technical note). HOWEVER, in the physical world, there ARE factual probability laws. "Something" - but what ?? - implies that certain sets of events are provided with specific factual probability laws. This point is mysterious until further notice, but belongs to the foundations of physics. Without this strange "something" physical science would not be possible, whether it may be statistical mechanics, control of experimental error or what you call "quantum mysteries." Or, taking the notion of physical reality in the broadest sense, without this mysterious "something" all insurance companies would go bankrupt.

Regarding the notion of infinity, I also agree with you agree that in the light of the current state of knowledge, the physical reality does not comprise anything that could match this infinite. HOWEVER, without the notion of infinity as MATHEMATICAL TOOL, physical knowledge would not be what it is. Relating to experimental error, for example, the notion of infinite values allows to write ideal laws, i.e. limits to what tend "sufficiently often repeated" empirical measures. Certainly, since the number of measurements effectively taken is always finite, we generally note a gap between ideal laws and empirical data. But the effective observation and appreciation of this gap presupposes the presence of an ideal law, i.e. a limit that could not be written without the notion of infinity as mathematical tool. And finally we would not have any knowledge very close to ideal laws if these latter were not there. Here, the example of insurance companies escaping from bankruptcy can still serve.

Unfortunately, I can not respond to all of your article, and a too long post on my part would take too much of your time. Permit me just yet to return to logical positivism.

This doctrine advocates the "elimination of metaphysics". That is its right. But personally, I reproach to logical positivism not having seen that its own doctrine is in turn undermined by metaphysics. The latter is everywhere. When we open a door, when we put a pan on the stove, etc. we are already doing metaphysics by adopting ontological realism which Carnap, the main reference of positivism, range himself within the same metaphysics than competing theories of realism, such as idealism. HERE, I agree with Carnap. But how, in these circumstances, can we be interested in foundations of physics - including the links between physics and mathematics - while denying dogmatically any consideration of metaphysics?

My position - I defend my article posted feb. 25 - is this. Since all knowledge regarding foundations, whether we like it or not, is metaphysically undermined, we must take note of it, rather than perpetuate the positivist legacy considering all metaphysics as a kind of mental illness. On the other hand, a metaphysical proposition, by definition, is neither provable nor refutable. All we can do is (i) determine the body of the various metaphysical conceptions behind EACH theory dedicated to the foundations of physics and (ii) compare these metaphysical conceptions under epistemological criteria such as simplicity, economy of assumptions, consistency and so on. Since, in most cases, we put our pans on the stove without asking ourselves why our physical reality - including pans and stoves - exists finally, knowing that it could also not exist, I wonder why it would be forbidden to note that some aspects of this physical reality are in turn provided with ideal laws interpreting at least a part of mathematical structures we are knowing. I believe that this position - a kind of Platonism - can be defended, unless the dogmas of logical positivism are regarded as absolute truths.

The article I posted on Feb. 25 is diametrically opposed to yours. But for my part, I participate in this contest with the sole order to seek discussion confronting opposites. Within a philosophy of science which is - according to my personal and obviously debatable vision - undermined by metaphysics, only such an approach may be legitimate.

If you have the time, and provided that this discussion interests you, I would be obliged if you would take notice of my paper and let me know your comments and objections.

With best regards

Peter Punin

Russell has discredited himself by declaring causality a relic of bygone time as is monarchy too and by suggesting a preventive war which could have killed me.

If philosophers like Russell are denying causality then I blame them for taking idolized do called basic theories for granted. Of course, the block universe implies denial of causality.

You might wonder why my favorite essay has been written by Phipps. I need no modern philosopher as to conclude that the conjecture of causality is indispensable and spacetime therefore wrong. While I often used non-causal tools as lazy approximations myself, I maintain that the conjecture of causality is the only alternative to futile mysticism.

Kind regards,

Eckard

Dear Roger,

I found your essay to be one of the rare ones having significant quality (among those I reviewed for now).

I agree about the difference of view of randomness between maths and physics, as I also expressed in my essay (that is, coexistence of possibilities with weights in maths, vs. realization of only one possibility in physics). I agree that randomness in physics does not make absolute sense as opposed to unpredictability, which may depend on the range of considerations to which the considered event may be related. However we do have a law of quantum physics that gives some probabilities quite successfully.

You wrote: "There are deterministic interpretations of quantum mechanics, so not everyone agrees with quantum randomness."

Indeed it is interesting to wonder what is behind quantum randomness, since randomness does not make absolute sense. The main interpretation of quantum physics that actually tries to be deterministic is Bohmian mechanics and other hidden variable theories, which I criticize (one of the reasons being that I see their claim of determinism as meaningless). As I explained in my essay, I see the source of quantum randomness as metaphysical, which, depending on circumstances, may either be the expression of free will by individual minds (diverging from the quantum probability law), or of a hidden, impersonal aspect of universal consciousness (usually obeying the quantum probability law, as far as "obeying a probability law" is relatively meaningful). So I disagree with the argument that "quantum mechanics adds only randomness to decision making processes, not freedom".

"Statisticians have taken the task of interpreting probability theory so it can be applied to the real world. Interpretations range from probability being a physical entity like temperature and called propensity, to being just a subjective measure of how persuaded you are of something. The major interpretations are the frequentist and Bayesian."

I see no sense of "interpreting probability theory" in the absolute. I can agree that it is an intrinsically unclear concept (a defect which can be seen as a quality, that is how I see mathematical probability laws as the perfect formalism by which mathematical laws of physics can leave a door open to the non-mathematical laws of free will), but I still consider it as a primitive concept in physics, i.e. I do not see a sense in trying to reduce it to something else. For example, frequentism suggests to set a limit to how far may frequency depart from average expectations. The fact is that probability laws induce values of the probabilities for different frequencies to occur in any given sample, so that frequencies away from the probable average just have a very low probability to occur, but a very low probability is not an impossibility, so that we still need an a priori concept of probability to interpret the frequentist interpretation of probability.

Instead, I see more sense to discuss more specifically about interpreting quantum theory: you wrote "A physicist might say that [some things] are random if current theory cannot predict them."

Sorry, I do not see things so vague as this. Lack of prediction does not mean randomness because randomness is a precise concept that refers to a specific probability law, which needs a theory to be specifically formulated. We are not in generic unknown universes with long series of successive speculative theories that might more or less be tried to fit, but in a specific universe where the specific probability law of quantum theory was found extremely successful. This law is the reference by which physicists can meaningfully speak about randomness, instead of simple ignorance. So, I consider the need to distinguish whether a considered probability law comes from quantum theory or not. And I actually do not see well where can serious probability laws come from, if not as particular cases of quantum probabilities. I mean, I see most probability laws that emerge in practice in this world, as actually particular cases of quantum probabilities, even if they do not directly look like such. I commented this further in my page on the problems with Bohmian mechanics.

"To the patient, a cancer seems like bad luck whether it came from genes, smoking, or mutation. All three factors presumably have completely causal explanations, if cancer were better understood. The reason they call the mutation bad luck is just that they have no good way of modeling it as a causal factor."

For most phenomena where microscopic physics or the butterfly effect is involved, deterministic explanations cannot exist in a non-deterministic world (do you mean anything else by "causal" ?), but in guise of causality, only probabilistic laws ultimately apply. In particular, I see mutations as directly coming from quantum randomness. Smoking is a conscious choice, which comes from free will, which uses quantum "randomness" as a medium of expression but departs from quantum probability laws. But I guess that genetic mutations are not subject to psychological bias away from quantum probabilities, since otherwise I would not understand why it is not also manifested in the form of intelligent design.

"A common view is that quantum mechanics describes true randomness, while all the other sciences have a pseudo randomness that results from complexity or uncertainty. Physics also has pseudo randomness, such as in the study of statistical mechanics."

There are good reasons to consider quantum randomness as fundamental in physics, since alternatives (hidden variable theories) have lots of troubles as I said. Statistical mechanics and other sciences express a practical randomness, and can happily remain agnostic about the nature of their randomness. This practical randomness can be logically compatible with explanations by pseudo randomness from complexity or uncertainty, but there is no point for positively claiming it to be pseudo randomness, so this is usually not claimed either ; and most cases, especially statistical mechanics, actually have their source or randomness in quantum randomness, so that this conceivable difference between the nature of randomness of diverse sciences is usually not real.

"Regardless of the branch of science, attributing causality to randomness does not explain it at all. Randomness is just a buzz word to replace an admission that the some causal factors are unidentified."

Hilbert spaces, at the basis of the formulation of quantum physics, are not a buzz word, but a very high, rigorous and elegant mathematical concept that is amazingly effective in explaining physical observations with a high degree of accuracy. Quantum probabilities are their direct logical consequences. Quantum theory is a well identified theory, leading to well identified mathematical evidences that any try to "explain" its randomness by hidden variables would lead to a lot of troubles. And, as I showed in my essay, we can find a well-identified logical connection between the paradoxes of quantum theory and what, in my view, can be naturally expected for the universe to allow the presence of consciousness, which I see as strongly suggesting a well-identified source for quantum randomness which is a metaphysical one (consciousness, which is non-physical and non-mathematical).

"When a uranium atom decays, it is often assumed that it is a spontaneous event that is independent of the history of the atom. But we have no proof of that. We can collect a large number of apparently similar atoms, and notice that they decay at much different times, but we do not truly know that the atoms are all in the same quantum state."

We do know it, not just assume, as the proof is found from the mathematical formalism of quantum physics: a system of rigorously identical particles behaves very differently in how they mix together (by the interferences between them), than would behave a system of different particles with only superficially similar properties that we would fail to distinguish by measurement.

I did not notice that "Physicists believe that causality is fundamental to physics, and philosophers reject that idea." On the contrary, I once saw a philosophical work followed in academic philosophy, which insists that causality is fundamental in physics, while I notice that the notion of causality is only an indirect one in the fundamental equations of physics which are time-symmetric (and, in many cases do not even fundamentally distinguish time from space), while causality is a philosophical concept which is fundamentally bound to the time dimension and is time-asymmetric; still I see a sort of concept of causality as important to describe the quality of quantum physics as "causal" in the sense of letting the probabilities of measurement results only depend on a "finite number of causes" from the state of what is there at a previous time. Otherwise, as people, physicists may talk about "causality" but I would say this is only a philosophical interpretation from outside the equations of physics in a strict sense.

It seems to me that the Bayesian/psi-epistemic view is actually a position of agnosticism with respect to the idea of hidden causes, and thus a non-interpretation, so I would not really classify this in the list of views, except if taken as a case of logical positivism.

You point out the diversity of views on quantum physics, but these divergences are internal to the small part of the community of physicists who care, and thus does not point to any idea of opposition between maths and physics which you took as the main topic of your essay, or does it ? (We might also find "controversies" in the foundations of maths if we search well)

I agree about the difference between math and physics on the role of infinity. I also commented this in my essay : how quantum physics, despite being a mathematical theory formally involving infinite sets, avoids any effective dependence with respect to actual infinity and its undecidabilities that can be found in other branches of mathematics.

We have the same interests in the foundations of mathematics and its paradoxes :)

Since the fine structure constant is only the macroscopic limit of the effective value of the charge, while some possible determination, if it exists, would rather come from the Planck scale, there is no surprise that it is not algebraic ; its deduction from the renormalization process would make it algorithmic but not algebraic (even though it would be very hard to write down the relevant algorithm). But I'm not even convinced that mathematicians would be troubled at the idea that physical constants are just arbitrary real numbers without any specific definitions (and thus possibly escaping countable models of set theory). After all, that would leave the axiomatic system of physical laws incomplete, just in a similar way as axiomatic systems of arithmetic or set theory are. Do you know, the most naturally "constructed" countable models of ZF also have wrong arithmetical properties (with a nonstandard model of arithmetic). The failure of countable models of ZF to contain the correct values of physical constants would be quite a similar phenomenon.

I also (moderately but for many practical purposes of truth research) agree with logical positivism. Your position seems unclear as you seem to promote logical positivism at the end, yet you argued about the impurity of the concept of randomness (the difference between pure randomness and pseudo-randomness) at the beginning, a difference which logical positivism would dismiss as senseless metaphysics. Some physicists do argue about it, as they look for interpretations (other than the logical positivist non-interpretation of Copenhagen and Bayesianism), but they are a minority. Having pointed them out, suggests that you give it importance yourself, in seeming contradiction with your final expression of support for logical positivism.

I guess your 2012 essay should be interesting as well, but for now I wish to focus on reviewing other essays of this year :-/

Fear Dr. Schlafly,

You began the abstract of your essay with a wrong assumption when you wrote: "Mathematics and physics are entirely different subjects, both in their methodology and results. The differences are illustrated with how they view randomness, enumeration, and truth."

Accurate writing enabled me to write sensibly about unified reality: Proof exists that every real astronomer looking through a real telescope has failed to notice that each of the real galaxies he has observed is unique as to its structure and its perceived distance from all other real galaxies. Each real star is unique as to its structure and its perceived distance apart from all other real stars. Every real scientist who has peered at real snowflakes through a real microscope has concluded that each real snowflake is unique as to its structure. Real structure is unique, once. Unique, once does not consist of abstract amounts of abstract quanta. Based on one's normal observation, one must conclude that all of the stars, all of the planets, all of the asteroids, all of the comets, all of the meteors, all of the specks of astral dust and all real objects have only one real thing in common. Each real object has a real material surface that seems to be attached to a material sub-surface. All surfaces, no matter the apparent degree of separation, must travel at the same constant speed. No matter in which direction one looks, one will only ever see a plethora of real surfaces and those surfaces must all be traveling at the same constant speed or else it would be physically impossible for one to observe them instantly and simultaneously. Real surfaces are easy to spot because they are well lighted. Real light does not travel far from its source as can be confirmed by looking at the real stars, or a real lightning bolt. Reflected light needs to adhere to a surface in order for it to be observed, which means that real light cannot have a surface of its own. Real light must be the only stationary substance in the real Universe. The stars remain in place due to astral radiation. The planets orbit because of atmospheric accumulation. There is no space.

Warm regards,

Joe Fisher

Thank you for not reporting the post as being inappropriate. I rely on the reports written by qualified scientists and published in accepted scientific journals for my contention that each snowflake so far investigated has been unique. As has every fingerprint and dollop of DNA.

Cheers,

Joe Fisher

Re: randomness in math and physics. Putting aside ignorance-randomness and pseudo-randomness, as well as the issue of whether "randomness" given its multiple employments is all that coherent a concept, we're still left with the specter of irreducible randomness. Mathematically, per the algorithmic information approach, that's represented as numerical information which can't be algorithmically compressed, full-stop, although in the view of many in the field it can be expressed as a Chaitin Omega in which form it has even been "computed" by means of some really smart hacks to 64 digits. Anyway, a concern that arises from your essay, at least for me, is whether that stuff is actually in the same category as the irreducible physical randomness held as an article of faith by many physicists -- represented for example by radioactive decay and the informational output of beam-splitters.

(I know for a fact that Greg Chaitin and Anton Zeilinger perceive an identity. They worked together formulating the Quantum Omega Number. They also share enemies.)

Finally, a question: in your opinion is there any possibility that either or both of the two irreducible randomnesses -- the one of physics and that of mathematics and AIT -- might represent (1.) actual features of nature, if not indeed (2.) an identical feature of nature?

The Scarani paper you link to in your refs mentions Antoine Suarez. The two have done a lot of physics work together over the years and remain affiliated with Nicolas Gisin's hugely prestigious Geneva group. They're respected physicists and Suarez is undoubtedly the go-to guy on Quantum Free Will. Watch out for Catholic theology under the asphalt but once warned you can steer around it unless you want the full-on experience.

.0000001000000100000110001000011010001111110010111011101000010000 are 64 digits of an Omega, actually has Chaitin's imprimatur. Why couldn't the zeros and ones be the two possible directions taken when 64 lined-up photons encounter the interferometer? Some claim it's possible. The math is complicated and controversial.

I'm not a Platonist, a Tegmarkian. But even empirically, Aristotley, Froglike, just maybe ...

Dear Roger Schlafly

Your clear and nice essay came to me in the right moment to know in detail references, which are contrary to my way of thinking. When I am reading your section of Free Will, I can accurately see the trends of thinking in this area. However, my model is not yet indirectly commented in your essay. Namely, in my essay I defend panpsychism, where decisions of the basic units of consciousness are random according to outside observer. ''In basic units'' means in every qubit, so it is also outside of the brain. Otherwise, the ''free will'' in the brain is more correlated, but there deviation from randomness has not yet been measured officially. (Otherwise, it is claimed by Sylvain Poirier, who knows for some parapsyhological measurements.) If you dislike panpsychism, you should to know that it is advocated also by Tononi and Koch.

And I claim also that QM is incomplete because consciousness is not explained and QG is not yet known.

My old essay about this topic is. As a detail I have added this year that consciousness does not exist without Free Will. So my theory is distinct from Tononi's one.

For the rest, I argue (in the essay) that axioms are not the essence of the of math, but the germ of formation of math is physics. So I defend naturalism, so, similarly just as Smolin in this contest, but as distinction from him, I believe that the basic math of QG is simple, so I believe in reductionism. What about you?

I also claim, tham infinity in physics do not exist. You claim for both options. Why?

p.s. By the way about pi: I think That its number structure is not random, Because the rule for its calculation is simple. What do you think?

Best Regards

Janko Kokosar

Dear Roger Schlafly

As correction, we disagree about quantum consciousness. But, I agree if QM is assumed not to explain consciousness, ''I doubt that anything else will anytime soon. ''

But, I like positivism, but at physics is a problem of selection of words and sentences, where a little changed sentence tell some clearly distinct things. Thus, because of some details, our opinions are distinct. Thus, I am positivist, but not 100%. (My phrase in this contest.)

In prolonged version of essay (ref [1]) you can see my positivisic explanation of free will: ''Let us suppose that Turing experiment gives distinct answers of a human versus computer. (Otherwise free will does not exist.) If we respect non-quantum physics, then explanation of free will needs new physics. But a quantum computer always gives distinct answers than a human, thus free will does not need new physics.''

Best Regards

Janko Kokosar

Dear Roger,

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

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rujing_tang at yahoo com

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Roger, I'd like to get your idea on my thoughts on simplicity.

Your view of probability requires some time to digest but appears to be along the line of what I'm thinking.

Thanks,

RJ

Simplicity is that a relative few theories and mathematical models can explain a number of phenomena. While complexity is the opposite where there seems to be an unending need to invent new theories. By this definition, physics and astronomy are in the former camp and social science and biology belong to the latter.

Why is the universe is even understandable? This itself is hard to understand according to Einstein. I propose a line of reasoning here. Simplicity is a result of long term evolution in a close system. The resulting equilibrium gives rise to simplicity. The infinite possibilities of any member of the system have been largely reduced to a highly confined options. Most of the possibilities are prohibited due to forces that have long been cancelled out during the long evolution. Because of this simplicity, there appears to be causal effect. In other words, causal effect is a direct product of simplicity. Take our universe as an example, the universe is in equilibrium by and large. Only a handful forces remain. Because there are relatively few forces and laws, the universe appears to be orderly and thereby allows mathematics to even exist and work. Mathematics owes its existence to the equilibrium of the universe. Equilibrium brings orderliness and slowness to change. Just imagine, if one puts one stone by another stone, and because the stones decay so fast, by the end of this action of moving them together, one counts zero stone. The law of addition will be forever different from what we know today. In this sense, math and physics have 'this worldliness' feature, and is a localized knowledge to this universe at this phase of equilibrium. It could be vastly different in other possible states of the universe or other universes.

A corollary is that the rules governing a simple universe is discoverable and free of controversy. The simplistic nature of the rules make it hard to miss the mark, so to speak. Once the framework of the rules is tested true over numerous times, what's left is refining of the details. Contradiction between the rules and the reality should be worked away over the time. This is good news to scientists because it solves the age old anxiety of finding all theories are invalid one morning.

One notable exception to the simplicity in universe is the complexity in bio-sphere. Because the bio-sphere is inherently expansive and interactive, we cannot reduce the theories to a few laws and mathematics models. The bio-sphere is NOT an equilibrium system. Therefore it is very hard to apply causal effect to explain human society for instance. It is very hard to generalize theories or apply mathematics in bio-sphere or human society, as we are able to in cosmology.

Humans' brain is wired to understand simple things and not complex things. We seek patterns and generalize. This skill helps tremendously in our evolutionary past. For instance, our eyes are adept in figuring out patterns like straight lines. Our eyes are especially good at spotting moving object in a static background. The predisposition to seek simplicity gave humans survival advantage in its evolutionary history. We appreciate simplicity over complexity. Humans process limited computational power. It is most efficient to apply the limited resource to a fast algorithm. The design principal of the fast algorithm is simplicity. There is an aesthetic side from human eyes for simplicity, whether be a new physics theory or a design of a gadget. The propensity of seeking simplicity is a very human specific trait, and has nothing to do with the reality whether the world is simple or complex.

The coincidence of the simplicity of the universe and human's preference of simplicity is fortunate and fruitful. Specifically in the math and physics the coincidence yielded amazing results. There is no reason to doubt that more amazing discoveries will surface in the future. However, a grain of salt must be added so that we are conscious that there is less mysterious processes or agent involved in the coincidence. This article hopefully explained why. In fact, if we are blindly led by our pursuit of simplicity, we might fall into traps of naturally complex traps. For instance, any attempt to gain simplistic insight into a complex system is not a good idea. Our brain comes into my mind as an example of complex system. There are so many facets to this simple object that no one can claim a brain can be modeled with a finite number of rules.

However, the simplicity on the surface for the natural world might be just a disguise of a chaotic and unpredictable reality. The equilibrium masks over much of the chaos and most noises or complex nuisances cancel each other out. What's left is the poetic simplicity skin. Underneath the skin, things might not be that smooth, or elegant or simple after all. It is a possibility. We probably are able to see some hints as we get more refined data, better models and more powerful observation tools.

Roger,

You approach the subject in a nicely different way to your previous essays and to others. Your prose is as good as ever and I still agree both with your viewpoint, and with 'vive la difference'! You're still not quite alone in suggesting maths can't faithfully model everything, though I take a slightly subtler line saying (and showing with an important case) that it often 'DOESN'T do so. Not adopting the absolute 'can't' is to me like saying it's complexity is so beyond all conceivable computational possibility that it's as good as impossible for humanity. I don't like absolutes, and that case the trust we put in present maths is as equally misplaced as in the 'absolute' case. The difference needs recognizing.

I'm glad I made it to your essay which I think has been well undervalued. The reminder of the philosophical variants was also useful. I hope you'll also make it to my essay as I'd value your thoughts and comments.

Best of luck in the last few days.

Peter