Hi Lee,

I'm puzzled about the status you ascribe to the fundamental principle enunciated here. It seems as if your basic idea is to try to figure out the consequences of accepting a "strong form of Einstein’s principle of no unreciprocated action according to which there can be no entity A which plays a role in explaining an event B, that cannot itself be influenced by prior physical...

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Hi Lee,

I'm puzzled about the status you ascribe to the fundamental principle enunciated here. It seems as if your basic idea is to try to figure out the consequences of accepting a "strong form of Einstein’s principle of no unreciprocated action according to which there can be no entity A which plays a role in explaining an event B, that cannot itself be influenced by prior physical events." There are various questions on could raise about such a strong principle: logical (does it apply to itself, so it can't remain the same?); metaphysical (why should it have such a foundational status?) and epistemological (why think it is true?). Let's leave aside the first two and focus on the last. There are three possible positions here. The Heraclitean position is that everything real is in flux, which seems to be your position. The Parmenidean position is that nothing real ever changes. And the mixed position is that some real things change and some don't. We can reject the Parmenidean position since the physical world is real and changes. Newton, Einstein, etc. all hold the mixed view, and you are trying to hold the radical Hericlitean view, it seems.

Now let's grant that the view can be made logically consistent (which is not clear). The mixed view has no such problem of self-application: according to the mixed view, the truth of the mixed view itself can be one of the things that never changes. So unless you have some mystical source of knowledge, you can't know that the mixed view is wrong. And there is powerful empirical evidence that at the least the basic physical principles governing material objects have been effectively constant and unchanged over billions of years. We know that stars as far away as we can see produce exactly the same spectral lines as the Sun, so the chemistry is identical. In fact, if the laws of nature themselves changed substantially then we would not be able to accurately account for the processes in the cosmological past at all. So you have to admit that the laws are effectively unchanged as far as we can tell over cosmological scale. On what grounds, then, can one dismiss the claim that the laws do not change at all? That is, why believe the "strong form" of the principle that you advocate? One can speculate about the consequences of denying it, but you seem to think that there is some necessity to it. What is the basis of your confidence?

Cheers,

Tim

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Dear Lee Smolin,

It is a pleasure to observe your evolution toward 'realism', with one natural universe making up a unitary whole, existing in the objective Now, distinct from past and future. And a corresponding rejection of mysticism in physics, whether strings, or Platonic ideals outside time and space, or a multiverse. I do not believe I have ever seen such a devastating analysis of the...

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Dear Lee Smolin,

It is a pleasure to observe your evolution toward 'realism', with one natural universe making up a unitary whole, existing in the objective Now, distinct from past and future. And a corresponding rejection of mysticism in physics, whether strings, or Platonic ideals outside time and space, or a multiverse. I do not believe I have ever seen such a devastating analysis of the sheer uselessness of the Platonic idea of a mathematical realm outside of space and time. As Tejinder Singh notes, it is an 'act of faith' at best! And I suspect it is far more harmful to physics than helpful. Pianos and banjos typically exist before Fourier, almost never otherwise.

You state that logic is the distillation of the fact that we can reason about (concepts). I see logic as the essential property of physical reality that allows structural AND-gates and NOT-gates, however implemented or constituted, to combine to produce ALL-gates, which are combined combinatorially in space and sequenced serially in time to produce, in effect, all mathematics and all control mechanisms, interfaced, where appropriate, to analog mechanisms. It is difficult to find an area of physics, from molecular to bio-molecular, to organic to silicon to neural, etc., where this sort of logic does not apply. Thus mathematics is eminently reasonable, arising from logical structure subject to time-based evolution, including the trigger events for counters composed of logical, real, physical subsystems that yield the 'next' natural number. This addresses Kronecker's "God made the integers, all the rest is the work of man." Counters exist naturally, from telomeres on chromosomes to crows counting; the Number operator is the counter at the heart of quantum field theory. I present a brief overview of such in my essay.

My essay addresses another intrusion of mysticism into physics -- the non-locality that Bell "invented", based on (what I claim to be) oversimplified physical assumptions. His math is correct, but physics that follows from false assumptions is not. I invite you to read my essay and very much hope that you will find time to comment upon it.

My very best regards,

Edwin Eugene Klingman

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Dear Sir,

Mathematical reality is the quantitative aspect of Nature, which is logically consistent – hence unchanging - and harmonizes with other aspects. But the problem arises when we try to manipulate them. In one of the essays here, the final equation is consistent with the figures given. But if the same sets of figures are applied to the initial equations, it shows 1200 = -1250. The...

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Dear Sir,

Mathematical reality is the quantitative aspect of Nature, which is logically consistent – hence unchanging - and harmonizes with other aspects. But the problem arises when we try to manipulate them. In one of the essays here, the final equation is consistent with the figures given. But if the same sets of figures are applied to the initial equations, it shows 1200 = -1250. The author has not cared to reply to our comment. With such basic flaws, even if the final equation turns out to be right, the theories become questionable.

Mathematical space-time structure is the intervals between objects that change according to the time evolution of those objects including motion due either to inertia (determined by energy at the point of application) or application of force (influenced by mass at the point of application), which change continuously due to interaction with its environment and determines the structure of free fall. Thus, the curvature does not belong to space-time, but to the position of objects that determine the interval. Geometry cannot tell matter how to move and in turn – only energy moves matter. Geometry is determined by such motion. We use alternative symbolism of such evolution of objects to describe the interval.

The Principle of no unreciprocated actions emanates from Leibniz’s principle that there should be nothing in the universe that acts on other things without itself being acted upon. This is essentially Newton’s third law. Einstein used this principle in GR when rejecting Newton’s ideas about absolute space. His interpretation forbids any reference to a fixed-background and entities whose properties are fixed for all time, regardless of the motion of matter, thereby reducing interactions to relationships with other objects. But space itself is not only intervals, but also background for everything. All motion takes place in space in time. All observations are made at “here-now”, which is referred to as space-time. Thus, by implication, Einstein’s interpretation of the Leibniz’s principle makes everything dependent on observation only. An object does not exist unless observed by a conscious observer – which concept of Bohr he opposed! Einstein based his conclusion on the M & M experiment, which used light. But light is a transverse wave, which is background invariant. Thus, his conclusion is faulty.

Chess was invented in India by the warrior class from their war moves. Like a poet writing poetry, the basic concepts were always there. But the processes of its codification for alternative use by emphasizing different aspects differently or choosing specific components, which can be infinite, were created. Your conclusions are identical with our essay, though the presentations are different. Best wishes.

Regards,

basudeba

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Lee,

 Let me first say, my critical point of view was derived from the inspiration of reading your essay. It has ignited within me the motivation to address, in a separate paper, the many misconceptions we have regarding time. Hopefully we will debate my theoretical and hypothetical intuitions constructively and thereby provide a genuinely effective iteration of these conclusions at...

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Lee,

 Let me first say, my critical point of view was derived from the inspiration of reading your essay. It has ignited within me the motivation to address, in a separate paper, the many misconceptions we have regarding time. Hopefully we will debate my theoretical and hypothetical intuitions constructively and thereby provide a genuinely effective iteration of these conclusions at some time in the future (excuse the pun).

With your sections addressing the effectiveness of mathematics in mathematics and physics, you lead the reader into the assumption we currently understand the fundamental laws governing both studies and their comprehensive connections between separate deviations. Mathematicians are on a path to derive a cohesive fundamental structure connecting Algebra to Geometry to Logic just as Physicists are attempting to unify the laws constituting observable physical forces. Ultimately the goal will not only connect the separate entities individually, but also unify these distinct disciplines into a decisive understanding of nature. As my essay attempts to illustrate, mathematics is abstract, arbitrary, and purely a fundamental tool - we then apply it to a properly structured interpretation of reality - we describe this process as the discovery of the laws of physics. The idea that nature or reality can be described or mirrored mathematically or in physics is not a “mystical” conjecture of philosophy. Artists are capable of painting images observed in reality. In time, the art evolved discovering better techniques to make paintings an accurate description of observation. This evolution was brought about by the application of “discovered” techniques using fundamental tools (i.e. physics using mathematics as tools for observation). The limitation or effectiveness of their mirrored representation of reality depends solely on the applications of tools “invented “or applied by humans and our competent abilities discovered by the art form. Photography led to realism, Motion Pictures led to temporal realism and now we have 3D HD Projections which is more “effective” at capturing and describing nature, but we are not satisfied, we require more information to describe the enormous information needed for temporal realism. The information needed to recreate nature or a temporal event using Mathematics and Physics is infinite. We possess the necessary mathematical tools, Integrals and Calculus for temporal states, we simply do not have enough information to predict probability from possibilities, or we are too lazy to consider the enormous amount of information needed to accurately calculate and depict nature. Therefore our observations as mathematical representations are lacking in its description prior to an event, leading us to assume probabilistic and uncertain future events based on biased accrued approximations within our mathematical equations which lead to misinterpreted phenomenon or unexplained events. For the most part, we are simply satisfied describing nature to an acceptable limit, but without including every physical representation of the information concerning the system of observation, we cannot call this an assumption a direct interpretation of nature. It is lacking, but it is not the fault of the applied mathematics that already “existed” after which humans “discovered” and “invented” arbitrary imaginative symbols to represent. It’s lacking, but not because of the interpretation of mathematics described as physics (although we must clarify a preferred theoretical methodology). It is lacking because we do not include enough information to describe an object “O”, and therefore we have an abstraction we (as the interpreter) hypocritically claim is based on the limitations mathematics and physics pose on nature.

As unbiased investigators of nature (mathematicians, artists, theorists, and physicists), we must not assume a provocative or unconventional approach abstract in resolving a preferred method of depicting nature, is assumedly flawed or insignificant for discussion and interpretation until thoroughly proven otherwise by analytical means of exploration and experimentation. The approach necessary for discovery is a derivation of fact from fiction - truth from falsehoods – limited “gauged” probabilities from infinite uncertain possibilities we seek as discoverers of our reality.

All in all, it was a great addition to this discussion. Thank you for contributing.

Best Regards –Keep in touch!

D.C. Adams

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Lee,

Your ideas on loop space with Astekhar and Rovelli in the 90s were fascinating. Your present ideas fascinate once again.

I think the Platonic view can be appropriately tweaked to agree with your view of a "unitary whole." Actually, I think that by default the view has always been that of the "unitary whole." I call it the view of an "all-encompassing existence."

My...

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Lee,

Your ideas on loop space with Astekhar and Rovelli in the 90s were fascinating. Your present ideas fascinate once again.

I think the Platonic view can be appropriately tweaked to agree with your view of a "unitary whole." Actually, I think that by default the view has always been that of the "unitary whole." I call it the view of an "all-encompassing existence."

My view is that there is one and only one totality of the existence. However, the one totality of the all-encompassing existence has two "initially" separate realms that evidently progressively get connected "inseparably" in the unified whole.

The following "table" illustrates my tweak of the Platonic view that involves the two fundamental realms (which are named in the header) into which the fundamental essences (which are listed under the header) are categorized.

The Realm of Phenomena –––––– The Realm of Noumena

–––––––––––––––––�
�–––––––––––––––––––�
�––––––––––––––––

Space (the dimension) –––––– Time (the dimension)

The Aethereal Substance –––––– The Ephemeral Instance

Motion –––––– Duration

The Corporeal Forms –––––– The Abstract Ideals

––––––––––––––––––
––––––––––––––––––––
––––––––––––––––

My view is that the all-encompassing existence has both the phenomena and the noumena. The strictly phenomena being the corporeal cosmos, which we observe with its full spectrum that range between the kinematic vacuums of dark voids and the kinematic singularities of super dense black holes. We see within that range the electromagnetic spectra of phenomena and the particulate spectra of phenomena. As far as my view goes, the corporeal cosmos exists within the space dimension, and the corporeal cosmos is the space-occupying substance that is inherently rendered the kinematic definitions by the essence of motion. The space-occupying substance is aethereal if without the kinematic definitions; but it is never without the kinematic definitions (in string parlance, it always has branes and underlying branes ad infinitum).

Note that my Forms and Abstracts no longer follow the meanings of the Platonic terms. My "Corporeal Forms" are no longer the Platonic universals of "Abstract Ideas." They are now exact opposites. My Corporeal Forms are strictly categorized as phenomenal realities, while the Abstract Ideals are strictly categorized as noumenal realities. To me, both the phenomena and the noumena are real.

However, the corporeal is the more real than the abstract because it is the manifestation and embodiment of the ideals. In other words, the corporeal forms are the complete or thorough realities, the already connected phenomena and noumena, the embodied truths, the combined unified fulness of existential realities.

The laws of nature, the laws of motion that we try to discover, are the abstract ideals. In the abstract is our mathematics. In the corporeal is the execution of the mathematics.

My view is that the abstract ideals are static and only await their discovery or fulfillment. So, there is no evolution of the laws of nature. On the other hand, the corporeal forms are dynamic since the fundamental essence that defines the corporeal forms is motion (flux). Motion is that which is being constantly governed to conform to the ideals – to the laws of motion described by our mathematics. (Here of course is the bit of my tweaked Parmenidean and Heraclitean.)

The tweak that brings agreement with your idea of the unitary whole should now be obvious. As much as we understand, the mind, the nous, that perceives the noumena, resides in the brain-and-body that perceives the phenomena. We have the mind and the brain-and-body as the unified mind-and-body.

If the idea is extended in its application to a pan-cosmic or pan-existential view, the whole cosmos would be a sort of "super mind-and-body" – a unified whole of the mindset and the body-set that pursues the execution of the abstract ideals towards the continuous fulfillment of existential realizations in the corporeal forms.

Yet, the noumenal is apparently inherent in the phenomenal. The inherently unified corporeal-and-abstract reality is fundamental. There are the simple corporeal-and-abstract realities. And there are the complex corporeal-and-abstract realities. But, evidently, the simple corporeal-and-abstract realities are progressively and continuously transformed to form and sustain the complex corporeal-and-abstract realities.

It is apparent that the noumenal and the phenomenal may be established as a unified inseparably connected, or sustained, reality. All that is needed is an inherent and fundamental bias in the existence, in order to have an established cycle that sustains the connected reality. With a cycle limits are set, in which the excesses are spun off the sustained complex realities, and with the spun off fragments eventually grown into new complex realities. The spin off process actually looks like the emergent mechanism in the corporeal that bring about replication. Now, it appears that gravity is that necessary fundamental bias that is indicated in the mathematics of physics.

Lee, my submitted essay is more illustrative of the relationship between mathematics and physics, instead of being explanatory. But I have a book/ebook that is sold at my www.kinematicrelativity.com website and a few pages there explaining my work.

I have been focusing on the ramifications of the genesis formula that I discovered. I derived the genesis formula from the 3-d tensor transformation equation. I clarify in my work that the 1-d Galilean transformation implies mass increases, that the 2-d Lorentz transformation implies mass increases, and that mass increases because of the universal gravitational acceleration is implied by the 3-d Castel transformation (tongue-in-cheek, Lee).

The genesis formula implies that mass increases inherently and continuously occur for every mass domain in the cosmos, and hence for the whole cosmos, because of gravity that is a fundamental bias in the corporeal realm. The genesis formula implies a few other radical ideas.

A bit of an exchange of ideas and critiques between us would be nice.

Regards,

Castel

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Hello. You come to propose a conception of things coherent with naturalism. Great ! I stand for the opposite view ;-)

I actually never found a formulation of naturalism that seemed coherent, as it seems to me logically impossible, somehow already in principle, and then even more with quantum physics. So I am very curious when I see such a proposition announced ! For now most of the essays I...

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Hello. You come to propose a conception of things coherent with naturalism. Great ! I stand for the opposite view ;-)

I actually never found a formulation of naturalism that seemed coherent, as it seems to me logically impossible, somehow already in principle, and then even more with quantum physics. So I am very curious when I see such a proposition announced ! For now most of the essays I reviewed here in support of such a view seemed to be amateur-level. I was full of hope for discussions to become at last serious and challenging, at the first sight of an essay with this purpose by a reputed physicist coming to the list.

One thing I was puzzled with when reading some naturalist views, is how they dismiss any idea of considering consciousness as fundamental, by calling this an "explanation by a mystery" and thus no explanation at all. Indeed it may look like this, in the sense that consciousness escapes all mathematical description. So if your condition to call something "non-mysterious" is to have a mathematical, deterministic description of it then indeed consciousness is "mysterious" in this sense. Which does not mean that noting can be said about it (as I did express some important features of consciousness for its connection with physics). However, on their side they claim to explain everything as "Nature". But what the heck do they mean by "nature", and, in lack of a clear definition for this kind of stuff and its working principles, how is an "explanation" of the world by an undefined "nature" assumed to be primary, be any less mysterious than the view taking consciousness as primary ?

I once saw an "argument" that if a miracle is real then by definition it must be part of nature because nature is "all what exists" so that nothing can be meaningfully called "supernatural". Then well, if "all what exists" is the definition of "nature" then it makes naturalism tautological, but no more informative. To be informative we need to specify what kind of stuff is "nature" supposed to be. It seems supposed to mean "physical stuff". Well if we were in the 19th century, and still with General Relativity, it could indeed look like there was such a thing as "physical stuff" that the universe could be made of. However, quantum physics broke that.

Namely, an important question I would have, is whether "nature" is supposed to be finitely or infinitely complex, or maybe just locally finitely complex, in case it could be considered locally (which you seem to reject as you seem to favor non-locality in interpretations of quantum physics). So for example if it is locally finitely complex but not locally causal then, finally, it is infinitely complex if the universe is infinite (in hope that the dependence of local stuff on the rest of the universe converges). Quantum physics makes the physical world locally finitely complex indeed. I consider consciousness infinitely complex. But if "nature" was physical and infinitely complex, how could it have definite causalities that depend on infinitely complex stuff ? Bohmian mechanics describes things as infinitely complex, but I suspect its laws to diverge when considered in their globality.

Here are points of interest I found in your article:

"The effectiveness of mathematics in physics is in [Platonism] mysterious because proponents of this view have failed to explain both how there could be such a correspondence and how we, as beings trapped in time bound physical reality, can have certain knowledge of the hypothesized separate realm of mathematical reality."

What failure to explain ???? I do not see the slightest problem here: it is a one-way dependence. Anything that exists must be coherent with itself, so that whenever we can discern mathematical structures somewhere, they have to be coherent with themselves, thus obey the laws of coherence which are the mathematical theorems. So it is "affected" by the mathematical world, but does not affect it in return (nothing can change the facts of what is coherent and what isn't). It is possible for mathematical structures to be more or less involved by contingent (non-mathematical) realities.

"if you believe that the ultimate goal of physics is to discover a mathematical object, O, which is in perfect correspondence with nature, such that every true fact about the universe, or its history, is isomorphic to a true fact about O, then you are also not a naturalist because you not only believe in the existence of something which is not part of nature, you believe that everything that is true about nature is explained by a true fact about something which exists apart from nature. You are instead a kind of mystic, believing in the prophetic power of the study of something which exists outside of time and apart from nature."

All right, so this means naturalism rejects any possibility to describe nature in mathematical terms. In this case, nature escapes any rigorous mathematical description and is therefore assumed to be fundamentally "mysterious". Like consciousness in my view.

You wrote: "Mathematics thus has no prophetic role in physics, which would allow us an end run around the hard slog of hypothesizing physical principles and theories and testing their consequences against experiment". Then you "hypothesize two principles which we take to define temporal naturalism". Are these two principles not supposed to have any prophetic role in physics, that would allow you an end run around the hard slog of hypothesizing physical principles and theories and testing their consequences against experiment? Because in the rest of your essay I did not find any big care to test these principles against experiment, or against the body of modern science which sums up so many experiments already done, in the sense of a possible challenge to the truth of your principles.

"All that exists is part of a single, causally connected universe. The universe and its history have no copies, and are not part of any ensemble."

Right. I would qualify the spiritual multiverse (where souls can migrate between universes) in these very terms, though the connections between parts (universes) can sometimes be poor.

"There is no other mode of existence, in particular neither a Platonic realm of mathematical objects nor an ensemble of possible worlds exist apart from the single universe." And why not ? You seem to have quite a faith in this negation.

"All that is real or true is such within a moment, which is one of a succession of moments"

You already multiply the modes of existence, between past, present and future existences, and where the time-status of the existence of any particular event... depends on time. So you admit multiple possible modes of existence, but you deny the possibility for still another mode of existence than these (the mathematical existence).

"The activity of time is a process by which novel events are generated out of a presently existing, thick set of present events. "

How thick is the set of present events, and how do you measure this thickness, both in space and time dimensions ? My view of the spiritual reality would be similar except that I take all past events as still presently existing and indestructible, and from which novel events are generated.

" we adopt a strong form of Einstein’s principle of no unreciprocated action according to which there can be no entity A which plays a role in explaining an event B, that cannot itself be influenced by prior physical events."

That is quite an assumption, of trying to generalize a principle far beyond the form in which it was initially considered and justified by experiment ! But is it really just a plausible strengthening of a well-defined principle, or rather an endless multiplication of fanciful assumptions only superficially similar to the initially successful version ? Something like justifying philosophical relativism as "a strong form" of the Special Relativity principle.

Of course you cannot understand the possible relation between mathematical and physical realities if you exclude by principle the possibility of one-way influences, and by "satisfying explanation" you mean "explanation that agrees with this principle", assumed to have such a prophetic role in physics, that it allows you, in your own words, "an end run around the hard slog of hypothesizing physical principles and theories and testing their consequences against experiment". By the way, how do you apply this principle to the dependence between past and future ? How can the past affect the future without being affected by it in return ?

You wrote " Among the things that violate a strict definition of naturalism are (...) absolute, timeless laws," yet you defend the view of "the singular universe" which seems to fit absolute timeless laws. It seems quite hard for these laws to vary inside the same universe, both theoretically (the formal rigidity of the physical laws that do not easily let coherent ways to glue together parts of space-time that do not obey the same laws) and as we did not see them vary, but it would be much easier between different universes. Don't you see it hard to reconcile both principles of uniqueness of the universe and contingency of the laws ?

I will write more remarks later.

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"So a new conception of mathematics is needed which is entirely naturalist and regards mathematical truths as truths about nature. In this essay I sketch a proposal for such a view. The key it turns out is the conception of time."

If mathematical truths are "truths about nature", they should be consistent. If the deductive consequence is wrong, the premise is wrong as well (the combination...

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"So a new conception of mathematics is needed which is entirely naturalist and regards mathematical truths as truths about nature. In this essay I sketch a proposal for such a view. The key it turns out is the conception of time."

If mathematical truths are "truths about nature", they should be consistent. If the deductive consequence is wrong, the premise is wrong as well (the combination "true premise, wrong consequence" is forbidden by logic). You teach that the special relativistic time (the consequence) is wrong but both the premise from which it is deduced (Einstein's 1905 constant-speed-of-light postulate) and its deductive consequences are gloriously true:

"And by making the clock's tick relative - what happens simultaneously for one observer might seem sequential to another - Einstein's theory of special relativity not only destroyed any notion of absolute time but made time equivalent to a dimension in space: the future is already out there waiting for us; we just can't see it until we get there. This view is a logical and metaphysical dead end, says Smolin."

"Was Einstein wrong? At least in his understanding of time, Smolin argues, the great theorist of relativity was dead wrong. What is worse, by firmly enshrining his error in scientific orthodoxy, Einstein trapped his successors in insoluble dilemmas..."

QUESTION: Setting aside any other debates about relativity theory for the moment, why would the speed of light be absolute? No other speeds are absolute, that is, all other speeds do indeed change in relation to the speed of the observer, so it's always seemed a rather strange notion to me. LEE SMOLIN: Special relativity works extremely well and the postulate of the invariance or universality of the speed of light is extremely well-tested. It might be wrong in the end but it is an extremely good approximation to reality. QUESTION: So let me pick a bit more on Einstein and ask you this: You write (p. 56) that Einstein showed that simultaneity is relative. But the conclusion of the relativity of simultaneity flows necessarily from Einstein's postulates (that the speed of light is absolute and that the laws of nature are relative). So he didn't really show that simultaneity was relative - he assumed it. What do I have wrong here? LEE SMOLIN: The relativity of simultaneity is a consequence of the two postulates that Einstein proposed and so it is deduced from the postulates. The postulates and their consequences are then checked experimentally and, so far, they hold remarkably well.

Pentcho Valev

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"...a big problem for me is that here Smolin is not taking a provocative minority point of view, but just reinforcing the strong recent intellectual trend amongst the majority of physicists that the "trouble with physics" is too much mathematics. As I've often pointed out, the failures of recent theoretical physics are failures of a wrong physical idea, rather than due to too much...

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"...a big problem for me is that here Smolin is not taking a provocative minority point of view, but just reinforcing the strong recent intellectual trend amongst the majority of physicists that the "trouble with physics" is too much mathematics. As I've often pointed out, the failures of recent theoretical physics are failures of a wrong physical idea, rather than due to too much mathematics..."

Correct. And the wrong physical idea is... Einstein's 1905 constant-speed-of-light postulate of course:

Lee Smolin, The Trouble With Physics, p. 226: "Einstein's special theory of relativity is based on two postulates: One is the relativity of motion, and the second is the constancy and universality of the speed of light. Could the first postulate be true and the other false? If that was not possible, Einstein would not have had to make two postulates. But I don't think many people realized until recently that you could have a consistent theory in which you changed only the second postulate."

"As propounded by Einstein as an audaciously confident young patent clerk in 1905, relativity declares that the laws of physics, and in particular the speed of light -- 186,000 miles per second -- are the same no matter where you are or how fast you are moving. Generations of students and philosophers have struggled with the paradoxical consequences of Einstein's deceptively simple notion, which underlies all of modern physics and technology, wrestling with clocks that speed up and slow down, yardsticks that contract and expand and bad jokes using the word "relative." (...) "Perhaps relativity is too restrictive for what we need in quantum gravity," Dr. Magueijo said. "We need to drop a postulate, perhaps the constancy of the speed of light."

Joao Magueijo, Faster Than the Speed of Light, p. 250: "Lee [Smolin] and I discussed these paradoxes at great length for many months, starting in January 2001. We would meet in cafés in South Kensington or Holland Park to mull over the problem. THE ROOT OF ALL THE EVIL WAS CLEARLY SPECIAL RELATIVITY. All these paradoxes resulted from well known effects such as length contraction, time dilation, or E=mc^2, all basic predictions of special relativity. And all denied the possibility of establishing a well-defined border, common to all observers, capable of containing new quantum gravitational effects."

Pentcho Valev

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Lee,

A very nice essay. I wanted to focus on the last two points of the paper:

1. In the real universe it is always some present moment, which is one of a succession of moments. Properties off mathematical objects, once evoked, are true independent of time.

2. The universe exists apart from being evoked by the human imagination, while mathematical objects do not...

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Lee,

A very nice essay. I wanted to focus on the last two points of the paper:

1. In the real universe it is always some present moment, which is one of a succession of moments. Properties off mathematical objects, once evoked, are true independent of time.

2. The universe exists apart from being evoked by the human imagination, while mathematical objects do not exist before and apart from being evoked by human imagination.

I agree these two points get to the heart of the conundrum we find ourselves in. We can intuit timeless mathematical entities. These of course are not "physical" in the sense that the have a discernible direct energy and momentum, however we can indirectly assign the storage of mathematical items as information having some energy and momentum requirement. Certainly, we can say that as artifacts of human thought, there is a level of energy and momentum transformed to develop these concepts. We know we have developed this in some discrete number of operations. So is there a spectrum of energy and momentum we can assign to the development of a mathematical concept?

Certainly there is no reason the development could not have followed some other path. There is nothing a priori that necessarily restricts someone from coming up with an idea, although it might be absent the requisite context. Regardless, a person's thoughts must be seen in a prismatic sense; some spectrum of possible mental states that tie back to the physical world.

I am staring at a young pine tree in my neighbor's yard being buffeted by a cold wintery wind, and I think about the fractal regularity of how it grew. Did the tree know before hand how to grow so it would survive the onslaught of the weather?

I have pondered the same points above for some time, and understand I am only seeing a tree because there is some function that tells me I am likely to see the tree there. So the regularity of the math associated with the tree must be buried somewhere in the function does it not?

Would be interested in your thoughts.

Cheers!

Harlan

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Lee, Tim and Pentcho,

The trouble with physics is not so much the volume of the mathematics that we have. The trouble is mainly the application and the interpretation of the mathematics.

The troublesome application is that regarding the arbitrary transformations that Einstein proponed based on the Lorentz transformation equations. Einstein actually proponed the following three...

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Lee, Tim and Pentcho,

The trouble with physics is not so much the volume of the mathematics that we have. The trouble is mainly the application and the interpretation of the mathematics.

The troublesome application is that regarding the arbitrary transformations that Einstein proponed based on the Lorentz transformation equations. Einstein actually proponed the following three transformation equations in special relativity:

(1) the space transformation equation

x=x'(1-v²/c²)^-½

(2) the time transformation equation

t=t'(1-v²/c²)^-½

(3) the mass-energy transformation equation

m=m'(1-v²/c²)^-½

In (1) the space transformation equation, the transformation factor is applied to the essence of space as implied by the space variables x and x'. Here Einstein made space a medium of motion.

After discarding the ether medium of motion, Einstein tacitly proposed other mediums of motion, because as per the erroneously interpreted Michaelson and Morley experiments, no motion can be ascribed to the ether. It is obvious that the Michaelson and Morley experiments were erroneously conducted and interpreted because the experiments did not and probably could not account for the doppler shifts.

In (2) the time transformation equation, the transformation factor is applied to the essence of time as implied by the time variables t and t'. Einstein made time another medium of motion; this ignored the fact that the duration process that occurs in time is NOT a motion process. The motion process occurs only in space, with infinitely many varied rates of displacements expressed as distance per unit time.

It is incorrect to apply the transformation factor to the essence of time because the transformation factor indicates only velocity or motion transformations and there is no such thing as the velocity of time - the duration process occurs as a 'displacement' through the time dimension strictly at the 'universal' rate of one moment per moment.

In (3) the mass-energy transformation equation, the transformation factor is applied to the concept of mass (and energy) as implied by the mass variables m and m' and the resultant entry of the kinetic energy variable in the famed K.E.=mc².

In the mass-energy transformation, Einstein apparently did not know what medium of motion was involved and did not understand the foundational reason why he substituted the mass variables into the equations. But he saw the connection with the classical K.E. and made a momentous interpretation regarding mass and energy.

Einstein must have somehow understood that the medium of motion need necessarily be ascribed some motion for it to be an appropriate medium of motion. This is implied by the reason he gave as to why he discarded the idea of the ether. But because Einstein discarded the idea of an ethereal space-occupying medium of motion, he also discarded the idea of space whose sole function is that it gets occupied.

Pure kinematics points to the idea of the motions of motions, which is the reason why the medium of motion must be ascribed some motion in order for it to be an appropriate medium of motion.

The idea of a space-occupying substance as the medium of motion is still the more appropriate idea because motion is the displacement through space. When this idea is embraced, the space and time dimensions may simply be 'fixed' (assumed as absolutes) as the classics did.

The picture then presented is that of the transformations of motion rendered on the space-occupying medium of motion, according to the accelerations and rotations indicated by the transformation factor. The space-occupying medium of motion can then even be spoken of as ethereal, because then the focus will only be on the motions of motions (i.e., the various configurations, formations and transformations) suggested by pure kinematics.

The velocity of light is then simply the reference velocity for what is observable in nature, which is exactly in accordance with Maxwell's proponed variety in the electromagnetic phenomena and the experimentally verified unvarying velocity of light.

As I have explained in my post above, the cosmos is observed "with its full spectrum that range between the kinematic vacuums of dark voids and the kinematic singularities of super dense black holes"; and that range includes the electromagnetic spectra and the particulate spectra.

These are according to the proposition from the mass-energy transformation (3), which is actually the more practically successful proposition; nothing has so far been practically proven regarding the space-time transformations.

This rather radical view presents a cosmos that is observable as having strictly the varied motion formations and transformations.

All these are in consonance with my post above, my submitted essay, and the materials at my website www.kinematicrelativity.com.

The new perspectives that I am presenting could correct and resolve "the trouble with physics" that involves the application and interpretation of the mathematics. But it is sad that, as far as I know, I still remain very much alone in these views.

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Paul,

The evoked things are first technically the Platonic abstracts (also remember Kant's "thing in itself"). The evoked is first a state of the mind. In saying "first", I am of course already making a choice regarding the chicken-or-egg question. The abstract idea before the corporeal embodiment... (Note, however, that Lee's evoked things are already of the compound mind-and-body, since...

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Paul,

The evoked things are first technically the Platonic abstracts (also remember Kant's "thing in itself"). The evoked is first a state of the mind. In saying "first", I am of course already making a choice regarding the chicken-or-egg question. The abstract idea before the corporeal embodiment... (Note, however, that Lee's evoked things are already of the compound mind-and-body, since he somewhat rejects the Platonic.)

The state of the mind is directly related to the state of the brain-and-body - e.g., neuron and synapse states. It therefore would require the 'cycling' of the brain-and-body state to make permanent the mind state.

A cycled brain state, is a cycled mind state. A cycled part of the brain remembers/stores the information - i.e., the evoked things/properties. The brain-body circuit should be there to recall the memory. Wack the brain and you have a wacked mind.

Extend that to the observable pancosmic reality, and logically there would be the suggestion of the retained information or the lost info as the case may be. It is the state of the pancosmic reality (Lee's "single universe") that renders permanent the evoked properties.

It appears that the mechanism you asked of is the brain-and-bodyset for the mindset that renders permanent the properties of evoked things.

Sometimes the info also sort of get stored outside the brain-and-body. Photographs, or some other bodies, and etc., help one recall the info. The outside storage is sort of part of the circuit.

But in the pancosmic, once the info is forgotten - i.e., cut off the circuit - the info is lost because outside of the pancosmic reality is the panchaotic reality where the info continually gets decayed, where, so-to-speak, eternal death occurs - e.g., the scapegoat is sent to the wilderness never to be seen again.

There is of course the idea of an all-encompassing existence, the all-encompassing reality, which can be tricky, but the logic remains.

Just my own take.

It would be nice if Lee Smolin will also answer your question..

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Dear Lee,

I enjoyed your essay and do not disagree with anything you said. In fact I am glad to know that renown physicists like yourself are willing to stand up to, what I humbly consider ridiculous ideas, like multi-Universes, and timeless reality (in the sense of prior or predefined and unchanging) that some seem to actually advocate… (how they do it with a straight face is beyond me)....

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Dear Lee,

I enjoyed your essay and do not disagree with anything you said. In fact I am glad to know that renown physicists like yourself are willing to stand up to, what I humbly consider ridiculous ideas, like multi-Universes, and timeless reality (in the sense of prior or predefined and unchanging) that some seem to actually advocate… (how they do it with a straight face is beyond me). I also enjoyed your books and considering your celebrity status, I’d be honored if you read and reply to this post.

With that said, I have to admit that I thought the word “timeless” meant time-independent or static in the sense that you said “… records of past observations are static and that the properties of a mathematical object are, once evoked into existence by their invention, static.” I know of at least one person who has had a “mystical” experience (altered state of consciousness) in which he perceived timelessness in a way that did NOT imply a prior or predefined world. Instead, it was a perspective from which he could “see” or intuit the unity of space and time as different aspects of motion. As a result, he went and got an M.S. in physics and a Ph.D. in Nuclear and Radiological Engineering.

There’s nothing mystical about motion; motion is a state and the moving state is a form of change. The word “motion” represents a relative, complementary concept, i.e. “motion” is a single word used to express complementary antonyms (moving and not moving or at rest). When a person is in a rest state, without any outside interference, he or she can experience a wonderful, blissful state of consciousness that is so profound that it may dramatically change their life. During that experience, they might have an epiphany about something and then, unfortunately, some people consider themselves qualified to “make mystical pronouncements that attempt to explain” all sorts of things that are well beyond their epiphany. Some may have special insight or perspective, but to lay “claim to special authority”, I think is a criminal. So kudos to you for keeping us honest.

Now back to motion: It is my simple hypothesis (please see “A Space-Time-Motion Model” at http://vixra.org/abs/1402.0045) that space and time are both conformal projections of motion. Mathematically, the moving state can be expressed in terms of gradable parameters (displacement (s) and time (t)). The gradable parameters, s and t numerate (i.e. quantize) and denominate (i.e. reference to standardized time scale) the moving state of motion to provide a gradable spectrum of motion, v=s/t yet I submit that space (i.e. all of space, call it S = s^2 = x^2 + y^2 + z^2) and time (T) are also complementary concepts that are expressed in terms of gradable parameters, s and t, where (S=s^2) and (T=t^2). And here is “the trouble with physics”. It seems to be universally accepted that T = t = one-dimensional concept while space is unfolded into three. My argument is that time is a scale that denominates motion and is therefore an “evoked” parameter inspired by observations of motion. The STM model is a modification of the Minkowski diagram with an important difference: space and time are treated a equivalent concepts, i.e. space is not unfolded and time is not mirrored about the origin. It is naturally symmetrical.

So the moving state is represented by the linear parameters, s and t, and the rest state, i.e. zero motion, is represented by the inverse parameters, i.e. spatial frequency and temporal frequency (to give E=hf). The result is a clear and concise relational model that accurately depicts the well-known relationship for total relativistic energy of a particle. It includes the Lorentz factor as the magnification that results from projection of the rest-frame units onto the moving reference frame; and provides a reinterpretation of the “event horizon” as an “event reference” that is a perceptual separation between past and future. The model suggests that matter is thus “evoked into existence” by motion.

I’d like to submit a slightly condensed version of “A Space-Time-Motion Model” for publication and would immensely appreciate it if you would review it for me. I will send it to you off line; please contact me at stjohntheodore@gmail.com. Then if you get the chance, I also submitted an essay with an artistic bent for fun called “Doctors of the Ring - The Power of Merlin the Mathematician to Transform Chaos into Consciousness.”

Respectfully,

Ted St. John

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The essays are generally illustrative and explanatory regarding the merits of mathematics in physics. My essay is more illustrative than explanatory. Smolin's is more explanatory with little of the illustrative maths, focusing on the logic of premise and of thesis/hypothesis.

But Smolin's main proposition is illogical.

Smolin puts forth the following "to define temporal...

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The essays are generally illustrative and explanatory regarding the merits of mathematics in physics. My essay is more illustrative than explanatory. Smolin's is more explanatory with little of the illustrative maths, focusing on the logic of premise and of thesis/hypothesis.

But Smolin's main proposition is illogical.

Smolin puts forth the following "to define temporal naturalism."

2. The inclusive reality of time: All that is real or true is such within a moment, which is one of a succession of moments. The activity of time is a process by which novel events are generated out of a presently existing, thick set of present events. There are no eternal laws; laws are subsidiary to time and to a fundamental activity of causation and may evolve. There is an objective distinction between past, present and future.

Smolin apparently says that the 'universe' evokes temporal laws (his FAS) that emerge when new physical realities emerge, such that, in sum, all laws are accordingly short-term temporal laws that evolve. Outright it can be seen that his idea contradicts itself.

Smolin's proposition that "there are no eternal laws" is itself a law that Smolin propones. Since his proposition is that the laws are temporal, then, if this law is functional, it implies that his proposition negates itself in time; when the law's term ends, the implication would be that of the return to the idea of eternal laws.

Thus, Smolin's main proposition is illogical. And he does not show any mathematics with a generalized scope that illustratively supports his proposition.

In contrast, my idea is that the universe replicates and establishes its parts as predicated by eternal laws that govern its progression from the infinite past towards the infinite future; it changes only in conformity with eternal laws; it looks generally the same since it abides by the same eternal laws predicated according to the premise that the observer (i.e., the universe) always existed in essentially the same complete form.

To illustrate and support my view, I presented the genesis formula that implies an infinitely hierarchical kinematic cosmos instead of a cosmos from a singularity; it indicates that mass and energy are kinetic constructs; and it explains the eternal nature and origin of gravity.

I identified two fundamental essences of change, two fundamental currents or flows (flux) or processes. They are motion and duration. As fundamental processes, motion and duration proceed in a unison of phenomenon and noumenon.

Duration is the CONSTANT essence of change, because there is no other flow that interacts with the duration process. Duration (time) flows uninfluenced by anything else.

Motion is the VARIABLE (transformable) essence of change, because motions interact with other motions and get accelerated.

I have put forth that motions, including light, may be transformed upon interaction with other motions. And the velocity of light is simply the reference velocity by which the transformations are 'measured'. The c=wf formula suggests that the wavelength w and frequency f may change, while the velocity c is simply the referenced threshold for the effected motion transformations.

When the mass or energy variables are substituted into the transformation equations, the genesis formula is derived and it indicates motion being transformed into the cosmic mass and energy observables; and the suggestion is that these observables may be perpetually preserved in their existence as part of an eternal and infinitely hierarchical kinematic cosmos.

In sum, the genesis formula contradicts Smolin's idea of evoked FAS and temporal laws, because the genesis formula implies an eternal and infinitely hierarchical kinematic cosmos.

The only way to discredit the propositions of the genesis formula is by falsifying or disproving its mathematics and logic... I doubt that anyone can successfully do that.

The indifferent and idiotic may of course simply ignore or ridicule or becloud the merits of the genesis formula. But the astute will make pertinent comments.

I await Smolin's comments (among others'), since I sort of challenged his view and he represents a sector of establishment science...

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And since we are at FQXi, I'd like to respectfully challenge the great FQXi minds like Tegmark, Aguirre, Greene, Susskind, Randall, Carroll, Turok, Hawking, Guth, Linde, Weinberg, Rees, Tong, Randall, Wilczek, Levin, Silverstein, Wolfram, Seager, Hooft, and etc., to try to falsify the mathematics and logic of the genesis formula. Let's see if that can be done successfully.

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To continue my remarks from last time. In trying to argue against the idea of preexistence of mathematical realities, you mention a wide spectrum of things ranging from the somewhat mathematical to the non-mathematical. Your argument seems to be that since you can find some (non-mathematical) things that do not preexist some act of creation and you can also go "continuously" from these to...

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To continue my remarks from last time. In trying to argue against the idea of preexistence of mathematical realities, you mention a wide spectrum of things ranging from the somewhat mathematical to the non-mathematical. Your argument seems to be that since you can find some (non-mathematical) things that do not preexist some act of creation and you can also go "continuously" from these to mathematical systems, you conclude that mathematical systems do not preexist some act of creation either. However I see this fallacious : just because you want to believe that different stuff are the same kind and you can look for intermediates between them, and pretend you find some which make the spectrum continuous, does not mean that they are really of the same kind. Discontinuities in this range can be found, that can justify to not put all these things in the same category.

Rules of poetry also implicitly require sentences to be meaningful and appropriate for poetry, a condition which cannot be mathematically defined. So the complete expression of its rules may depend on time (as language and cultural context evolve, modifying the condition of meaningfulness of sentences), thus making this incomparable to the case of mathematical systems.

For example, chess is an exact problem, but the rules of chess are rather complex and arbitrary, so that it is just one game in a range of billions of possible games with a similar degree of complexity of their rules. Civilizations on independent planets have only a very small probability of having the same game of that complexity level becoming popular. Still, from a mathematical viewpoint, this game exists as a game among others, just like any number between 1 and 10¹⁰ exists as a number among others in this range, no matter that it has only a very small chance of being picked up by a particular person who is choosing a number at random in this range. The only thing in chess which is not strictly of this kind (of existing in the abstract but having a very small chance of being picked up), is not the game itself but the names and pictures of the pieces involved.

Question : if Chess does not exist before a civilization "invents" it, then, did any number between 1 and, say, 10¹⁵, remain non-existing until someone uttered it ? You seem to not adopt that view, however, in the sense that you admit that all possibilities inside an axiomatic system exist as soon as the rules of the system were fixed. So, as soon as we have a theory of arithmetic, all natural numbers must exist. More precisely, at least the standard ones, and even more precisely those lower than a number we can tell, such as for example, all numbers between 1 and 10¹⁵. This makes your concept of existence of an object independent of the degree of conscious awareness of people towards this object, unlike the rules of chess, whose heavy "existence" in this world above other possible games of similar complexity, actually consists in the conscious attention of people towards it. As explained in my essay, I hold conscious awareness as forming the other component of existence aside mathematical existence, that is where "novelty" as we know it resides (the act of becoming aware of a mathematical object that mathematically existed, but that one did not think of before).

In biology, things are picked up in a landscape of possibilities that is explosively huge because of the high complexity of everything there. So it would be completely impossible for someone to enumerate all possibilities one by one. But then what ? If that was a reason to deny the preexistence of possibilities not yet picked up, should we also claim that most numbers between 1 and 10¹⁰¹⁵ are non-existing just because nobody ever paid attention to them ? If we recognize the existence of all these numbers just because we have a theory of arithmetic for them, no matter our concrete inability to enumerate them all, then we should also recognize the existence of all biological possibilities because we have laws of physics which, in principle, determine this landscape of possibilities.

Now about axiomatic systems, and the idea that the whole infinity of truths from an axiomatic system are being born at the time when the particular axiomatic system is being uttered. I'm sorry but this is so ridiculous to draw the line of existence here (I was tempted to say it is one of the most ridiculous places to draw the line, however I'm not here to try arguing that a less ridiculous defense of naturalism is otherwise possible, either). Because, as is well-known in mathematical logic but as you may have missed if you are ignorant in this field (since you admitted that you only recently happened to accidentally discover that a respectable account of a philosophy of mathematics also needs to tell something about the rules of proof, while it might have been better if you went as far as caring to seriously inform yourself on the core concepts and works actually done by specialists of this well-established field of mathematical knowledge, instead of just assuming that, just because you are a renowned physicist and famous blogger, your random baseless speculations on the foundations of maths should be seen just as plausible as anything else), there is a well-known general concept of axiomatic systems and their logical consequences, whose rules are universal and independent of the particular axiomatic system. Somehow you even also implicitly admitted yourself the Platonic existence of this universal system with its absolute concept of proof, that you awkwardly tried to condone and reduce to some pragmatic stuff.

But, since, in fact, these universal rules of the game of writing axiomatic systems and deducing their logical consequences have been discovered (or "evoked" if you prefer), according to your philosophy, this automatically gives existence to the whole of mathematics, with the totality of possible axiomatic systems and all their consequences. Bingo ! The whole truth of mathematical Platonism is now accomplished.

Indeed, in case you didn't know, we can easily write down a computer program whose function is to automatically enumerate all possible axiomatic systems one by one, only restricting the possibility for particular axiomatic systems to be included there by the practical limits of computer resources. (We can also enumerate all algorithmically enumerable infinite axiomatic systems by automatically generating and emulating all programs able to generate axioms).

If on the other hand we considered particular axiomatic systems as not yet created as long as they are not actually uttered by a computer, but created when they are uttered, a problem would be, just uttering is not enough. If a program utters an axiomatic system, it is not yet really an axiomatic system that is uttered as long as it is not functionally used in the intended way, otherwise there would be no objective truth on which axiomatic system was really uttered at at time (it all depends, for example, whether a given logical symbol is interpreted as meaning "and" or "or", just like uttering "1464" remains ambiguous on which number this chain of symbols is supposed to represent, unless we specify some conventions on how numbers are denoted). However it is just a matter of adding one more piece of software and a lot of computer power, for a program of automatic generation of axiomatic systems to also actually give their full meanings to these axiomatic systems, by starting to deduce all logical consequences of these systems in parallel. Then, is it that latter piece of software which, when put in conjunction with the utterance of each axiomatic system, provides these uttered axiomatic systems their actual existence with all their truths ?

I will still add more remarks later.

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I continue. You call "mystical" the belief in the independent existence of mathematical entities. You point out that they "add nothing and explain nothing". Well, I do not see the idea of independent existence of mathematical entities as trying to add or explain anything, as if it was any kind or addition or speculation. It is not. Mathematical facts are necessary facts. I cannot see any sense in...

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I continue. You call "mystical" the belief in the independent existence of mathematical entities. You point out that they "add nothing and explain nothing". Well, I do not see the idea of independent existence of mathematical entities as trying to add or explain anything, as if it was any kind or addition or speculation. It is not. Mathematical facts are necessary facts. I cannot see any sense in which the truth of 2+2=4 can be said to be or have been "non-existing" at any time. It is the belief in the possibility of non-existence of such truths, that I would call a mystification.

What is the problem ? You have the problem that you think that whenever such ideas are raised, it "involves us in a pile of questions that, unlike questions about mathematics, cannot be answered by rational argument from public evidence."

Which questions ? I looked at the questions you listed on page 5, and sorry, this is just laughable. You call these "questions" ? Well of course it is always possible to feel uncomfortable with any idea or any truth, by the sickness of reacting to them by asking tons of "questions" which may be naively thought of as legitimate but which are in fact senseless, just a psychological reaction of inventing problems where there is no problem, because the truth that is seem "problematic" was not grasped in the correct manner. Such reactions are frequent in the crackpot world. For example those who cannot accept relativity theory may ask questions such as "What causes the slowdown of time ?" "What causes the contraction of length ?". On other topics, one can ask "What is an electric charge", "what is a number", "how dense is a black hole", "what happened before the big bang", "what is a specie", trying (as I saw science philosophers do) to make sense of "structural realism" so as to define what is the reality of the structures that are studied by biology and other sciences; and wonderiong a long time about whether light and other quantum substances must be "explained" as waves or as made of particles.

Example: "If the FAS existed prior or timelessly, what brought it into existence?". Well, nothing, why ? If it existed timelessly then there is no need of any such thing as an event of bringing it into existence. It would only be needed under the assumption of existence of a previous time when that FAS did not exist. But the idea of such a time is a belief I would call a deep, crazy mystification. There never was a need of any physical event to create an FAS because there never was in the first place any physical time when it did not exist and remained to be created. As simple as that.

"How can something exist and not be made of matter?"

Well, and how can matter exist and not be made of something else ?

You choose to call "mystification" the belief of existence of something else than matter. But, well, can we reject as "mystification" the belief of existence of anything at all ? Of course not, as we are aware of our own existence. So we can only reject a belief in the existence of some specific kind of things in favor of that of another kind. The question is to know which are the kinds of things that exist. The only mystification would be to misattribute our existential beliefs in ways not supported by evidence. Our own existence, as conscious beings, is something clear, that cannot be denied. The existence of mathematical truths is also clear as we can study and understand them. But the existence of matter, what the heck is that ? We cannot access it, all we have is sensations about it. These sensations naively suggest to the layman a real presence of material things by means of their coherence (logical patterns). These patterns can be described mathematically. But when analyzed in details, we discover quantum physics, which strongly indicates that material things do not really exist at a fundamental level, but are created by our conscious perceptions of them. Indeed: for example I even heard in this debate on interpretations of quantum physics, all of whose participants are hardcore materialists, a report that many physicists tend to dismiss the reality of the wavefunction, and at the same time hold that "nothing else is real", which would imply that "nothing [exists] at all" (since they did not make the step of admitting another kind of fundamental reality). So I'm not inventing the idea that quantum physics denies the existence of matter, even materialist physicists somehow acknowledge it.

So we have evidence (or at least strong indications from experience) that matter is not real. Now if a belief in the existence of something we clearly see (mathematical truths) is "mystification", then, how can we call the hard unshakable belief which you expressed in your text, that only one kind of things that we cannot see (matter) exists while other kinds of things which we clearly perceive (our own self and mathematical truths) don't, in spite of the evidence from modern physics that matter is not real ? Maybe "total insanity", why not ?

(I still didn't finish...)

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The Lorentz transformation is not the culprit. Its interpretation is. Remember that the famed E=mc² was derived according to the tacit assumption that space and time are absolutes (i.e., not influenced by anything - no fluxions or motions influence space and time); and because of this, the mass or energy variables are substituted into the transformation equations in order to indicate...

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The Lorentz transformation is not the culprit. Its interpretation is. Remember that the famed E=mc² was derived according to the tacit assumption that space and time are absolutes (i.e., not influenced by anything - no fluxions or motions influence space and time); and because of this, the mass or energy variables are substituted into the transformation equations in order to indicate the effects of motion transformations that depart from the classical velocity transformations. I have persistently stated this for many years now.

Einstein's idea of space-time transformations is bunk. What nature is showing us is the idea of motion transformations. The whole cosmos is a motion (kinetic) construct - formations of motions, configurations of motions. The idea of configuration space or spatial configurations is an illusion. Einstein led us to an undecided view of reality with his idea of the arbitrary transformations of space and time, and that of the transformations strictly of motion, which he never explained. Perhaps, he knew it, or perhaps he didn't know it. But the equations suggest the transformations of motion - which is why the Lorentz equation is an equation regarding motion.

Apparently, to cover all bases, Einstein put forth the arbitrary space-time transformations idea, but the substitution of the mass variables into the Lorentz equations is according to the 'classical' idea of motion transformations, which has clearly indicated to us that mass is a kinetic construct. Mass is a kinetic energy configuration, which is why we are able to release so much motion from our nuclear reactions where mass is lost.

Descartes and Maxwell were closer to truth when they considered the idea of motions in the space-occupying ethereal medium - which is never really 'ethereal' because it is always imbued with underlying motions; the idea of the ether and motion together complete the idea of substance (i.e., matter or mass-energy) in space.

The maths of our science will never get clarified until we thoroughly embrace the idea of motion transformations and altogether disregard Einstein's arbitrary space-time transformations idea, calling it as it is - an illusion.

But present-day scientists and theorists are too afraid to champion the idea of strictly the motion transformations. It remains to be seen whether our FQXi bunch will muster the courage and good sense to finally clarify the facts and evidences and raise their hands to vote for the truth.

It will not be surprising if eventually somebody will say that what they mean when they say space-time transformations is the idea of motion transformations. But then it would likely be hogwash if they do not acknowledge the ideas presented here.

I have stated all along that physical reality has been according to the laws of motion (the transformations of motion), not the pseudo-laws of space-time transformations that Einstein put forth. In all that I have written on the 'physics' of reality, I have always proponed the idea of strictly the motion formations (i.e., configurations/constructs) and motion transformations...

All matter, mass, energy, forces, fields, gravity, all phenomena can be explained as motion constructs - all according to the comprehensive laws of motion.

I think Smolin, Tegmark, Aguirre and the whole FQXi gang should say something regarding these. Otherwise, they'll prove themselves not really true to the professed cause of FQXi... I am not saying that they are exploiters who simply gather our ideas for their own use and glory; I am saying that they should at least take some responsibility by giving answers to the comments here since they started this FQXi thing... So, come on. Why so quiet?

I wish I could say these things in a milder way. But it is difficult because of the hardness of the scientific community...

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Now about your page 7.

You wrote : "the answer to Wigner’s question is that mathematics is reasonably effective in physics, which is to say that, where ever it is effective, there is reason for it". This claims comes as logically deduced from your philosophy, in the traditional way of philosophers, that is, as a pure theoretical (but not even so carefully logical) blind guess, that...

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Now about your page 7.

You wrote : "the answer to Wigner’s question is that mathematics is reasonably effective in physics, which is to say that, where ever it is effective, there is reason for it". This claims comes as logically deduced from your philosophy, in the traditional way of philosophers, that is, as a pure theoretical (but not even so carefully logical) blind guess, that proudly comes as self-sufficient reasoning with no need to check it against any review of how things were observed to be : here, the measure of how mathematics was found to be effective in reality. Indeed, where is your review of these observations ? Instead of observing or checking anything, you satisfy yourself to prophesy: "There will never be discovered a mathematical object whose study can render unnecessary the experimental study of nature". Still you are coming with philosophical principles whose study seem to suffice for you to deduce in the abstract how effective should math be to the study of nature. Just like usual (bad) philosophers, your confidence in your principles makes you see unnecessary not only to abstain concluding and humbly consider to wait and see what future discoveries may show (maybe giving your claims a status of falsifiable predictions to be tested and eventually refuted), but you also see it unnecessary to check their compatibility with the present record of the state of things actually found by modern science: whether the effectiveness of mathematics that was actually "observed" by the development of modern science fits these expectations of effectiveness you are presenting. Does the self-evidence of your principles and prophecies carry sufficient logical or metaphysical reliability to give you such a faith in their truth that this confidence can legitimately supersede for a rational mind, any concern for experimental check, any verification against any past or future research, such as a search for a counter example to your claims (some mathematical object that might be successful enough to make some experiments unnecessary) ?

Actually, theoretical physics happened to be so successful that, well of course there is still some place for experiments, but this place is now quite reduced either to very complex (macroscopic) systems (where computations would be too complex for our supercomputers, so that the studied properties are only consequences of known laws in principle but not in practically computable ways), or to the case of extreme conditions that are very hard to explore (with particle accelerators, some subtle aspects of astronomy and cosmology to analyze the properties of dark matter... not mentioning the mind/brain interaction that I expect, as I explained in my essay, to involve subtle processes, linked to the nature of quantum measurement, beyond established mathematical physics, that have not yet been well investigated); in many other cases, such as gravitation, theory suffices. Fortunately indeed we do not need to send hundreds of probes in space all over again for each space exploration mission until finding out by chance which trajectory may actually lead to the desired destination.

After this, in guise of illustration of your belief, you give examples from modern physics, so as to make it look as if your principles were not pure abstract principles disconnected from modern science, but compatible with it, or even supported by it. I am deeply amazed at what a badly distorted report you manage to make of how things go in modern physics, so as to make it look as if it supports your philosophy. This is so ridiculous, and just the same style of absurd distortions and misinterpretations of modern physics as what is usual from the part of cranks who claim to refute Special Relativity by criticizing Einstein's book and finding a "new explanation" for the Michelson-Morley experiment (or rather an old one, always the same : a "mechanically explained" Lorentz contraction of moving things and absolute slowdown of clocks with respect to an absolutely still ether), or who similarly "explain" quantum physics by classical waves, or who claim there must be a local realistic deterministic explanation of quantum randomness because they believe that any randomness must hide such a determination (assuming that physicists just did not try to look for one but lazily and dogmatically preferred to "shut up and calculate") and they did not learn about the logical and experimental arguments against it.

You see "a large degree of arbitrariness" in mathematical physics. Of course there is some arbitrariness in the list of particles in the Standard Model and the values of all constants there as we know them (about 20), but this is nevertheless often qualified by many physicists as quite elegant as compared to the amount of observations this theory explains, far from "a large degree of arbitrariness" as you say. The Higgs boson, like many other particles (such as antiparticles), was predicted before being observed.

You wrote "In most cases the equation describing the law could be complicated by the addition of extra terms, consistent with the symmetries and principles expressed, whose effects are merely too small to measure [by] given state of the art technology. These “correction terms” may be ignored because they don’t measurably affect the predictions, but only complicate the analysis". Sorry I do not see well what kind of example you are thinking about here.

On the contrary, I see in most cases that such "correction terms" you mention, such as "correcting" classical mechanics by Special Relativity and then General Relativity, indeed complicate the work of numerical computation of results with "additional terms" from the viewpoint of numerical analysis, however the corresponding theoretical picture is simplified instead. What they actually reflect is a more unified, simple and elegant theory. They are not arbitrarily added for complications, but they come as more or less theoretical necessities. Indeed I explained in my web site how, for example, Special Relativity is simpler as a theory than Galilean space-time. Consequently, Relativistic mechanics is also simpler than classical mechanics, as it comes from a simple principle (the least action principle, more elegantly applied to the space-time of Minkowski than it was to the Galilean space-time) and unifies all conserved quantities (mass, energy, momentum, angular momentum, center of mass) in a unique mathematical object (an antisymmetric tensor in the 5-dimensional vector space associated with the 4-dimensional affine space-time). General Relativity is very elegant too, should I develop this point ?

"every one of the famous equations we use is merely the simplest of a bundle of possible forms of the laws". Please list 10 possible non-equivalent theories of speed and movement that behave approximately the same in many practical cases of experiments, and among which Galilean space-time and Special relativity are non-remarkable particular possibilities. If for any reason you do not like this example, please do a similar thing for other problems such as electromagnetism, gravitation, quantum physics or whatever. You say the only advantage of admitted versions is their simplicity just because it is convenient for us ? But how to explain that in so many cases of theories, among all possible alternatives, there happens to be one that is both extremely simpler than any alternative that can be thought of, and extremely well-verified by observation, with no need of correction by any alternative (no arbitrary complication that we may naturally think of for the sake of complication rather than for the sake of elegance, ever turns out to be better verified, as far as I know) ? Or do you claim this is not the case ?

So I'm sorry but this is bullshit : "Often we assert that the right one is the simplest, evoking a necessarily mystical faith in “the simplicity of nature.” The problem is that it never turns out to be the case that the simplest version of a law is the right one". First, we do not assert by faith that the right one is the simplest we think of. Instead, we conclude it as we verified it by observation. Second, when we had a seemingly simple equation which worked (such as Newton's law of gravitation), the new one that turns out to be more correct to replace it (General Relativity), turns out to be conceptually simpler (more elegant) than the first one; only it was not thought of at first because it is a more subtle, sublime kind of mathematics that requires some familiarity with high mathematics to be grasped. Finally thus, it remains true that the right one is the simplest, except only that we did not know at first the theory which turned out to be both simplest and better verified.

You gave another example : "Maxwell’s equations received corrections that describe light scattering from light-a quantum effect that could have been modelled-but never anticipated-by Maxwell". This example is supposed to illustrate your claim of possible complications and "under-determination" of laws among multiple possibilities. It doesn't. The truth is that these corrections by light scattering from light are not an option among alternative possibilities, but a logically necessary consequence of inserting electromagnetism in the framework of quantum field theory. Of course Maxwell could never anticipate it because quantum theory was not known at that time, but this impossibility to anticipate it before the birth of quantum physics is completely irrelevant here. It does not change the fact that this effect is a necessary consequence of quantum physics. This quantum physics had to be introduced for very different (and necessary) reasons than looking for corrections to electromagnetism. There is no logical possibility for this "correction" of electromagnetism to be not there with its exact necessary amplitude as soon as we live in a quantum world with all its other, more direct consequences (such as the stability of atoms). There is no trace of any "radical under-determinacy" here. To take a related example, consider the measure of the anomalous magnetic moment of the electron, where the calculation as logically determined from theory was verified by observation to an amazing degree of accuracy. We did not need to adjust anything in the theory to put it in agreement with this observation.

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Dear Mr. Smolin,

I appreciate your reliance upon common sense; a conception that is not as common as commonly believed. I also concur with your view that there is "no perfect correspondence between nature and mathematics."

You state that "it is essential to regard time as an essential aspect of nature". While I endorse this statement as being correct, I find it difficult to imagine...

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Dear Mr. Smolin,

I appreciate your reliance upon common sense; a conception that is not as common as commonly believed. I also concur with your view that there is "no perfect correspondence between nature and mathematics."

You state that "it is essential to regard time as an essential aspect of nature". While I endorse this statement as being correct, I find it difficult to imagine how time or nature could be represented otherwise.

As the prefix "Uni" clearly implies, there is only one all-there-is. We agree on the existence of a singular universe which embraces everything that exists, whether we have acquaintance with such "things" or not. Your statement that "There are no eternal laws" also rings true insofar as laws are too rigid to accommodate eternal changes in nature's performance. The concept of "principles" better describes the causes or natural biases that effect change.

While, as you state (with regard to biology and mathematics) that in a timeless platonic world "there is a potential infinity of FAS’s (formal axiomatic systems)", such potentials are merely infinite opportunities to exist, not existences per se. In the natural world the notion of timelessness evokes senselessness!

I suspect that in editing your essay you overlooked the need to delete the statement "How can something exist now but also exist timelessly" - though you did omit the question mark (?) .

Again, "How can something exist and not be made of matter?" is questionable. Time, space, energy, relations, the intellect, volition and the affections are not made of matter. No matter!

The statement "mathematical arguments are just finely disciplined cases of the usual rational thinking that all humans constantly engage in to understand their world" seals the fate of your naturalist position in your favour, i.e. that mathematics is reasonably effective in physics.

In reducing nature to its ultimate quality, all that exists are relations. That is exactly what mathematics and physics deal with and why they are complementary visions of the same world.

Congratulations, and thanks for the trip.

Gary Hansen

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Dear Lee,

You have mentioned "By that I mean the hypothesis that everything that exists is part of the

natural world, which makes up a unitary whole. This is in contradiction with the Platonic

view of mathematics held by many physicists and mathematicians according to which, mathematical truths are facts about mathematical objects which exist in a separate, timeless realm of...

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Dear Lee,

You have mentioned "By that I mean the hypothesis that everything that exists is part of the

natural world, which makes up a unitary whole. This is in contradiction with the Platonic

view of mathematics held by many physicists and mathematicians according to which, mathematical truths are facts about mathematical objects which exist in a separate, timeless realm of reality, which exists apart from and in addition to physical reality."

So a new conception of mathematics is needed which is entirely naturalist and regards mathematical truths as truths about nature. In this essay I sketch a proposal for such a

view. The key it turns out is the conception of time. I propose that to get a conception of mathematics within naturalism it is essential to regard time as an essential aspect of nature, in a sense to be specified shortly. I thus propose to call this new view, temporal

naturalism.

1. The singular universe: All that exists is part of a single, causally connected universe.

The universe and its history have no copies, and are not part of any ensemble.There is no other mode of existence, in particular neither a Platonic realm ofmathematical objects nor an ensemble of possible worlds exist apart from the single

universe.

2. The inclusive reality of time: All that is real or true is such within a moment, which is one of a succession of moments. The activity of time is a process by which novelevents are generated out of a presently existing, thick set of present events. Thereare no eternal laws; laws are subsidiary to time and to a fundamental activity ofcausation and may evolve. There is an objective distinction between past, present and future.

This is what I have emphasized in my Mathematical Structure Hypothesis that mathematical and physical reality don't exist independently and both are creation of Eternal Vibration which creates the entire Universe. thats why mathematical structures and physical reality both are effective to solve each other. This further sorts out your concern that "If we give up the idea that there is a mathematical object existing in a timeless Platonic realm which is isomorphic to the history of the universe, we still have to explain why mathematics is so effective in physics."

The paradoxes, inconsistency,contradiction exist because physical reality has been equipped with time and frame dimension but mathematical reality are taken into timeless, frameless dimension. But as my MSH states that both originate from Eternal Vibration, mathematical reality should also be extended in time/frame dimension like physical reality and made dynamic. Skolem had also shown that axiomatization of set theory leads to relativity.

In the Absolute there are no space,time & causation but we allow them in physical reality and take time into timeless space without causation. This fundamental discrepancy must be removed so that mathematics could evolve beyond paradoxes,contradictions dynamically.

Anyway you have written great essay.

Regards,

Pankaj Mani

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Dear Lee Smolin

I could never accept that math is only what is defined with axioms, but I think that math is predefined without axiom. But, here I do not think so a Platonistic world, but a Physical world. Thus naturalism agrees with my intuition.

I agree a lot of with your ideas. This your ''evoked'' can be described a little differently. A lot of options in Platonistic world, for...

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Dear Lee Smolin

I could never accept that math is only what is defined with axioms, but I think that math is predefined without axiom. But, here I do not think so a Platonistic world, but a Physical world. Thus naturalism agrees with my intuition.

I agree a lot of with your ideas. This your ''evoked'' can be described a little differently. A lot of options in Platonistic world, for instance chess rules, mean a big entropy, which cannot be applied, similarly as perpetum mobile of the second kind cannot used heat if temperature differences do not exist.

Beside of this entropy, here is also time, which should to run, logic needs time, and consciousness which should think about this Platonistic space. Thus Platonistic world exist on some way, but it is ineffective, similarly as you described with your ''evoked''.

One essential distinction between you and me is, that I am reductionist, thus I claim that math of fundamental physics is simple. (It is also one essay about this in this contest.) Admittedly, special relativity (SR) is a correction of Newtonian physics (NP), but Newtonian physics also gives some information; SR does not mean complete correction of NP. Thus I also claim that quantum gravity should be simple.

Admittedly, transitions from Newtonian physics (NP) to special relativity (SR), to General relativity mean complication. But, c at SR gives connection between space and time, and G gives new explanation for gravitational force. Besides, SR is not so complicated as we think, a lot of is our familiarity with NP. One special example is the complexity of quantum field theory, but it is a consequence of quantum gravity, thus I suppose that it should be simple, as it is written in my essay. Postulates of SR and GR are simple, and it seem by Zeilinger, that postulates of quantum mechanics can also be simple.

You worked a lot of on this question, thus you can give a lot of anti-arguments. I am interested in them.

Thus, I claim that mathematics is a consequence of physics, but physics is also a consequence of mathematics. I gave two opposite examples in the second section, Planck spacetime and Pythagora theorem.

You even prove that Feynman and Mermin were wrong with ''Shut up and calculate'' and ''philosophy is not usable in physics''.

You mentioned that ideas are not massless. I mentioned in my reference [1] that time and mass are connected in dimensionless quantities, thus this makes your idea still more clear.

But, the problem is also to use right words. These essays gave a lot of improved essential sentences.

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Hi Lee,

You said, “In particular, there is no mathematical object which is isomorphic to the universe as a whole, and hence no perfect correspondence between nature and mathematics.” As an example to defend this viewpoint you said, “In the real universe it is always some present moment, which is one of a succession of moments. Properties off[sic] mathematical objects, once evoked,...

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Hi Lee,

You said, “In particular, there is no mathematical object which is isomorphic to the universe as a whole, and hence no perfect correspondence between nature and mathematics.” As an example to defend this viewpoint you said, “In the real universe it is always some present moment, which is one of a succession of moments. Properties off[sic] mathematical objects, once evoked, are true independent of time.”

If the universe was known to be discrete and finite at any given moment of time, (and time itself was also discrete) would this change your view that there is no mathematical object that is isomorphic to the universe? Do you think if we saw the universe as a computation that the notion of “time” might stand out more? Could time just be the step where the system/universe is in the calculation?

You said, “The alternative to believing in the timeless reality of any logically possible game or species is believing in the reality of novelty. Things come into existence and facts become true all the time.” Is this analogous to adding an axiom to a math system?

With regard to this view, what are your thoughts on the following two statements?:

2^192748098245-1 is prime number.

2^192748098245-1 is not a prime number.

From your point of view, would you say one of these statements will be “discovered” to be true, but the truth of these statements did not exist before the notion of numbers, primeness, and the meaning of these symbols were “evoked”? Does “evoke” relate to something being defined or given meaning? Does this relate to how the meaning of a string of symbols created by a formal axiomatic system should be looked at as being devoid of meaning? (e.g. See Douglas Hofstadter's discussion on his p-q system)

Do you think metaphysics plays no role in science? Can we not know something about chess, haiku, or the blues even before they are invented if their rules which govern their structure/definition fall into a certain class?

Your statement that “honest wonder about our world seems a better stance than mysticism” seems to contradict your notion of “novel” events being evoked. It seems like if these things are really “novel”/random there wouldn’t be a reason that explains why they came into existence, so at that point we could stop wondering about the reason and just be mystified by their existence.

Thanks in advance for your comments on these thoughts, and please check out my Digital Physics movie essay if you get the chance. There are some questions posed at the end of the essay that may interest you. (e.g. Do you think there is an analogy between the following relationships: a “class” vs. a “set” and “true” vs. “provable”? )

Thanks,

Jon

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Dear Lee,

Here my comments, questions, and suggestions about your essay.

Contents

1 A pleasant essay.

2 Platonisms, and making one's ideas clear.

3 The explanatory power of a formal system.

4 Some room for improvement.

5 A path to improvement.

6 A Question.

7 Two quotations.

1. A pleasant essay.

It is a pleasure...

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Dear Lee,

Here my comments, questions, and suggestions about your essay.

Contents

1 A pleasant essay.

2 Platonisms, and making one's ideas clear.

3 The explanatory power of a formal system.

4 Some room for improvement.

5 A path to improvement.

6 A Question.

7 Two quotations.

1. A pleasant essay.

It is a pleasure and even a relief to find a contribution by an accomplished physicist that integrates time as something substantial.

It pleases me of course because it is closer to my views than many others. I even have the feeling that it is congruent, it combines well with what I have tried to express (in particular, a central rôle of time, as we experiment it, `irreversible').

The essay is well written, it is easy for the reader to follow the author, and... it answers the question, which is worth mentioning since not all essays do.

Most of the statements touch on things that I feel right and I am sympathetic to. All the pieces fit well overall to form a pleasant discourse. The result is then that we ask more from it, we want to put that framework to the test, we want to try using it.

2. Platonisms, and making one's ideas clear.

The form of Platonism that you attack —aptly I believe— is quite extreme.

Once I witnessed on one occasion Jean-Pierre Changeux trying to take the upper hand against Alain Connes in a conversation, by treating him of Platonist, for the mere reason that he had said that the solution to a mathematical problem is fixed, you can do whatever you want, it won't change, and that's a characteristic of mathematical objects. What Alain Connes was saying is just what everybody has to agree about, as you write: ``if any person can demonstrate it, any one can'', these are ``properties which can be discovered or proved, about which there is no choice''. Mathematical objects show like inescapable invariants.

In this situation, you would have been termed a Platonist. As usual, not much interesting can be said unless we define precisely what we mean by each term we use, and that implies getting closer to a formal system, and giving pragmatic criterions to define the key concepts, so that someone else can virtually reproduce, at least mentally, each experiment and ascertain semantic correspondence with what we signify.

3. The explanatory power of a formal system.

About formal systems, everyone is free to decide what rules he wants. Only, some decisions are really unfruitful.

One way of being unfruitful for a formal system is the inability to explain some classes of facts, by its inherent structure. In the present case, of course, if you make `mathematics' and `the existing universe' two completely separate domains, by construction, you have difficulties articulating them: there is by construction no natural connection between them. That's in summary what happens to Wigner. It is merely a consequence of the axioms.

Only should one be conscious that it is useless asking unanswerable questions, in a given system. So, more specifically, some decisions about a formal system are unfruitful in that they prohibit specific explanatory schemes.

Of course, even while a Platonist states the axiom of complete separation between `mathematics' and`the existing universe', he does enunciate the existence of both, and hence their connection, if only through himself because he names them, he has ways of connecting them, of interacting with each one, so he does recognise they both belong to a larger world. Most of the ensuing confusion stems only from occasional shifts to the general discourse in which you nested your formal system, when you should only be talking from within the formal system itself. If you stick to our axioms, you cannot ask about the effectiveness of mathematics in representing the world. If you want to explain the effectiveness of mathematics, you need a general, abstract domain in which objects that you observe in the world and objects that you meet in mathematics are both produced from a common root, and hence display natural symmetries.

Incidentally, the extreme Platonism you oppose to would fail to pass the test of defining pragmatically the terms it uses. That's another failure.

4. Some room for improvement.

First, you include causality as a constituent part of your principles. Causality is a human concept, in the best case, a theory. To me your sentence would sound better to me ``All that exist is part of a single, connected universe''. Or Simply ``the universe is everything''.

It is worth avoiding causality at this stage, because it is indeed absent of most of (the formal part of) physics. Let us take an example as simple as possible, to avoid being distracted by technicalities: Newton's law F₁₂ = -F₂₁ is completely devoid of causality. It says that the forces between two objects are permanently —and sort of magically, almost fortuitously— equal in modulus and opposed. According to the equation, things, if they happen to change, change simultaneously; therefore, not causally. Writing an equation means suppressing any idea of causality. In spite of that, most explanations accompanying this and other equations do speak in term of causes, included in physics textbooks. You then have a complete strangeness between the actual theory and the discourse seemingly explaining it. See, e.g. John Clement. Student's preconceptions in introductory mechanics. American Journal of Physics, 56:1 (January), pp. 66-71, 1982. Or, even better (but in French) Laurence Viennot, Raisonner en physique : la part du sens commun. De Boeck Université, 1996.

You may like the following quote, which I I understand well matches you notion of being evoked: ``To say that truth is not out there is simply to say that where there are no sentences there is no truth, that sentences are elements of human languages, and that human languages are human creations.'' (Richard Rorty Contingency, irony and solidarity, 1989.)

Of course, a fastidious reader would require you give a pragmatic definition for `exist'. Mathematical objects, or properties, exist once their question is `evoked', but then they appear as completely invariant. The pattern is: we produce a change, and then we see that invariant phenomena appear, any one at any time would witness it. The pattern is the same when I bump into a stone: I produce a change (a step), and my toes find an invariant, that I call a stone. Any one at any time would find the same. Hence in some respect, the situation is the same, but I don't think we would say that the stone did not exist until it was `evoked' by bumping into it. However, we can certainly say something like that we were unaware of it.

There are similar small difficulties (I don't want to go into those set-theoretical-like paradoxes, whereby I would talk about Borges's Library of Babel which contains all the possible mathematical books, and pretend I evoked all the possible mathematics —that is not correct, since the exact invariants do not show yet): for instance, Ramanujam is famous for having `re-evoked' a lot of mathematics that others knew of already: obviously evocation does not `work' forever. It seems that we must make explicit the relativity of any mathematical object to those who know about it, and maintain it.

5. A path to improvement.

I think there is a way out of this difficulty. It requires, as is suggested by the above parallel, that we include explicitly in our axiomatic framework the processes of perception by which both stones and mathematics can be said to exist: They all appear as a sort of invariant, under particular conditions. This way of making explicit what it means to be `evoked' for mathematical objects is what I have attempted in my essay.

6. A Question.

You take some length to discuss, on one hand, games (typically board games like chess), and on the other hand, formal axiomatic systems.

For me, the two statements ``there are an infinite number of games we might invent'' and ``there is a potential infinity of FAS's (formal axiomatic systems)'' are simply equivalent. When I want to explain to someone not acquainted what a formal system is, I equate it to a board game like chess or go, and I deem it perfectly exact. (There is a sheet of paper in the Turing archive, where he has written down the rules of go strikingly in a formal system, axiomatic manner.)

Do you make any difference? Was that just rhetoric redundancy?

7. Two quotations.

That I feel fit particularly well here.

``And, moreover, we have found that where science has progressed the farthest, the mind has but regained from nature that which the mind has put into nature.

We have found a strange foot-print on the shores of the unknown. We have devised profound theories, one after another, to account for its origin. At last, we have succeeded in reconstructing the creature that made the foot-print. And Lo! it is our own.''

—Sir Arthur Stanley Eddington. Space, Time and Gravitation: An Outline of the General Relativity Theory. Cambridge University Press, 1920.

``A man sets out to draw the world. As the years go by, he peoples a space with images of provinces, kingdoms, mountains, bays, ships, islands, fishes, rooms, instruments, stars, horses, and individuals. A short time before he dies, he discovers that the patient labyrinth of lines traces the lineaments of his own face.''

―Jorge Luis Borges, The Aleph and other stories

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Dear Lee,

First of all, it is great to see essays from noted physicists in this contest. It's an honor to be participating among them. Although I don't agree with your thesis in many ways, you make cogent critiques of a lot of fashionable notions. Outstanding among them is of course "the multiverse" - for which we don't have any genuine evidence. (I guess if that "bruise" in the CMB holds...

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Dear Lee,

First of all, it is great to see essays from noted physicists in this contest. It's an honor to be participating among them. Although I don't agree with your thesis in many ways, you make cogent critiques of a lot of fashionable notions. Outstanding among them is of course "the multiverse" - for which we don't have any genuine evidence. (I guess if that "bruise" in the CMB holds up we could have a clue that we bonked into another universe, but really - how can we be sure?) Your defense of traditional, flowing time really appeals to me. I have long thought that making a "block" out of space-time is just a representational indulgence with no deep ontological significance. (And what alternative predictions would be made, or is that just an interpretation?) I agree that time is active in some sense, and that the physical distinction with space dimensionality is profound.

I do not agree about mathematical Platonism. It is hard for me to imagine that we are not discovering truths about Platonic solids and in various dimensions, including more than our physical space has. It is "true" that no fraction squared can equal 2, and so on. Even if you don't like furniture-like scenarios, the logical structure about math is that of discoverable truths about something that we only get rolling. We can't invent it to be what we want. Start walking, it leads where it must go ...

However, it looks like you are aiming for a contextual view of the world itself, which I consider a good thing. I think such a picture is the only way to get a handle on quantum weirdness. No-collapse theories simply cannot fairly derive the Born probabilities. Consider: structurally identical scenarios (with the same counts of contents) but with different relative amplitudes, can't be fairly tricked up to show the correct ratios of event frequencies. Pretended solutions like measure weights (stumbling around since Everett), are like coloring the sides of coins to have more heads in the same pattern of falls.

I consider the following point of yours most relevant to working physics:

In this context we use the simplest equation that expresses a law, not because we believe nature is simple but because it is a convenience for us-it makes a better tool, much as a hammer with a handle moulded to the hand is a better tool, Moreover in this context every theory is an effective theory which means that the limitations on the domain of applicability are always explicit and the correction terms are always there and ready to be exploited when a boundary of the domain of applicability is approached.

It underlies my argument that uses consistency relations in electromagnetism, to show why space has three dimensions. This requires taking a look at the nuts and bolts of the stress-correction to momentum instead of just taking "it works as a correction" for granted. We look at how that would play out in spaces of various dimensions, and it only gives consistent results for electromagnetic inertia in a space with three large dimensions. I think this effort of mine is the best contribution I offer, altho I appreciate the many commenters who like my overall perspective. I hope you and others will take a look at it. I also highly recommend the essays by the Burovs and George Gantz. Thanks.



Regards.

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To complete my criticism, in reply to the last 2 pages of the essay, while I replied to the previous pages earlier (see my previous replies above): why I see this essay a rather laughable illusion of argument for naturalism, not worth being taken seriously by any scientifically educated person, at the antipodes of the above expressed beliefs by some who lazily enjoy the claim that arguments for...

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To complete my criticism, in reply to the last 2 pages of the essay, while I replied to the previous pages earlier (see my previous replies above): why I see this essay a rather laughable illusion of argument for naturalism, not worth being taken seriously by any scientifically educated person, at the antipodes of the above expressed beliefs by some who lazily enjoy the claim that arguments for naturalism are given, as, just like in religious apologetics, they love to dream in the existence of arguments to validate their belief, but are too lazy or incompetent to think logically about which argument can be actually valid. They dream it would be able to convince some platonists ? Of course it cannot. It can only convince those who are already convinced.

"There are four of these core concepts: number, geometry, algebra and logic."

This description looks as if there was nothing more interesting in the maths of theoretical physics, than school-level mathematics. As if the school-level concepts already gave the essence of all the main mathematical ideas needed in physics. They don't. Very far from it. Just the fact that some of the high-level maths used in theoretical physics (tensors, spinors) can be called "algebra", and that gauge theories can be called "geometry", does not mean that they are as boring as school math. And Fourier transforms, which are essential to quantum physics, clearly do not enter these school-level categories.

Finally, this "argument" is here to be praised and high rated by the public, for the precise reason I gave in my review of this contest: "Obscurantism = Deny the amazing efficiency of mathematics observed in physics; stay ignorant about it. Such people usually hate mathematics because they cannot understand it, so they need pseudo-arguments to feel proud of their ignorance."

This way of pretending that theoretical physics is just as boring and conceptually down-to-earth as school math, so as to make ignorant people feel proud and sufficient of the boring little school math which is all they know, can be a good way to be popular indeed. But it is just an expression of ignorance (may it be true ignorance or pretense of it, doing as if the wonderful stuff of theoretical physics was not there). To see how wrong is this view, see the section "Arguments for Mathematical Platonism" of my review, and the 4 essays I referenced there, which develop the observation of how amazing is the mathematical understanding of physics.

Now the last page : "we still have to explain why mathematics is so effective in physics. It will be sufficient to..." (just blindly pretend that there is nothing remarkable about the effectiveness of maths in physics). Well, just like so many other naturalist essays, the main idea there is to believe that the connection between maths and physics is best explained by pretending that it does not exist, i.e. that there is nothing remarkable about it, that it is nothing else than an illusory impression from what would just be the remarkable efficiency of the naturally evolved human brain to understand mathematics, together with the fact that it should be possible to mathematically analyze anything that happens because finding mathematical structures in anything is what the scientific activity is about, and the reader is not supposed to have any imagination to figure out anything else than this which the remarkable connection between maths and physics might be about. Well, if that was all what the connection between maths and physics was about, why would anyone have come to declare amazement at this connection in the first place ? It would have been simply stupid to do so.

Now the closing "examples". When it was first announced on page 1 that "There indeed may be properties enjoyed by physical reality which have no counterpart in mathematics. I will mention two below", I expected (not paying attention to the restrictive "may be") that the examples would come to make a point showing that such things actually exist, giving good reasons to see physical reality and maths as different. I expected these to be scientifically well-founded, such as reports of scientifically well-established facts. I had one particular example in mind, which I expected to be given in the list : the wave-function collapse, that is found physically real but does not admit any coherent mathematical description.

But it turns out that the given 2 examples of differences between mathematical and physical reality are very disappointing. They are not reports of any scientifically well-established facts. They are only examples of the author's fanciful assumptions introduced earlier in the essay. And not only this, but they are purely metaphysical assumptions, where by "metaphysical" I mean what logical positivism (which is the usually good scientific methodology) dismisses as senseless : it is neither logically well-structured, nor intended as a reference to any possible observational verification.

In reply to the first example "In the real universe it is always some present moment, which is one of a succession of moments. Properties off mathematical objects, once evoked, are true independent of time.": in the details of the sentence, the comparison is unfair between the "real universe" and "mathematical objects", as the difference that is presented does not come from the difference between reality and mathematics, but between a universe and an object inside it. If we reverse the correspondence, comparing between a mathematical universe and a physical object, the stated difference remains between a universe and an object, no matter which one is mathematical.

Indeed, in my study of the detailed properties of the foundations of maths, I showed that the universe of set theory is not fixed but expands in time. During this expansion, its properties never stop evolving, as established by the truth undefinability theorem.

As for "In the real universe it is always some present moment", it still begs for a specification of the mathematical shape of the present moment : in which direction does it slice space-time ? What determines the choice of this direction ? Does it span the whole universe ? I have the same "problem" with my own interpretation of quantum physics, except that I clearly admit that the real answer is in a metaphysical reality that escapes the laws of physics. And finally, as I asked earlier : how thick is the slice of the present ? do events vanish into non-existence as soon as they are past, only remaining temporarily real in the form of a destructible memory ? In my view they don't (the past reality keeps eternally existing as a past reality).

"The universe exists apart from being evoked by the human imagination, while mathematical objects do not exist before and apart from being evoked by human imagination." Did the universe exist before the Big Bang occurred ?

Now coming back to my wonder, of : why did he not give the example of the wave-function collapse as a difference between reality and mathematics ? Well, it may be because his work on the foundations of quantum physics is precisely about believing hard in the possibility, and actively searching for, a mathematical description of the wave-function collapse. Since, no matter the pretense to believe in the metaphysical or any conceptual differences between maths and physics, the fact is, in which sense can anyone conceive of a naturalistic explanation of the wave-function collapse (or generally, any naturalistic law of physics), if not in the sense that it is expressible as a deterministic law ? Which, of course... ultimately has to take the form of a mathematical equation in order for it to be a deterministic law at all (no matter his insistence, in some other articles, on the difference between linearity and non-linearity : this does not constitute any essential difference in the sense of the fundamental difference between mathematical and non-mathematical laws or realities).

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