A naturalist account of the limited, and hence reasonable, effectiveness of mathematics in physics by Lee Smolin

...cosmic mass-energy increases because of the universal gravitational acceleration are implied by the 3-d Castel transformation (tongue-in-cheek, Lee).

(gotta correct that..)

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.

"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

"...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

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

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.

What's the mechanism by which envoked things' properties are permanent?

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..

Your purpose illumines semi-quantised conceptualism which dots the big picture from reality.

Sincerely,

Miss. Sujatha Jagannathan

I quote what Basudeba repeatedly wrote:

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.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. END of my quote.

Having several remarks, I nonetheless agree on that light in empty space is background invariant.

However, shouldn't we at least avoid obvious incorrectness like "Michaelson and Morley experiments"? It was Michelson, not Michaelson, and not not Morley and hence also not M & M, who performed three belonging experiments. Already the first in Potsdam in 1871 had a null result. The third measured the Sagnac effect.

In contrast to my ally Lee Smolin, I consider the present also incorrectly listed between past and future.

Eckard

Harlan,

You quoted the sentence "Properties off mathematical objects, once evoked, are true independent of time."

Since my native language isn't English, I am not sure whether "off" should read "of". In this case I understand the properties as belonging to mathematical objects. Otherwise, I feel forced to speculate, the author might mean properties that do not belong to mathematical objects.

Perhaps, I did not yet fully grasp the conception of evoked reality because I consider already my distinction between measurable elapsed time and the abstracted from it usual event-related notion of time (cf. Fig. 1 in topic 1364) an appropriate alternative to what Lee Smolin criticizes as timeless.

I would appreciate if you or Lee Smolin himself could tell me how to understand the "off".

Regards,

Eckard

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

Dear Lee Smolin,

Your approach in this excellent paper is not, as you're undoubtedly aware, incompatible with that of Hubert Dreyfus, Evan Thompson, Alva Noë and others and which stands dubbed as Embodied Cognition. Both Logic and Mathematics are expressions or representations of life's interaction throughout maybe a billion years or longer with the physical environment of this planet. After a while, in the course of ongoing informal experiment, regularities in the surrounding world begin to be perceived. Rules are intuited and generalized and communicated and refined by new tools and discoveries. Pretty much Bottom-Up. Definitely more Aristotle than Plato.

So there's a lot that gets addressed and undoubtedly an immensely greater amount that doesn't and won't. Michael Peskin's remark that "Physics is that subset of human experience which can be reduced to coupled harmonic oscillators" comes to mind. Fortunately that's still a fair amount of stuff.

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...

-

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.

-

Smolin's illogical "there are no eternal laws" eventually negates itself. But the idea of temporal naturalism, although grossly flawed, is a clarifying 8-year brain exercise.

The fruit of my own 20 years of brain exercise also needs scrutiny. So, I challenge the FQXi minds to falsify the mathematics and logic of the genesis formula.

Here are the pertinent links regarding the genesis formula.

The Idea of Motion Transformations as the Foundation of the Laws of Nature

www.kinematicrelativity.com

A Summary of the Propositions of Kinematic Relativity

Questioning the foundations of modern physics

If the genesis formula and its implications withstand the scrutiny, then the 100 years of spacetime transformation and big bang delusion will finally be done in and we will have a better understanding regarding the nature of the existence.

Let's see what the following champions of the search for knowledge have to say:

Tegmark, Aguirre, Greene, Susskind, Randall, Carroll, Turok, Hawking, Penrose, Guth, Linde, Weinberg, Rees, Tong, Wilczek, Levin, Silverstein, Wolfram, Seager, Hooft, Vilenkin, Smolin, Ashtekar, Rovelli, Ellis, Davies, and etc from the FQXi Membership...

If FQXi is true to the foundational search of Big Answers to Big Questions, we will have answers.

Cheers!

Point taken, Eckard. Michelson.

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.

Dear Basudeba,

The Eleatic Monism was a denial of the doctrine of flux. They are not complimentary unless you submit to a dualistic account of reality. Monism tells us that physical reality cannot be explained by raising change to the status of a primitive notion. In other words, change is an epiphenomenon.

Regards.

The following links to an earlier FQXi essay I submitted:

http://fqxi.org/community/forum/topic/1273