The term "sophistication" in math/logic

1. M. Koppel, Complexity, depth, and sophistication, Complex Systems , 1(1987), 1087-1091.

2. M. Koppel, Structure, The Universal Turing Machine: A Half-Century Survey , R. Herken (Ed.), Oxford Univ. Press, 1988, pp. 435-452.

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Timothy Y. Chow wrote:

> I was wondering if FOM readers have any comment about Stephen Wolfram's

> announcement today: > http://blog.wolfram.com/2007/10/the_prize_is_won_the_simplest.html

Wolfram's Principle of Computational Equivalence (PCE) states that "when

one sees behavior that isn't obviously simple,

it'll essentially always correspond to a computation that's in a sense

maximally sophisticated".

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https://www.scottaaronson.com/blog/?p=762 (Shtetl-optimized??!!)

sophistication M Koppel: Regarding Bennett’s logical depth versus (Moshe Koppel’s original notion of) sophistication: under certain formalizations of the notions, these are actually equivalent. Of course, Koppel’s notion of sophistication looks much different than Antunes and Fortnow. It’s been a while since I’ve read the Antunes/Fortnow paper, so I forget the nuances of the connection to Koppel’s work.

In particular, studying infinite sequences instead of finite strings, one can qualitatively define some sequences as deep or sophisticated, and the rest as not. There are two ways that Bennett defined depth and two ways that Koppel defined sophistication for infinite sequences.

Sean also delivered the opening talk of the conference, during which (among other things) he asked a beautiful question: why does “complexity” or “interestingness” of physical systems seem to increase with time and then hit a maximum and decrease, in contrast to the entropy, which of course increases monotonically?

My purpose, in this post, is to sketch a possible answer to Sean’s question, drawing on concepts from Kolmogorov complexity.

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The information in an individual finite object (like a binary string) is commonly measured by its Kolmogorov complexity. One can divide that information into two parts: the information accounting for the useful regularity present in the object and the information accounting for the remaining accidental information. There can be several ways (model classes) in which the regularity is expressed. Kolmogorov has proposed the model class of finite sets, generalized later to computable probability mass functions. The resulting theory, known as Algorithmic Statistics, analyzes the algorithmic sufficient statistic when the statistic is restricted to the given model class. However, the most general way to proceed is perhaps to express the useful information as a recursive function. The resulting measure has been called the "sophistication" of the object.

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Can Neutrinos Kill Their Own Grandfathers?

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Sophistication Revisited

Kolmogorov complexity measures the amount of information in a string as the size of the shortest program that computes the string. The Kolmogorov structure function divides the smallest program producing a string in two parts: the useful information present in the string, called sophistication if based on total functions, and the remaining accidental information. We formalize a connection between sophistication (due to Koppel) and a variation of computational depth (intuitively the useful or nonrandom information in a string), prove the existence of strings with maximum sophistication and show that they are the deepest of all strings.

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https://ieeexplore.ieee.org/document/1705018?signout=success " We develop the theory of recursive functions statistic, the maximum and minimum value, the existence of absolutely nonstochastic objects (that have maximal sophistication-all the information in them is meaningful and there is no residual randomness "

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Ideas for book: Maximal sophistication of the universe; new physics discoveries, principles to use to find them; astrology & synchronicity

Below are examples of "maximal sophistication of the universe".

After reading this, see also the old email to you (Jan 2017) below.

Examples:

• A sophisticated understanding indicates that the EPR effect does not violate SR and causality, ie it can be true despite initially seeming impossible (this is 'sophistication'), and so the universe 'prefers' to include it (ie there is a principle of 'maximizing sophistication').

• And similarly: a sophisticated analysis shows that QP-indeterminacy etc can be true despite the seeming determinacy of what we generally observe (ie the macro universe), so the universe 'prefers' QP as part of its basic structure.

• Similarly for the effects of SR and GR, non-existence of 'absolute time' etc.

• A sophisticated analysis (eg Blum's book) shows that life does NOT violate entropy, so a constant increase in the complexity of the universe's structures is consistent with growth of entropy, as long as there is an energy reservoir to draw from etc, so the universe 'prefers' this.

WHen I say the universe prefers this, I don't mean it literally, anthropomophically, but rather that it is an axiom we can use in trying to discover new theories - search for the most sophisticated posiblity consistent with what we observe.

And why is the universe this way? Perhaps it has something to do with why there is somethign rather than nothing - there is a minimax principle governing emergence of a universe, only the maximamlly-sophisticated emerges.

To find new theories therefore, in some sense one needs to investigate deeply the assumptions one makes about what is and is not possible, what is and is not logically necessary inorder for the universe as we know it to function, and then after a sophisticated analysis eliminate the assumptions which have been revealed to be unnecessary.

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Additional idea for book:

Just as a logical exercise, and to indicate to people one reason why science is sceptical about these issues: I am also interested in analyzing what would need to be true in order for astrology to be valid, and in order for synchronicity to work, and maybe other such.

For example: let's say we take as true that the pattern of the lights in the sky (some are stars, some are galaxies) as seen from this particular angle (ie viewed from Earth), contains information about future events, and specifically related to date/location of birth, what would have to be the structure of the physical universe what type of mechanism would there need to be to enable this? What constraint would there have to be on our allegedly free will or the natural cause-effect of Earthly physical interactions in order for the stars to predict events correctly?

Similarly re synchronicity.

It is somewhat similar to asking what mechanism/algorithm/laws would there need to be in the universe which would guarantee that if there is time travel there would not arise paradox-inducing situations. If there was an intelligent entity supervising, this could be a mechanism, but if it was some 'natural phenomenon' what could it be? Though of course an intelligence is natural - perhaps time travel can exist only in a universe in which an intelligence emerges which can supervise and prevent potential paradoxes in this way; this itself is a type of time-loop phenomenon.

See the old email below:

---------- Forwarded message ---------

From: Avi Rabinowitz <air1@nyu.edu>

Date: Thu, Jan 5, 2017 at 11:13 AM

Subject: ideas: book: new physics discoveries, principles to use to find them, or maybe not

To: Avi I Rabinowitz <air1@nyu.edu>

Cc: Noson S. Yanofsky <noson@sci.brooklyn.cuny.edu>

Can a human mind find new theories in this way? if not, why not?

..........................................................................................................

find the hidden assumptions: parallel postulate --> curved space

placing things in the same context, space, time --> spaceitme, and thinking how to make this make a difference, eg straightness in spaceitme.

finding the underutilized principles, like the EP in newtonian gravity.

seeing the structure of tidal tensor gravitaiotnal vector accleeraiton, potential scalar and then adapting it to a diff geom context.

checking the experimental basis for major assumed aspects of a theory: that the universe's expansion is slowing (it isn't!)

finding ways to adapt more modern theories to produce the results the previous model assumed: epigenetics produces some of what otherwise was assumed to require Lamarckian theory.

This is kind of an application of something else: to really understand inertia, one needs to recapitulate the thinking of the ancients(Greek philosophers etc) on the subject, they weren't stupid, they were the einsteins of their era. same for other concepts. Figure out why the previous theory seemed so reasonable, and then you understand the new one better, and also perhaps you can think of something in the new theory which can produce something like the older model.

Allow the universe maximal sophistication, think of structures it should have which are consistent with what we see. Think of assumptions which are true for what we see but which could be violated in oters scales or realms etc without violating what we see.

Quantum physics assumes a greater sophisticaiotn of the small than classical physics does of the large, and the compatibility is exactly in the transition from small to large, in other words the classical theory of the large arises merely as a statistical averaging of ensmebles of large numbers of the small.

If the universe allows us to neglect something, or makes something not count, like Birkhoff (a spherically-symmetric mass can pulsate without producing any effect outside of it), there will be a compensating phenomenon which utilizes this in a way which makes the measure of the sophisticaiotn of the universe larger (ie overcompensating for the lost complexity due to the lack of effect),in this case it is that the universe expands, which I hold would not be defineable if not for Birkhof. If one assumed that there needs to be a compensating complexity or sophisticaiotn-raising effect, could one have somehow 'deduced' the expansion from knowing Birkhoff in Newtonian gravity?

Note: the field in a charged spherical shell is zero etc, which is Birkhof, due to the same 1/r2 law of electric theory as for gravity, but in GR it arises in a more subtle way which reduces to 1/r2 in Newtonain gravty. So: in the overall newer field theory of qed etc how does the effect arise for the interior of a charged shell? is there a compensating effect like the the universal expansion in gravity/GR?)

AR’s idea: Indistinguishability leads to possibilities of sophisticated aspects of the universe:

Birkhoff indist between oscillating and not, leads to expansion of un (which allows un to exist)

Indist of Galilean rel allows no center, no absolute space, and fff curvature, an that is bg bang which

allows un to exist.

Pauli explusion is via indist of particles, and also particle history is irrelevant, and idea of affine

connection with car returned to garage, it neverhtless fits in irrespective of where it was, what speeds,

acceleration etc, Two clocks, diff heights, come back to same height and their rate is the same.

minimal coupling in email

https://chq.io/g/jy7dcmhoe6xdydjpnwcdq3ubypvscw8

https://chq.io/g/tabphnke6ksojoelsttfwgked27tail

Mentions baez, re minimal coupling, gives example: https://arxiv.org/pdf/1902.07287.pdf

Simplicity

Simplicity and beauty are important to physicists, but they are subjective, culture-influenced of course, etc.

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Physicists agree that general relativity is much simpler than newtonian physics. because we now know that newtonian is not really consistent and one needs all kinds of patches to get it to make sense, and the result is ok but much less beautiful than GR, and takes a lot more math, and it is ugly. But it is simpler because it doesnt involve paradigm change. And GR needs tensors etc.

Only after learning all the math and defining everything carefully, the physics of GR is very simple and beautiful. So is it simple or not?

But the bottom line is experiment, verification of predictions, new phenomena, and that conclusively chose GR over Newtonian.

If there is no experimental difference between two very different theories, then one ought to try to find out why, it will give something interesting.

See re Eddington: so what is the information content of an equation? And what is the information supplied by the mind reading and 'understanding' the equaiton? As before, where I mentioned simplicity, need to factor in the sophisticaiton of the mind seeing the equaiotn; some of that is due to the sophisticaiton of the brain, which is due to the sophisticaiotn of the universe, and therefore of 'the laws of nature'. So the sophisticaiton of the underlying patterns creates the sophistication of a brain capable of representing it mathematically.

The model of the sun-Earth system is simplest with sun at center, and the euqations/calculations therefore are very simple, but it is no more 'valid' than taking any other frame, most of which are horribly hopelessly complicated, and which would obscure what is happening to human eyes. For exmaple, looking from Earth at the planetary system, there are many strange motions (retrogade etc) of the planets, took thousands of years of observations to deduce that these are actually several bodies orbiting the sun. Ptolmey Earth-based equaitons which describe the motion from the Earth-based perspective can predict everything, but it would not occur to anyone seeing those equaiotns that it is bodies orbiting the sun. So I think 'simplicity' is more than just a 'subjective' easure, there has to be something more to special frames than is accorded by GR. And there are examples in GR, where the expression is particularly simple, and that is when one utilizes all the symmetries, but of course one must first discover/recognize the symmetries.

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Simplicity is very deep (complex?), and objectivity is subjective (not every mind agrees on what is objective).

Chapter title: "The complexity of the truly simple, and the subjectivity of the objective".

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It is important to stress the difference between a mind state, of being certain about something, even being convinced that it is objectively true, and the 'actual objective' truth. But how distinguish them? All such will also be subjective. Even all physicists agreeing about something scientific, is a sociological (or anthropological) statement about psychology, the states of mind of a group of people.(usually white European males :) )

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three complex aspects of 'simple'

i) simple means that even if there is more information to give, it is general info, and the amount of info needed for any given specific case might be less: eg tensors is useful for many things not only GR, and once one has that and differential geometry and SR, it is a short simple step to GR.

ii) simple means "after thinking deeply and when not allowing fuzziness to creep in", ie Newtonian fudges so much when one thinks about it deeply, so its alleged simplicity is an illusion - who needs a 'simple' theory that ignores the depth and breadth of the situatiom and does not encompass all the phenomena.

iii) Simple means compared to any other theories which are sufficient to describe what is, at all levels

'simplicity' ties to intuition and therefore to human judgement, and therefore like Godel completeness etc

the Copernican model being simpler, despite the 'equal validity' of any reference frame (which in GR is a 'coordinate system' since we use spacetime, so velocity and accleraiton are results of transformations of the 4-d coordinate system)

Simplicity is not enshrined as a physcal principle officially, but it really is, informally, and see Einstein

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Symmetry considerations: also based on "intuition": the remarkable parallel between Einstein’s addition of this term and Maxwell’s addition of the “displacement current” to Ampere’s law.

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Special coordinate systems, minimal coupling, intuition, what's 'real'

I think that there is more significance to special coordinate choices than is usually granted in GR.

The core of the measurement problem is that we can only know of things as they are in a particular state, whereas theory tells only of processes in the abstract. And both are necessary. The problem is the transition form the regime of 'theoretical', ie unobserved, to that of known.

I think it is similar to the idea in GR that all coordinate choices are equivalent, but of course any knowledge of a system is in the end obtained via a particular coordinate choice.

Also, the heliocentric coordinate choice is obviously the 'correct' one rather than the geocentric, yetGR says there isnt any such correct one - I think the simplicity points to 'correctness'. Not that GR is wrong, but rather there is something additional.

There is also a articular coordinate choice of 4-d spacetime metric which makes things incredibly simple, makes it almost newtonian formulae, and it is the same type of coordinates as in Special Relativity. I am pretty sure there is a pointer here to something fundamental,

And it all in the end comes down to us and how we know things etc, and simplicity, all subjective [and mental-realm-related.The fact thatthought arises in the most complex arena in the universe, the neural interconnections of our brains, is significant.]

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An interesting article: http://www.mathpages.com/home/kmath588/kmath588.htm

There are several references to issues I discuss here:

the Copernican model is simpler, despite the 'equal validity' of any reference frame (which in GR is a 'coordinate system' since we use spacetime, so velocity and accleraiton are results of transformations of the 4-d coordinate system)

Simplicity is not enshrined as a physcal principle officially, but it really is, informally, and see Einstein quote below (in the article)

Excerpts from the article, and how the tie in to the topic I am interested in:

Role of "intuition": We must simply rely on an intuitively plausible choice,

"Simplicity" (AR: which is also a judgement based on 'intuition'): "distinguished by the fact that the laws of physics can be expressed in particularly simple form in terms of such coordinates. " And later "coordinate systems based on geodesics are “distinguished” in the sense that the laws take a particularly simple form when expressed in terms of such (local) inertially “free-falling” coordinate systems" and "a very elaborate formula, hardly recognizable" "There is a huge difference in complexity (and intelligibility) between" "Although it is true that one can put every empirical law in a generally covariant form, yet the principle [of general covariance] possesses great heuristic power… Of two theoretical systems, both of which are in agreement with experience, that one is to be preferred which, from the point of view of the absolute differential calculus is the simpler and more transparent."

Complexity: "we could devise many different generally covariant formalisms, of which the tensor formalism is only one, and each of these would have its own set of “simply expressible” laws. (Compare this with the impossibility of proving the absolute complexity of a string of binary digits.) "

Symmetry considerations: also based on "intuition": the remarkable parallel between Einstein’s addition of this term and Maxwell’s addition of the “displacement current” to Ampere’s law.

The nature of time, or our definition of it: "This is ultimately because the fundamental notions of spatial distance and temporal duration underlying those physical laws are essentially defined in terms of inertial coordinate systems.

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not the same as the measurement issue of qp, but reminiscent in some sense: "We never observe abstract tensors; we observe the individual components of tensors with respect to some explicit basis."

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"Simplicity" (AR: which is also a judgement based on 'intuition'): "distinguished by the fact that the laws of physics can be expressed in particularly simple form in terms of such coordinates. " And later "coordinate systems based on geodesics are “distinguished” in the sense that the laws take a particularly simple form when expressed in terms of such (local) inertially “free-falling” coordinate systems" and "a very elaborate formula, hardly recognizable" "There is a huge difference in complexity (and intelligibility) between" "Although it is true that one can put every empirical law in a generally covariant form, yet the principle [of general covariance] possesses great heuristic power… Of two theoretical systems, both of which are in agreement with experience, that one is to be preferred which, from the point of view of the absolute differential calculus is the simpler and more transparent."

Complexity: "we could devise many different generally covariant formalisms, of which the tensor formalism is only one, and each of these would have its own set of “simply expressible” laws. (Compare this with the impossibility of proving the absolute complexity of a string of binary digits.) "

A bad answer is NOT better than NO answer

I always make the following point: it is important that science - as opposed to religion or new age etc - is self-limiting, it deals with verifiable statements; and also, it doesn;t have opinions about the other types of statements (so while it is not religious, is is also not atheist; it is not spiritual, but it is also not materialisitc). The fact that other systems can talk about these other things doesnt make them less limited, or of greater applicability, or make them more reliable sources of information or insight into those phenomena. From the scientific perspective, making potentially false statements, or ones that are unverifiable in the scientific sense, is not impressive - from within its perspective science is not 'limited' in its realm of validity compared to religion: religion allows for statements than cannot be verified in the scientific sense, but form the scientific perspective religion is not thereby more highly qualified to make these statements.

"Physics A Priori":

Derivation of Basic Physical Theories from Paradoxes of Natural Philosophy

Introduction

Over the centuries natural philosophy has often arrived at a paradox in its conception of nature. With hindsight one can see that these paradoxes were actually due to a major misconception about very fundamental aspects of nature. Resolving the paradox usually ushered in a major advance in scientific knowledge.

We would like to point out various paradoxes and difficult points which plagued physics over the years and which could perhaps have led to immediate advances which in actual fact took many years.

Non-Euclidean Space and General Relativity

It was clear to all that space could not be finite [Leibnitz], for then it would be bounded, and that it also could not be infinite [Newton], since infinitude is not a property of physical entities.

Had the solution to this dilemma been the supposition that space was finite but unbounded, a great advance towards the theory of general relativity might have been made.

In a gravitational field, all bodies fall with the samecceleration, regardless of their mass. That is, inertial mass equals gravitational mass. It might have been concluded as a result that a geometric property of space was involved, and this would have been a pointer in the direction of general relativity.

It might also have been realized that forces of inertia and of gravitation are interchangeable, and that therefore gravitational fields could be transformed away in differing frames of reference. This would also have been a pointer in the direction of general relativity.

Special Ralativity

If infinitude is not a property of physical entities, and if the universe is not infinite, then nothing can move with infinite speed. Since in theory an entity can accelerate continuously without limit [unless it uses up the universe as fuel], but it must always have a finite speed, this means that either time is finite or that there is a maximum speed.

If there is a maximum speed however, an entity moving at close to this maximum sent from a moving frame which is itself moving close to the maximum, would move faster than the maximum - therefore there must be some reason that velocities do not add in the Galilean manner. From this one could derive the Lorenz transrormations, which would be a clear clue to special relativity.

The earth spins very quickly, and moves quickly around the sun. At times twelve hours apart, the speeds add and subtract - so that the difference in tangential speed is great. Nevertheless physics experiments do not indicate any difference, and therefore one can conclude that all equations of physics must transfornm invariantly between frames moving with relative velocity between them.

The Maxwell equations indeed transformed invariantly under the Lorenz transformation. However this was taken as an indication of a property of the non-existent ether rather than as a property of space-time.

Quantum Physics

Newton claimed that light is particulate, Huygens claimed it was wave-like. It might have been realized that it was both - and that therefore since being wave-like and being particle-like can be two aspects of one entity - and that this is indeed the case for light - that perhaps all matter is also wave-like. This would have led to the development of quantum physics.

That matter is divisible seems obvious, yet if the division process could be continued indefinitely, this would imply that all matter is infinite. It might then have been realized that matter must be indivisible at its most fundamental level. However there can be no reason that a basic piece of matter is indivisible unless it is infinitely hard - which is impossible since physical entities cannot have any infinite properties. It therefore must be that its most basic level, matter cannot be thought of as a localizeable entity. This could have led to the direction of quantum physics.

Free will exists, yet physics is deterministic. Therefore, one could have supposed that nature would, at its most fundamental level, be non-deterministic.

Miscellaneous Theories

Physical experiments give identical results irrespective of the time and place. Invariance under space-time translations imply conservation of matter-energy.

Particles are identical and indistinguishable - therefore there is an exchange force [see Jammer "Concep. ..Q.M." p338-345 [I have copy]

Spin. Have to rotate by 720 degrees to get back to start.

Zeno's paradox could have been developed to show that ....

Free will, therfore Godel, Church, Chaitin etc.

[Some intuitive feelings are true but unprovable ---- Godel.]

Olber's paradox showed that the universe must be expanding.

Second law of thermodynamics is implied by ???

Entropy, perpetual motion,

What of a single particle stationary in space = [same thing as] moving with uniform speed . How does its entropy increase? It must decay radioactively. And then? It decays further and further, and then disappears. Vacuum energy ??

Orbiting objects in space - no friction etc. Where is the increase in entropy. There must be tidal forces, or radiation because it is accelerating. Or the elementary particles are radioactive, or it loses vibrational energy - and then after all the energy is gone ??

The existence of a horizon which constantly recedes - especially noticeable at sea - is clear evidence that the world is round.

Indeed it had been known even in antiquity that the world is round. Had it been realized that people on opposite sides would fall of unless held by some attractive force, the idea of gravitation could have been discovered thousands of years before it was.

See Whitehead."Science and the Modern World" p.180-190

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Bohm Ahraonov; Minimal Coupling etc

What is ''real' ? As in Bohm Ahraonov. Also: Einstein consuidering the 'conneciton' as real, not just the riemann tensor; and what surprisingly does not 'couple' eg in GR re the EP/minimal coupling (see below); and which theories can be arrived at via manipulations of other theories, eg obtaining curved spacetime equaitons form the fat ones via the EP/minimal coupling; also the relaiton to of duality; and dulaity, category theory, EP/minimal coupling.

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Minimal coupling (MC): like Weyl gauge invariance

An equation can be much more powerful than originally intended: (see Feynmen quote re this).

Once one realizes that one can consistently define curved spaces, and then realizes that flat space is simply curved space with curvature zero, then it becomes clear that equation derived for flat space may also be valid for curved space.

If the equaiton is decoupled from the curvature (it is minimally coupled), ie has no terms dependent on the curvature (which one might not know from the flat space form since they would be zero?) then the equations should be valid for any curvature.

Geodsic equaiotn is minimally coupled: Of course Cartesian coordinates or any other choice in flat space is a specific coordinate choice and so the equation which will be valid needs to be coordinate-choice independent, so one needs to find for example the equation of a straight line not just in cartesian or polar coordinates but a general formula for any coordinates, which is the geodeisc quation in flat space for curvilinear coordinates (where cartesian coordinates have curvilinearity zero).

So it turns out that this flat-space curvlinear coordinate geodesic equation is then valid for curved space with any coordinate choice.

What hints of higher-level theories exist in the lower-level limits of those theories?

How expected are the similarities of the equations for the different levels? (eg newtonian gravity and GR)

Or for completely different phenomena? (e electric fields and gravitaitonal fields in Newtonian theory) [this is somewhat similar to the quesiton of why the golden ratio emerges ubiquitously, or fractals ; chaos theory and strang attractors; etc)

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Prosaic reasons for a Minimal Coupling:Newtonian + SR --> GR mapping to work

The mysterious parallelism comes out in a particular coordinate system rather than being an invariant property and so it may all be coincidence or manifestations of constraints : eg:

· There are limits to the amount of ‘simplest’ linear differential equations which can be produced to describe natural phenomena via a field theory and so if ‘nature loves simplicity’ unrelated mechanisms may be described by the same field equation.

· Any effect which decreases with distance, if conservation laws apply, will in a 3-d (spatial) universe, for cases of spherical symmetry, constrain the possible field equations, resulting in equations for unrelated phenomena which have to depend on r in a somewhat similar manner.

· the dimensionality of our 3-space;

· One can see also from a certain element of dimensional analysis etc, whatever the theory one uses, the solution has to be dependent on r, and diminish with r; the question is what would one expect, ie what has to be the case, and how different is the Newtonian result from what it anyways has to be even in GR.

The prediction of the big bang emerges from Einstein's theory applied to a universe in which everything is neglected

A cosmological theory can treat the universe as a whole as a cloud of non-interacting particles- termed 'dust' - neglecting specific smaller-structure like galaxies and planets and people, emptions, justice, compassion, morality etc.

A cosmological theory then investigates what happens to this cloud of dust over time, makes predictions, and they are verified.

It was certainly not obvious to geniuses of the past that one could understand large-scale aspects of the physical universe despite ignoring everything that is important. (Nowaday one would say not "despite" but "only by"). One would not even have imagnied that one could understand the motions of the lights in the night sky (moon, planets, stars) without taking into effect human moral behavior etc. But all that turns out to be completely irrelevant.

This division between the idea-level of morality and compassion etc and the physical level is incredible, but taken for granted today.

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When the validity of a lower level theory is established by its higher-level version

A homogenous isotropic dust-cloud is so highly-symmetric, that the model and the mathematics required for it is very simple. Using Newtonian theory one can create a Newtonian cosmology, specifically a field equation governing the expansion or collapse of a cloud of dust (the universe), and it turns out to be quite simple. Even in GR, the Einstein field equaiotns for this case reduce to very simple field equaiotns. Indeed, the situation is even simpler than that, as explained below:

As we mentioned, using Newtonian theory one can create a Newtonian cosmology, specifically a field equation governing the expansion or collapse of a cloud of dust (the universe), and of course there is no theoretical justification a priori for assuming this has any validity within the context of a non-trivial-metric-based spacetime theory. However as it turns out , using general arguments in GR (Birkhoff's theorem and aspects of the EP) one arrive as at the conclusion that this aspect of Newtonian theory can indeed be legitimately utilized, after of course re-interpreting appropriately the dynamics as spatial expansion (rather than collapse/explosion), and suitably reinterpreting the coordinates and constants in the equation.

However one does not need the entire apparatus of GR in order to arrive at this justificaiotn for the use of Newtonian gravity in this way. The metric-based spacetime theory we mentioned above is adequate, and so one can use a more generic or simplified theorem than Birkhoff's to make the justificaiotn. And once we do, we find that the Newotnian equivalent is valid, and so we use that. And we find that the Newtonian equaivalent of our field equaiotn is valid, and so we use that. Thus the result is that we have a field equaiotn which is derived using Newtonian gravity theory, but which is justified by our metric-based spacetime theory, and without requiring recourse to the Einstein field equaiotns. Note carefully that the field equaiotn describes the dynamics of the field-quantity of the metric-based spacetime theory, namely the metric components [in the case we treat, the dynamic quantity will be written as R(t)] not the field quantity of the Newtonian gravity theory utilized to derive it (using the EP, the field equation for Newtonian gravity for exterior vacuum can be written for example as Div a(r) = 0, so a(r) is the field quantity).

So in the rest of the paper wherever we talk about using Newtonian results, it is only because we know from the non-trivial-metric-based spacetime theory that these results are valid, and we need to see the variables in their more sophisticated guise as field quantities of the metric-based spacetime theory, ie as metric components.

Entire content sof file "Nature Maximizes Phenomena, Minimalism, Nn"

“Geometric Structure”: Does Nature Maximize Phenomena?

We cannot assume that nature is boring: maybe if we rotate a ruler it will change overall length, and perhaps even the scale (!), and/or twist as it turns around, and maybe it will even maintain some difference after we bring it back to its original position (and location) so that it is of different length and so on compared to a ruler which was not rotated; if we move a clock around a closed path perhaps it will show a different time when it returns than a watch left stationary. Perhaps it will even work at a different rate.

Maybe even without moving the mutual separations of objects can change, and change in different ways

Which possibilities does the universe realize (does it maximize possibilities)? Eg:

• Charge of the electron: is it a function of time? Fine structure constant change with time?

• Universe emerges into existence by itself? Continuous creation?

• Rotate something 360 degrees, will it return to original state? 720 degrees!?

• Gauge field.

• The value of pi: function of position, of time.

We know that when a car returns from a drive it fits in the garage it left behind; one can rotate a 2-d plane hand and thumb to reverse the handedness, but not a 3-d hand: all this tell us something about the ‘structure’ of the space we live in. The greater our sophistication the more we realize the possibilities, and when we see how many are NOT exploited we can see how much structure there is to the geometry of our space, and we can speculate as to the possibility that under certain conditions these CAN be exploited.

Space time has a structure: it is 3+1-d, it is ‘Euclidean’ etc. We shouldn’t take any of this for granted.

One can simultaneously measure both location and momentum for large objects, however quantum physics shows that one cannot assume that this is so for objects smaller than a certain size. Prior to quantum physics no one assumed that the size of the measured item was relevant in this way, and that such an obvious-seeming fundamental truth as the simultaneous existence of a unique position and velocity was really only an approximation valid for macroscopic entities.

It was assumed that microscopic entities operate under the same rules as do the macroscopic ones with which we are all familiar – especially as they are the components of the familiar objects, however it is possible for this not to be the case since measurements are performed only on macroscopic entities.

The same is true for the probabilistic determinism of quantum theory: at the microscopic level events can unfold in a random manner as long as the overall statistics follow the patterns familiar in the macroscopic world; nature takes advantage of the averaging which occurs in the transition from microscopic to macroscopic. [indeed nature takes advantage of this possibility and in constructing macroscopic values the properties of the microscopic constituents are averaged out].

Nothing travels faster than light: but we believe this not simply because it is part of the theory of SR but because (within the theory of SR) it leads to paradoxes. However one cannot simply assume there is no “no action at a distance”: some type of action at a distance is logically possible and therefore cannot be ruled out.

Nature maximizes phenomena, but doesn’t exploit all possibilities

One of the most astonishing results of electric theory is that there is no electric field within a charged conducting sphere, and a very powerful demonstration of this fact is given in science museums ……

Watching someone sit in a Faraday cage bombarded with lightning is a hair-raising experience – but the person inside the cage will not have the same bad hair day …. not even static electricity.

There is no discernable distinction electrically between the interior of the “cage” and a place far from any electric source. In some sense the two regions are ‘disconnected’ from each other in terms of their electrical properties. (This is a type of topological effect.)

On the one hand it seems surprising that Nature does not utilize the possibility of making a distinction between these two very different situations; on the other hand the laws of nature thus make possible this very interesting phenomenon of a Faraday cage.

If the sun were to begin pulsating (while maintaining spherical symmetry), how would the orbit of the Earth be gravitationally affected? The answer is that it would not be gravitationally affected! Similarly, if the Earth began pulsating the moon would not be gravitationally affected. It is a simple matter to show (see Appendix) that in Newtonian gravity theory the gravitational field outside of an extended spherical mass is the same as it would be if the entire mass were concentrated at its central point, or even if it is pulsating. (We will refer to this principle as “Birkhoff”. Again, this is a type of topological effect.)

On the one hand this is a very beautiful result, but on the other hand it seems surprising that the laws of nature do not allow for pulsations of a gravitational source to have a gravitational effect. The universe is not maximizing the potential for diversity - one might have imagined that Nature would take advantage of all types of differing conditions and have these give rise to differing results.

[In a different sense, Nature does seem to take advantage of possibilities: if pulsation is physically possible without violating the laws of nature, it will likely occur somewhere.]

On the other hand this is a type of maximization as well, a loophole allowing unexpected phenomena: one cannot assume that the gravitational field is different outside a pulsating spherical mass than it is outside a static mass just because inside the pulsating mass it is very different than inside the static mass. (this is something we will see a lot in topology…) Although it seems as though Nature is wasting possibilities we’ll see the great ramifications of this – it allows for even greater maximization of startling possibilities.

[1]

The EP

From Nn gravity we know that all particles fall at the same acceleration in a gravitational field, irrespective of their mass, and so the possibility of distinguishing different cases is lost.

However, again, although the possible distinctions are seemingly wasted ie nature doesn’t maximize the possibilities, later we’ll see great ramifications of this: the loss is offset by a greater gain, the enabling of a very beautiful principle of Nature (the ‘equivalence principle’ which underlies the connection of gravity and the nature of spacetime)..

Principles

Perhaps the universe utilizes any loophole which is not logically contradictory, and which does not contradict fundamental principles of physics, as long as this loophole can give rise to phenomena with measurable consequences.

Given some mathematical law of nature, “any increase in generality which can be brought about by the removal of previous restrictions will be of advantage in increasing the range of possible applicability”. The resulting models may be “mathematically more complicated” but “the history of human endeavors to understand the universe would certainly indicate no a priori right to demand mathematical simplicity of nature” if this simplicity means less complexity of phenomenon. [2]

So it is not true that the laws of nature take the simplest possible form; instead they take the simplest forms which allow complex phenomena to exist.

Like the Sherlock Holmes story where the famous detective inferred the crucial clue from what did NOT occur, namely that the dog didn’t bark, so too in Nature: what is NOT is also an important clue. eg no flood of cosmic light à the universe does not contain a static array of an infinite amount of eternal stars spread out with in a finite density (Olber). etc.

We can propose principles of versatility and minimalism:

• Anything is possible as long as it does not lead to paradoxical measurements in the lab.

• Some causes will not lead to all its possible effects

• Assumptions that are unnecessary, unmeasurable (insert re solipsism etc) lead to paradoxes, inconsistencies or incorrect statements.

• The laws of nature take the simplest possible form which allow complex phenomena to exist;

• Since Nature tends to exploit possibilities one can infer properties of the nature and laws of nature when one realizes the existence of possibilities which are NOT exploited.

We can’t know a priori whether or not a phenomenon exists, it is a matter of measurement.

One’s intuition alone is not sufficient to determine whether or not some situation will be realized, and whether or not it will have this or that effect.

From file: “Models”

Model Building: We Can’t Trust Intuition which is based on specific circumstances, Nature Maximizes Possibilities: Force Model vs Spacetime Curvature Model

At one point in the development of science it was believed that there was some medium, called “the ether”, which pervaded all space and was the medium through which light traveled as a wave. But it was later realized that there was no need to assume the existence of such a substance: one simply had to accept that a wave could travel through empty space without a medium to transmit it.

One attempts in physics to minimize the use of constructs – if an entity is not indispensable we jettison it. This is a very important principle.

For example: the concept of a gravitational force field: we see a mass responding to gravity caused by another mass, and since they are not touching, but rather are separated by empty space, we assume that there must be a force field of gravity in the empty space between the masses intermediating between them. We do not see the force field, but we feel something and then invent ‘a force field’ as a sort of explanation. But Instead let us proceed as follows: the two masses definitely exist, and the space in between them exists, so let us attribute the effect we call ‘gravity’ to the space itself, and in this way dispose of an unneeded concept/entity “the gravitational field”.

But how can it be that space does the job? One place in empty space is like any other, especially if there is no such thing as a gravitational field! How would the space near the sun know how to get Eath to move around the sun if the space near the sun is he same emptiness as the space far from the sun, in itergallactic emptiness? Space would have to be different in different places in order for it to be the source of the motion we formerly attributed to “gravity”.

The same for time…. And therefore for spacetime. So, using spacetime as the source of gravity rather than space alone is no help.

Well we’d need to know if spacetime has any non-trivial properties, if these properties can be different at different places and times.

Certainly spacetime does not seem to be different at different places and times….. but wait….. if that which we called ‘gravity’ is actually a manifestation of the properties of a spacetime location then spacetime IS different at different places and times!

What is it about spacetime that can vary? What is space, or more to the point in physics, how do we measure it, or more precisely, what is it exactly that we measure when we talk about space and time? The answer is that we measure distances and elapsed times, ie “intervals”. So if something is different in different places/times, it must be that the measure of the interval is different. But surely if spacetime intervals are different at different places and times, ie it is a field quantity, and with a magnitude related to the amount of mass nearby, this will have other ramifications, for example the value of pi should have different values at different places nearer and further from a large mass.

Indeed Gauss and Riemann discussed the possibility that physical space may be warped, as mathematical space can be. And there is no reason that we should expect that nature will not utilize this possibility. Indeed I would suggest that one take it as a very central tenet of physics that unless otherwise proven one should assume that nature does indeed manifest all possibilities; only that which is mathematically inconsistent is physically impossible. And, if nature manifests the possibility, it may be in a manner and to an extent that will be un-noticeable to us in ordinary circumstances, and so our intuition will argue against its existence.

But we cannot simply argue from physical intuition, because our intuition about what can or cannot be true about the physical universe derives from experience, and our experience is limited to phenomenon which are accessible to our unaided senses; we don’t have good intuitions about the microscopic biological world, or about fundamental particles. So we have to be open to the possibility that the spacetime field is strong enough to cause the effects we attribute usually to ‘gravity’ but is not strong enough to cause deviations form the well-known 3.14 value that is usually measured. Could this be?

Well, spacetime has the value of the speed of light built in intrinsically into it, and therefore to balance the units the amount of time measured has a factor of 3x10⁸ built in relative to the amount of space measured, and so if the value of p dependes on the space measure whereas the value of the gravitational field depends on the time measure, this could work! And indeed this is how it turns out!

Think also of the actual strength of gravity that we witness: to us it is tremendous, strong enough to cause the earth to orbit the sun at 50,000 miles an hour. But compared to the natural speed, that of light, 750 million miles an hour, this is incredibly slow. And however strong gravity feels to us after we’ve completed a heavy meal and can barely stand, the mass of the Earth causing it is tiny relative to that of a large star, so small that we cannot expect to measure changes in pi here. So, spacetime can have field quantities which give rise to gravity strong enough to cause the Earth to orbit the sun and yet be so slight that its effect on p be un-noticable on Earth. Gravity seems so strong to us because we are exceedingly slow-moving creatures of tiny mass, with mass and speed commensurate with the small slow-moving Earth from which we were brought forth.

This is a very important physics principle – we cannot assume what is true and what not, what can and cannot be the case, and if we have not measured something we cannot know whether or not it exists, and if some phenomenon – like the variation in p – is not familiar to us, we cannot assume that in different conditions it would not appear either – we only know what we have measured.

..

We have to be sufficiently sophisticated to realize how many properties there are which are NOT realized by our spacetime each tells us something fundamental about spacetime, but we need to be aware of all the possible aspects which COULD in THEORY change, and then their non-changing can tell us something.

Inside a pulsating mass, gravity is very different than inside a static mass, but the outer region does not feel this distinction. (this is something seen a lot in topology: one cannot assume that things are different in one region simply because they are different in another region).The fact that the gravitational field is NOT different outside a pulsating spherical mass than it is outside a static mass tells us something important about s+t.

In a different sense one can see this as an example of the exact opposite: this phenomenon shows also that Nature does take advantage of possibilities: this is a type of maximization as well, a loophole allowing unexpected phenomena: since this type of unfelt-pulsation is a physically and logically possible aspect of laws of nature, it indeed occurs.

……..

Ramifications of Birkhoff’s Theorem

As in Newtonian gravity, so too in Einstein's GR the spacetime curvature outside a spherical mass depends only on the mass of the and not on the distribution as long as it is spherically symmetric, ie if the star were to inflate of deflate with the same mass, the spacetime curvature (metric) outside the star would be the same. Therefore, a star which has collapsed all the way to a black hole will still have the same external space as it had before it became a black hole [thus the Schwarzchild metric is also that of the space outside a black hole].

Cosmology

Another example has application to cosmology. The vacuum of a spherical cavity hollowed out inside a sphericaly symmetric distribution of matter has this same Schwarzchild metric. And, since there is no matter which the vacuuum surrounds, the spacetime (metric) is flat. That is, the space inside a spherical cavity is flat, no matter how much matter-energy there is outside the cavity! [Similar to result in electromagnetic theory.]

We now look at the case of a spherical distribution of matter-energy within which we take a spherical volume of matter and collapse it into a point source, so that there is a point source at the center, a cavity outside it, and a spherical distribution of matter-energy outside that. The metric in the newly-created vacuum cavity outside the point source and inside the rest of the spherical distribution necessarily has the static Schwarzschild form. There is no contribution at all from the surrounding matter [and the constant in the metric term is given by the mass of the point mass which the vacuum surrounds]. The metric in the vacuum there is the same a it would be if it were not surrounded by the spherical distribution of matter-energy! [3]

Application: If the universe is considered to be a homogeneous distribution of mass-energy, then if we consider any part of the universe, and collapse the matter there to a point, the metric in the vacuum created there is static, and has the above form. However, this will hold true even where the space as a whole has a non-static metric.

This means that although the universe may be expanding for example, at any point in this expanding universe there is no expansion locally, since one can arbitrarily demark a volume of space as a sphere with oneself at a distance r from the center, so that all the matter further away has no effect, and one is affected only by the matter inside the sphere. Of course the volume of the sphere is arbitrary and therefore so is the mass, but the metric will give the same result as the center of mass for a further centered sphere is more distant so that while it contains more mass it has the same effect as a closer centered sphere with less mass.

In any case, if the sphere is smaller than a critical size so that the mass enclosed is less than a critical amount (like for black hole formation) there will be no expansion. It is only at the global level that the local patches of non-expanding spheres become unified into an expanding universe.

…….………………..……

In order to know which possibilities are NOT realized by our spacetime one has to be sufficiently sophisticated to realize how many properties are possible! eg handedness doesn’t change when go on a closed path, size doesn’t change etc, each tells us something fundamental about spacetime, but we need to be aware of all the possible aspects which COULD in THEORY change, and then their non-changing can tell us something.

………………

Sometimes a theory can point to conditions in which it is not needed: quantum physics contains relations which can help us determine whether or not quantum physics need be employed in a particular situation , or one can use classical physics (to obtain results within given range of required accuracy). In the same way, general relativity can indicate when it can itself be dispensed with and Newtonian mechanics can be safely employed (with the needed accuracy): we’ll see this example when applied to cosmology (and to some other situations). [Also, we will see that the existence of tidal accelerations – ie the fact that they are large enough to be measurable - is an indication that the Equivalence Principle will fail and one needs to take gravity into account.]

………

Implications of the Staticity of the Spherically Symmetric Vacuum Metric

A) No matter how the distribution of matter-energy serving as the source behaves, changing with time, oscillating, shrinking etc, as long as it stays spherically symmetric the geometry of the vacuum space-time outside the source is static. This is called Birkhoff's theorem.

In Newtonian gravity the gravitational field set up by a spherically symmetric source is the same as though all its matter-energy was concentrated at a point. We will see that we can obtain the same result in general relativity as a consequence of the staticity of the vacuum.

Imagine a collapsing mass. At all times as it shrinks, (instantaneously) the vacuum metric has the same form. (Since for arbitrarily small changes in t this is true, we can say that the vacuum metric remains the same). The metric is static all throughout the collapse, and is therefore the same at the beginning of the collapse when it is an extended spherical mass-energy distribution, and at the end of the collapse when it is a point source.

that is, (since the geometry remains the same) a mass which has shrunken to a point gives the same solution as (resulted from) an extended spherical source.

The constant c in the Schwarzschild metric is obtained from a boundary condition, and turns out to be the mass of the source which the vacuum surrounds, that is, the mass encountered while going from r=r to r=0.

In Newtonian gravity the matter outside the sphere

has no gravitational effect at the point x. In general relativity the effect at x is indicated by the term m/r in the metric, but since m is the integral over the space within the sphere the effect of the matter is the same as in classical theory.

C) The implication of this is that - in analogy to the case of Newtonian gravity - for a vacuum inside a spherical cavity inside a sphericaly symmetric distribution of matter, since there is no matter which the vacuuum surrounds, c=0 and the metric is flat.

If we take a volume of matter and collapse it into a point, the metric in the newly-created vacuum necessarily has the static Schwarzschild form, with no contribution at all from the surrounding matter, and with c given by the mass of the point mass which the vacuum surrounds.

.............

Linearity and radiation

Spherical symmetry precludes dynamical gravitational degrees of freedom. Ie no monopole gravitational radiation.

…………

AR NOTES

However, again, although the possible distinctions are seemingly wasted ie nature doesn’t maximize the possibilities, later we’ll see great ramifications of this: the loss is offset by a greater gain, the enabling of a very beautiful principle of Nature. (EP)

[We’ll also see the connection between these two (Birkhoff and EP: local flatness, global curvature]

………..

What things are possible (Can things be known a priori)? Which possibilities does the universe realize (does it maximize the possibilities)? Eg:

· Charge of the electron: is it a function of time? Fine structure constant change with time?

· Universe emerges into existence by itself? Continuous creation?

· Rotate something 360 degrees, will it return to original state? 720 degrees!?

· Gauge field.

· The value of pi: function of position, of time.

…………………

(that they are all at rest is the meaning of the co-moving frame in cosmology, that their mutual separations would change is cosmic expansion).

· Don’t think of spatial expansion as the space itself moving, rather it is the particles within that space which give meaning to this, ie it is that there is geodesic separation (time-dependent spatial separation) of neighboring stationary particles.

· ..

Why should space have Euclidean structure? Maybe something else? But if it is different at different places/times, we certainly expect that this is correlated to some other difference, a “cause” (eg in Cartan N’n affine theory and in GR the cause is matter-energy).

Space w/ a connection need not have a metric etc: Topology: set of points, not nec’ly a ‘distance’ bet points of the set, or ordering. Give ex’s. A “space”.

To distinguish bet connection and metric connection etc., introduce idea of topological and (diff’l) geometric ‘structure’ to a space. A set of objects, points or people or etc can impose a metric on it, ex of train tracks changing a metric, metric measuring relationship distance bet people. Or degrees of separation etc..

Our physical space:

Can define parallelism. This is a structure on the space, called a “connection”.

Distance between 2 infinitesimally close points: ds² = dx² + ….

Define word “metric”: metric measurement, meters vs inches etc. meter.

But also for distant points the formula is (Euclidean formula) s² = x² + …, ie one can integrate this all the way to any limit. This tells us a lot about the space. We call it a Euclidean space, it has a Euclidean metric.

Nature exploits possibilities: Can’t assume that physical space is NOT warped:

………….

[1] Not all things which seem different necessarily are: eg Birkhoff, therefore pulsating star is same outside as static one etc. so the universe is not maximizing the diversity? But nevertheless this is a loophole, cannot assume that they are different outside just because elsewhere it is very different. (topology…)

Cannot assume things like “no action at a distance”. No FTL only bec it leads to paradoxes.

[2] [words in quotation taken from Tolman p361 (beg’g Ch10) in context only of cosmology]

[3] INSERTED FROM PREVIOUS CHAPTER FOR COSMOLOGY SECTION

(Standard conclusion) As long as we are considering the space outside the mass, since the mass only enters the metric through the integration constant, the effect of a mass is the same if it is all concentrated or spread out, as long as it is spherically symmetric.

As we saw from the form m/r, what is important is the distance r from the center of the mass, not the distance from the edge of the mass. Therefore a hollow shell acts the same as a solid ball - what is relevant is the amount of mass-energy and the distance from the center of the shell or ball, and that we are considering the space outside the shell or sphere.

This will have important consequences for cosmology - and will enable us to find models of the universe simply, and to derive the age of the universe!

Full content of file: "Derivation of Basic Physical Theories from Paradoxes of Natural Philosophy"

Introduction

Over the centuries natural philosophy has often arrived at a paradox in its conception of nature. With hindsight one can see that these paradoxes were actually due to a major misconception about very fundamental aspects of nature. Resolving the paradox usually ushered in a major advance in scientific knowledge.

We would like to point out various paradoxes and difficult points which plagued physics over the years and which could perhaps have led to immediate advances which in actual fact took many years.

Non-Euclidean Space and General Relativity

It was clear to all that space could not be finite [Leibnitz], for then it would be bounded, and that it also could not be infinite [Newton], since infinitude is not a property of physical entities.

Had the solution to this dilemma been the supposition that space was finite but unbounded, a great advance towards the theory of general relativity might have been made.

In a gravitational field, all bodies fall with the samecceleration, regardless of their mass. That is, inertial mass equals gravitational mass. It might have been concluded as a result that a geometric property of space was involved, and this would have been a pointer in the direction of general relativity.

It might also have been realized that forces of inertia and of gravitation are interchangeable, and that therefore gravitational fields could be transformed away in differing frames of reference. This would also have been a pointer in the direction of general relativity.

Special Ralativity

If infinitude is not a property of physical entities, and if the universe is not infinite, then nothing can move with infinite speed. Since in theory an entity can accelerate continuously without limit [unless it uses up the universe as fuel], but it must always have a finite speed, this means that either time is finite or that there is a maximum speed.

If there is a maximum speed however, an entity moving at close to this maximum sent from a moving frame which is itself moving close to the maximum, would move faster than the maximum - therefore there must be some reason that velocities do not add in the Galilean manner. From this one could derive the Lorenz transrormations, which would be a clear clue to special relativity.

The earth spins very quickly, and moves quickly around the sun. At times twelve hours apart, the speeds add and subtract - so that the difference in tangential speed is great. Nevertheless physics experiments do not indicate any difference, and therefore one can conclude that all equations of physics must transfornm invariantly between frames moving with relative velocity between them.

The Maxwell equations indeed transformed invariantly under the Lorenz transformation. However this was taken as an indication of a property of the non-existent ether rather than as a property of space-time.

Quantum Physics

Newton claimed that light is particulate, Huygens claimed it was wave-like. It might have been realized that it was both - and that therefore since being wave-like and being particle-like can be two aspects of one entity - and that this is indeed the case for light - that perhaps all matter is also wave-like. This would have led to the development of quantum physics.

That matter is divisible seems obvious, yet if the division process could be continued indefinitely, this would imply that all matter is infinite. It might then have been realized that matter must be indivisible at its most fundamental level. However there can be no reason that a basic piece of matter is indivisible unless it is infinitely hard - which is impossible since physical entities cannot have any infinite properties. It therefore must be that its most basic level, matter cannot be thought of as a localizeable entity. This could have led to the direction of quantum physics.

Free will exists, yet physics is deterministic. Therefore, one could have supposed that nature would, at its most fundamental level, be non-deterministic.

Miscellaneous Theories

Physical experiments give identical results irrespective of the time and place. Invariance under space-time translations imply conservation of matter-energy.

Particles are identical and indistinguishable - therefore there is an exchange force [see Jammer "Concep. ..Q.M." p338-345 [I have copy]

Spin. Have to rotate by 720 degrees to get back to start.

Zeno's paradox could have been developed to show that ....

Free will, therfore Godel, Church, Chaitin etc.

[Some intuitive feelings are true but unprovable ---- Godel.]

Olber's paradox showed that the universe must be expanding.

Second law of thermodynamics is implied by ???

Entropy, perpetual motion,

What of a single particle stationary in space = [same thing as] moving with uniform speed . How does its entropy increase? It must decay radioactively. And then? It decays further and further, and then disappears. Vacuum energy ??

Orbiting objects in space - no friction etc. Where is the increase in entropy. There must be tidal forces, or radiation because it is accelerating. Or the elementary particles are radioactive, or it loses vibrational energy - and then after all the energy is gone ??

The existence of a horizon which constantly recedes - especially noticeable at sea - is clear evidence that the world is round.

Indeed it had been known even in antiquity that the world is round. Had it been realized that people on opposite sides would fall of unless held by some attractive force, the idea of gravitation could have been discovered thousands of years before it was.

See Whitehead."Science and the Modern World" p.180-190

Full content of file "Physics a priori via paradoxes"

Introduction

Over the centuries natural philosophy has often arrived at a paradox in its conception of nature. With hindsight one can see that these paradoxes were actually due to a major misconception about very fundamental aspects of nature. Resolving the paradox usually ushered in a major advance in scientific knowledge.

Non-Euclidean Space

It was clear to all that space could not be finite [Leibnitz], for then it would be bounded, and that it also could not be infinite [Newton], since infinitude is not a property of physical entities.

One solution to this dilemma is the supposition that space is finite but unbounded; this was a great advance in mathematics and physics that in some sense might have been made earlier.

Quantum Physics

Newton claimed that light is particulate, Huygens claimed it was wave-like. It might have been realized that it was both - and that therefore since being wave-like and being particle-like can be two aspects of one entity - and that this is indeed the case for light - that perhaps all matter is also wave-like. This would have led to the development of quantum physics.

That matter is divisible seems obvious, yet if the division process could be continued indefinitely, this would imply that all matter is infinite. It might then have been realized that matter must be indivisible at its most fundamental level. However there can be no reason that a basic piece of matter is indivisible unless it is infinitely hard - which is impossible since physical entities cannot have any infinite properties. It therefore must be that its most basic level, matter cannot be thought of as a localizeable entity. This could have led to the direction of quantum physics.

Free will exists, yet physics is deterministic. Therefore, one could have supposed that nature would, at its most fundamental level, be non-deterministic.

Miscellaneous Theories

Physical experiments give identical results irrespective of the time and place. Invariance under space-time translations imply conservation of matter-energy.

Particles are identical and indistinguishable - therefore there is an exchange force [see Jammer "Concep. ..Q.M." p338-345 [I have copy]

Spin. Have to rotate by 720 degrees to get back to start.

Zeno's paradox could have been developed to show that ....

Free will, therfore Godel, Church, Chaitin etc.

[Some intuitive feelings are true but unprovable ---- Godel.]

Olber's paradox showed that the universe must be expanding.

Second law of thermodynamics is implied by ???

Entropy, perpetual motion,

What of a single particle stationary in space = [same thing as] moving with uniform speed . How does its entropy increase? It must decay radioactively. And then? It decays further and further, and then disappears. Vacuum energy ??

Orbiting objects in space - no friction etc. Where is the increase in entropy. There must be tidal forces, or radiation because it is accelerating. Or the elementary particles are radioactive, or it loses vibrational energy - and then after all the energy is gone ??

The existence of a horizon which constantly recedes - especially noticeable at sea - is clear evidence that the world is round.

Indeed it had been known even in antiquity that the world is round. Had it been realized that people on opposite sides would fall off unless held by some attractive force, the idea of gravitation could have been discovered thousands of years before it was.

See Whitehead."Science and the Modern World" p.180-190.

Science and Religion

..................

Topics for a book: synchronicity, free will, mind etc (some of this I wrote to RUdy Rucker)

contradictions, impossibilities: as of course you know well: manipulations that are impossible in 2-d are possible in 3-d and etc for higher dimensionalities, so although there can be something impossible of even self-contradictory in our level of physical reality, prhaps it is not contrdictory in the full reality, only in the limited perception of this 4-d spaceitme causal turcture, or when our awareness is limited by it.

...

synchronicity that is programmed into the universe seems to imply that the OS of the unverse i more mind-like, and if the synchronous events are meaningful not just similar, then the meaning seemingly has to be not jus tnour minds but in the system, so the 'universe' has menaing programme dinto the las of its operation etc, and oerhas just like theres a law oflest action and energy onservation etc, theres a lw of maximal sophistication, and also of maximal meaning (in potentia).

rudy@rudyrucker.com , rudytheelder@gmail.com

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Rudy, hi

Some background: I'm a theoretical physicist, perhaps you'll have an interest in seeing my lectures on general relativity given to the SPS there when I was a visiting scholar [btw, I'm not affiliated now with NYU].

Thanks so much for putting in the time and mental effort to write "Infinity and the Mind", which made a huge impression on me way back when I read it. And for the poignant revealing honesty I found in the later edition's statement "I thought I had so much time to finish my thinking. The ideas I developed were, in many respects, my complete and finished thoughts, e.g., on robot consciousness via evolution, but at the time I thought I was still just roughing out a start. I didn’t realize it was a high-water mark, and that I would never again think so deeply about the philosophy of mathematics." I appreciated it more and more as the years passed and looked back at my own experience.

Your writings are very much on my wavelength - 'ultimate causes' at variouslevels have always fascinated me [and a paper I co-authored touched on this topic in a way: we found a way to overcome a problem in the process of emergence of a universe from nothing (overcome via tunneling, catalyzed by topological transition via a specific source-term which its kind of topological (a 'defect')]

Now in corona-times at home I'm reading or re-reading the last two chapters of your terrific "The Fourth Dimension" and wanted to get your feedback on various ideas.

• Examples in physics of ours being a "maximally-interesting" universe (what you call a 'first class universe' 'a beautiful & interesting world"): this has relevance to what you wrote (on p188 of the edition I have) re the EPR etc: "The fact that two widely separated elementary particles can act in concert has no explanation" To me, the reasoning which allows it, ie since there is no transmission of information possible using it as a mechanism, is a great example of what it means that ours is a maximally-interesting universe.

• Synchronicity: re (p185) "It seems evident that a first class universe must include a mizture of both sorts of spacetime patterning. What I am suggesting, in short, is that our world contains synchronicity because it is a beautiful and interesting world!" Perhaps you will be intrigued by my proposal to employ HiTech methods to test Synchronicity & Dream sources;

• I'll bet you have been frustrated forever with those who claim minds is an illusion, is just software etc. My conclusion is that such people simply do not possess a mind; I mean that literally;

• The crucial cosmic (or cosmogenetic) role of a "true free will": I think the essential aspect of our reality is not awareness but rather the mechanism whereby it can influence the physical universe, ie free will; rather than us being 'conscious robots', we have a will which is 'free' in a sense that is impossible both logically and in terms of cause effect. You propose synchronicity as an example of a phenomenon which is beyond the usual type of cause & effect, and I similarly propose free will & true creativity as examples of acausal phenomena, directly related to the acausality of the emergence of the universe into existence These ideas are expressed at the beginning of this webpage which are based on an article I published in an obscure journal in the 80's; the conclusion of that article relates free will, acausality, the measurement problem. The home page of that site attempts to define what I mean by "a truly free will".

• That which is called "the conflict between religion & science", and the possibility of connecting to a "higher Mind".

A little more about consciousness, free will, and also re

Awareness: Basically in this sense the world is divided into two, those who with Descartes (and you and I) enfranchise consciousness, and those who don't, the real "hard materialists". My essays about my belief that intelligent people who do not believe as we do are simply not conscious are inevitably removed - here is a cached web-entry listing my article but it is cached because it disappeared as do all references to my idea, probably because it is a potentially problematic assertion about the "humanity" of those who deny awareness, eg perhaps they don't "feel" pain as we do.. etc.

http://webcache.googleusercontent.com/search?q=cache:dlHkaNxOpmAJ:www.statemaster.com/encyclopedia/Consciousness+&cd=8&hl=en&ct=clnk&gl=us See the last sentence of the section "Phenomenal and access consciousness" , a ref to me:

"The possibility has indeed been proposed that those denying the existence of qualia, hence denying the existence of a "hard problem," do so since they do not possess this faculty^[13]."

See ref 13, but that link is broken. There used to be various sites quoting me, but I don't see any more left.

Of course, perhaps there are other levels known to "Mindless materialists", but however it may be, there's no use to arguing with them on this topic.

The next level up (from 'awareness') is 'free will', which is what makes it possible for a conscious being to not just be a passive observer, a conscious robot vs the materialists who are non-conscious robots. A free willed being can affect the chain of cause and effect in an 'independent' manner. But this idea is completely counter to logic and physics and is impossible to actually define, and so is generally rejected by philosophers and scientists. Also, as opposed to consciousness which someone who is conscious knows exists by definition, free will CAN be an illusion, we CANNOT say for free will (as we do for consciousness)"I know it exists without having to prove it exists".

re what is called "the conflict between religion & science"

Religion is based on free will, since true morality is based on it, but there are religions (Calvinism?) which perhaps avoid this, and in any case philosophers are not interested in "true morality" but rather in showing that a brain state can exist which correlates to the thought "I am morally responsible for my action" even in a completely deterministic universe without awareness and without free will.

As a young physicist I used to try to "reconcile" physics and religion, the spiritual etc, thinking that physics had all the answers and religion had to fit inside physics somehow. Some of my writings on consciousness within this mindset are here:

• https://sites.google.com/nyu.edu/andgodsaidlettherebemeaning/the-retroactive-universe-intro-to-book

• https://sites.google.com/a/nyu.edu/avi-rabinowitz/creation-big-bang-evolution-the-retroactive-universe/fullbook_the_retroactive-universe

But eventually. When I realized that what is most fundamental, awareness and the passage of time, are totally not encompasses within physics, physics did not at all enfranchise awareness (contrary to the new age claims that it does),

and that very many physicist I spoke with were not interested and didn't understand and we're materialists etc to me

and that most theoretical physicists were entirely uninterested in the topic, and so I came to the opposite conclusion, that physics was inadequate to the task of describing reality, and one need not be overly concerned with "reconciling" it with religion.. meant eventually that I would not hold all my beliefs accountable to science. This liberated me to express views which could not be reconciled with science, but still to use scientific ideas to illustrate concepts, or to demonstrate possibilities etc ..

...

Science and the Modern World by Alfred North Whitehead (1925):

“Western peoples exhibit on a colossal scale a peculiarity which is supposed to be more especially characteristic of the Chinese. Surprise is often expressed that a Chinaman can be of two religions, a Confucian for some occasions and a Buddhist for other occasions . . . . But there can be no doubt that an analogous thought is true of the West, and that the two attitudes involved are inconsistent. A scientific realism, based on mechanism, is conjoined with an unwavering belief in the world of men and of the higher animals as being composed of self-determining organisms.

This radical inconsistency at the basis of modern thought accounts for much that is half-hearted and wavering in our civilization…It enfeebles [thought], by reason of the inconsistency lurking in the backgroundIt enfeebles purpose itself, and consequently policy which necessarily presupposes purpose. …For instance, the enterprises produced by the individualistic energy of the European peoples presuppose physical actions directed to final causes. But the science which is employed in their development is based on a philosophy which asserts that physical causation is supreme, and which disjoins the physical cause from the final end. It is not popular to dwell on the absolute contradiction here involved.

Alfred North Whitehead, Science and the Modern World, p.73 (New York: The Macmillan Co., 1925).

p.91: p180-190

....

recently Nagel

Thomas Nagel: Thoughts Are Real | The New Yorkerwww.newyorker.com › books › page-turner › thomas-nagel-thoughts...

Jul 16, 2013 - The widest implications of Thomas Nagel's new book involve art and ... waves that give rise to a person's momentary complex of awareness, ...

Thomas Nagel is not crazy | Prospect Magazinewww.prospectmagazine.co.uk › arts-and-books › thomas-nagel-mind-...

Oct 23, 2012 - The philosopher Thomas Nagel thinks the materialist scientific ... why the mind feels free, or why we feel we are self-aware and conscious.)

...---------- ......

Whitehead process philosophy

Bridgman, universe is as we measure, no preonceptions

My idea of solipsism as minimalistic, all else adds unprovable aspects. By addong other minds it is complicated. Our model of reality should take into account that this is so! Take into account that by definition we cannot know of others directly.

Also, we assume that 'reality' is amenable to description, and by us!

...

all is about synchronicity except first quote:

but much of his defence of synchronicity can also be about FW in the sense that (my words) "Just because FW seems impossible or contradictory, doesn;t mean it isn;t so".

my page re synchronicity: https://sites.google.com/nyu.edu/deep-learning-synchronicity/home

...

For my Q ch 4 of evo: re to guarantee the eventual mergence of humans moral beigs etc would require constant intervention or inst un at moral stage (and then maybe also other interventions?) : he writes in a diff context:

ch 10 "time travel and telepathy": p180: "If there were a God directing the world's history, thenit would not have been enough for him to set up the world billions of years ago and then walk off. He would have to work over all of spacetime, weaving the random blips into a pleasing pattern".

.....

I write about emergence into existence etc, and Rambam and Ramban worry about all that, and also RR:

ch 10 "time travel and telepathy":

p172 "Maybe contradictions are rare but not totally ruled out. After all, there is a sense in which the very existence of our world is a contradiction: for how could something come from nothing" so he is willing to conceive of contradicitons" of some sort, such as existing and not existing in some sense both, though then he kind of waffles on that.

He is open to the notion of synchronicity since it doesnt involve contradictions (or impossibilties), and "since the process of cause effect does not account for all th world's structure we might as well look for other kinds of patterning"

meaningful coincidences, life is full of them", Jung "synchronicity" acausal conection".

P184 presents spacetmie diagram, vertical structure is cause effect.

"One might think of our world's synchronicities as a sort of "horizontal" spacetime structuring... that is there for reasons that might be thought of as artistic" !!

p185 "It seems evident that a first class universe must include a mizture of both sorts of spacetime patterning. What I am suggesting, in short, is that our world contains synchronicity because it is a beautiful and interesting world!" (he has ! there) !!

He asks:who built in all this deep meaning?

Ans: p186 According to the quantum-mechanical world view it is we ourselves who create the world event by event, instant by instant. the universe is in a sense a book writtne by its haraqcters, a dream dreamed by its own phantoms"

He asks: why should they exist?

He answers: "Qp requires synchronistic events" by which he means not causally related, but connected..

.....

RR: This finally is the essense of synchronicity, he world we live in is filled with harmonies and coincidences that have no explanation in terms of cause and effect..the world is a given it is full of cause and effect full of synchroniciy.

p191 last paragraph of chapter: "This is a first class universe we're in.It's loaded with symbolic events, deep meanings, and heavy coincidences...synchronicity is a fact of life"

...................

Science is about provable statements etc, and philosophy strives to do that as well. S since i am talking of the unprovable, I do not refer to this as philosophy, and since it is about our reality at its most fundamental I refer to it as metaphysics (& cosmogony rather than cosmology etc).

One of the interesting photopies I have is of Ayer who wrote that essay in '84, which is when i was just starting to get into the subject, reading, buying used books in Ylm, so I was at that cusp, but do not have anyhting to say that has not been said from the technical philosophical perspective, but I think I do have osmehting uinteresting to say form the metaphysical perspective.

One distinction is important to make: there;'s no point in arguing about that which is impossibe to prove, eg awareness etc. And no sense in trying to incorporate it into 'philosophy/ since it is not provable. So it is beeter to stay in metaphysics.

..

Progression:

1. Mind exists: my contribution is my original proposition re 'mindless materialists': say I am addressing the book onl to those who agree with me :)

2. Mind is primary: my contribution is as a physicist who understands what is accepted and what is not, what is scientific fact and what is not, but who KNOWS awareness exists, is fundamental and is not included in physics. ie I am led to all this as a physicist, ie from the desire to understand the fundamentals of our existence but from the same introspection anyone alse does not just physicists, but as a p I know that what I am noting is a fact that belong at the foundaiton of physics.

So I state unabashedly that Mind is primary, but successful physicits were those who concentrated only on experimentallly-measured etc phenomena. So we don;t study Mind quite yet.

3. FW: Bridgman put the situaiotn vis a vis FW very well, no counterfactual etc, so I know that is is not worth investigating at this level of our ignorance. But FW is the way that the existence fo mind makes itself felt in the physical realm. Maybe it doesn;t exist, but in a Mind-primary universe I am not convinced that logic and cause-effect based arguments are good enough reasons to reject it outright.

One day soon perhaps we'll be able to experimentally-deterrnine whether any brain-events occur which are not implied in the purely-physical brain state.

This is a type of god of the gaps, but...

4. Cosmological implicaitons of the existence of true FW: (notion of acausiality etc): collapse of wavefunciotns etc, and emergence of universe into existence All this is my original stuff and should be first in the book.

5. The implicaitons of FW is moral responsibility etc: There are various ways that thinkers have grappled with what one ought to do if there really is FW. Eastern mystcism way, 'western' = Greek?, Jewish = Genesis (the outsider perspective). Understanding Gensis in this context is my original contribution, so place it first. [The relevance of Genesis to this discussion. I see it as a presentation of a compete worldview underlying an objective morality etc, and a theodicy etc (contained in a poem, not presented as a minimalistic philsophical or metaphysical axioms-set.).]

6. Meaning & Purpose: my contribution is the concept of stratification outlined here:

Let's assume there are statements provable to every raitonal person (ie physics depts at major universities exclude people they call crackpots, but tha tintroduces subjectuivity, but we ignore that :) , I'll call that physics.

To me anyhting beyond that may be in the categogory of 'religion'.

But 'mind' is in a grey area, so there is a stratificaiotn,

1. Physics;

2. mind

3. FW, Morality.

These are levels of what can be proven etc.

ie that which is accepted in physics depts is level 1.

Then there is level 2. awareness, which is accepted by some in those depts, they KNOW it exists, but also know they acannot prove it exists (especially not to those colleagues in their dept who claim it doesn't exist).

Then level 3. FW or etc, a direct intuition but which may be false so it is less than awareness, but may be a universal intuition which would make it not necessary to prove tha tthe intuition exists, but that is not necessarily a level-changer, since it is the referent we are interested in (ie whether FW actually exists or not) and not simply the intuition about its existence. And similarly regarding morality, 'ought', good/evil, meaning & purpose (noone disagrees that humans have these feelings or intuitions, what we are concerned wiht are the referents not the intuiotions about the referents).

...

Connecting to a higher "Mind"

Einstein’s “Religion” is far from Naive

People tend to dismiss Einstein’s religious beliefs as naןve, and perhaps logically inconsistent. However they do deserve greater scrutiny.

At first glance the Spinozic conception of God seems empty, as totally synonymous with the laws of nature. However Einstein stated clearly that he believed in the existence of a Mind ..... of the ultimate unknowability of the universe, .... of the need for morality (but separate from religion?) .......

He simply did not attribute human characteristics to this Mind, nor did he believe in divine communication with humanity in the form of speech etc, but he did feel that it was the ... inspiration ..... guided scientists to the great discoveries ....

What is inconsistent in this?

And if one would ask: well what relevance does this God have to our lives, Einstein could answer that God does not exist to be of relevance to us, nor should we expect to understand God’s motivations or actions etc.

Einstein simply tells us facts about the universe, facts he knows via contemplation, observation, deduction, experiment etc: that there is a Cosmic Mind, that the universe is expanding etc - what the relevance of all this is to humanity is not an issue, it may have no relevance, it is simply true. And, if we do not like that morality has no anchoring in Einstein’s religion, this is not a failure of that religion. It is sophisticated and minimalistic, far from naןve.

To him morality follows from logic and observation of human nature (or at least of his analysis of his own nature!) (we can check to see if this belief is consistent).

His religion is minimalistic in the extreme. It is religion because it involves unproven beliefs about the universe etc, it involves the belief in a God-like entity....

His religion does not involve morality, ritual, revelation (other than the basic revelation of the existence of the Cosmic Mind) etc, but is no less a religion for all that.

He had his goals and drive in life, and his convictions, without connection directly from his religion; for most people their religion gives them these; for us they are seemingly necessarily connected, whereas for him they seemed not to be, at least according to his claims. One suspects however that his feeling for the dignity of life etc was affected by his religious beliefs.

Perhaps we feel that he should have tied one to the other, and determined what religious beliefs are implied by these humanistic beliefs; if it is true that life is precious etc then what does this necessarily imply about the universe or the cosmic Mind or its connection to human minds ..... (i.e. his religion may be sophisticated but too minimalistic - it is perhaps missing something and therefore inconsistent.)

One needs to take into account the fact the E was able to feel/deduce the existence ofthis Mind, that implies some form of conneciton between tem.

One should not assume that E's level of conneciton is maximal, maybe others experienced greater conneciotn and therefore further insight in the nature of reality, or of the Mind..

Maybe it is only in a universe in which Mind is fundamental and which is underlayed by Mind, that brains can think that morality is self-evident.

ie the act thatE felt it was not necessary to have tehc sonic Mind be the bedrock o fmorality exist, is itself an indicaiotn of the pervasive influence of the MInd.

..

to Noson Y:

given Brian Greene's success, and yours, maybe "the outer limits of a maximally sophisticated universe" is a good book title?

The Elegant Universe - Wikipediahttps://en.wikipedia.org › wiki › The_Elegant_Universe

The Elegant Universe ... The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory is a book by Brian Greene published in ...

..

In any case, I understand that this project will have to wait its turn, if at all... and given your experience with co-authors, I would not insist on being one, especially as you are capable of unusual generosity of attribution as evidenced by your reference to me in The Outer Limits (which I usually indeed inhabit)

..

To Rudy Rucker

Your great books; my comments & ideas

Rudy, hi

Some background: I'm a theoretical physicist, perhaps you'll have an interest in seeing my lectures on general relativity given to the SPS there when I was a visiting scholar [btw, I'm not affiliated now with NYU].

Thanks so much for putting in the time and mental effort to write "Infinity and the Mind", which made a huge impression on me way back when I read it. And for the poignant revealing honesty I found in the later edition's statement:

"I thought I had so much time to finish my thinking. The ideas I developed were, in many respects, my complete and finished thoughts, e.g., on robot consciousness via evolution, but at the time I thought I was still just roughing out a start. I didn’t realize it was a high-water mark, and that I would never again think so deeply about the philosophy of mathematics."

I appreciated your comment more and more as the years passed and looked back at my own experience.

Now in corona-times at home I'm reading or re-reading the last two chapters of your terrific "The Fourth Dimension".

Your writings are very much on my wavelength, and It would be great to get your feedback on various ideas I've written about (see the links below) which relate somewhat to topics you discussed.

• You wrote about emergence of the universe into existence, and certainly 'ultimate causes' at various levels have always fascinated me, especially the notion of acausality, as in true creativity, true free will (see more about this below), and the origin of existence. About the last, you write in chapter 10 "time travel and telepathy": (p172) "Maybe contradictions are rare but not totally ruled out. After all, there is a sense in which the very existence of our world is a contradiction: for how could something come from nothing". A paper I co-authored (with EG: see mention here, and in this book) touched on this topic in a way: we found a way to overcome a problem in the process of emergence of a universe from nothing (overcome via tunneling, catalyzed by topological transition via a specific source-term which its kind of topological (a 'defect'). However, there is still of course the next level of 'nothing' . And if the fundamental reality of our existence is the mental realm, this casts the issue of origins and how something comes about 'from nothing' in an entirely different context (eg the acausal origin of the universe is more like the origin of a truly-creative thought as it arises in a mind). In any case, below you'll see rerences to my writings about mind, and about free will, which to me is the ultimate expression of acausality.

• Regarding your notion that ours is what you call a 'first class universe' 'a beautiful & interesting world": What I am suggesting, in short, is that our world contains synchronicity because it is a beautiful and interesting world!" Indeed there are several examples in physics of ours being what I call a "maximally-sophisticated" universe: one of those I discuss has relevance to what you wrote (on p188 of the edition I have) re the EPR etc: "The fact that two widely separated elementary particles can act in concert has no explanation" To me, the reasoning which allows it, ie since there is no transmission of information possible using it as a mechanism, is a great example of what it means that ours is a maximally-sophisticated universe.

• Synchronicity: You write (p185) "It seems evident that a first class universe must include a mixture of both sorts of spacetime patterning. What I am suggesting, in short, is that our world contains synchronicity because it is a beautiful and interesting world!" Perhaps you will be intrigued by my proposal to employ HiTech methods to test Synchronicity & Dream sources;

• I'll bet you have been frustrated forever with those who claim minds is an illusion, is just software etc. My conclusion is that such people simply do not possess a mind; I mean that literally;

• You wrote: "since the process of cause effect does not account for all the world's structure we might as well look for other kinds of patterning" "The world we live in is filled with harmonies and coincidences that have no explanation in terms of cause and effect" "meaningful coincidences, life is full of them", Jung, synchronicity and "acausal conection". Many of my writings center about what I feel is the crucial cosmic (or cosmogenetic) role of a "true free will": I think the essential aspect of our reality is not awareness but rather the mechanism whereby it can influence the physical universe, ie free will; rather than us being 'conscious robots' living in a reality totally bounded by randomness + determinism,, we have a will which is 'free' in a sense that is impossible both logically and in terms of cause effect, which is fundamentally transcendant of the bonds of "randomenss+determinism", and thus is the sole generator of truly new events, which to me are the most interesting. Just as you propose synchronicity as an example of a phenomenon which is beyond the usual type of cause & effect, I similarly write about free will & true creativity as examples of "impossible" or "contradictory" phenomena which might I believe neverthless be real. They are aspects of a fundamenta acausality in the operation of our relaity, directly related to the acausality of the emergence of the universe into existence. These ideas are expressed at the beginning of this webpage which are based on an article I published in an obscure journal in the 80's; the conclusion of that article relates free will, acausality, the measurement problem. The home page of that site attempts to define what I mean by "a truly free will".

• I imagine that not all math or science departments were always receptive to some of your directions of thought. Re contradictions, impossibilities: you wrote about manipulations that are impossible in 2-d but which are possible in 3-d and etc for higher dimensionalities; you state or imply that although there can be something impossible of even self-contradictory in our level of physical reality, perhaps it is not contradictory in the full reality, only in the limited perception of this 4-d spaceitme causal structure, or when our awareness is limited by it. My interests also transcended the confines of physics, and I stopped limiting my search for the Ultimate Truth to the notions accepted by physics. Perhaps you will be interested in some of what I wrote regarding "the conflict between religion & science", and the possibility of connecting to a "higher Mind" (Section not yet complete, being edited). You also wrote about 'meaning' and its origin; certainly if there is indeed synchronicity programmed into the universe, it would seems to imply that the Operating System of the unverse is more mind-like, and if the synchronous events are meaningful not just similar, then the 'meaning' seemingly has to be not just in our minds but in the system, so the 'universe' has meaning programmed into the laws of its operation etc, and perhaps just as there's a law of least action, and energy conservation etc, theres a law of maximal sophistication, and also of maximal meaning (in potentia).

Thanks so much,

And wishing you and your family much good health,

Avi (Dr Avi Rabinowitz)

...

Hi Avi,

Nice that you noticed that remark in the I & M preface about high water mark. I'm impressed by the breadth and depth of your writings. But, regrettably, I'm not in a state of mind to delve into them and make useful comments. Too old and tired!

But, yes, a synchronstic universe makes sense. We might as well assume, this is a really GOOD cosmos! I wrote about this idea in terms of successive "drafts" of our spacetime in my novel "Mathematicians in Love," I'll send you an ebook download link.

All the best,

Rudy

...

Rudy, hi,

Great to hear back from you, you made my week! last week and this one :)

And thanks for your very kind remarks about my writing.

BTW: The Foreword of your "4thD" by Martin Gardner impressed me - specifically your decision to include a foreword in which there was an explicit mention of disagreement with your approach. I was struck by the wisdom of being able to enfranchise a divergent opinion, the courage or self-confidence not to be intimidated by it, and the modesty of openly showing that not every 'expert' agrees with what you say.

I wish I had had that wisdom a few decades ago when I was faced with a similar issue.

And I noticed how on the cover etc you were branded as a science writer, scifi writer, rather than insisting on being labeled "mathematician" everytime your name was mentioned, and I guess this freed you to present speculative material close to your heart.

Of course I'm sorry to hear that you are not up to "delving" into those topics....I wonder if at some time you'd be up to a video-conversation which could be recorded and edited, with material then appearing in a book or article or video presentation I would make, or perhaps an exchange of emails would be more convenient.

I may be collaborating with my good friend Noson Yanofsky on some writing project, perhaps you may have seen his book "The Outer Limits of Reason" , and I was thinking that perhaps you could participate in a few of our discussions in some way, live or via email etc.

I'd also like to include other mathematicians; perhaps you can recommend some who have interests beyond that which fits exactly into "math". (BTW: Do you know John Baez?)

For example of one topic: true creativity - if it really exists - goes beyond deterministic cause & effect. Mathematical "Platonists" seem comfortable with enfranchising a realm beyond that of the purely-mechanistic/materialistic, while remaining "rational", and Einstein spoke of a Mind whose existence one could somehow sense. So, can a human mind on occasion connect to some higher level and gain insight in an acausal manner? Wigner wrote about the unreasonable effectiveness of mathematics in describing the physical universe, and some math/physics geniuses seem to "intuit" new theories. It's certainly interesting that the universe seems to grant those with unusual physical intuition a hint at a new theory, eg Maxwell, Einstein & Dirac. I'm interested in all that, as well as a more prosaic equivalent, the ways in which there is a sort of nesting hierarchy, where high-symmetry solutions of a higher-level theory are surprisingly similar to sophisticated representations of the corresponding solutions of the lower-level theory they replaced (see my site's discussion of this in the context of "minimal coupling", and discussions by Bernard Schutz).

And various other issues. Although I'd like it to be a book which investigate the topics of interest to me - like the one I outlined above - it doesn't have to be a book with only my views on those topics; divergent views will only make it more interesting for the reader.

What do you think? (Not to burden you, it can all be very informal....)

Thanks,

Respectfully,

Avi

...

Correspondence with Stanger

jdstanger@verizon.net

Thu, May 20, 5:25 PM (13 days ago)

שלום וברכה אבי

Yes, it really has been a long time.

I am semi-retired, living in Israel and spending a good part of my learning-time deeply immersed in the תלמוד עשר ספיות and other works of the בעל הסולם.

I find his approach to be the most comprehensive, coherent and transcendent of the different approaches I am familiar with.

By “transcendent” I mean that by deeply engaging in the seemingly analytical approach of the material (like learning a Tosfos but more so) there is periodically a transcendence into a super conscious reality where the intuitions I referred to in my email (among others more profound) become experiential. Thus the limud is essentially meditative which, apart from generally re-orienting the wiring of the brain, also transports not infrequently to really higher consciousness.

Rav Ashlag refers to that as subjectively empirical (he was very well acquainted with the philosophical milieu of his time) also as muda’ut nevu”

‘it. We are standing at the threshold.

Hope you are doing well. Are you still in the states?

jdstanger

Sun, May 23, 4:37 PM (10 days ago)

to me

No I don't recall that although I've been always intuitively very leery of lucid dreaming

can you briefly tell me what his reason was?

Sent from my Verizon, Samsung Galaxy smartphone

Avi Rabinowitz <air1@nyu.edu>

Sun, May 23, 5:27 PM (10 days ago)

to jdstanger

He had some type of frightening experiences..

You might be interested to see his book "the 4th dimension", he placed it on a site: http://www.rudyrucker.com/thefourthdimension/

I found this, but I think there was something else, specifically about lucid dreaming:

"Staring at the Neck-A-Cube too much before bedtime can lead to really unpleasant dreams. Although the fourth dimension is of great theoretical and philosophical interest, there is something frightening and mind-warping about it when it starts to get too real. I remember in particular a series of dreams I had in 1976, soon after I carne to understand that left and right are concepts as relative as up and down, or front and back.

In these dreams I would be walking down a street with someone on either side of me — my wife, Sylvia, let us say, on my left, and my friend Greg on my right. I would move out of my body and watch the three of us from a distance, first from a point in our space, then from a point entirely outside of space. What struck me was that depending on which half of hyperspace I looked from, the order of the three people would be Sylvia-Rudy-Greg, or Greg-Rudy-Sylvia. In my dream of walking down the street, I would begin to internalize such a shift, and the whole city around me would change back and forth between itself and its own mirror image. Some mornings I would wake up convinced that I and the whole universe had been replaced by our mirror images overnight. The worst day of all was when I sat up in bed and actually saw the reversal taking place: the whole room, furniture and all, rambunctiously do-si-do-ing about into mirror reversal. But, of course, I couldn’t prove anything … I’d turned over, too."

..

Here is what I wrote to him, not about dreaming:

Some background: I'm a theoretical physicist, perhaps you'll have an interest in seeing my lectures on general relativity given to the SPS there when I was a visiting scholar [btw, I'm not affiliated now with NYU].

Thanks so much for putting in the time and mental effort to write "Infinity and the Mind", which made a huge impression on me way back when I read it. And for the poignant revealing honesty I found in the later edition's statement:

"I thought I had so much time to finish my thinking. The ideas I developed were, in many respects, my complete and finished thoughts, e.g., on robot consciousness via evolution, but at the time I thought I was still just roughing out a start. I didn’t realize it was a high-water mark, and that I would never again think so deeply about the philosophy of mathematics."

I appreciated your comment more and more as the years passed and looked back at my own experience.

Now in corona-times at home I'm reading or re-reading the last two chapters of your terrific "The Fourth Dimension".

Your writings are very much on my wavelength, and It would be great to get your feedback on various ideas I've written about (see the links below) which relate somewhat to topics you discussed.

• You wrote about emergence of the universe into existence, and certainly 'ultimate causes' at various levels have always fascinated me, especially the notion of acausality, as in true creativity, true free will (see more about this below), and the origin of existence. About the last, you write in chapter 10 "time travel and telepathy": (p172) "Maybe contradictions are rare but not totally ruled out. After all, there is a sense in which the very existence of our world is a contradiction: for how could something come from nothing". A paper I co-authored (with EG: see mention here, and in this book) touched on this topic in a way: we found a way to overcome a problem in the process of emergence of a universe from nothing (overcome via tunneling, catalyzed by topological transition via a specific source-term which its kind of topological (a 'defect'). However, there is still of course the next level of 'nothing' . And if the fundamental reality of our existence is the mental realm, this casts the issue of origins and how something comes about 'from nothing' in an entirely different context (eg the acausal origin of the universe is more like the origin of a truly-creative thought as it arises in a mind). In any case, below you'll see rerences to my writings about mind, and about free will, which to me is the ultimate expression of acausality.

• Regarding your notion that ours is what you call a 'first class universe' 'a beautiful & interesting world": What I am suggesting, in short, is that our world contains synchronicity because it is a beautiful and interesting world!" Indeed there are several examples in physics of ours being what I call a "maximally-sophisticated" universe: one of those I discuss has relevance to what you wrote (on p188 of the edition I have) re the EPR etc: "The fact that two widely separated elementary particles can act in concert has no explanation" To me, the reasoning which allows it, ie since there is no transmission of information possible using it as a mechanism, is a great example of what it means that ours is a maximally-sophisticated universe.

• Synchronicity: You write (p185) "It seems evident that a first class universe must include a mixture of both sorts of spacetime patterning. What I am suggesting, in short, is that our world contains synchronicity because it is a beautiful and interesting world!" Perhaps you will be intrigued by my proposal to employ HiTech methods to test Synchronicity & Dream sources;

• I'll bet you have been frustrated forever with those who claim minds is an illusion, is just software etc. My conclusion is that such people simply do not possess a mind; I mean that literally;

• You wrote: "since the process of cause effect does not account for all the world's structure we might as well look for other kinds of patterning" "The world we live in is filled with harmonies and coincidences that have no explanation in terms of cause and effect" "meaningful coincidences, life is full of them", Jung, synchronicity and "acausal conection". Many of my writings center about what I feel is the crucial cosmic (or cosmogenetic) role of a "true free will": I think the essential aspect of our reality is not awareness but rather the mechanism whereby it can influence the physical universe, ie free will; rather than us being 'conscious robots' living in a reality totally bounded by randomness + determinism,, we have a will which is 'free' in a sense that is impossible both logically and in terms of cause effect, which is fundamentally transcendant of the bonds of "randomenss+determinism", and thus is the sole generator of truly new events, which to me are the most interesting. Just as you propose synchronicity as an example of a phenomenon which is beyond the usual type of cause & effect, I similarly write about free will & true creativity as examples of "impossible" or "contradictory" phenomena which might I believe neverthless be real. They are aspects of a fundamenta acausality in the operation of our relaity, directly related to the acausality of the emergence of the universe into existence. These ideas are expressed at the beginning of this webpage which are based on an article I published in an obscure journal in the 80's; the conclusion of that article relates free will, acausality, the measurement problem. The home page of that site attempts to define what I mean by "a truly free will".

• I imagine that not all math or science departments were always receptive to some of your directions of thought. Re contradictions, impossibilities: you wrote about manipulations that are impossible in 2-d but which are possible in 3-d and etc for higher dimensionalities; you state or imply that although there can be something impossible of even self-contradictory in our level of physical reality, perhaps it is not contradictory in the full reality, only in the limited perception of this 4-d spaceitme causal structure, or when our awareness is limited by it. My interests also transcended the confines of physics, and I stopped limiting my search for the Ultimate Truth to the notions accepted by physics. Perhaps you will be interested in some of what I wrote regarding "the conflict between religion & science", and the possibility of connecting to a "higher Mind" (Section not yet complete, being edited). You also wrote about 'meaning' and its origin; certainly if there is indeed synchronicity programmed into the universe, it would seems to imply that the Operating System of the unverse is more mind-like, and if the synchronous events are meaningful not just similar, then the 'meaning' seemingly has to be not just in our minds but in the system, so the 'universe' has meaning programmed into the laws of its operation etc, and perhaps just as there's a law of least action, and energy conservation etc, theres a law of maximal sophistication, and also of maximal meaning (in potentia)

• true creativity - if it really exists - goes beyond deterministic cause & effect. Mathematical "Platonists" seem comfortable with enfranchising a realm beyond that of the purely-mechanistic/materialistic, while remaining "rational", and Einstein spoke of a Mind whose existence one could somehow sense. So, can a human mind on occasion connect to some higher level and gain insight in an acausal manner? Wigner wrote about the unreasonable effectiveness of mathematics in describing the physical universe, and some math/physics geniuses seem to "intuit" new theories. It's certainly interesting that the universe seems to grant those with unusual physical intuition a hint at a new theory, eg Maxwell, Einstein & Dirac. I'm interested in all that, as well as a more prosaic equivalent, the ways in which there is a sort of nesting hierarchy, where high-symmetry solutions of a higher-level theory are surprisingly similar to sophisticated representations of the corresponding solutions of the lower-level theory they replaced (see my site's discussion of this in the context of "minimal coupling", and discussions by Bernard Schutz).