In order to conceptually bridge the Wigner MATH-PHYSICS GAP, it is helpful to see how deeply embedded quantitative and structural properties are in the physical world. The phase space approach is helpful, and a vid on how colliding blocks compute digits of pi (under ideal circumstances) will help. The vid:

It helps to look at some screenshots:

In this first shot (from a part 1 vid) we see a setup where we have a frictionless plane with a rigid wall to the left and two masses that collide. On the first hitting the second, it will hit and bounce back (elastically) from the wall. A second collision with the first block follows and rebound from the wall. This will continue until the second block cannot catch up with the first. Amazingly, depending on the mass ratio, the number of collisions between blocks or with the wall will give digits of pi.

Such suggests that there is a hidden circle, and there is, in an associated phase space — which allows us to see the dynamics from a geometric viewpoint in an associated abstract space:

Here, we see blocks moving so that kinetic energy and momentum are conserved. The circle shows constant kinetic energy and the zigzag jumps come from momentum conservation during collision — the vertical one being due to collisions with the wall of effectively infinite mass (rigidity). Due to collisions, they are switching directions and points on the circle on collisions. And, the angle at the centre will be twice that at the circumference standing on the same arc, here marking three successive collisions:

This continues until a critical value is left. It turns out, that this is when the arc-jump around the circle can no longer achieve a critical value:

The result of all this is that we move, depending on mass ratio, from 3 to 31 to 314 collisions and onward. Which computes pi’s digits.

Of course, we have idealised the system to be friction-free. (In the video, clacks are added as an audio effect, with energy conservation there would obviously be no noise.)

We see here how a physical situation (admittedly idealised) obeys laws of physics which were empirically discovered. These reveal a deeply embedded logic of structure and quantity manifest in phenomena of the world. Where, we may freely move to an abstract, phase space which allows further insight and analysis.

In this case, geometry counts.

Counts to the point that an idealised case would allow computation of digits of pi.

Of course, we could not actually build such a system, but the laws we infer from the observed world help us to form abstract model logic worlds that give us insights and which often help us to understand real world cases with friction etc.

Why all of this is possible is because the physical world is governed by logic of being constraints that are structural and quantitative. Laws, that turn out in aggregate to be fine tuned in ways that enable C-Chemistry, aqueous medium, cell based life. **END**

PS: Mobius strip cutting exercise:

Logic & First Principles 8: Bridging the Wigner MATH-PHYSICS GAP (with help from phase/ configuration/ state space)

Things like this make me look forward even more keenly to being able to question the designer.

F/N: Maybe I should add a note on kinetic energy i/l/o kinematics and some basic dynamics of force and work.

1: It is easy to see from uniformly accelerated motion:

v^2 = u^2 + 2*a*x,

2: So, rearranging:

v^2 – u^2 = 2*a*x,

1/2[v^2 – u^2] = a*x,

3: Where F = m*a (where m is constant) and increment of work, dW = F*dx, so too:

1/2*m*[v^2 – u^2] = m*a*x = F*x = W

–> Work done by F applied to a body is linked to change in a velocity-square term, so set u = 0:

1/2*m*v^2 = m*a*x = F*x = W

–> 1/2*m*v^2 or kinetic energy, is the net work done to give a body of mass m its velocity v, starting from rest and it is manifest also in the forced motion through relevant distance moved, x.

This gives some background to the OP.

It also helps us see why kinetic energy will be conserved in the idealised case, KE change comes from forces changing the speed of massive bodies. (BTW, this can be extended to rotational motion.)

KF

PS: Momentum conservation can be similarly analysed, given that empirically bodies interact in pairs, exerting equal magnitude, oppositely directed forces, where too momentum is in effect cumulative effect of force acting across time. So momentum change in body A of an interacting pair will be equal size but oppositely directed to that of body B. In the cases above, the rigid wall has effectively infinite mass and all momentum change is in the body that hits it. The two moving bodies interact in ways dependent on relative masses and velocities. All of this then has its dual in the phase space view.

I like applied math. 🙂

Actually, after watching further, I see that this is all pure math, using a theoretical model. Still neat, though.

It’s way beyond me. But, possibly, that is the point.

Ed, it’s a model of an idealized situation based on formulas that are known for the movement and energy of objects. It is all pure math.

What it doesn’t do is add to kf’s arguments. No one has disputed that math can, to varying degrees (sometimes to remarkable degrees), provide accurate models of things that actually happen in the physical world (although I think this particular situation would be hard to actually set up.) That was the whole point of Wigner’s essay on the Unreasonable Effectiveness of math, which I don’t think anyone has disputed.

But kf claims that pure math concepts exist outside of the individual minds which understand them, and use them, and that the pure math existed before (“antecedent to” is his phrase) the existence of the physical world. Examples like this one, or even examples where a mathematical model accurately describes actual events in the physical world, do not establish, with “demonstrable warrant”, his philosophical claims about abstract math concepts existing outside and prior to the physical world.

H,

we have here a case study on how an abstract, dual space that brings out the significance of major conservation laws is intimately involved in the framework of behaviour we see in the time-space domain; the embedding of key domains of structure and quantity in the logic of being in any possible world having already been demonstrated. Where, notice, Geometry in the abstract space is directly relevant to physical world behaviour — the breakout that allows a count of collisions depends on the double-angle circle theorem exhausts the circumference of a circle. Where, too, such domains in an auxiliary space that demark criteria for crucial behaviour changes are pivotal in other similar analyses. For material example, in the Laplace domain, poles drifting to the right half of the space imply instabilities, and as that threshold is approached, we see ringing behaviour etc. Which is related to the issue of being outside the unit circle in the Z-transform domain.

This case study also continues the exploration of how abstract, logic-model possible worlds draw out entities, relationships, structures and quantities which then provide bridging archetypes for the physical world — hence ways in which we can better understand through case studies how the Wigner Math-Physics gap is bridged.

All, in a context of exploring logic and first principles of thought of interest to design theory and wider thinking on serious matters; thought which would not normally be controversial but for the sort of ideologies on the loose in our day. In that explicit context of logic and first principles, the OP introduces a key analytical tool, phase or state or configuration space, which is of great value for itself and which is an extension of how logic — rational principles — of structure and quantity are key to the reasoning process we undertake in addressing scientific and other important matters.

It specifically serves as a case study that sets the context in which we can see how energy and mass conservation laws lie implicit in the logic of force-based interaction of bodies acting in space and time — a big result in its own right, and one that in my view should be better brought out in early exposure to physics.

This example of a dual, abstract domain and its relevance is also significant as opening the way for consideration of other cases of state/ phase/ configuration spaces and similar uses of abstract domains such as Fourier, Laplace and Z transforms.

KF

PS: The case study also puts on the table two out of three crucial conservation laws and how they arise: momentum, energy and angular momentum (an extension of conservation of momentum through the analogy of translational and rotational motion). This in turn highlights the physical significance of an abstract, structurally embedded quantity or three. That is already an embedded abstraction — conservation laws — that mark major cross-cutting and unifying/bridging themes in Physics. It also puts on the table the significance of three linked abstracta: momentum, angular momentum and energy. Where, too, we see the embedding of a core calculus concept (and fundamental theorem), as momentum is the cumulative effect of force is time, and kinetic energy is the cumulative effect of force in space — rates and accumulations being key abstracta that thanks to hyperreals and nonstandard analysis, bring back infinitesimals. Angular momentum, per the analogy, is the cumulative effect of torque in time. Where, too inertial quantities play a regulatory role on rates of accumulation. This points to the interesting questions as to what mass, moment of inertia, momentum and energy are. Let Wikipedia speak as a witness testifying against known ideological interest:

Notice, how the operational definition on the unit of energy gives a big clue on its abstract nature.

PPS: Notice, now that our eyes are sensitised, how Wiki similarly speaks about momentum:

In this context, the intimate fusing of abstracta of structure and quantity and concrete manifestations in space and time is patent.

F/N: I should speak to potential energy, that which is locked into position (in a force field) or state — chemical, nuclear — etc.

In this case, consider an old fashioned cannon, elevated at an angle.

First, in vacuo — a simple ideal case. Fire a ball, and away it goes, projected with initial velocity [muzzle velocity], with mass, at an angle. A simple analysis will see its velocity breaks into vertical and horizontal components. The latter, leads to steady horizontal speed. The former undergoes uniform gravitationally induced acceleration downwards, leading to climbing to a peak and descending symmetrically again.

This shows how the initial KE of vertical motion is converted gradually — at the rate that follows from PE = m*g*h — into positional energy in the gravity field and then returns to KE under conservation of energy. Rich onward aspects lurk, including how a gravity potential well marks a warping of the spacetime fabric due to mass. The result of the two is that the projectile follows a parabola, and in many cases where air resistance is not material, that can be seen pretty directly. A parabola of course being one of the five conic sections.

(I used to look at such using conically tapered drinking glasses: circles, ellipses, parabolas, hyperbolas. Straight lines are trivial. Also note, “orbital” paths for objects in a gravity well follow conic sections (unless perturbed, which then leads on to butterfly effects and chaos!)

Coming back, we can consider air resistance (an example of taking an ideal model and bringing in further factors to more accurately address complexities of cases) and how it affects the components, leading to complex ballistics models, which bleed over into modelling flight (often, by way of rockets and guided missiles these days). And of course, we see more and more structural and quantitative abstracta embedded in physical reality.

Going back to PE, capillarity provides a striking case study which I originally encountered by accident. For some reason I now forget, I was using two optical glass blocks sitting in water tinted with ink, to illustrate the effect. Somehow, I set the blocks in a narrow, v-shaped wedge. Instantly, the liquid that had been pulled up above the surface ran up into a sharply defined, instantly recognised hyperbola.

Why?

I went to the board and did a live modelling exercise. We know, liquid molecules wet glass showing adhesion, and they stick together [balanced by intermolecular repulsion that sharply rises as they are compressed and molecular electron clouds begin to overlap]. So, consider that the surface adhesion at the meniscus is lifting an entrained column of liquid through h consistent with force balance, F_adh = – mgh. So, now, consider an increment dx along the blocks of width z is lifted to h, where dx * z*h is the lifted volume, of mass density * lifted volume. At this level, in effect this is a tiny rectangular prism. It soon drops out that h is inversely proportional to x, length along the face of the block from the apex of the V.

A striking case that brings together infinitesimals, structural and quantitative constraints and more, yielding to close approximation a well recognised mathematical result. (I soon realised that if done carefully, the curve would remain on separation and could be transferred to a paper.)

I of course then routinely used this case in further classes.

Again, we see how anstracta of structure and quantity are deeply embedded in the fabric of the world.

KF

PS: I recall, too, exercises of gluing together a Mobius strip and cutting around the loop then cutting again: double length strip then two interlocked circles. (See vid here, with bonus on cutting at the 1/3 width point: https://www.youtube.com/watch?v=XlQOipIVFPk and the two-cut discussion here: https://www.wikihow.com/Explore-a-Mobius-Strip then that which is here: http://www.exo.net/~pauld/acti.....ction.html see actual video here https://www.youtube.com/watch?v=f-19NLKxNUc ) Likewise, that cutting out a circle then folding over a sector or cutting it out will then lead to forming a right circular cone. An astonishing spatial transformation almost as impressive as the strip, if you think about it. I have already talked about doing a string and half-circle exercise — pinning threads to the ends of the diameter and along the arc that brings out circle theorem and pythagorean spatial properties. Maybe, I should add, build the squares on the sides and see how the theorem works. Toss in the Euler identity 0 = 1 + e^i*pi for good measure. Space inextricably embeds in itself deep abstract structures and quantities.

F/N2: My objective here is to hammer home through accessible and undeniably relevant case studies just how pervasively the Wigner Math-Physics gap is bridged. Understanding deep in our bones through seeing a pervasive pattern is necessary to break the spells of Kantian ugly gaps and associated subjectivism, relativism and nominalism. That’s what will have to be done to rescue Math, Physics, logic and understanding of being from what we have been seeing for weeks. We have been bewitched. KF

PS: I added a Mobius strip cutting exercise to the OP — simple case.

hazel:

What? ID says the Intelligent Design was from a Mind. And if math was used to design the physical world then it is obvious that the Designing Mind understood them.

That Intelligent Designer, again.

Except it is not a philosophical claim.

ET (attn H):

First, the warrant laid out in the other thread, which pivots on the inescapably true principle of distinct identity as a core premise of being and on the linked premise that if two things W1 and W2 are indistinguishable they are merely labels for the same entity W, thence what the implications for a world-distinctive A are, not assumptions or assertions about minds — this is an argument to necessary abstract entities embedded in the fabric of any distinct world . . . thus that certain quantities and structures are substantially present once any world is:

To date, no-one has provided a counter-demonstration. Where, to deny LOI and its immediate corollaries is intellectually immediately absurd.

Next, the above case studies demonstrate facts of discovery that in this world where Newtonian dynamics have a realm of validity, we can see that in fact we discover many embedded abstract quantities and structures. The case on number of collisions showing successive digits of pi turns on influences of energy and momentum conservation which are observable and mathematically demonstrable on pondering cumulative effects of forces [pushes or pulls — already, vectors] across space and time. In turn, that brings to bear infinitesimals and the key operations of calculus, rates and accumulations. Energy is abstract as is momentum, force by contrast is tangible. Further, its phase space shows how geometric abstract considerations on conservation of kinetic energy and momentum (already abstracta) lead to a geometric pattern that produces the result. Going to projectiles we see vector components and different force effects thus dynamics of projectile motion. The case of the capilliarity between wedged glass blocks producing a hyperbola shows calculus again and patently direct embedding of quantities and structures. The semi-circle and string thought exercise would show embedding of abstract geometrical structures and patterns in space. The Mobius strip, spectacularly so.

These things are manifesting such properties in contexts that are not merely conceptual, they are concretely physical.

And we could continue.

KF

Hazel objects that KF’s model is an ‘idealized situation’ that is ‘pure math’. Hazel further objects that “Examples like this one, or even examples where a mathematical model accurately describes actual events in the physical world, do not establish, with “demonstrable warrant”, his philosophical claims about abstract math concepts existing outside and prior to the physical world.”

Basically Hazel is arguing that the applicability of mathematics to the physical world, no matter how uncanny and accurate it may be, is just a ‘happy coincidence’ that needs no further explanation. Hazel is hardly the first of the atheistic persuasion to do so. Rosenberg did so in his debate against Dr. Craig.

And while I agree with Hazel overall sentiment that abstract mathematical objects, being causally inert as they are, do not exist independently, all by their lonesome, ‘outside and prior to’ the physical world, but are dependent on the Mind of God in order to ‘breathe fire into the equations’,,,

,,, While I agree with that overall sentiment of Hazel’s, I certainly disagree with her overall atheistic sentiment that the uncanny correspondence is just a ‘happy coincidence’.

Besides Wigner, Einstein himself also rejected the notion that the applicability of mathematics to the physical world is ‘just’ a ‘happy coincidence’ but also regarded the uncanny correspondence between math and the physical world to be a ‘miracle’.

And again, to repeat Wigner’s original ‘miracle’ quotes,,,

Amazingly, in the original Wigner thread Hazel tried to claim that “I can’t find anything about Wigner attributing the unreasonable effectiveness of math to God.”

To which I had to remind her exactly what the definition of a miracle actually is:

Also in the original Wigner thread I noted that Darwinian evolution, based on materialism as it is, denies the reality of anything beyond the the physical world. This denial extends to the timeless immaterial ‘Platonic’ world of mathematics.

And as was further pointed out in that thread, Darwinian materialists, although they deny that anything beyond the material realm exists, need this transcendent world of mathematics in order for their theory to even be considered scientific in the first place. The predicament that Darwinists find themselves in regards to denying the reality of this transcendent, immaterial, world of mathematics, and yet needing validation from this transcendent, immaterial, world of mathematics in order to be considered scientific, should be the very definition of a scientifically self-refuting theory.

But it is hardly surprising that Darwinists ignore the fact that their materialistic theory, which denies the reality of the immaterial realm altogether, is dependent on this immaterial realm of mathematics in order to be considered scientific in the first place, Darwinists have a long history of ignoring the fact that their theory has been shown to be mathematically impossible by many different methods.

Which is again proof that, when it comes to Darwinian evolution, we are basically dealing with a unfalsifiable pseudo-scientific religion for atheists, rather than dealing with any mathematically well defined and rigorous theory of science that can be ‘potentially’ falsified by empirical testing:

Hazel went further than just saying that KF’s model was an ‘idealized situation’ that neglected friction, (the second law and such as that), but Hazel also further claimed that even if ‘a mathematical model accurately describes actual events in the physical world’, that still would ‘not establish, with “demonstrable warrant”, his (KF’s) philosophical claims about abstract math concepts existing outside and prior to the physical world.”

Hazel’s use of the term ‘idealized situation’ gives her hand away. If she rejects KF’s model because it is an ‘idealized situation’ that only exists in the mind of man and not in the physical world, then she should accept the fact that when a mathematical model is found to ‘accurately describe’ that “idealized situation” of math within the physical world, with no discrepancies, then by all rights she should accept that that “idealized situation” of math and the physical world is the product of an ‘Idea’ that originates in the Mind of God, not by some unfathomable physical process.

Hazel, inadvertently and unavoidably, with her use of the term ‘idealized situation’ revealed her philosophical bias against God when that ‘idealized situation’ of math is actually reached in the physical world.

Moreover, science has a long history of looking for ‘platonic perfection’ in the physical world and assuming the Mind of God to be behind that ‘platonic perfection’.

Copernicus, (who was heavily influenced by Platonic thinking), imagined (incorrectly) that the planets move in perfect circles (rather than ellipses). Later, Newton, for allowing God could adjust the orbits of the planets, was chastised by Leibniz, (and Laplace) for having a “very narrow ideas about the wisdom and the power of God.”.. i.e. For having a narrow view of the perfection of God.

In fact, Laplace, contrary to atheistic folklore, cited with approval Leibniz’s criticism of Newton’s invocation of divine intervention to restore order to the Solar System: “This is to have very narrow ideas about the wisdom and the power of God.”, to them, it would count as evidence against intelligent design if God had to intervene to prevent the solar system from collapsing. So intelligent design could just as easily be a motivation to prove the stability of the solar system.

Even according to wikipedia (hardly an ID friendly website), Laplace paraphrase is shown to be based on folklore not on fact,

Moreover, contrary to what is commonly believed, Laplace did not really solve the problem of planetary perturbations in the end, (he only solved for for first degree approximations), but Haret showed that orbits are not absolutely stable using third degree approximations.

Moreover, I hold that if Newton and Leibniz (and even Laplace) could see our science today they would be very pleased by what modern science has now revealed about the wisdom and power of God in solving the problem of ‘perturbations’:

Since Albert Einstein’s General Relativity equation reduces the chances to just 1%, and since KF referenced pi in his OP, it is interesting to note that pi is integral to Einstein’s General Relativity equation:

Since science has a long history of looking for the ‘idealized situation’ of ‘platonic perfection’, and since KF referenced pi in his OP, it is interesting to note where in this universe ‘platonic perfection’ for spheres is approached rather closely,,,

The delicate balance at which carbon is synthesized in stars is truly a work of art.,,, Years after Sir Fred discovered the stunning precision with which carbon is synthesized in stars he stated this:

And ‘platonic perfection’ for a sphere is also approached rather closely in the Cosmic Background Radiation (CBR). ,,, Of the supposed “imperfections” in the sphere of the CBR, the following author comments, “the discovery of small deviations from smoothness (anisotopies) in the cosmic microwave background is welcome, for it provides at least the possibility for the seeds around which structure formed in the later Universe”

And indeed, these imperfections in the the sphere of the CMBR, (which ‘provides at least the possibility for the seeds around which structure formed in the later Universe’), ‘surprising’ line up with the earth, and thus overturns the Copernican principle by showing the earth has a ‘privileged position’ in this universe. This fact is touched upon in further detail in the following post:

The one exception to this rule of ‘no platonic perfection’ for 3-D Euclidean objects within this universe is the axiomatic ‘primitive object’ in Euclidean geometry of the line.

That is to say, the place where “platonic perfection” is, not only approached, but, (as far as our best scientific measurements will allow us to see), ‘perfectly reached’ in the universe, is for the ‘flatness’ of the universe.

Moreover, this ‘insane coincidence’ of ‘platonic perfection’ being reached for the axiomatic ‘primitive object’ of the line just so happens to be necessary for us to even be able to practice math and science, (and apply technology in our world), in the first place:

Simply put, if the universe were not ‘ever-so-boringly’ flat (and if the universal constants were not also ‘ever-so-boringly’ constant), but the universe were instead governed by randomness, as atheists presuppose, or governed by some other of the infinitude of ‘platonic topologies’ that were possible, modern science and technology would have never gotten off the ground here on earth.

Nor, if platonic perfection were not present for the flatness of the universe would we have eventually been able to deduce the ‘platonic perfection’ that is revealed in the ‘higher dimensional’ mathematics that lay behind Relativity and Quantum Mechanics.

Simply put, no experimental test to date has ever been able to detect any ‘imperfection’ for what the “platonically perfect’ theories of Special Relativity, General Relativity, Quantum-Electrodynamics, and Quantum Mechanics predict.

To give a glimpse of just how insanely precise the measurement of 120 standard deviations is for Leggett’s Inequality in Quantum Mechanics,,,

And again, as far as our best scientific instruments will allow us to measure, we can find no deviation whatsoever from what the ‘platonically perfect’ mathematical theories of Special Relativity, General Relativity, Quantum-Electrodynamics, and Quantum Mechanics predict.

In regards to the ‘platonic perfection’ revealed by Quantum Mechanics in particular, Heisenberg stated,,,

In regards to further establishing that the Mind of God is behind the insanely precise 120 standard deviation ‘platonic perfection’ of Quantum Mechanics, it is interesting to note Quantum Mechanics is more foundational to our description of reality than either Special Relativity and General Relativity are.

As Vlatko Vedral states, “space and time are two of the most fundamental classical concepts, but according to quantum mechanics they are secondary.,,, We must explain space and time (4D space-time) as somehow emerging from fundamentally spaceless and timeless physics.”

And indeed, to further back of the claim that the Mind of God is behind the ‘platonic perfection’ of Quantum Mechanics, ‘the experience of the now’, which is a defining attribute of the immaterial mind, (and which corresponds to to the ‘timelessness’ of the platonic realm), is found to have a consistent correspondence to quantum mechanics no matter how we might choose to perform our measurements in Quantum Mechanics:

As Professor Scott Aaronson quipped, “Look, we all have fun ridiculing the creationists,,, But if we accept the usual picture of quantum mechanics, then in a certain sense the situation is far worse: the world (as you experience it) might as well not have existed 10^-43 seconds ago!”

And to further back up the claim that the Mind of God is behind the insanely precise 120 standard deviation ‘platonic perfection’ of Quantum Mechanics, the quantum wave, prior to measurement, is mathematically defined as being in a ‘infinite dimensional-infinite information’ state,

Simply put, in order to adequately explain quantum wave collapse we must postulate something with the causal sufficiency within itself in order to explain the ‘effect’ of the ‘infinite dimensional-infinite information’ quantum wave state collapsing to a single bit of information. In other words, we must postulate the omnipresent and omniscient Mind of God in order to explain why the ‘infinite dimensional-infinite information’ quantum wave state collapses to a single bit of information.

Moreover, with the refutation of hidden variables, there is no cause that materialists can possibly appeal to in order to ‘explain away’ this ‘timeless activity’ that is constantly witnessed in quantum mechanics. As the following article states, “Our result gives weight to the idea that quantum correlations somehow arise from outside spacetime, in the sense that no story in space and time can describe them,”

Whereas, on the other hand, I, as a Christian, have a beyond space and time cause that I can readily appeal to in order to explain the timeless effects of quantum mechanics:

Thus in conclusion, the ‘idealized situation’ of platonic perfection is reached to its highest ‘insane’ degree in quantum mechanics, and this ‘idealized situation’ of platonic perfection being reached in Quantum Mechanics gives every indication of being reached by none other than the infinite Mind of God. There simply is no other postulated cause by atheists that is remotely capable of explaining what we see in Quantum Mechanics (which is, by far, our most accurate and foundational mathematical model of reality).

Supplemental note:

kf, you are wasting your time posting all these examples. We all know that math can describe the world, and that modeling relationships between pure math and actual events in the physical world exist, and that there is a mystery, in Wigner’s words, as to the unreasonable effectiveness of this relationship.

The

onlyissue that I am addressing is your claim that the abstractions which exist in our minds as parts of pure math areembeddedin the physical world. I am claiming that another way to look at it is that the physical world contains physical things which behave in certain ways that can be described by our mathematical abstractions, but those abstractions don’t themselves exist in the physical world.This is a philosophical point of view, and your position is also. Your Platonic premise that the abstractions exist antecedent to the physical world, are embedded in it, and constrain it may be true, but it is not demonstrably true. Other premises lead to different conclusions, and may also be true. The history of philosophy shows clearly that there is no definitive way to resolve this issue.

So no further amount of examples of neat math and neat examples in the physical world will add any more weight to your perspective.

Bornagain writes,

That is not what I think. Please don’t put words in my mouth.

hazel- then correct bornagain77 instead of just denying what he said. That would go a long way to support your claim of “That is not what I think.”

If not a “happy coincidence”, then what (if math was invented by us)?

If you have something other than the infinite Mind of God that can ground ‘platonically perfect’ mathematics, then by all means clearly lay it out. Please do be explicit in your definitions and don’t hide in a haze Hazel.

My case for the infinite Mind of God grounding mathematics is laid out in posts 13-17, and is certainly clear for all fair minded readers to see.

Folks, let us go get some paper, glue or tape and scissors, or at least watch the Mobius strip in action. If that does not demonstrate to our satisfaction how structure and quantity are embedded in space and figures in space, nothing will. And further to all this if Matrhematical, logical and directly observable empirical demonstrations meet with such a wall of objections on what should not be controversial, then that tells us utter volumes on why evidence of signs of design meet with similar walls of unyielding objection. The time has come to stand non our epistemic rights, pointing to how insistent objectors are utterly unresponsive to essentially any degree of warrant so they have locked themselves out of the circle of evidence-responsive discussion.. KF

kf writes,

So be it: I stand “locked out”. 🙂

H, that is truly sad. I simply ask you to set up two Mobius strips and an ordinary loop of paper then proceed to cut one strip and the loop in half, going around the loop. Then, cut the other M-strip at the 1/3 across point. For the first M-strip, cut it in the middle a second time. Ponder on how the results are plainly independent of what you or any other human being cares to think, but are readily confirmed by doing the experiment oneself. Then, please think again on whether rationally intelligible properties of structure and quantity are or are not to be found in space and in bodies in space, embedded in ways that must go to the roots of reality. KF

I know how Mobius strips work, kf.

H, then you have the evidence figuratively in hand. If that does not make it patent to you that structural, quantitative, rationally intelligible properties are embedded in space and in bodies in space, independent of our views, perceptions, claims or arguments, then no degree of warrant will. KF

It’s the ” properties are embedded” part that I am arguing against as certain. You don’t seem to be able to sort out what we do and don’t agree about.

hazel:

Denying isn’t arguing.

If not a “happy coincidence”, then what (if math was invented by us)? What is your positive case and supporting evidence?

H, start by taking a sheet of paper, loop with a twist and cut around the loop in the middle. Set up a second, and cut at 1/3 width. Notice the difference. I think the structural and quantitative properties revealed cannot be in our minds, it is paper in our hands here. Paper, in space, with certain form factor. Other than when the paper is arranged in space in this way, it will not behave like that. Space, an aspect of our world, has properties in it — embedded if you will — that manifest in this way, exhibiting structural and quantitative features. This is an empirical demonstration and on a scale that makes it a property of a 3-d spatial domain; here manifest to moral certainty (what empirical observation delivers). Similarly, the distinctness for any particular possible world entails the natural numbers as embedded, with further things associated. Whether you agree or object is at this point immaterial, as you have no warrant to the contrary. Especially when the root premises are inescapable first principles such as distinct identity. KF

PS: Should I note that two properties, permeability and permitivity of free space were measured and then were found working together as a wave velocity suspiciously close to the speed of light.

The following observation is found in Omne’s book Quantum Philosophy.

Assuming that mathematics is a by-product of human evolution gives a circular argument, that goes like this:

1) Humans evolve mathematical ability over time. We invent ever deeper math structures and objects to explain natural phenomena.

2) During the 20th century we learn about Hilbert spaces (the math underlying quantum physics).

3) We find that all matter obeys the mathematical laws of quantum mechanics, including our own brains!

4) So the abstract math we “invent” to study the world already exists in the subatomic structure of the (supposedly solely material) brains that are doing the “inventing”!

MG, I think I am reduced to pondering peculiarities of paper loops and cutting along the loop [having given several less direct illustrative cases]. Where, a twist and whether you cut centrally or close enough to one side can make a big difference. Last I checked, paper loops, a pair of scissors and a spot of glue or tape were not figments of anyone’s imagination, nor are their properties sensitive to our axiomatisations, philosophies, contemplations, etc. We are talking about bodies in space with the interesting result of having one surface due to the twist. So far as I can see, the Mobius strip is a direct demonstration of embedded structural and quantitative phenomena in our world, here tied to space and to bodies in space. With that in hand, we can go back and re-think, seeing how certain core math facts, properties, entities lock into the distinct identity needed to set up any particular possible world, and how many consequences flow from that. KF

Math Guy your post on the circular argument that is found within quantum mechanics when holding that mathematics is ‘merely’ a by-product of human evolution, reminded me of this article by Steven Weinberg entitled “The Trouble with Quantum Mechanics” in which he stated,

“the instrumentalist approach turns its back on a vision that became possible after Darwin, of a world governed by impersonal physical laws that control human behavior along with everything else. It is not that we object to thinking about humans. Rather, we want to understand the relation of humans to nature, not just assuming the character of this relation by incorporating it in what we suppose are nature’s fundamental laws, but rather by deduction from laws that make no explicit reference to humans.”This is simply devastating to the atheistic worldview on so many levels.

Steven Weinberg, an atheist, rejected the instrumentalist approach in quantum mechanics precisely because it undermines the Darwinian worldview from within since “humans are brought into the laws of nature at the most fundamental level”. But, regardless of Weinberg’s a-priori atheistic bias against the reality of Agent causality and/or free will within quantum mechanics, the ‘free will loophole’ has now been, for all practical purposes, experimentally closed.

That is to say that advances in quantum mechanics itself now demands that agent causality and/or free will be let into physics.

In regards to the Kochen-Speckter Theorem we find, as leading experimental physicist Anton Zeilinger states in the following video, what we perceive as reality now depends on our earlier decision what to measure. Which is a very, very, deep message about the nature of reality and our part in the whole universe. We are not just passive observers.”

And with contextuality we find, “In the quantum world, the property that you discover through measurement is not the property that the system actually had prior to the measurement process. What you observe necessarily depends on how you carried out the observation” and “Measurement outcomes depend on all the other measurements that are performed – the full context of the experiment. Contextuality means that quantum measurements can not be thought of as simply revealing some pre-existing properties of the system under study. ”

Moreover, the final ‘free will’ loophole in quantum mechanics has now been closed. As the following article states, the “creepy” and “far-fetched” possibility that the “physicist running the experiment does not have complete free will in choosing each detector’s setting” and that “a particle detector’s settings may “conspire” with events in the shared causal past of the detectors themselves to determine which properties of the particle to measure”,,,

,,, that “creepy” and “far-fetched” possibility, (which is exactly the “creepy” and “far-fetched” possibility that atheists hold to be true), has now been, for all practical purposes, closed.

Anton Zeilinger and company have now pushed the “free-will loophole” back to 7.8 billion years ago using quasars to determine measurement settings.

Moreover, here is another recent interesting experiment by Anton Zeilinger, (and about 70 other researchers), that insured the complete independence of measurement settings in a Bell test from the free will choices of 100,000 human participants instead of having a physical randomizer determine measurement settings.

Again, this is devastating to the atheistic worldview on so many levels.

Bringing humans “into the laws of nature at the most fundamental level” has some fairly profound implications. First, by allowing Agent Causality of God (and ourselves) back into the picture of modern physics, as quantum physics itself now demands, and as the Christian founders of modern physics originally envisioned, (Sir Isaac Newton, James Clerk Maxwell, Michael Faraday, and Max Planck, to name a few), then a empirically backed reconciliation, (via the Shroud of Turin), between Quantum Mechanics and General Relativity, i.e. the ‘Theory of Everything’, readily pops out for us in Christ’s resurrection from the dead.

And secondly, besides the reality of ‘free will’ and/or Agent causality within quantum theory bringing that rather startling solution to the much sought after ‘theory of everything’, there is also another fairly drastic implication for individual people being “brought into the laws of nature at the most fundamental level’ (S. Weinberg)” as well. Although free will is often thought of as allowing someone to choose between a veritable infinity of options, in a theistic view of reality that veritable infinity of options all boils down to just two options. Eternal life, (infinity if you will), with God, or Eternal life, (infinity again if you will), without God.

And exactly as would be a priori expected on the Christian view of reality, we find two very different eternities in reality. An ‘infinitely destructive’ eternity associated with General Relativity and a extremely orderly eternity associated with Special Relativity:

Verses: