What is the Point of Reality? by Doug Bundy

Dear Eckard,

You wrote: "Thank you for your hint to John Baez. Unfortunately, he is an overly prolific interpreter of sometimes rather unrealistic mathematics in terms of physics, and I did not yet find his "clarification" you are alluding to. Hopefully someone else can give me a clue. Is a Baez always correct?"

Most of the things he writes about, I can't understand anyway, but he has a fascination with Octonions, and that got my interest. I believe that the ad hoc invention of imaginary numbers in algebra, while useful in some ways, is counter-productive in the end, as particle theorists found out in SU3 studies, but, what I like to call the tetraktys, the binomial expansion, up to dimension 3, is key to understanding a true R3. Among other things, it has an inverse!

You wrote: "When you compared my essay with a whirlwind tour in a museum, I sadly did not reach you. I tried to investigate where mathematics started to become arbitrarily rather than logically founded."

Please don't misunderstand me. I did not mean your essay was museum-like. I meant that my reading of it was tour-like. My daughter is having her baby today and that's just one of many pressing things I have to attend to, which doesn't leave me enough time to study your essay, but I will! I read the two Joyce documents and can hardly wait to comment further.

You wrote: "I am not surprised that even the very cautiously thinking Ian Durham in his new essay ignored the possibility of mistakes when he wrote: "... while results from ... WMAP have demonstrated that the geometry of the universe must be flat ...and thus 'Eucildean,' we of course have long known that it is locally curved.""

In the new physical system of theory that I advocate, the major assumption is a space/time progression, but it included the assumption that the universe was flat and I had to defend that assumption vigorously. The WMAP news was very welcome on that score.

You wrote: "What about your multidimensional small-signal numbers I recall a Dutch outsider who seems to be close to your approach. I got aware of him when he was quoted from a participant of a previous FQXi contest. I also vaguely remember of a peculiarity in theory of acoustics waves: Solutions for even spatial dimensions (0, 2) behave differently from those for odd (1, 3) spatial dimensions. Did you know that?"

No, I do not know about that. I also don't know of the Dutch outsider you refer to.

I have to run now, but I will be back tomorrow. I just wanted to tell you how much I appreciate your knowledge of things and your belief and attitude toward things fundamental. I support your insistence on re-instating Euclid's view of number as measure and Peirce's view of the continuum as infinitely divisible, full heartedly.

Regards,

Doug

The above anonymous post is from me, in case it's not obvious. I forgot to log in, before posting it.

This info was posted in a thread earlier, but people had a hard time finding it, so I am re-posting it here:

A lot of the essays in this contest have to do with the issue of mathematics versus reality. While numbers can be used to count things, they are not those things, but I'm not sure why it's important to make that obvious distinction. I don't recall that it was ever a big issue in geometry.

In my case, what is being counted are units of space and time. The 3D expansion of space upon which it is based is an observed physical phenomenon. The operational interpretation of the mathematical expression s3/t = 23/1 describes how many measures of space per measure of time are generated from a given point, as the progression continues. Thus, after n linear measures of time pass, (n*2)3 volume measures are generated, giving us the mathematical progression, 8, 64, 216, 512, ... quantitatively, corresponding to the linear march of time, 1, 2, 3, 4, ....

Geometrically, the time units are constructed as the radius of the inner circle of figure 1 in my essay (considering only one of the two constructions there). The volume units are the volume of the 2x2x2 stack of 8 one-unit cubes, which grows to a 4x4x4 stack of 64 one-unit cubes, a 6x6x6 stack of 216 one-unit cubes, an 8x8x8 stack of 512 one-unit cubes, and so on, ad infinitum, as time marches on.

Admittedly, these discrete volume units in the progression correspond to nothing real, since space doesn't expand outward cubically, in only eight "directions," but outward radially, in an infinite number of directions. However, the inner and outer radial volumes are determined by the 3D stack of one-unit cubes and the ratio of their volumes is equal to R3, where R = 21/2. Hence, the progression of the ratio of the two volumes of the expanding spheres (technically balls) is, (n*21/2)3, or 81/2, 5121/2, 58321/2, 327681/2..., as time marches on.

It may not appear at first that these numbers correspond to anything real, but the fact that their squares are integers, and very familiar integers at that, indicates otherwise. Indeed, when we look at the ratio of the surface areas of the spheres, the formula for the progression of which is (n*R)2, the numbers are very curious: (1*21/2)2 = 2, (2*21/2)2 = 8, (3*22)2 = 18, (4*21/2)2 = 32.

These are the numbers of elements in the half-periods of the periodic table, something we might be tempted to dismiss as conincidental, smacking of numerology, if it weren't for the fact that Le Cornec has made what C.K. Whitney calls "a stunning demonstration:" Le Cornec discovered a previously un-noted pattern underlying all ionization potential data: the square roots of all ionization orders, when plotted as a function of atomic number Z, lie on a straight line. (See Whitney's "Relativistic Dynamics in Basic Chemistry")

That the IPs are something real is undeniable, but that their order appears closely related to a natural numerical progression is astonishing, in my view.

More on this later.

The feedback I'm getting privately indicates that people do not understand the concept illustrated in figure 1 of my essay, in several respects. Given the constraints of the contest rules, I found it very difficult to include all the explanatory detail I would have liked to have included.

One of the difficulties has to do with background. There is no background. There are two, reciprocal aspects of one component, motion, which are 3D space and 3D time, but since time has no direction in space, and space has no direction in time, one of the reciprocal aspects of motion is always zero-dimensional.

However, just as, strictly speaking, natural numbers and energy are zero-dimensional measures, and, to be useful, they have to be regarded as one-dimensional, so also the 0D aspect of motion has to be one-dimensional.

In the case of numbers, any number raised to the zero power, n0, is equal to 1, because any number divided by itself is equal to 1, by virtue of the law of exponents. Hence, n/n is actually n1/n1 = n(1-1) = n0.

In the case of energy, any magnitude that does work has to be one-dimensional, because magnitudes that have no direction are scalar (i.e. 0D), while magnitudes with direction are vectorial (i.e. 1D). Energy per se is scalar. It has no specific direction in space, but in its form as work, it must have direction, and therefore it is regarded as a one-dimensional quantity.

In the geometric constructions of figure 1 in my essay, we see the discrete (digital) and the continuous (analog) expansion of 3D space (or 3D time), after one unit of 0D time (or 0D space) has elapsed. Though the 0D time (space) aspect of the expansion cannot be represented geometrically in any direct fashion, the 1D radius of the inner circle is equal to the time duration, in the same sense that a time line on a space and time graph, or the 1D sweep of an oscilloscope, represents a duration of time.

With this much understood, the radii of the inner circles are 1D representations of the 0D time (space) of the expansion. Now, the digital and analog representations of the two, inverse, expansions in the figure, each contain the 1D, 2D and 3D components. The digital representations are contained in the 2x2x2 stack of one-unit cubes, while the analog representations are contained in the ratio of the two balls that are determined by the stack of cubes.

In the digital case, the 1D magnitude is the width (or the height, or the depth) of the stack, while the 2D magnitude is one of the faces of the stack, and the 3D magnitude is the volume of the stack.

In the corresponding analog case, the 1D magnitude is the ratio of ball diameters, the 2D magnitude is the ratio of the spherical surfaces (or else the cross-sections of the balls), and the 3D magnitude is the ratio of the volumes of the balls.

The reason that the analog magnitudes are taken as the ratio of the two balls is because the magnitudes of the inner ball are necessarily less than the magnitudes of the stack, while the magnitudes of the outer ball are necessarily greater than the magnitudes of the stack. It turns out, however, that their ratios are integers and square roots of integers, which means that the digital magnitudes can be directly related to the analog magnitudes, not just approximated!

As the expansion continues beyond the one unit elapsed time stage, the digital and analog magnitudes follow their respective geometric progressions, part of which is explained in the previous post above. The key point is that these units can be arranged in the customary mathematical forms called groups. The usual 1D digital groups of integers and rational numbers apply, plus a new group with the square root of 2 as the 1D unit, instead of the number 1 as the 1D unit, applies.

However, this new group contains 2D and 3D elements as well as 1D elements, which provides for 1D, 2D and 3D scalar algebras called division algebras, which have all the properties an algebra needs to have to be used in physics.

Ultimately, this means that the 3D oscillations of these units, and their mathematical combinations and relations between their combinations, can be used as building blocks, called preons, to build the particles of the standard model of physics, at least in part. The hope is that the entire model will eventually emerge, including gravity. If this turns out as hoped, it will be very strong evidence that the physical universe consists of one component, motion, existing in three dimensions, in discrete units, with two reciprocal aspects, space and time.

I hope this helps.

I've been asked to provide a graphic depicting what I mean by the "common origin" of the 3D oscillation. Here is the best I can do for now:

3D Oscillation

I'll try to improve it when I get time, but it should be good enough to convey what is meant by the common origin of the two, reciprocal, volumes that define a true point of no spatial extent and no duration.

BTW one cycle of this motion is equivalent to 4pi rotation (something inexplicable until now.

Thanks Eckard,

I'll check out the book. I'm familiar a little bit with Miles. He's a prolific writer. I don't think Oostdijk is an alias, but could be. You never know.

In the earlier drafts of my essay, I included a chart that showed how one cycle of the 3D oscillation is equivalent to a 4pi rotation, but I had to take it out to fit the essay into the contest space requirements.

I have posted an updated copy of the essay on my website that includes the chart here.

As far as I know, this is the first time the physical and mathematical explanation of how one cycle of oscillation "around" a point of no extent can be 4pi has been given. Bruce Schumm wrote "...a particle of no extent shouldn't possess angular momentum, and the axis about which it spins shouldn't have to be rotated through 720 degrees to return the particle to its original state. We don't really have a clue about the physical origin of [quantum] spin. To describe [quantum] spin as 'intrinsic angular momentum' is like your best buddy describing how your car's differential works by explaining 'that it employs mechanical linkage;' The only useful information contained in this statement is that its author probably knows next to nothing about how a differential actually works."

Of course, I'm not saying that, because the 3D space/time oscillation is equivalent to one cycle of 4pi rotation, it is a photon or it is an electron. It's a bit more complicated than that, but what I am saying is that the physical basis for what appears to be 4pi rotation is found in the 3D space/time oscillation. To see how this concept can be employed in a preon theory of the standard model of particle physics, see here.

However, There's another, more fundamental issue being discussed in Eckard Blumshein's forum that has to do with negative numbers. Eckard rightly asserts that negative quantities don't exist physically, in the sense that we can subtract more from a quantity of entities than that which exists. For example, it's ridiculous to think that five people can leave a room of three people.

However, when we are thinking in terms of motion, or the "order of progression," the idea of negative operations is perfectly acceptable. In the case of the swinging pendulum, for example, or 2D oscillation in general, the point at zero separates the two inherent "directions," or poles, of each of the two dimensions. In the illustration I offered Eckard, we are justified in labeling these poles as positive and negative, even though there is no such thing as negative quantities.

I have elaborated on the subject in the attachment to this post.Attachment #1: More_On_3D_Oscillation.doc

Hi Peter,

I'm pleased you took time to read my essay. I had already read your essay and many of the abundant comments on your thread. I also have followed your discussion with Eckard.

The reason I haven't commented on it can be understood when it is recognized that I have a different mind set when it comes to theoretical physics. What I like about your essay is that it is based on both observation and reasoning. So many essays in the contest do not have both components.

As far as your conclusions go, on the one hand, I am very receptive to them, as far as I understand them, but on the other hand, the issues involved with the CSL as a measured phenomenon, and the deductions made from those measurements and procedures are most relevant to those who regard the universe as a space-time container of objects. Not only do we start with the idea of the existence of EM waves and interacting particles as given, but then we seek to reduce these particles and interactions to an elementary set, the properties of which can explain our observations.

It has to be admitted that this program of scientific research, initiated by Newton, has yielded spectacular results, since his day. But for theoreticians and philosophers, the trouble with physics goes to some profound depths, concerning the very nature of space and time. Experiments and analysis helps shed light on these contradictions, but they generally only emphasize the problems. If I can, I will try to elaborate on your essay in this context, over at your thread.

For those interested in my thinking, with regards to the theoretical and philosophical challenges that are perplexing to physicists, I will just say that I favor a change in the program of research itself; This means abandoning the notion of the universe as a space-time container of interacting particles, and the effort to reduce our understanding of it to the fewest interactions of the fewest particles, based on their relative motions.

I know how heretical this must sound, and I realize that one cannot take such a position, without first having some idea of what program could replace the current program of research. The justification for my taking this position is found in the works of the late Dewey B. Larson.

For Larson, the key to understanding the physical universe is the acceptance of the idea that it all stems from one simple relation, the relation of space and time. When we consider this idea in the three dimensions (four counting zero) that we can observe, the CSL becomes the datum of all physical activity. The logical deductions that we can draw from the idea seem endless, but compelling.

The observed fact is, Peter, space and time are expanding, from the perspective of all matter, regardless of the size of its aggregation, or the magnitude of its vectorial motion relative to another aggregate. This universal expansion is moving all galaxies and all clusters of galaxies away from each other, and, in the case of those separated by great distances, they are moving away in all directions at nearly the speed of light. The attribution of this phenomenon to the concept of an infinitely small point of infinitely dense energy, exploding outward, not into space over time, but as space-time itself, is untenable, in my mind, for many reasons.

However, the concept is firmly entrenched in the minds of the practitioners of the current program of research, by many confirmations that seem to point to it. This is unfortunate in that it prevents us from seriously considering the possibility that this theory has no basis in fact. If it is false, then what explains the space and time expansion?

If we consider the mystery of the nature of space and time, and don't take the great knowledge of its continual expansion into account, recognizing that gravity is the opposite of this type of scalar motion, within its geometric limits, our efforts cannot be fundamental enough, in my opinion.

All the best,

Doug

Interesting - Someone voted for my essay! Thanks to you, whoever you are. I wish I could start over. I know that I could do a much better job.

One of the things I would do is make a more explicit connection with the topic. Even though I address the most important aspect of the topic, It's not explicitly clear why the redefinition of the point is so relevant to it.

The point is, that there is no use trying to define a point in space that has any extent, or an instant of time that has some duration. This contradiction at the foundation of our science and mathematics cannot help manifest itself in terrible ways later on. Our concept of the electron is the best example, but there are many others.

A really advanced alien society would no doubt laugh at our pathetic theories that we take so seriously that we build silly machines like the LHC, going to astronomical expense to look for figments of our imaginations.

Why look for the Higgs, when we can't even understand the electron? If there is a discrete unit of space, then, by definition, it means that it cannot be subdivided. Yet, we can represent any magnitude with figure 1 of my essay. ANY geometric length magnitude whatsoever, including the so-called Planck length, can be represented by the radius of the unit circle. This means that the radius of the square root of 2 circle can be represented as well. With these two radii and the eight cubes between them, we have both digital and analog 1D, 2D and 3D geometric quantities such as circumference, area and volume, represented. So, how can we say space and time are doomed at some length, as today's leading theoreticians contend?

Just because we can't build a machine to probe that magnitude, or ever hope to generated the energy to do it, doesn't mean that we can't continue to subdivide it even further. As long as any magnitude can be squared, doubled and the square root extracted from it, the validity of the geometric construction of figure 1 stands.

Of course, when we regard it as a representation of motion, its collapse/expansion (c/e) occurs over time, so once we choose a reasonable unit, any subdivision of that unit has to have a c/e time faster than the whole, so, at the Planck length or smaller, the elapsed time for the c/e of a subdivision of a unit corresponding to the value of the speed of light c, is small indeed, relative to our scale, but that doesn't mean squat. It can still be further subdivided mathematically, ad infinitum.

What is significant is that this ability to infinitely divide the continuum in our minds compels us to pick a discrete unit to represent physical reality. A minimum unit of space and a minimum unit of time, which cannot be subdivided physically. Once this is done, then the problem of collapsing the unit to zero is solved, because such a collapse cannot continue beyond that selected unit.

Yet, this is good news, because a change in an inverse affects the ratio of the two in a compensating way. In this case, an increase in time is the equivalent of a decrease in space, so if time expands, space seems to collapse and vice-versa, providing a way out of our logical dilemma. Consequently, it's not a minimum unit of space that we should be looking for, but a minimum unit of space/time.

Clearly, we know the minimum unit of space/time: It is the speed of light, c, relative to matter. We can choose any magnitude of space, in this ratio, as long as we then choose the appropriate magnitude of time that will maintain the minimum ratio, the c ratio, we might say.

Whatever the space magnitude chosen, then the two constructions of figure 1 can be used to represent these inverse units and their ratios. When the left one collapses, the right one expands and vice-versa. Once appropriately assigned, we are left with the unit oscillation of the physical universe. Using this discrete unit of motion as a building block, we can presumably build all the physical constituents of the universe, from bosons and fermions, to their aggregates, as large as quasars and the Sloan Great Wall.

What a task that thought presents! Who knows how long it would take to complete it, but even if it means nothing more than we could obtain a working, consistent, model of the electron, in our lifetimes, it would be worth it.

Feynman would be happy, I think.