The turn isn't another dimension. It's a change of trajectory within space, which you forgot to add. You have the dimensions for the object and its velocity but you didn't indicate any spatial dimensions for the space it's in. Velocity in which direction? Turn in which direction?

You have an interesting question there, but asked in the wrong manner.

The velocity is usually in a straight line, requiring one dimension of space, when you add a spin moment, you vear off into two dimensional space, and multiply the term by the constant 2 Pi.

The interesting thing is that there are at least 6 paired families of spins represented by Quarks, yet the one family far out populates the rest. Some think that this implies that there are 12 dimensions instead of just 5.

GS:

How are these paired spin dimensions related to geometric space?

They appear to be independent variables, which define mathematical space dimensions - but not (necessarily) geometric dimensions.

Geometric space dimensions involves coordinates of location. In what geometric space are these extra dimensions providing coordinate information?

?

Well, I don't claim to be an expert on dimensions in all their ramifications. Just a searcher in the wilderness with a dim flashlight.

However, the reason that I assume that 1 dimensional objects cannot have spin, is simply that spin requires a planar surface on which to orient. The minute you define a planar surface, you imply 2 dimensions.

When we describe 6 families of spins in pairs, this describes at least 6 planes on which spins can orient. I believe it describes 12 such planes, since each quark in each pair might be on an opposing plane. Thus the spins influence each other and one spins clockwise and the other counter clockwise on their respective planes. So while 12 dimensions would be possible the likely geometry is 24 dimensions to explain 12 planes However if one dimension is common to all such planes, such as time, we can reduce the collection to 13 planes..

There is a tendency to attempt to collapse these planes into a three dimensional construct, but my feeling is that this is counter productive, in that it doesn't explain the geometric requirements of the construct that makes 6 families of Quarks practical.

Now on to the question of Spacial versus Mathematical dimensions. If the spatial dimensions wrap around the 4 dimensions, One might expect that there would be planes on six sides of the cube defined by 4 dimensions, and that these planes would wrap around more than once, allowing opposing planes. Since the dimensional complexity would be opaque to the inside four dimensions it could be mathematically described as if it were part of the 4 dimensions, without much difficulty, but the complexity of the structures within the 4 dimensions would not make much sense mathematically since the math needed to properly explain them would have more dimensions than the nomenclature used to define them.

Hans: "Dimensions must correspond to observables" Is this a new law? Or a preferred convention?

How do you define observables? Is complexity not observable but confusing?

Hans: "Observables must correspond to eigenvalues of operators" another new law? Or another new preferred convention?

I am not sure I understand completely what an Eigenvalue of Operator is when it is at home.

Currently I am trying to deal with an arbitrary length string of complex numbers. (1 real and innumerable complex) but I am not sure it is working. The problem is to determine what needs its own complex number, and what doesn't. Proliferation of complex numbers seems somewhat more radical than dimensional complexity would suggest.

'Observables', esp. as eigenvalues, is another way of saying 'independent variables'.

These refer to dimensions of mathematical spaces - not necessarily geometric spaces.

To suggest that these dimensions are "opaque to the inside four dimensions" really translates to 'we don't how these could be geometric dimensions' so we will wave our hands and pretend they do.

If these really are geometric dimensions, or theorists construe them to be such, then they need to be appropriately described with geometric properties - in particular as position coordinates along mutually perpendicular axes (where the perpendicular direction can be identified).

In the case of "Wrap Around" dimensions the mutually perpendicular dimensional aspect is suspect. As is the convention that all dimensions start at the origin. Please be advised that the hand waving as you call it, depends more on a lack of commonly agreed ways of dealing with a new system of thought, rather than an attempt to keep things vague.

The problem lies more in the building of conventions when there are only a small number of thinkers who can even claim to understand the questions, let alone come up with answers.

Mathematics is mostly about conventions. I don't claim to be a Mathematician, and so when I have a thought that doesn't fit the current conventions I do not feel constrained to define it in the form of the current conventions. Having said that, I do have a preference for using the common conventions where they apply, I am just not sure in all cases where they apply.

the concept of an independent variable changes depending on the system that it is imbedded within. For instance Green as a color is seen as independent from biology, but green as the color of an eye, is seen as chosen by DNA. Philosophically one can question whether there are ANY independent variables.

Having said that, I take the issue very seriously, when new elements emerge as the result of phase changes, are the new variables independent? They are independent of the former phase, for sure, but if the phase change didn't happen, would they exist?

Consider the concept of a "Constructed Geometry" that is formed by field effects. As the complexity of the fields is increased, new dimensions are needed to describe the new complexity of the system defined. The origin of the new dimension can be seen to be offset from the dimensional system before the phase change to a higher dimension. in such a system, it is possible that a new dimension might not lie along the same axis as the old one that might have paralleled it. When we try to define such a system using a common point of origin for all the dimensions, we find that the points on the old dimension and the new dimension both seem to correspond to points in one of the arbitrary dimensions, and so the complex geometry collapses into a figure that looks like a complex object in a simple geometry.

This then is my problem, how do I define the complex geometry without collapsing it into the simple geometry and losing track of the complexity involved.

Phew. I'll try otherwise. It is known that the Universe is asymmetrical. If we wanted to make it symmetrical, we need to dispel all matter (all that exists) into one superstructure. But in this case there will be no difference in this one, that could be used for comparison to show any object (then it will be only one object, which itself can not define). Now, having this "something" we are dealing only with the concept of movement and nothing more. If we examine, in how many directions the movement takes place, it turns out that in the system of straight orthogonal x, y, z, you can plan a sphere which is perpendicular to these axes, whose size will change with a change in value of the other axis. Therefore, I think, we have five directions, because the sphere is also changing the size (area comes in the additional two-way), like the other axes.

Interestingly, the layout, which showed, in my opinion, can serve as an absolute standard (Clock), because, although it is moving, the move cannot be demonstrated. There is a lack of differences in movement. The result of any comparison is zero. Time does not expire. From this perspective one can say that we are dealing with a point, although this is not a point commonly understood.

Then, if we stop the movement at any point, will appear a waste. This waste can be used to build a mass, and is associated with a change of axis of motion (dimension). It appears the opposite phrase of movement (what does not growing it goes back).

Of course, it isn’t all yet, but for first I’m interesting if this construction of dimensions in your opinion is in some way wrong in its basics?

There are two items of note, directly related to 'dimension'. Hans has just brought up the second.

The first is the distinction between dimensions of mathematical 'spaces', which involve the number of independent variables in use, and the 'dimension' of geometric spaces, which involve the number of positional coordinates needed to locate a point in that space.

The axes of a geometric space must be mutually perpendicular and the positional coordinates measured from some origin.

It is quite possible that a mathematical space maps to a geometric space, however the requirements of geometric space need to be met for this mapping to be correct. This is what I do not see in the discussions of 'higher-dimensions' in physics - even though there is an attempt to make this mapping - usually by some waving of hands. These higher-dimensions remain mathematical space dimensions.

The second item comes from attempts to take abstract geometric spaces and map them to the real world. If the real world is 3-dimensional (plus time), then we have three mutually perpendicular axes and three coordinates (x, y, z) to locate - now an object rather than a point - in space. This is an important distinction as reality is comprised of objects, not abstract points. The same abstract point can exist in 3-D, 4-D, etc. dimensional spaces. An object in reality isn't 2-D in a 3-D space or 3-D in a 4-D space. An object in reality extends in all the dimensions of that space. If it didn't, we would not need all the dimensions to locate that object.

If we have a 5-dimensional reality (topic of this thread) - of 4-D geometric dimensions plus time - then the objects in that reality extend in all four dimensions (plus time).

(I separate 'time' as a dimension, since it also doesn't fulfill all the characteristics of a geometric dimension, although more than just an independent variable.)

So where is this 4th geometric dimension with a fourth coordinate required to locate an object in space and with a mutually perpendicular axis?

For the record, I think scale fulfills the requirements of a fourth geometric dimension.

To measure the distance between a book and a molecule, each object needs the coordinate of scale to locate the position of the object in order to measure the distance between them. Taking the 3-D volume of an object at different scales (think of a 3-D medical image of our body at different levels of scale - e.g. organs, cells, proteins), we will need a 4-D hypervolume to combine these different 3-D images of the same object.

Further, if we take a 3-D volume of an object, we can 'slide' this volume in the direction of scale, which is mutually perpendicular to the 3-D volume.

All physical objects extend in scale, thus all objects are 4-D.

LOL. I just realized that this discussion has backed into the subject of the book I'm trying to finish this weekend. Actually you can break time down to being attached to any arbitrary amount of dimensions you want. The result is that time has as many dimensions as does the space your object is in. The proof of that is the fact that time for one part of an object can be different from another part, i.e. the examples given of an astronaut being stretched by the gravitational field of a black hole. Time at the head of the astronaut will not run at the same rate as time at his feet.

As for scale being another geometric dimension, I can see the argument but it doesn't get us anywhere. Scale is already dealt with in physics. But I will say that I like this question from Donald:

"So where is this 4th geometric dimension with a fourth coordinate required to locate an object in space and with a mutually perpendicular axis?"

and my book answers it precisely - Solving The 4th D Puzzle: The Continuum of Unified Elements from Euclidean Geometry, Relativity Theory, Quantum Mechanics and Cosmology

I'll post an excerpt in my blog section after it's done...

I think that the problem I have with Palmers assertion that geometry always requires mutually perpendicular axis that join at an origin, is the assumption that the only valid geometry is Euclidean Geometry.

Why are we not allowed to think up new geometries if they are needed to deal with physical constants that are not well dealt with by previous geometries? Hans at least is willing to work in Mathematical Geometries, although his insistence on Quaternions leaves him overexposed to the 4 dimensions of observable space. His discussions of 2^n ions at least opens the discussion for how to deal with higher dimensional spaces, but points out a very interesting mathematical limitation on the use of advanced complex numbers, in that the spaces described tend to have reducing similarities to real number algebra as n increases.

Axes that meet at some (relatively defined) origin do need to be perpendicular at that origin. There is nothing that limits this to Euclidean geometries, however. Two lines that intersect on the surface of a sphere do so perpendicularly. Those two lines might intersect at more than one place - both of which will be perpendicular intersections.

The concept of perpendicular does have different characteristics in Euclidean and non-Euclidean geometries - however both do include the 'perpendicular' concept.

The issue with Quaternions and other 2^n ions is less a theoretic problem than an applied problem. In a sense it bridges both theoretic and applied mathematics.

This is the problem of adequate representation of theoretic number systems. Currently the most powerful numeric representation system we have is the decimal numeral system and it's helpful side-kick logarithms. This numeric system is only capable of representing values of real numbers.

Note that 3.8125 is a numeric real value. (3.8125 + 3.45i) is not a numeric value - even though it is considered a complex number value. Currently we seem quite satisfied with the decimal numeric system and its limitations of not being able to handle complex numeric values. However there is reason to suspect that more powerful numeric systems exist - which can represent a complex numeric value.

If (3.8125 + 3.45i) could be represented by a singular numeric value, then computation of complex values would result in another singular complex numeric value rather than the increasingly complex algebraic expressions we get using decimal numeric values.

In essence, where we currently multiple (3.8125 + 3.45i) * (1.259 + .056i) and end up with (4.6067375 + 4.55705i), we would have the equivalent of multiplying decimal numerals with singular values for each value and the result. (like 3.8125 * 1.259 = 4.7999375).

This requires a numeric value for i = sqrt(-1). Differently, we have (-1)^ 1/2 = i or

log (-1) i = 1/2.

This requires a negative base for logarithms - something that is currently undefined in mathematics. That doesn't mean it cannot be defined - only that we have not found a way to do so yet.

One more point - decimals are defined using addition, multiplication, and powers - thus

1.259 = 1 * 10^0 + 2 * 10^-1 + 5 * 10^-2 + 9 * 10^-3

This numeric system involves three reversing operations - addition-subtraction, multiplication-division, and powers-logs.

A more powerful numeric system would need to incorporate an additional (fourth) reversing operation - best bet would be integration-differentiation (probably using base 'e').

This thinking strongly suggests such a numeric system would not be a 'pencil scratch' type of numeric system but require computers to manipulate.

Even if the above has flaws:

I will suggest that more powerful numeric systems exist than our decimal numeric system. These numeric systems can represent - can provide singular values for - number systems beyond the reals.

This is an area of mathematics that holds the potential to expand not only mathematics, but also most areas of science.

well, yes, but, you still require the same sort of dimensions. While I am not sure of perpendicularity, I am sure that in a constructive spacial geometry you cannot have a common origin for each dimension. The only geometry that can have the common origin, is one where space is taken as an axiom. Because it is axiomatic, the dimensions are projected through the origin, because they pre-exist the geometry. In a constructive spacial geometry spacial dimensions are part of the construction of space, and therefore likely do not project back to a common point, since their origins fall at different times in different dimensions.

Well Hans, If what you want is the classical description of space, then Wikipedia is where to go.

"Space is One of the few fundamental quantities in physics"

But, what if Dark Energy is MORE fundamental than Space?

Now there is no way that I can prove that it is, Maybe there will never be a time that I can. However, if I don't take the time to develop my idea that it might be, and define the type of space that might exist as a result, we will never know because we will never be able to compare the two geometries to determine which one is more realistic to actual observation.

You seem to imply that I am not using logic in my reasoning. Perhaps not, I have seen the dangers of logical inference in a system where you start with a false statement. But in a minimal axiom system, any axioms that exist are there to separate the system from the assumptions of previous logical developments. If you don't base your system on the assumptions in an axiom but merely point out where other axioms do not apply, Logic does not assure that you preserve falsity. On the other hand, if you fly too far from the main flock, you have to expect to spend a lot more energy going back and forth over the same issues time and again, trying to see if you got the inferences right.

#H1-217. Ref Hans van Leunen. I read the wikipedia/space link provided by you, and from there wp/abs s t. From that:

I have read this many times, but it never fails to beat me: >.

@*. What travels, light or information?

Ultimately, it is not so important to me, whether this sphere I wrote about will bring two additional dimensions physically. They would be needed if we treated the elementary particle, as already three-dimensional (by nature), which most people do. I think the impression of a three-dimensional body can be created by moving a single dimension, so we still could have enough space to hold the rate of movement and phrase, using the other two.

I’d like to draw attention to a matter of mass. In particular, the possibility to define mass as the difference in movement between any given layout and the standard system (mentioned diffuse movement). But even between local layouts. Not necessary perfectly symmetrical. This arrangement provides the standard layout of all motion at rest, a truly inertial “navel of the Universe” (the layout of absolute resetting), where the movement expresses simply energy. If we could (what is not impossible at all) to see such a system, we would see the body perfectly transparent (not white and not black). Although the system is moving is not possible to demonstrate this motion because all the elements (in this case the three axes of motion) are in constant relationship to each other. In this state there is no mass, no radiation, and time does not expire, because the time as a result of comparing things with each other (differences in movement) is equal zero. However, if there is a loss of movement of any axis, (as indeed it is quite natural: there is no reason that the symmetry is preserved and no reason not to have been preserved) shall a measurable change appear. Color and shape pattern will change. The mass understood in terms of difference of motion allows to show the reaction (where the object is merely an "external" effect of reaction) as a result of summing of mass value: movement1 - movement2 = movement3 (three axes, so the solution is very simple), where the word (-movement2) expresses lack (absence) of movement, so its character (mark) is natural. Mass (-movement2) as the inverse of movement has the characteristics of connecting (acts), so it can be identified with gravitation. It is immediately quantized (energy is a quantum, so its opposite as well). Moreover, such understood gravitation will not take infinite values. It’s reset by alignment differences of motion (and off expiry of time), where the limits set c. The object (here: the Universe as a whole) may be collapsed or stretched to a point understood as no differences in motion (not classic, mathematical point), or split into unequal parts (which is what is taking place). Mass is then also a relative value. What matters is phrase of movement, so from the perspective of one the mass is growing, but from the other point of view decreases, although the total value (for the entire Universe) remains constant, and the overall difference (between the mass and energy) acts as the engine driving the whole movement. There remains the question of belief as to the possibility of conversion of mass into energy. According to the shown solution it’s impossible, because you can’t get movement from the immobility. You can only replace them (complete a lack of movement with help of existing motion, but this is not trivial, since the movement must match the value of motionless). Conversion the whole mass into energy would mean the annihilation of the drive mechanism - the engine - turning off the Universe.

All this description makes the movement, space (distance), the facility must, of course, viewed from another perspective. Understand the reality otherwise than it is commonly understood. However, I think we could gain a lot if it was a good idea (in general, because in my opinion, is acceptable). We could move quite differently but also to cure the disease and communicate in other way. As an inventor I can’t see any error that disqualifies a solution, so willingly find out, what can’t be thus described. Maybe basic rules aren’t so complicated as one can think?

Only in my own: "Mechanics of Time". But, I'm sorry, not in English, yet. Maybe never need :)

G.Smith said:

"But, what if Dark Energy is MORE fundamental than Space?

Now there is no way that I can prove that it is, Maybe there will never be a time that I can."

come on, yes you can, just by showing us how do you use "space" and "dark energy" according to what?

With regards.

Hans,

when you said:

"Traditional quantum logic contains a single axiom that differs from classical logic."

I don't understand what you are comparing with what here.

Are you trying to compare QM's axioms with the axioms of let's say Predicate Calculus?

With regards,

Grand Sen~or.

Hans,

I think what you want to say is:\:

Theory of QM adopts such and such mathematical structure but not so and so.

Right?

With regards,

Grand Sen~or.

Thank you Hans,

I found it intriguing that you said that nature travels between Hilbert spaces and Fourier spaces.

I had, I believed discovered that there was a shift between Field Generation and dynamic readjustment of spatial relationships, but I hadn't realized that this shift, could be easily calculated in a spatial transform. If we assume that Hilbert spaces are State oriented, then the Fourier spaces are where the adjustments happen?

It was also nice to hear that Birkhoff is the father of quantum Logic, since I had never heard the term before you mentioned it, and hopefully Birkhoff's work will be searchable via the net.

Hans,

are you talking about another theory of QM or a model of the theory of QM?

Regards,

Grand Sen~or.

Hans.

so it is just another model of QM based on the modification of the QM Theory.

Regards,

Grand Sen~or.

Well that is good,

"None of them IS physical reality!"

I was beginning to think that everyone thought either that the current status quo on theories was everything, or that the moon was made of blue cheeze.

So am I wrong in thinking that Fourier space has to do with frequency?

If so it doesn't match my model, and I will have to look for another transform....

Sorry, but I very dissappointed by level of the discussion. Instead of consideration the theme here we have competing of egos. So, I'll add my 1 cent to the discussion. The discussion about enveloped Riemann and enveloping Euclidean spaces.

Let's consider the simple example - a surface z=z(x,y) in three dimensional Euclidean space with metric tensor G=(100;010;001) or the interval ds^2=dx^2+dy^2+dz^2.

By taking into account an equation of the surface we can get an appropriate metric tensor in two dimensional Riemann space with metric tensor g=(1+z1^2,z1*z2;z1*z2,1+z2^2), here z1,z2 are partial derivatives of z. On the base of this metric tensor we can reconstruct the initial equation of the surface from equations of a full differential dz=z1*dx+z2*dy, which determine the initial surface with arbitrary shift on the z.

The same speculations can be applyed to General Relativity. It's about the fifth dimension. Here we have no physical ideas, only some math exercises. There is a question: Have these exercises any practical meaning, may be for simplification of calculations, or they are only a fun.

Hans,

I think what you want to say is:

"QM and QL are models based on the theory of QM, physicists can make and use more than one model based on the Theory as they need while practicing physical research, experimentatiuon, observations to communicate meaningfully among themselves."

If tht is what you want to say I agree with you, but wher is "reality" here?

I mean "reality" is not a defined/undefined term of the Theory of QM, so how can physicists talk about it meaningfully? I mean when physicists talk while doing/practicing physics they talk meaningfully if and if what they tell is according to the Theory. If they cannot talk according to the Theory, then it is not physics yet.

Well, then feel free to talk about reality but don't tell us you are talking physics or "physicsl reality" in physics for there is no such a term in the theory unless you are talking according to a physical theory which "reality" is either a defined or undefined term of such a theory.

With regards,

Grand Sen~or.

Actually there are 8 models of quantum reality, according to physicist Nick Herbert...

@Mark:

If the math exercises don't translate to physical reality, then they are only fun. Mine have a direct correlation with physical reality and involve both Euclidean and Riemann geometries...

@Hans:

Good points. That's why the proper description of it is the Continuum of Unified Elements from Euclidean Geometry, Relativity Theory, Quantum Mechanics and Cosmology. In fact, the portion of Riemann geometry that I use is not "observable" in the everyday sense of the word at all. I discovered where elements from these various models connect seamlessly to reveal a new understanding of space and time. None of it violates any known laws of physics nor tries to undue Einstein, etc. or over reaches to try to explain everything in the universe. In fact it reinforces Einstein is surprising ways...

M.Barnes said:

"Actually there are 8 models of quantum reality, according to physicist Nick Herbert..."

I think you wanted to say:

"Actually there are 8 models of quantum theory, according to physicist Nick Herbert..."

otherwise it doesn't make sense what you said. Because physisicts make models based on theories.

With regards,

Grand Sen~or.

@Grand Sen~or:

I said what I meant. English is not my second language and I'm no stranger to QM.

http://www.amazon.com/Quantum-Reality-Beyond-New-Physics/dp/0385235690

http://www.globalmind.info/quantum_reality.htm

M.Barnes said:

"I said what I meant."

he said:

"Actually there are 8 models of quantum reality, according to physicist Nick Herbert..."

and I ask:

"are you saying that you didn't mean "Actually there are 8 models of quantum theory, according to physicist Nick Herbert..."?"

If "yes" then what is this "quantum reality" that you are talking about which you make models according to it ignoring/bypassing any theory of QM?

With regards,

Grand Sen~or.

@Grand Sen~or:

I gave you links, why don't you read them? And for the record, I'm not making any models, I'm referring to the work in QM that you're obviously ignorant of. Physicists have been referring to models of quantum reality for decades now. Where have you been?

M. Narnes said:

"Physicists have been referring to models of quantum reality for decades now."

No! physicists are not "referring to models of quantum reality". Physicists are making models based on the Theory of QM to use a meaningful language among themselves while they are coducting experiments and observations formulated according to the models based on the theory of QM. Physicists have nothing to say by using "reality". "Reality" is not a term of the theory of QM. Hear, for example, what Bohr _can_ so much say as a physicist what is physics:

"Physics tells us not about what _really is_, but what we can _say_ each other concerning the world."

However, if I question him "What is the world?" most probably he would withdraw it and replace it with "about our experiments and observations conducted according to the theory in use". Let me rephrase what Bohr would say;->

"Physics tells us not about what _really is_, but what we can _say_ each other about our experiments and observations conducted according to the theory in use".

With regards,

Grand Sen~or.

#H1-227. Ref Hans van Leunen, Feb 1, 2011 4:51 pm. 1.

@*. Why sir, have to use such words as annihilation (though it mightn't've been uncommon). You could say that's the happening, but what is the use of such implied work involved? Certainly again-creation is not a sufficient reason/purpose.

2.

@*. Logic usually has the Yes/No binary. Dynamics can have any such pair?

#H1-229. Ref Hans van Leunen, Feb 1, 2011 10:02 pm :

@*. If i see SUPERFLUOUS waste of effort in it, would it be wrong?$ I find it difficult and am lost at anything that uses a more than minimum work/effort/intention for a purpose.

$ Nature cannot make anything such that EVEN i might call it wrong!

As to your statement, Hans," "Is this the item?" is a valid QL proposition" I can doubt, because in a nucleus you can't determine it is a proton or neutron.

As to my preliminary post about enveloping Euclidean spaces about enveloped Riemann ones (fifth dimension), I found a one important benefit of the such approach. it is in setting of limitation on a metric tensor in Riemann space as: d(sqrt(gii-1))/dxk=d(sqrt(gkk-1))/dxi, (c=1).Here d is a partial differentiation, and is no sum on repeating indexes. May be it is in some way an additional continuation condition. It can be useful in GR.

@Grand Sen~or:

So you're telling me that Nick Herbert, Michael Talbot, Fred Alan Wolf, Jack Sarfatti, and dozens of other scientists aren't physicists. That's rich. The bottom line is that you're playing a semantics game here and in the end you're the one that's going to end up unsatisfied. Those of us that understand reality don't go chasing after it, like a dog chasing his tail...

@Hans:

What's the difference between a strand and a string? (that's a rhetorical question - no need to answer). My eyes immediately glazed over when I read "However, dimensionality is not a parameter, but a result of the model: other numbers of dimensions are impossible." since I know that that's not true and by known experiments, which is part of my model. But I'm not trying to do a final theory model, which is what Strand theory is.

It will be interesting to see how far it goes. In the meantime I'll be sure to reference the flaw, over higher dimensions than 3, in my book...

@Hans:

This guy's strand theory rules out strings and is no comparison - according to him.

Just to be clear, I'm not trying to figure out the structure of the universe any more than a painter tries to figure out the structure of a canvas that's stretched over a frame. I've come to the conclusion that a number of other researchers have as well - that the structure can be manipulated without having a paint by the numbers understanding of what it is. In that regard, I'll let the physicists bang out their number theories. I'm an engineer but I know enough physics to be able to figure the engineerable solutions that enable me to see things that are possible that most physicists miss.

But I appreciate the link because it forced me to look at something that could impact my work and resolve any applicable issues with it...

@Hans:

Oh. I thought you knew what you were posting. That's why I said my question about the difference between strands and string was rhetorical. They sound similar but this guy says that his strand theory is totally different.

At any rate, he serves as an excellent model of the difference between my theory of space and time and the approach of trying to determine a final theory. These are the kind of challenges I like and are worth my time...

@Hans:

I just want to know when the experimental evidence will be available...

@Hans:

Well that's good because I have a $100 bet with Stephen Hawking that the Higgs Boson will be found. Schiller doesn't include a possibility for a Higgs, but I'm not sweating it. I took the bet just on the odds, because Hawking makes so many mistakes, the odds were too good to turn down...

How can any thing - in nature - have infinite length?

I think we are misunderstanding what we do when mathematical models are considered the same as reality.

It is okay to Model reality with mathematical tools that include concepts like infinite length. Believing this mathematical model IS reality is a mistake.

Has physics, in its theories, adequately accounted for the assumptions and theroems inherent in the mathematical tools used?

Consider that probability includes the 'Law of Large Numbers', which explicitly states that some characteristic we are concerned about is being averaged out. That the measurements of this characteristic are admitted not to be known for any specific object under consideration. Only averages for this characteristic across large numbers of objects is being included.

The consequence of this mathematical law is that any model using probability admits there is some characteristic which is only averaged out and the specific details not known.

So any Theory Of Everything based upon probability must be incomplete and cannot be a true Theory of Everything.

To make the sort of quantum leap progress in physics - and mathematics - many people are looking for, we will need new mathematical tools. The ones we have are not up to the task.

A good first place to start would be a critical review of the impact of the mathematical tools being used on the current (and projected) models and theories of physics.

As stated, probability is not adequate to the task of producing a Theory of Everything.

Hans, the ordinary continious three dimensional Euclidean space is an example of the Hilbert space. It has only three base vectors. And what is followed from the fact? On my opinion, it is nothing.

One problem I have with this approach, is the idea of tangles of 1 dimensional objects. To have an object that can "Tangle" it has to be either linear but in a higher dimensional space, or to be able to twist out of a strict one dimensional space, which in turn suggests that it cannot be described as 1 dimensional. Now I understand that some spherical dimensional structure have been used for geometry, but one dimensional objects were still projected as linear just conforming to the higher dimensional surface of the sphere. In other words they were not one dimensional at all but one dimensional projections on a three dimensional surface.

If you are talking about 1 dimensional projections on a convaluted surface (space) then I wish you would call them that, instead of 1 dimensional objects.

I like Palmers statement that Probability is not adequate as a basis for a theory of everything.

The problem as I see it is the loss of information created by Probabilistic Mathematical tools. In essence we are saying that the "Noise" that we damp out by probability, has no value. What we need are tools that are more accepting of noise, but analyze it to see if there is any information content before throwing it away.

I see this for instance in the Science of Medicine, where often probabilistic tools are used to decide whether there are links between diseases, with out regard, to the complexity of the links. If there is data linking two diseases that lies just below the noise threshold by the applied mathematical processes, it is lost in the process, and no one looks again until they find a bio-chemical connection.

Since what is signal and what is noise is determined to some extent by the paradigm under which the test is done, to some extent the paradigm determines whether or not a link is made during probabilistic mathematics. One aspect of this, is that Outliers that have both the diseases, are often seen as sports, and no attempt is made to link the diseases, because the probability of the person having both diseases is considered too low. I wonder if this is one reason why "Multiple Universe" and "Sequential come and Go Universes" are so popular now.

Personally I don't think you need multiple Universes to describe reality, merely something squishy that increases complexity with energy density and entropic effects.

Two items:

1) No object that we find in reality extends in less than the number of dimensions of reality.

We don't have 2-dimensional surfaces in reality. This is a mathematical construct. To suggest that 1-dimensional objects exist in reality violates all evidence before us.

To use 1 or 2-dimensional concepts as a mathematical model of reality is fine. Just don't expect it to BE reality.

2) A particular problem that exists with the study of reality, at the moment, is that our mathematical tools are slim for measurement that crosses scale. How can we measure the distance between a book and a molecule of the table upon which the book sits?

The decimal numeric system we have - our most powerful numeric system - is unable to provide this measurement. The error term at our scale, even with 6 digits of precision, completely dwarfs that of any measurement on the molecular scale. The (mathematical) measuring tools we have today are not up to the task we attempt to use them for.

Given the above problem with decimal numeric values, the primary mathematical tools we have for crossing scale are probability and statistics. This is why these are the tools of choice for small scale physics. They have proven quite useful - until we start getting into 1-dimensional objects that supposedly exists in a 3 or 4-dimensional universe.

There is also the problem of 'noise' and the use of probability.

This is were we need to step back and question whether we even have the tools to adequately describe the universe before us.

It is quite clear to me that we do not have the appropriate tools (in particular mathematical) for describing our universe. The most important tool missing is the ability to represent a complex value as a singular numeric value. We do not have a numeric system capable of representing complex number values.

The decimal numeric system is more than 1000 years old and is an assumption of pretty much all science. It is only capable of representing values of real numbers.

Science has moved beyond real values and deals with complex values as a matter of course.

Why, then, have we not found a numeric system that can adequately represent complex values?

Because we have not stepped back and questioned the mathematical tools we use in science: Where are these deficient? Also, how do these tools impact the theories and interpretations we are generating in our search to understand reality.

50 years hence, there will be a more powerful numeric system that can represent complex values and will transform both mathematics and science.

Dear Donald, I agree with you as to your first point and partly with the second. But I have some remarks:

1. Experimentally proven Maxwell equations are invariant relatively four dimensions. What is a sense of this time/space? (Philosophical question)

2. Any measurements have errors. Thus, we have noise and statistics. But the measurement itself is carried out in time/space frequences and spectral limitations. So, we have to solve ill-conditioned inverse tasks, which requests additional limitation in any case. Then any physical model consider object, which isolated from external (not included in the model) interactions. So, we have a lot of sources for statistics. Thus, such math models as: plain waves, pass to limit, Fourier transform, and others, where we have infinite limits, have limited applications. On my opinions for these models are more applicable Karunen-Loeve basises.

3. I disagree with you that the cause in the numerical system. Any math models of physics system are independent of a choice of a numerical system.

There is a very significant difference between a number system (e.g. real number, complex number) represented as some value-less variable and the hard value of a specific measurement requiring a specific value. In theoretic equations one can ignore the numeric system since specific values are not obtained. In practice (e.g. use in practical or experimental physics) it is hard to distinguish the two, but specific values are required.

To address certain of both Hans & Mark's points, the most advanced numeric systems we have are the decimals (and their sidekick logarithms) which can only provide a singular value for a real number. I have looked at the 2^ons and they do not provide specific singular values. It is not the theoretical Maxwell equations that are the point - it is the specific values that would come out of applying the equations.

There does not currently exist a numeric system that can, as a singular value, represent a complex number. To do so would require a log with a negative base, which is currently an undefined situation in mathematics.

The issue is not about the NUMBER system in use in generalized equations where specific values are not used (e.g. a complex number is represented as z_overline). It is about the NUMERIC system providing specific measurements and values when an equation is applied in a specific situation.

What is the complex value when an equation has values applied to the variables?

Currently the only VALUE we can assign is a real value represented by a decimal (or log) value.

When calculating electric circuit values and using complex numbers, the complex part is tossed out and only the "real" part (represented by a decimal) is retained.

This is not because there is no use for the complex part (since we required it in the equations that produced a result), it is because we have no way of handling this complex part as a value. Since we cannot handle it as a value, we have not looked at what it signifies or measures.

All we have is the decimal system to provide specific values. The error term we find also must be based upon the numeric system we use. Thus we can have 3.1415 +/- .00009.

Where is the complex error term of a complex measurement? Do we have (3.1415 + i4.259) +/- (.00009 + i.0005)? What is the meaning of +/- i.0005 in a physical measurement?

Specific measurements are not variables and cannot be represented by an undefined letter (e.g. "i"). We are unable to represent a complex value without an 'undefined' term.

As a measurement, we cannot provide complex values.

For William: Have you tussled with Kant yet - and his "I think therefore I am"?

What is it that you call reality and how can you know - for certain - that what you experience is accurate and correct? The brain interprets information - it is not presented apriori (as Kant believed for certain items). How do know you have a bowl or a hammer, let alone space inside the bowl?

William:

I think I get your idea of looking at boundaries, although I haven't done so before intentionally myself. Context appears to be one thing that separates us from computers - we intuit a context to most everything. Computers have to systematically build a context (at least as we have currently programmed them). Getting a computer to 'see' an optical illusion might be an interesting task.

So how do you understand mental 'tools' - like mathematics?

Do you think such tools impact the theories we build of reality? Do you think they would impact our experience of reality?

Why would we not be interested in 'better' tools?

Those 'better' tools need to appear at least vaguely familiar to tools we already know and perform a function similar to what we already know. We must have a context to understand them.

Give a caveman a rifle and he will have no context in which to understand it. Show him how to use it for food (or war) and he will understand it as a tool.

Interesting that you focus on boundaries, as I have been working on a paper entitled "Boundary Conditions". Numeric systems are tools that cross the theoretic-applied boundaries of both mathematics and physics.

An important perspective of this is that there are theorems about numbers and number systems that use properties of numeric systems in the proofs. Cantor's diagonal method on the un-countability of the reals uses the properties of the decimal numeric system in the proof. My math textbooks gave proofs that real numbers correspond to the points on a line by equating a decimal representation of a real with a point on the line.

Like objects in space, numeric systems have limitations and boundaries. These do not necessarily correspond to the limitations and boundaries of the mental abstractions we have of number systems. We call pi a transfinite number and give the infinite decimal expansion as a reason for why it is different. However, if I use pi as the base of my (decimal-like) numeric system, then pi = 1.0. All our 'normal' values might now be infinite 'decimals'.

By physicists delving too far into just mental models, they are loosing their connection to reality. They are crossing the boundary from applied, with its limitations coming from 'reality', to only abstractions - sans such limitations.

To go off on a 'current affairs' discussion:

If reality consists of multi-verses - only one of which we can actually experience - all the other 'verses' are strictly abstractions in the same sense as Russell's numbers (I have only read his Intro to Mathematical Philosophy). How we manipulate values, produce practical solutions, or determine boundaries and limitations in 'our verse' need not apply.

The abstractions of logic theory and the attempt Russell and Whitehead made to put mathematics on a firm theoretic foundation smacked into the reality of specific (applied) statements - like 'This statement is a lie'. We cannot operate only from a theoretic perspective. There might, however, be better 'applied' tools than we currently have before us.

What ever anyone thinks about "This statement is a lie", I think it's rather true in that it's not a statement of anything, so calling itself a statement is a lie and so in effect the sentiment overall is true. Like saying "That wall is green, but I'm lying". If the wall is green, then I'm lying about lying, if it's a different color, then the first statement is a lie and the second is true. The real question is what's the color of the wall?

No big deal really, when you really think about it...

"This statement is a lie". Rightfully: "Any statement is a lie" I think, the sense of this statement is that almost any statement about fenomena or things is incompleet, because it doesn't reflect them from all sides.

As to"That wall is green, but I'm lying", Here we have two different statements in the one expression. Second part of this expression can reflect the fact that "green" is very approximate expression of color of the wall.

@Mark:

per the green wall example, if the second part is in fact a statement, it can't reflect anything that it doesn't refer to, in this case any approximation of the color of the wall. It simply says, "I'm lying". The only reference to color is in the first part which clearly says it's green. Assuming information about the statement, which it doesn't address, renders the whole exercise meaningless because it could then be made to say anything...

"Any statement is a lie" actually is a lie, since it's not true. Again, trying to assign a meaning to it which it doesn't address, means that anything could mean anything...

Unfortunately, it appears you are not aware of the underlying issues at stake.

The self-referential "This statement is a lie." is the kind of statement Russell & Whitehead (and most mathematicians since) have been unable to address from a foundational position. This leads to a problem putting mathematics on a strictly logical foundation.

Hilbert identified 5 'theorems', which if they could be proved would essentially place mathematics on a firm axiomatic foundation. To most people's surprise, Kurt Godel found the 'theorem' that an axiomatic system was complete to be false and provided a very elegant proof of this.

What this means is that any axiomatic system, as complex as the natural numbers, includes statements that can not be proved true or false (or could be proved both). Any complex axiomatic system is incomplete (Godel's incompleteness theorem). To prove the other theorems requires essentially a superset of the axioms and theorems of the given system (however this 'super' system will have other unprovable statements).

The extrapolation of this to physical theories is that any theory derived from a set of axioms and having logical and/or mathematical derivations, will not be able to tell the truth or falseness of all theorems (equations) derived from the axioms.

Given how close certain theoretical physics theories have become to axiomatic theories, this issue could have a very significant impact of any 'Theory of Everything'.

AI programmers have been attempting to disprove Godel's theorem for awhile now - without luck.

A most interesting philosophical aspect of Godel's theory is that no axiomatic logical system (including axiomatic physical theories) can be complete. There will always be more to the story.

Knowledge does not 'bottom out' at some level with a nice all-encompassing set of equations. There will always be something more to work out.

I find this a very comforting thought.

@Hans

In terms of a 'Theory of Everything', I think the completeness does come into play. Since I don't believe any such theory can be complete, this is less of an issue for me. For those working toward such a theory, it could be a limiting factor in getting there.

So what if the mathematical tools to handle these situations doesn't yet exist. No matter what physicists do, the mathematical tools are not available to 'adequately' handle the situation.

The problem can be re-phrased: Will physicists recognize that the tools are either not available or not adequate? Will mathematicians recognize this?

What to do if it is recognized?

@William:

Yeah, it's time wasting alright, but for a different reason. My problem, with much that I see about philosophy, is its inherent reliance on misdirection in order to create it's favorite effect - the dog chasing it's tail. Though Donald said

"Unfortunately, it appears you are not aware of the underlying issues at stake.

The self-referential "This statement is a lie." is the kind of statement Russell & Whitehead (and most mathematicians since) have been unable to address from a foundational position. This leads to a problem putting mathematics on a strictly logical foundation"

what he and Russell and Whitehead et al don't get is that there is no foundational position because the subject is not complete. The comment - "This statement is a lie" is meaningless because it doesn't say anything. There is no statement. You could easily, and intelligent people would, respond by saying, "which statement?" and how do you suppose the smart-alec philosophers are going to reply to that? I know exactly how - with tail chasing. Any grammar teacher can show you why such comments are incomplete. Ignoring that gets you your paradox, but only if you ignore the obvious, but I'm sorry, as an analyst I don't do that, Russell and Whitehead be damned.

Oh, and please add Godel to the list! His procuring MacTaggert's A and B series to apply to SR and GR was the biggest farce I've seen in physics prior to Julian Barbour! And that's saying ALOT...

William said "All theories of Everything, must become theories of Nothing (that is entirely Useless)"

Hmmm.... Well as someone who started out with 0 dimensional objects, I have had to become an expert on "Nothing" but I find it far from useless, just really difficult to work in.