Five Part Harmony by Gary D. Simpson

Dear Sir,

You say: "The unit vectors i, j, and k represent the x, y, and z axes respectively. The unit vectors make it possible for the axes themselves to be a part of computations". In that case why complicate things by adding terms i, j, and k? The x, y, and z axes could have been sufficient by treating them as unit vectors. After all, vectors are different only because they have movement (energy) and direction. The axes provide direction. The axes have no meaning without something to represent. We also use mobile coordinates. Thus, what is the justification of adding i, j, and k? Further, x, y, and z are real, whereas i, j, and k satisfy i^2 = -1, which means complex. Why should we use complex numbers at all? They do not have physical presence. Anything that has no physicality cannot be a part of physics. Your statement that you have tried to "combine physical space, in the form of an arbitrary unit vector, with the complex plane..." presupposes that both do exist physically. Is there any proof in its support? Can you give examples?

Your statement: "Let x = 1 and let y = 1. It follows that x y = 2. This is a simple scalar result. Now let x = i and let y = j. It follows that x y = i j. This is a vector from the origin of length sqrt(2) at an angle midway between the x and y axes" only conforms our views. Addition is linear accumulation, which is possible between similars. Here x and y have the same value and belong to one class. But x = i and let y = j shows that they belong to two different classes. You cannot add 5 oranges and 3 apples. You can add them only as fruits. We have submitted an essay to physically explain 10 dimensions. Unlike your 5 -D inferred space, we have shown direct correlation, where we have used the same logic as you have shown here.

Regards,

basudeba

Dear Sir,

We have started showing the inadequacies of mathematical physics and argued for physical mathematics. You are silent on this aspect. Similarly, we took 8 pages to refute modern notion of extra-dimensions, which has not been physically found even after a century. This includes your notion of dimension also. Kindly comment on that. How long you will chase a mirage? In case you have any other notion of dimension, kindly educate us.

Our 10 dimensions are different from your 5 dimensions and are physical. But can you show your 5 dimensions physically.

A quaternion is a complex number of the form w xi yj zk, where w, x, y, z are real numbers and i, j, k are imaginary units that satisfy certain conditions. Firstly, complex numbers itself have no physical representation. All text book representations are manipulated. The concept of complex numbers was introduced by Euler, when he tried to solve the equation x^2 1 = 0. But is there any physical system where this equation is fulfilled? The answer is no. If we rewrite the equation as x^2 = -1, still then it will not lead to mathematics or physics because squaring is done with not only the numbers, but also signs. Two negative signs square up to positive as per the mathematical rules. Then how can x^2 be equal to -1? Further if i denotes square root of -1, what about the equations x^2 2 = 0, x^2 3 = 0, x^2 5 = 0, x^2 7 = 0, etc.? Why do not we invent suitable terms to explain square roots of -2,-3,-5,-7, etc? In that case, the required symbols will be infinite and doing mathematics will be impossible. For this reason, complex numbers cannot be used in computer programming. Some people say complex numbers include real numbers and more. In that case, dream should be used instead of observation, because dream includes what we observe and more. May be for that reason modern scientists are including dream with observation to formulate theories based on extra-dimensions, strings, foams, chamelions, axions, gravitons, sparticles, bare mass, bare charge, dark matter, dark energy, expansion of the universe (even though it is not observed in less than galactic scales and we observe blue-shift), inflation, etc. But their dream costs humanity huge costs, which could otherwise have been enough to eradicate poverty from the world. Should dreams get primacy over real sufferings of the world?

Hope you will educate us on these issues.

Regards,

basudeba

Hi again Gary. Not sure if this turns out to be useful, or even makes sense, but it jumped out because there is a chance it might relate to the factor of 1/5 which seemed to be missing from the speed in the CMB frame in your final conjecture.

I was just reading Jonathan Dickau's essay and was intrigued when he mentioned that the greatest hypersphere is produced in 5 dimensions. I don't know whether your 5-d construction is a hypersphere, but he refers to a Wolfram page Ball which has a formula V=S/n (Eq.2) relating the volume and surface area of a unit hypersphere to the dimension n. For n=5, the surface would be 4-dimensional. So it looks like there could possibly be a factor of 5 floating around in the math going between 5 dimensions and 4 dimensions.

I am still working on my essay involving the derivative of a conjugate quaternion, which I started fiddling with after reading your Calculus 2.0 essay last year. -cw

I can mention here..

Somewhat paradoxically; while the (hyper-)volume curve is maximal around 5.25-d, the (hyper-)surface is maximal at ~7.25-d. There is some interesting material to access here:

2.1.3 A Brief Look at "Complicating" from 'Mathematics Itself: Formatics - On the Nature, Origin, and Fabrication of Structure and Function in Logic and Mathematics' by David M. Keirsey.

It would seem that Hilbert's hotel results from using hypercubic expansion, instead of building on spheres. People who build brane-world models often forget that branes are a generalization of spheres.

Regards,

JJD

Dear Gary

I am thankful that you are with me! We must to join our efforts to push ahead what we believe are the right. I see one of important criterions of our rightness in that the different brains in the different times and in the different places may come to similar conclusions. So, I just felt myself very obligated to read your work to say something.

About of decay of freely neutron you are fully right. I have tried to explain it and I even calculated its time, based on my model (you can find it in good time in my ,,Rethinking ... (I),, )

I will answer you within short time!

Good wishes

Dear Gary,

You have used the the complex vector representation and the Euler's beautiful formula in your attempts to describe proton, in this case. You have the definite success on this. It shows just that you are on the somewhat right way. I am very agree with you that the dynamics and harmony should be the base to understand the microcosm. By the way, the solutions of Maxwell's equations (in macrocosm) and Schrodinger's equations (in microcosm) with its different modifications correspond with this. The main questions however, has become there - how need to interpret these solutions, since a what of physical values must to put there as the this or that members of equations? That is why I am calling to put the ideas first before of math! You know of course the merits of Faradei as well as Nikola Tesla ..... who was very weak in math! So, the math does not disturb them to RIGHT THINKING and to find the right answers by the same! Then their job was continued by whom who was more well with math ....!

So, I welcome your work and I will happy to help you.

I wait that we can be agree each with others.

Good wishes

Dear Gary,

I read your interesting essay and understood your intention.

You lose me when formula's are introduced, It is a language that I just have problems with.

You say : It is certainly possible - perhaps even likely - that these conclusions are false. However, if that is the case then the reader is left to explain the proton diameter calculation.

So in order to discuss your conclusions I have to calculate ? In my humble opinion the diameter of an instananeous excitation from the past called "proton"

is just trying to nail an idea onto a board with a screw.

That is why I like your essay , you are aware of its relativity...

I hope that you can find some time to read and maybe rate my essay : "The Purpose of Life"

best regards

Wilhelmus de Wilde

Thank you Gary for your instructive comments on my essay "The Purpose of Life".

Next time I will try to avoid acronyms (perhaps I like to mimic formula's...)...

Indeed there is more to explain but I could not realise it in nine pages. I have solutions for time-travel, black hole information loss and more that you can find in my article published in The Journal of Consciousness Exploration and Research Total Consciousness in Total Simultaneity

Your "Complex Plane" is indeed almost the same idea as Total Simultaneity, maybe I need your advise to mathematically explain my idea of Total Simulaneity which is both a not in our reality existing singularity without time and space as well as it contains ALL Eternal NOW Moments and contents also a "field" named Total Consciousness.

best regards

Wilhelmus

In regards to questions about non-integer dimensionality..

Hi Gary,

Non-integer dimension arises in causal structure theories of quantum gravity, which is referred to simply as a running D - compared to the case where D = n, where n = 0,1,2,3... Of course; this gives space a fractional dimension, and makes it a fractal - along the way - which is simply how surface roughness evolves into a new (whole) dimension or extent. So briefly; fractional dimension arises because of folding of space in the microscale. As Lawrence alludes, the Hausdorff dimension evolves.

One can also think of this as relating to emergent spacetime, because if the observed properties of space and time, this means that intermediate values are accessible between the onset of geometrogenesis and the current era. One can also see this as connected with a different root dimension for the microscale and macroscale, as with Rainbow Gravity (which was explored by Magueijo, Amelino-Camelia, and others). If space is 2-d at the Planck scale and 3-d at the common scale; what is it in between?

Lastly; this is a broad feature of what is called bi-metric gravity. There are many formulations in that family. There's too much to say simply, but as the name implies there are two co-existent descriptions of space - to deal with the weak-field and strong-field, low-energy and high-energy regime, or common scale and microscale, and so on.

All the Best,

Jonathan

Hi Gary. I think I see now what you are getting at with your equation 3.1 - it is a combination of two quaternions but having complex coefficients instead of real in the real quaternion basis. I recall that what you would get is a biquaternion. It turns out that a biquaternion 2x2 complex matrix is not a quaternion, and any 2x2 complex matrix can be expressed in biquaternion form. Like an octonion, a biquaternion has 8 independent real variables. A quaternion is a biquaternion with a specific combination of symmetries that allows only 4 independent real variables. I cannot see getting an octonion unless your 'complex i' was the octonion 'l' in the sequence of seven octonion imaginaries i,j,k,l,m,n,o - and then it would have to be checked for (or arranged to have) the appropriate symmetry.

Best to you,

Colin

Hello Gary, You say that the mass ratio depends on absolute velocity and suggest a satellite test. Would the ratio also vary as the Earth changes direction round the sun? If the absolute velocity is the sum of the sun's motion and the Earth's motion round the sun, would it change with the seasons?

Yes, the quaternion is fascinating, a lot of promises and makes you wander before you come to a path leading to the goal. This goal - the recognition of your merits by most mathematicians and getting your name in the books, at least for the fact that you are using the quaternions of his own invention, calculated the size of the proton.

I wish you success on this path, at least in this contest!

Because you went deep and put a lot of work to that branch of mathematics which looks to be a dead end, I'll put your essay the highest score.

New Cartesian Physic, which is based on the equivalence of space-matter, needs the theory of complex numbers not only on the plane, but mostly in space. After all, Descartes himself believed that the basis of physics must lie geometry.

From New Cartesian Physic great potential in understanding the world. To show this potential in his essay I gave materialistic explanations of the paranormal and supernatural. Probably, I made a mistake that has bound New Cartesian physics with the paranormal and supernatural, because it does not attract the attention of others. Visit my essay and you will find something in it about New Cartesian Physic. Note the drawing of geometric relationships in the atom.

Sincerely, Boris Dizhechko. (Note that I did not know English and use online translator)