Brought to You by the Number 10

Science has numerous unanswered and perplexing questions: How do electrons "tunnel" through resistors and suddenly appear where they shouldn't be? Why does the universe have much less measured matter (and energy) than it should given the astrophysical calculus (and thus, "dark matter" and "dark energy")? Are there such things as gravitons (minute particles that transmit the force of gravity)? Why does light behave as waves sometimes and, other times, as particles (photons)? If the speed of light is absolute and as fast as things can go, how can gravity have a seeming instantaneous effect over huge interstellar space? Why don't matter and antimatter annihilate one another.1 Why is time unidirectional? What causes magnetism to behave only over very short distances whereas gravity, a much weaker force than magnetism, can reach out over the vast distances of space? Why does magnitism manifest itself with flux lines … why not flux plasmas?

Mathematicians and physicists, who have been trying to answer these and many more perplexing questions and also run to ground Einstein's elusive snark, the Unified Field Theory (also known as the "theory of everything" -- the linkage of astrophysics with sub-atomic physics), have concluded that there must exist many more than four dimensions … and as many as ten or even twenty-six (where, according to the scientific literati, most UFT mathematic equations resolve themselves in sublime elegance). That is, most of us currently grasp the notion that our world is bounded by height, width, length and a time dimension (or X, Y, Z, and T)2. However, adding more dimensions to this set stretches our minds beyond normal comprehension.

Mathematicians have tried to help us visualize this hyperspace by proposing "string theory" where additional dimensions are teensy tiny3 vibrating strings that are curled up throughout the universe and manifest themselves only where they intersect our visible world … possibly as subatomic particles. Even though I don't understand the mathematics of string theory, this seems to me to be a silly explanation (like the Platonic notion of a crystal sphere surrounding the earth). For instance, how can all six additional dimensions be represented by a single physical entity, a tiny string? And why do we continue to think within the box (the space-time continuum). Can't additional dimensions be outside this paradigm? Certainly Einstein reached beyond space to include time. I don't believe string theory moves our universal understanding forward one iota. If anything, it seems to be a regressive rationalization. The number of space-time dimensions associated with various string theories varies from 10 to 24. But the preponderance of string theories requires 10 dimensions, so this is the number toward which my arguments are directed.

I often lie awake nights, trying to understand these conundrums with laic naiveté, particularly what might be the 5th through 10th dimensions of our existence. Fortuitously, part of my career has been spent creating software to manipulate and display multidimensional databases (also known as hypercubes). And so, I have thought quite a bit about how to visualize such multidimensional data constructs. One software product I was involved with was able to store, retrieve, and manipulate eight data dimensions and display graphically four dimensions (X, Y, and Z axes, as well as animation -- used to represent the fourth dimension, time). I also have followed what other graphics thinkers and developers (including Tufte) have proffered along these same lines. I also think that the basic units of measurement of physics (SSI) can offer useful insights. And, finally, animals' sensory apparati seem also to offer a notion of how our world is constructed. These three approaches have been useful for me in trying to understand what might be the further dimensions of our physical world. Let me explain:

1) A fifth dimension can be easily displayed graphically using colors. That is, if one uses animated planar surfaces to display the first four dimensions. (If one must visualize more than one value surface in four dimensions with say, a bar chart, then color must be used to differentiate these value surfaces and this option is negated.) Following this logic to the real world may suggest that the visual spectrum, or to generalize, the different wavelengths of the electromagnetic spectrum, might indeed be the fifth dimension.4 The following table (also from the Internet) represents the electromagnetic spectrum as we now know it. The Energy column represents the photon energy at each wavelength in joules (107 dynes*centimeter -- dynes are grams*centimeters/second). Wavelengths are in meters and Frequency is in hertz (cycles per second):

................Wavelength (m).............Frequency (Hz).............Energy (J)
Radio..........> 1 x 10^-1..................<3.x.10^11................> 2 x 10^-24
Microwave.1 x 10^-3 - 1 x 10^-1....3 x 10^9 - 3 x 10^11...2 x 10^-24 - 2 x 10^-22
Infrared......7 x 10^-7 - 1 x 10^-3....3 x 10^11 - 4 x 10^1..2 x 10^-22 - 3 x 10^-19
Optical....4 x 10^-7 - 7 x 10^-7...4 x 10^14 - 7.5 x 10..14.3 x 10^-17 - 5 x 10^-19
UV..........1 x 10^-8 - 4 x 10^-7.....7.5 x 10^14 - 3 x 1016..5 x 10^-19 - 2 x 10^-17
X-ray........1 x 10^-11 - 1 x 10^-8...3 x 10^16 - 3 x 1019..2 x 10^-17 - 2 x 10^-14
Gamma-ray.....<1.x.10^-11................> 3 x 10^19.................> 2 x 10^-14
2) A sixth dimension can be graphically displayed with color brightness. Brightness (or color intensity) is measured by the amplitude of an electronic spectrum wave.

3) A seventh dimension can be graphically displayed with color saturation. Following this logic to the real world suggests that luminous intensity (candelas) might be the seventh dimension. (Note: candelas are also used to represent the luminious intensity of radiation all along the electromagnetic spectrum.)

4) So far, graphical dimensions are differentiated by we humans with our eyesight. Why can't they be differentiated also by our touch? One could imagine a futuristic graphical image with a tactical component so that changing temperature would represent a spectrum of values along a dimension. Therefore temperature (Kelvin’s) might indeed be the eighth physical dimension. (note: temperature might be the measure of brightness and/or luminious intensity at the infrared spot in the electromagnetic spectrum … in which case this would NOT be another dimension.)

5) Another tactile (or rather kinesthetic) representation of dimensionality might be the weight of the object represented. Since weight is really the mass of an object within a particular gravitational field, then mass may be the ninth physical dimension … and gravity the tenth (if gravity isn't part of the electromagnetic spectrum). Gravity was described by Einstein as a warp in the space-time continuum. Why can't gravity's formula -- feet per second per second (or distance/time**2) be an addition to distance**3 as representing the first three dimensions. (Note: Gravity waves have recently been argued to travel at or close to the speed of light … just like all the waves of the electromagnetic spectrum. It is also believed that the force of magnetism also travels at nearly the speed of light.)

6) As suggested in the footnote below, a matter-antimatter dipole (or continuum) might be the tenth dimension if it is not gravity. (The tenth dimension might also be magnetism.)The preceding are my guesses for the makeup of ten dimensions. It is interesting to note that all the base SI units of measure have been included in this treatise … except for amperes that, it is claimed by some, is really derivative … and moles that are really a measure of molecular count. It is also interesting that all of our senses have been covered except for hearing, texture feeling, taste and smell. Why can't hearing also suggest a dimension? To me, this animal sense represents the lateral movement of molecules and not a true physical degree of freedom. Texture is primarily molecular arrangements, and smell and taste really discern the chemical character of molecules and not the nature of atomic or subatomic dimensionality. However, it must also be noted with interest that some animals have a sense of magnetic polarity, which leaves us with another tantalizing clue as noted above.

FOOTNOTES
1 Questions: Are matter and antimatter a dipole? Or is there a continuum of multiple states between matter and antimatter? Is this continuum, if it exists, another dimension?
2 This suggests the UFT is resolved with an equation in as many as 8 variables with one variable (distance) being cubed. However, there is nothing that prohibits other dimensions of the ten being represented by powers of any of the above (or other) dimension surmises (see the comment above about gravity).
3 University of Washington scientists using gravity measurements to hunt for evidence of dimensions in addition to those already known have found that those dimensions would have to occupy a space smaller than an electron. Note that photons are believed to be extremely small, if they have any mass at all.
4 It seems logical to generalize the visual spectrum into the whole electromagnetic spectrum the purpose of this exercise. However, this raises many other questions: Are there electromagnetic waves whose periods are infinitely small and/or infinitely large? Could electromagnetic waves that are infinitely large be gravity? Could electromagnetic waves that are infinitely small be magnetism? Or the weak atomic force? Or the strong atomic force? The fact that the electromagnetic spectrum can be represented both by waves and particles (photons) is another tantalizing clue to it being a dimension of our existence. If subatomic particles are theorized as the four-dimensional representations of the string dimensions in string theory, why can't photons be the equivalent four-dimensional representations of five or six dimensional electromagnetic waves?