The blog received a comment, containing what I, for the moment, call 'out-of-the-box' thinking. Non 'standard mathematics' at least. I have moved the comment to this post in an attempt to share this with as much as possible readers. I will reply. But later, I have to let it work on me first.
Regarding our active internal analog math...
I'm a civil/environmental engineer by education but I've been working off and on on a theory which takes the tact that all abstract math symbols and expressions are secondary and arise from a handful of internal analog "math" artifacts and processes. This may not be a very polite thing to say to a mathematician, but I am wondering if you have impressions along the same line?
It turns out that we all get energy to think and do math and other things from the respiration reaction (organics + oxygen -> water + carbon dioxide +energy). And basically, what that means, if you remember your biology or organic chemistry, is, body-wide, within our cells is a ~steady creative flow of about 10^20 water molecules per second -- coming from the 160 kg of O2 we each respire each year. Generally, each water molecule is sort of tetrahedral in shape with two positive and two negative vertices and so, it turns out that there are at least six ways each water molecule can orient within an enfolding field when it first comes into being at a respiration site. That also means that a chain of n-molecules can form in 6^n different ways. Thus a sequence of 12 molecules could form in 6^12, or about 2 billion different ways. A chain of eighteen molecules could associate with 6^18 or 10^14 different impressions. Now, in this analog math theory, I am assuming that repeating vibrations in the environment ought to result in formation of similar stacks and chains of structurally coded water molecules being formed. This gets us a rather crude image of the vibrations of our internal and external environment forming an internal echo or representation within this active internal analog "math", or "language".
I say it's active because the 6^n stacks of water molecules are really also structurally coded hydrogen-bonding packets and such things, when they unfurl, are connected with and influential in protein-formation and protein-folding, which is to say, memory formation and muscle movement, which is to say, in our case, ALL human expression, perhaps beginning with our nearly universal actions and impressions of counting each of our ten fingers and ten toes, and the like.
Bizarre stuff, huh? Lots of little internal Turin devices writing out structural coded signals.
I'm wondering if mathematicians are taught this type of internal analog math as the basis of the abstract math symbols and expressions, or if they are given different associations or impressions, perhaps leaving it that there is just an uncanny (and unknown) relationship between much or all of nature and math?
Also, I vaguely see the similarity between 2^n binary or boolean math and the 6^n "multiple-state structural coding" that I've made up or stumbled onto. I expect the trend continues with starting with other polyhedra which have limited orientations "within enfolding fields" -- when a containing structure is added. My general hunch is the initial condition IS actually significant for us and we can immediately get to multiple states (relevant to ~quantum mechanics/quantum gravity) by starting with tetrahedron and adding the enfolding cube container, rather than the way it's done presently of beginning with the xyz-cubic framework and adding variants.
Initial conditions do matter in mathematics, don't they?
Thanks you, Ralph Frost.