Foundations of Mathematics - How arithmetic and numbers are "quantum-like"

Bruno, 

Thanks for the clearer and more detailed summary of your thesis relating/associating p and [p] to concepts developed in other traditions and linguistic communities.  

I am curious whether you can add more detail or clarity on relating ~how you see/saw arithmetic contain 'quantum features', or that you came to "predict quantum logic and quantum computations"  and what you mean by that?  Does it have to do with some propositions being both doubtless and doubtful, etc.? And if so, what words came to you first?  

Also, when you say, """by justifying the quantum from a very old theory of consciousness (Mechanism, or its modern Digital form) """,  what are the traits you reference in "Mechanism"?   Also,  by "very old theory of consciousness", are you referring to the split into "subjective and objective" categories?

Additionally, are you saying that quantum features are implicitly "already"  embedded in arithmetic and numbers, as in, just like the ordering alternations between  addition and subtraction or multiplication and divisions,  or a number potentially having N+1 inner states thus predicting the numerical value of its successor?

It seems to me that  math or STEM education might greatly benefit from such a re-factoring since it might eliminate  the habitual starting out in teaching a seemingly non-quantum, classical 1,2,3,4... math perspective and then, after the die is cast,  trying to introduce the non-classical,  quantum mechanical inner states, artifacts and relations.  

If arithmetic and xyz-Cartesian numbers and math are ~already  quantum mechanical or having the "quantum logic", that would be a handy feature to accommodate and emphasize in the early steps of the K-12 educational process.  

It's rather obvious and easily conveyed in the magnetic or ~bipolar or ~binary tetrahedral analog math that I am marketing, but, other than pointing at the positive and negative numbers, I am not clear on how students  might observe or see arithmetic and numbers as "quantum-like".   Can you clarify?

I'm not doubting you did or can discern these relations, I'm just curious to discover what is entailed or involved in describing it and conveying it in the instance of nested structured~duality   that you are working with.

Best regards, 

Ralph Frost, Ph.D.

Changing the scientific paradigm.

https://magnetictetrahedra.com

Duality and "Bipolar Polyhedral Structures

[Bruno Marchal] But how do you relate that with you experience? You have not yet told me what is the duality in the nested structured duality. You need to try to explain this without using the terms “nested”, nor “duality”. You seem not trying to explain. 

[rf] Try this. Think of 'duality' as a pointer to 'quanta' or 'multiple states', and consider that such quantum features are and must be  inserted first in the foundationation of mathematics (even in arithmetic), rather than as a somewhat magical add-on after a classical, non-quantum, introductory prepi-cycle. In my first pass through this terrain back in 1975-1982 -- in the Bad Old Days, back in the Reagan eras,  I was imagining building a tetrahedron using four rod magnets. With my wife's metal-working help I soldered a center connector together and then played around with the five states of the inner magnetic tetrahedron.   Tetra- implies poly- and inner implies outer, so in a couple of moves on the gameboard I was considering the states of all inner and outer "bipolar polyhedral structures" (bps).  So, if you follow, I upgraded the term from 'bipolar' to 'duality'.  Originally, though, I came around to noticing that even forgetting about magnets and just making a structure out of anything, to my way of thinking there would always be a tiny, maybe what mathematicians might call "infinitesimal difference" between one end (half) of a radii or edge. One half could have a few more electrons or photons or quanta on one half than the other,  So the ends are different, similar to what is overtly present with magnets, but now more subtle, tending to the point of practically indistinguishable.

That's the original meaning/origin of "duality" as in "nested structured~duality", to me.  That's why I sometimes qualify it a "difference", and it could be a difference or duality in many different traits of features.

In the last few weeks, I have remembered that I used to think that ALL structures, even the highly idealized ones, are ~actually 'bipolar polyhedral structures' existing or having multiple states.  That is, that there are not the two categories: {regular, bipolar},  but just the one category: {bipolar}.  

Continued thread on the foundations of mathematics

Thanks, Bruno, for trying to understand reality being nested structured~duality.

On Wed, Mar 7, 2018 at 10:24 AM, Bruno Marchal <marchal@ulb.ac.be> wrote:

Hi Ralph,

On 4 Mar 2018, at 10:44, Ralph Frost <ralph.frost@gmail.com> wrote:

Bruno, 

I reply here below in attempt to convey to you an understanding of my term "nested structured~duality". 

Scroll down  a ways, below UTOPIA  to [rf Mar 4]...