Penrose / Hameroff and a note on Emergence

These diagrams (Boltzmann and Hopfield networks) put us in mind of the orthogonal view of a 16-cell Coxeter helix polyhedral net, while the Boerdijk–Coxeter helix featured in the same article puts us in mind of Hameroff’s Penrose’s microtubules under Orch-Or and if so, might there be for instance opportunity for correspondence between Numenta’s work that contained in the Orch-Or hypothesis?

(Hameroff seems to be pointing to a resonance taking place which puts us in mind of a Hopf bundle.)

" In the mathematical field of differential topology, the Hopf fibration (also known as the Hopf bundle or Hopf map ) describes a 3-sphere (a hypersphere in four-dimensional space) in terms of circles and an ordinary sphere. Discovered by Heinz Hopf in 1931, it is an influential early example of a fiber bundle."

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Sorry - not a fan of Penrose or his quantum consciousness.
I have a much simpler model that does not require mechanisms currently not known to be part of nerve behavior.

Best of luck with your theories.

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Perhaps not surprising given the premise of consciousness as prime; if we understand correctly, such talk may be heretical among specialists in artificial intelligence. Be that as it may or may not, we’re not dependent on nor here to promote Orch-Or as we’re hoping primarily for some interpretations on the designs we’ve shared within the Numenta community.

My biggest concern - I spent considerable time working though the Penrose stuff. Very pretty, very mathy. I could not match it up to the known functioning of the biology. If there is no way for it to actually work - well - that’s kind of a show-stopper.

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Again understandable given biology as model for AI, while from the perspective of Hameroff and Penrose, the biology may be hard-pressed to account for consciousness, at which point we might refer to the central object of the tetrahedral net and suggest such an emergence may be accountable by virtue of the arrangement such as in the whole being greater than sum.

(As a side-note; providing necessary constituents may be appropriately arranged and if it exists at all, the emergent central object in addition to both horizontally and laterally inverted may be either potentially illusory or ubiquitous.)

As we see it currently, we’ve been slowly moving through the application stage and since we’ve interpreted and applied the model sufficient enough to our needs, interpreters able to construct a functional correspondence between two, complex worlds such as two human beings, two languages, two academic disciplines or two hypotheses may be presented opportunity to move forward with their ideas.

When you say “we” is it just you or are there more people involved?

Such a notion as no other people involved, may be difficult to conceive; have you a better question?

(We’re producing notable results with a general model and sharing our findings to the most potentially appropriate group we’ve thus far come across and if we have an unreasonable expectation of the Numenta community making use of the ability to interpret and apply what may prove an informative design, any indiscretion on our part might be understood given what we know about the scientific method and the necessity of trial and error to experimentation. However, if our expectations may be reasonable then we stand open to constructive inquiry and look forward to continued success for the Numenta project, research team and community members.)

Have you had any success with the illusory contour problem?

It seems like it would be low-hanging fruit for your approach.


One may be unfamiliar with illusory contours as necessarily a problem, so perhaps a question may be raised in terms of why such a problem in relation to our approach may be given to the impression of low-hanging fruit?

(We can’t speak for others, but we’ve been producing some interesting illusory or otherwise ambiguous designs and find them quite satisfying and indeed informative.)

The “problem” is explaining why you see what clearly is not there.

The repeating triangles between island of recognition extending the brush manifold (fiber bundle) could well be an explanation.

I would expect at some point you could show the mechanism and whatever supporting theory that explains the phenomenon. If you are able to do this it could well attract attention to what you are doing.

I do understand the brush hyperspace manifold and it does have interesting possibilities with repeating Calvin tiles, particularly with the evolution in the patterns over time. This could bind the patterns as they evolve.

You will need to do more than draw triangles to make the work accessible and useful. I am doing other things and don’t have time to work in this area.

BTW: the Numenta mothership is not very interested in Calvin tiles. The TBT is all about lateral connections but taking the next step to forming Calvin tiles is not part of the canon. This has been a personal thing for me and I doubt that you will get much traction with Numenta unless you can demonstrate something very impressive.

There is an exceedingly important distinction to be made between the ability to read and write, and the ability to process information correctly in order to recognize something important. We’ve considered such a thing best described for lack of better as algebra, or our ability to fill in missing pieces of a puzzle through creative problem solving. We suspect such an ability as being essential to recognition especially in terms of distinguishing something as important.

(We look forward to hearing positive results pertaining to your work on Calvin tiles.)


Specific to Mathematics

I believe your best bet in this problem space lies with analytical geometry.
But what do I know anyway?
I am not a mathematician.

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Sure; we love that stuff and would love to hear from some geometers.

(In addition to mathematics, Algebra may apply to linguistics and relate to humour in the form of completing otherwise incomplete information such as that which got out through the sliding door and buried a bone in the flower garden, may likely be…
a companion alligator.)

Also not a mathematician - but I’ve had this Crampin and Pirani book sitting on the shelf taunting me with differential geometry for awhile (and Gray’s intro w/Mathematica) - and tangentially exposed to DOE’s ASCI/DMF Whitney Fields. Out of pure curiosity, can you expand a little on your thinking?


We too are looking forward to hearing more from Bitking and in particular something he mentioned pertaining to recognition occurring at juncture or convergence or something to that effect, which may play an important role in terms of how both mind and brain may be employing geometry in the process of recognition.

@GoodReason Actually, I was hoping that you knew something useful and could expand on my lead. You seem very passive when it comes to discussing the meat of the ideas you posted. Perhaps you will have more to say soon. So far I really have not gotten anything from your responses.

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Sure. Most of what was posted on the top of the page did not do much for me. I did pick up on the fiber bundle link as this was similar to a problem that was discussed in a recent Numenta research meeting.

Marcus was talking about how grid patterns repeat and that due to this they could be thought of a unit sphere, repeated from one grid module to the next. The information is phasic in that the location on the unit sphere repeats and perhaps, evolves, from one module to the next.

Numenta has very little interest in my hex-grid coding scheme inspired by Calvin tile but I could see that the same problem has to be solved in my coding scheme, the grids code phase, scale, and angle to represent something. The nodes within the grid also repeat on a regular spacing. They have many of the same properties as Moser grids.

As you move across the grid one way of thinking about this is that the hex-grids could be thought of as tiling the outer surface of the fiber bundle. The brush model collapses that to the core of the brush which could be thought of as a line that is the distilled center of this representation. This line in this map can be thought of as tracing the surface of a manifold. When multiple maps are interacting this forms a higher-dimension manifold. Hence the call out for linear algebra.

As far as the illusory contour problem - the spline of this fiber bundle could auto-complete as the hex-grid forms around the recognized ends. If the spline is the same as a perceived line then this fill-in could be perceived as a contour.

May we ask what the preferred general term might be for the lines of communication between cells and if it is safe to say we or the mind navigate(s) across those lines in such a way as to circumnavigate three-dimensional objects or in the case of a tetrahedron, in order to determine the object’s faces by circumnavigating along its edges whereupon coming to a vertex, a boundary may be established?

Thank you, or never mind as the case may be.

(Rather than the cells, we’re seeing the lines of communication as possibly more important and most notably where such lines may intersect as we suspect you may have alluded to in a previous discussion.)

Synapses and axons.

This really is very basic neurobiology.