How Might Columns be Shown?

Hello fellow newbies, seasoned veterans and those of the tangential,

There may be no better place where one might come to terms with the workings of the mind than the Numenta community forum and to that end hope we might be able to ask some questions without being offended nor offending anyone else.

For instance, at the moment, we’re attempting to identify which element or elements within our diagrams may be representative of the columns, if for instance the distinct triangular regions may represent cells or collections thereof and directional lines formed by cell groupings may be seen as nerve tracts?

Thank you most kindly for your time.

“In effect, the columns “vote” as to what is the most likely object, and quickly settle on cup. The same process occurs across senses, so cortical columns that process visual input can communicate with columns processing touch. In fact, there are connections in the cortex between low level sensory regions that don’t make sense in the classic hierarchical model of the cortex but do make sense in the Thousand Brains Theory.”

The Thousand Brains Theory of Intelligence

In our most recent peer-reviewed paper published in Frontiers in Neural Circuits, A Framework for Intelligence and Cortical Function Based on Grid Cells in the Neocortex, we put forward a novel theory for how the neocortex works. In this updated blog…

Low level processing in the old brain

@0:1:10 nine regions

The Circuit::

Nine Regions:
(terms may vary; these are examples within a given context)

We suspect three or more domains connected in such a manner that may suggest a compound of three or more tetrahedra.
(fig. 4)

Compound of three tetrahedra

“In geometry, a compound of three tetrahedra can be constructed by three tetrahedra rotated by 60 degree turns along an axis of the middle of an edge. It has dihedral symmetry, D3d, order 12. It is a uniform prismatic compound of antiprisms, UC23. It is similar to the compound of two tetrahedra with 90 degree turns. It has the same vertex arrangement as the convex hexagonal antiprism. A subset of edges of this compound polyhedron can generate a compound regular skew polygon, with 3 skew squares…”

" There are 3 types of dihedral symmetry in three dimensions, each shown below in 3 notations: Schönflies notation, Coxeter notation, and orbifold notation.

Thank you once again for your consideration in this matter of the columns and how they might be shown within the context of the diagrams we’ve provided.

Our model suggests a meeting of dendrite and axon other than than the synaptic gap and if so, what might such a vertex be representative of in terms of the brain?

Thank you.

(fig. 1)

Is there a reason not to also be concerned with the other two vertices?



Thank you for your question Paul,

Thus far as we’ve been able to determine, there may be reason enough to consider what the other two vertices might represent and no reason for concern, but rather than assume we’re correct; perhaps a question may be raised in terms of why one ought to be concerned about such a consideration as the other two and upon having no further concerns give consideration to a question of identifying the first of the three vertices? (surely, which ever order you prefer)

May I be so bold as to answer your question with another, and ask why one might be concerned about an intersection between the concepts of “dendrite” and “axon” which excludes the context of synaptic gap? Do you believe there is a physical interaction between axons and dendrites which is separate from synapses, or is your question about identifying the language semantics common between “dendrite” and “axon” and not in common with “synaptic gap”?


A fine distinction and a well-articulated question for which we are both impressed and grateful, Paul.

According to the design, we might expect some form of connection between dendrite and axon other than the synaptic gap and physical evidence suggesting interaction between the two may serve both as positive results for an informative design and a point of correspondence between two disciplines.

To what design are you and your associate(s) referring?


Good point!

We’ve included more than one in the message thread, and so thus labelled, (fig. 1).

Thank you.

Sorry, I am asking where that model came from and the thought processes behind it. I assume you didn’t randomly write three words on the sides of a triangle, and that it is based on some theory.


An even better question; Paul; thanks again!

We employed a creative method in order to inform our understanding of a force with which to be reckoned and began with a subjective description of the universe in which we found ourselves.

Why Triangle?
We assumed free will and a distinction to be drawn, and so depicted choice as two diverging lines stemming from a common origin, distinguished arbitrarily by color.

This is part of my question, yes. I have picked up that you are using the triangle to represent conflicting decisions. However, I think the more important part of my question is, besides the fact that you have depicted a triangle, why you have chosen to label that triangle’s sides as “axon”, “dendrite”, and “synaptic gap”. And secondly, why does this arrangement imply a form of connection between dendrite and axon other than the synaptic gap?

Is there more to this than merely placing three random words on a triangle and talking about what the vertices might represent? Is there some higher reasoning for selecting the three labels in the first place? For example, I assume the process wouldn’t be used to imply the existence of a connection between an arm and a hand which does not include a wrist:


Hopefully I am not insulting your intelligence by this question. I really do not yet understand the concept you are presenting, so hopefully this will demonstrate where the communication is failing. Is there more to this than just a drawing exercise that can be used to think about the relationship between three concepts from a different perspective?


To answer the question of thoughts on design; in the case of (Fig.1), we provided an example of a specific application intended to serve as a suitable point of reference from which another so inclined may find correspondence.

We love your arm, hand, wrist example otherwise such a thing might never have occurred and insult or not, we may be forever grateful. <3

You’re hitting the important points in terms of relationship, three, concept and perspective, and while there may be no shortage of ways with which to describe how a general model might be viewed or applied, we’re hoping to propose to the group an important question which we hope may shed light on the matter of recognition from which the tetrahedral net may come into play and in so doing may demonstrate how one might employ the design in such a manner as you so well described.

(On such a matter as proposing a question of recognition, we’ll be asking if we can ask the question but currently unsure where to ask and therefore unsure where to ask where; giggles.)

Since you have thus implied the question of where, and there no longer being a need to ask it, I will suggest the Community Lounge.


(To be fair to Paul’s point of hanging random terms on a framework; it may well be incorrect to assume such a connection in terms of the brain but for example quite safe in terms of body and nervous system. Again we’re attempting an example of how to use the model in a discipline far beyond our general knowledge set and so are reliant on those better qualified to correctly implement according to their preference.)

Ah, I see. Could you perhaps demonstrate in detail how you have used the model to solve another problem? I am still unclear on the details of your model, so I think such an exercise would be helpful (for me at least)


Unless instructed otherwise; we’re attempting such an experiment pertaining to recognition in the Community Lounge as suggested, which in all likelihood may only produce what may be an invaluable exercise where such details as you describe may be shown, however we’ve been pleasantly surprised by positive results on a number of occasions and look forward regardless.

(we’re currently proofing the article in question)

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Perhaps any demonstration of a resolution or discovery may always remain open to debate, but through an iterative process of trial and error some early successes were expanded upon which appeared remarkably effective in terms of both quality and quantity in the form of a considerable catalogue of original material covering a broad range of topics, some of which we share through a network of Facebook pages intended to engage a general audience in a self-directed, educational experience of discovery, or as one may prefer and depending on which page they may be visiting; an associated network of informative Facebook pages designed to entertain an audience in an engaging experience of educational self-discovery.

While entertaining ourselves with such a prospect, we’ve been anticipating what may be about to unfold and might be inclined to revelry, but as one may find themselves a happy, naked lunatic chasing butterflies in winter, they may be unable to speak in terms of what another finds satisfying and so look to those more suitable to the task at hand.

Thank you once again for providing such a great example and in this case a model of investigative inquiry. <3

If such a thing as quantity may be of greater consideration than quality, perhaps favour may be shown for a thousand tonnes of useless over a fractional gram of useful; but as creative difference may suggest, there may be no accounting for preference and if so, one may speak only of their own and through reason be prepared to defend it, and so to that end we offer the following for your consideration:

There may be no single answer to a question of how many triangles there are in the figure, but if an account of the number of line segments, vertices and colours may be definitive, then the matter may have more to do with the quality of the question or more accurately stated; a question of the quality of the question being asked.

Figure 2:

I see. So to rephrase this in my own words (to make sure I understand): If one were to rephrase the question from “how many triangles” to “how many line segments and vertices”, they would go from asking a subjective question to asking an objective one.

Could you provide an example where you have used this technique to solve a problem or provide a more objective view into a specific domain?


More or less the idea Paul; good example!

The figure may also demonstrate the notion of emergence and an important distinction between quality and quantity insofar as quantity may be meaningless without quality and in terms of quantitative analysis being dependent on the quality of the things being measured.