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.
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.
We had higher hopes for Bitking. (offers two terms instead of one, excludes dendrites and includes condescension)
The synapses are on the dendrites. Collecting the results of the connections of the synapses, which is precisely the question you asked.
The fact that you even asked sets up the response.
I have been working with neuroscience for 30 plus years. I spend time and effort for genuine questions from people that are making an effort to learn. If you need bona-fides feel free to read my many detailed posts in the nubie section.
I have given you the benefit of doubt and you have proven that to be wasted effort.
Troll someone else.
We learned a great deal.
(Tracts, may have been the term we were looking for, but regardless; we’re still hoping to arrive at a suitable description for such goings on within the brain.
In some cases, we’ve considered the regions as minds of their own which the Thousand Brains hypothesis may be inclined, but some descriptions we’ve found there may raise questions even among those well-versed in the discipline, such as “a grid cell-derived location”, or “locations over movements” ans so on. The latter may be favorable as we’ve found aesthetic terms and particularly those in music such as movement, favorable to positive results and perhaps necessary to provide a satisfying description for such goings on.)
Thanks for the reply - I think I need to review your previous posts before continuing. Is this where’d you suggest I start:
These two thread have most of what I have posted. The first thread include pointers to the post you just put up. There are a lot of moving parts and the hex-grids are just a part of the overall package.
But yes, the hex-grid post more directly addresses the coding method.
Risking asking something already answered elsewhere - I think you talked about Hopfield/Boltzmann pattern completion. Since creatures need to identity occluded objects (food behind leaves, predators behind foliage, mates behind rocks) would you expect phantom contours to be a very simple/primitive/well-conserved ability and something like a Hopfield net?
I expect this to be encoded in the visual stream in the cortex. V1 though Vx is where the visual illusions are found.
I expect that visual primitives are also encoded in the amygdala. This limbic bit is outside the purview of the cortex and not accessible to consciousness. Think of blindsight.
Like I said, it is a big system with a lot of moving parts.
The only helpful contribution by that guy to AI:
Feynman wasted a lot of time on the connection machine:
Generally physicists should keep away from AI.
We may be less than qualified to speak of the biological mechanisms, but the following paper may point out some key points to consider in particular Vyshedskiy’s figures 3, 4 and 8 in what may be necessary for such a complex function as may be demonstrated by the illusory contours problem.
Neuroscience of Imagination and Implications for Human
Evolution - Vyshedskiy Curr Neurobiol 2019; 10(2): 89-109 ISSN 0975-9042
Variation on Vyshedskiy’s Figure 4:
That was an excellent video. I had to put it on my playlist.
A few paragraphs into this reply I described the latest in regards to (where all the chemistry begins) Origin Of Life theory indicating that RNA came first, and DNA is most like a RNA created library not something that can be “selfish” as in old-school evolutionary thought. The “Confidence” requirement in what I quoted is essentially a “hedonic system” needed for the driving force of self-replicating RNA evolution to be pleasure:
I’m not sure about your other thoughts. What I’m looking for is a cell level 3 axis spatial vector map shown on the right side of the screen of this simulation, indicating direction around (nonpropagating) obstacles towards a place that starts a wave to attract it to what the body wants like (being the location of) food. For at least navigational purposes wave propagation makes it easy to model properties of what exists in an external environment. Only have to set hexagonal places (on surface of microtubules and such?) to propagate, not propagate, and optionally reflect a wave back to source as in echolocation. A wave generated in the map will travel out from a given location according to the shape of the navigable environment.
In the way a separate motor system works is a bilateral tug of war that can maintain stress on motors/muscles, working towards two horns of a bull like opposite bilateral rotational directions, according to heading vector of a given place in the vector map. The forward/reverse works the same way, to represent a magnitude from one opposite max value to another. It seems like you are taking that to higher level constructs like love, in what you draw out using triangles.
Everything that helps explain how our brain especially cortex works has correspondence to the mission of Numenta. We all only need to show how to code in what the HTM model of a neuron needs to include to be more biologically accurate, work even better. Current mysteries include cell level sequence memory formation and playback. Also each cell ahead of time responding to periodic events over time like in timed cold air blast experiments is not yet included, but can be added, to at least see what happens.
I thought I should explain what I have, to maybe help support what you have, then let you take it from here.
Awesome piece of work! Missed the introductory notes due to some buffering on my end but intently watched the video and by the end had a feeling for what was being depicted. (might come back to the video later with some questions)
Currently looking over your material to get a lay of the land and in the meantime might offer an early draft of what may equate with what Numenta refers to as the spacial pooler and some background on why we think the figures we’ve been sharing might be important.
(As they may equate with that which Numenta might reference as inference, in part or in whole the dotted lines of figure 7 may correspond with the random motor’s function or some aspect thereof within at least one context of IDL v6.1)
" Given a metric space (loosely, a set and a scheme for assigning distances between elements of the set), an isometry is a transformationwhich maps elements to the same or another metric space such that the distance between the image elements in the new metric space is equal to the distance between the elements in the original metric space. In a two-dimensional or three-dimensional Euclidean space, two geometric figures are congruent if they are related by an isometry; the isometry that relates them is either a rigid motion (translation or rotation), or a composition of a rigid motion and a reflection."
" While advantageous for architectural drawings where measurements need to be taken directly, the result is a perceived distortion, as unlike perspective projection, it is not how human vision or photography normally work. It also can easily result in situations where depth and altitude are difficult to gauge, as is shown in the illustration to the right. This can appear to create paradoxical or impossible shapes, such as the Penrose stairs."
If a single hexagon of the grid cell matrix equates to a single cell, then a tri-coloured triangle such as in (fig. 3a), may equate to a single hexagon of the grid cell matrix in which case the hexagon goes without being shown, otherwise the first hexagon appears at three units as in (fig. 3f) or at six units (fig. 3g).
Most of what you need is summed up here:
The (right side of screen) spatial network part is the result of my modeling what I sensed being described by this paper, from live rat data:
The network adds a best guess mechanism to the motor system, useful for navigating from place to place without bumping into things, which brought things to life like nothing I ever tried before.
That sounds like an excellent project. In the model I program it is assumed that the RAM in the circuit has at least (by default) binary addressing to store unique experiences, in unique locations, while for living neurons it’s not that easy they have to on their own sort out a fantastic amount of sensory information.
You will then be in an area the HTM model was meant for, where the model I have predicts you are then constructing an address decoder:
What Numenta is reverse engineering is the (neo)cortical part of the brain, added on top of the lower level trial and error motor system that most has to guess what works to coordinate motors/muscles, according to the vectors the upper level navigation system provide as best guesses for proper direction to go. So where the navigation network shown to the right in the video is taken as a best guess mechanism for magnitude and direction (to supply a forward/reverse and left/right angle) the guess is the wave direction at an associated place in a higher level map.
The lower motor system will use the upper level direction vector as a guess, even though to the upper level it’s all wave action with no guesswork required. In the same way HTM does not necessarily have to include motor level guesses. It would though work as a best guess mechanism for another that needs one. And a best guess does not have to be perfect, only needs to work better than a random alone, to be extremely useful to have. As with modeling a whole critter of any kind including RNA level actions guesses need to be accounted for, but for an add-on like a neocortex that’s covered, so for HTM don’t worry about it.
What I add is more like an opposite side of the modeling spectrum of the same basic process. When well compared (like you just forced me to) the two complement each other in a way that can help uncomplicate things, instead of complicating them. So hopefully that explained what you were wondering about, and it’s now easier for you to proceed towards HTM greatness.
We’ve been struggling to find a suitable landmark within the Numenta landscape and your request for a cell level, 3 axis, spatial vector map, led us to identify what may be a suitable starting point, in addition may serve to move our model forward.