posted to numenta forum
Back when there were only 2 white papers and a few videos I became interested in the HTM and saw a video of a 2D helicopter being detected and wondered about the relation between the layers they used and the ability to recognize objects. I remembered 6 equations with 6 unknowns (the degrees of freedom) are required to solve the dynamics of 3D rotation and translation. The layers of the helicopter HTM matched with what it was able to detect if they were unknowingly being used in a subtle 2-equations and 2 unknowns methodology. Of course this begs the question "Are the 6 layers in the cortex required to see the 3D world?" Numenta's view of the cortical column implies that the 6 layers have nothing to do with this but I would like to question that view. Jeff has also warned against pursuing the reverse black hole question no one has ever escaped: "Is the 3D world the result of a 6-layered brain?" But an understanding of the relation between mass and space-time prevents me from abandoning the reverse question. More importantly, physics has an elephant in the room that is rarely acknowledged and questioned: the only integers that appear in physics are the result of 3D spacetime and Feynman states no fundamental aspect of QED requires an extension beyond 1D. QED is sort of the core of all physics except for gravity and nuclear stuff. An expert in the area informed me that spin is what creates 3D space, so my line of questioning is suspect. But my view is that we may have invented spin to maintain the view that objects are independent of our perceptions. I admit I am immediately deep in a recursive black hole: the 6 layers is a mass of neurons that I'm proposing we can see only because we have the 6 layers. BTW, if we had 10 layers to support the perception of 4D objects in 4D space then I believe all velocities would be static positions and all accelerations would be velocities. instead of E + mc^2 = 0 we would have E+mc^3=0 (now really getting side-tracked on the physics: by keeping relativity units correct there is a missing negative in some equations. Another example is F+ma=0 where the "F" is more correctly defined as the reactive force of the object which is in the opposite direction of the "a". This comes from meters=i*c*seconds which comes from Einstein's "Relativity" appendix 2 which he stated allows use of Euclidean instead of Minkowski space-time which is in keeping with the Occam's razor requirement.)
What I'm suggesting is falsifiable. Others posting here will know if it takes 6 layers to fully recognized objects in 4D space time. The degrees of freedom is N translational plus N(N-1)/2 rotational. I tried testing the theory via observation and thought of ants. It seems to be supported there: their eyes that need to detect only 2D "shadows and light" without rotation have roughly two layers. And yet their feelers and front legs, having to deal with 3D objects in 3D space, have 6 layers. There's a great extension to this observation: wasps are the closest cousins to the ants and have 6 layers for their eyes.
I posted this question nearly a decade ago in the old forum, but I'll ask again. Is a 6 layer HTM required for fully characterizing 3D objects in 4D space-time?
I think a single layer would require a lot more new training on every object. For example, it sees a circle moving about and learns its behavior. Then it turns sideways and turns out to be a cylinder, and then it starts rotating, so training has to start over. I don't think it could conceive very well "this is the same object" and/or generalize the lessons learned on past objects to future objects. It just seems like it would have difficulty understanding objects like we do. I believe 6 layers would be able to perceive the laws of dynamics but 1 layer would not. These six layers are not an HTM but the foundation of a single cortical column. Each CLA layer of the HTM would require the 6 layers. So the CLA would need to be redone if you want it to think like mammals and see like wasps. The motor control of layer (5th layer of cortex) may serve may also serve part of this "inherent object modelling", not just motor control. The motor control part might be crucial to developing the concept of inertia (mass). Mass is another variable ("dimension") which implies 7 layers should be present. To get out of that mathematical corner, I have to conjecture mass is something special in the modelling like "the higher dimensions that 6 layers can't model and that have permanence".
I do not mean to say that 6 layers is necessarily inherently needed in A.I. to be superior to humans even in the realm of understanding physics, but that it is needed to think more directly like animals. But if 6 layers per HTM layer is actaully needed for a higher intelligence, then 10 layers to do 4D space should be even more powerful. 15 layers are needed for 5D. I do not accept the conjecture that objective reality, if there is one, depends on a specific integer of spatial dimensions like "3".
The visual cortex by itself with its 6 layers does not seem to have any concept of objects, but I think the 6 layers are still needed for encoding the information so that the concept of the objects is still extractable by the higher levels in the "HTM" of the brain (e.g. frontal lobes). But the concept of an object seems to be possible in the 6 layers just "behind" the eyes of flying insects: wasps certainly have a better concept of the object nature of people than ants, judging by the way they identify and attack. Ants are virtually blind to what people are, except for detecting skin and biting.