How big is the location space of an object?


#1

In the slide above from Dr. Hawkin’s latest keynote the point W is depicted outside the physical boundaries of the pen but within its location space. How big is its location space? I can close my eyes and think of a point G that is 2 meters away from the pen. Do I make its location space bigger this way? Am I using the room around me where the picture above is displayed on a screen as its location space when I place point G? If mentally I try to place a different point M 55 million kilometers away onto the surface of mars still relative to the pen in the screenshot above do I still utilize its location space? Was it that big or did it have this enormous capacity to represent space?

From the same keynote:

All possible locations are assigned in a room even though we might not have moved through most of them. A unique set of locations for the unique representation of the room.


#2

Note that many descriptions are given in angle, parsec being an example. ( A parsec is defined as the distance at which one astronomical unit subtends an angle of one arcsecond, which corresponds to astronomical units. One parsec is equal to about 3.26 light-years in length.)

From a personal perspective, things “out there” extend through some some visual angle and maybe some personal definition of a distance. The movement in this case is the angle you move your eyes when looking at features of the object.
BTW: This is why artists like to make very large or very tiny replicas of objects - it plays with our perceptual mechanisms.

Note that this is very different when it comes to what is often called "personal space.’ This is the distance that you have learned to manipulate objects in as part of learning to run your body. Your joint angles and sense of touch and vision all combine within this space to allow you to manipulate things easily as if they were part of you. The convergence of many senses feeds into a sense of agency in this space.


#3

I talk about this in this video. Look for the universe metaphors.


#4

Matt’s video provides an great explanation. Here is an additional explanation in words. A particular set of grid cells can represent a finite number of locations.

For example, say we had 12 grid cell modules, and each grid cell module had 20 neurons, one of which was active at a time. Then there would be 12^20 different possible locations that these cells could represent. That’s a ridiculously big number about 4x10^21. (It isn’t as simple as this, but this is a good approximation. BTW there was a very recent paper from David Tank’s lab that shows grid cell modules being about 360u x 240u, so 1 square mm would contain about 12 grid cell modules.)

You can think of this as a very large space (Matt’s universe). Each object you learn will occupy a tiny portion of this space. The cloud of points that include the object and the space around it, in theory, is very large, but in practice it is limited. You just aren’t going to move your finger 20km away from a coffee cup. Also the path integration ability of grid cells is noisy, so in practice, the system has to constantly use sensory cues to keep track of where it is. Moving too far away from an object becomes useless at some point.

The spacing of grid cell firings determines the granularity of the location representations. In the entorhinal cortex there are grid cell modules at one spacing, then another set with about 1.4x spacing, then another set 1.4x times that, etc. It is believed this allows the system to learn maps of small and large areas. In the neocortex we predicted that different regions would similarly have grid cells of different spacings.