Let’s assume I’m the HTM and I’ve learned the model of my room (with a cup as usual). I know some objects are at some locations but there is a location in the middle of my room, floating mid-air where there’s “nothing” in it. I have a specific location of that point in grid cells inside my brain and my eyes are sensing the visual features of objects behind it, but I also have a sense of “nothing” being there.
If “nothing” had no representation then I wouldn’t be able to sense it obviously, nor to make this post about it. I wouldn’t be able to have a window to build a model of what “nothing” is that would eventually evolve into the knowledge that air is in that point. And it doesn’t feel like I’m computing there’s “nothing” there, it just comes intuitively. What I might be sensing is both the location of that point in the room and the point as an empty object by itself, simultaneously. Essentially, that point in the middle of the room might be an empty room by itself.
Could it be that there is a cell or a population of cells in the brain that represent an empty room?
Space
Space is full of “nothing”. Literally, space is an ocean of nothingness that paradoxically has objects in it. So, it’s not something you 'd easily forget. We know that all location spaces of objects are larger than the object itself which would mean logically they would contain “nothing”. Since all objects contain “nothing” they also share this similarity. All composition starts as an empty room (documents as blank pages, paintings as a empty canvases, music as silence) which would mean that all composition is re-entrant structures of the empty room. All objects would share this similarity too.
Mathematics
John von Neumann’s definition of a real number is that it’s a set of it’s predecessors.
0 = {}
1 = {0}
2 = {0, 1}
3 = {0, 1, 2}
...
All numbers contain 0 which is “nothing” or an empty room. Are they all empty rooms? You would say yes because they all contain 0 but no because they are also not 0.
Language
This paradox is apparent even in the way language is structured. Why does the sentence this and that have nothing in common make sense? We can take the meaning of the sentence literally so it does come out that this and that do have nothing which is an empty room in common. This is something you must have observed to be able to relate to.
If I’m allowed to speculate, I think you have to break down this question in three steps.
Consider a real physical object. A Numenta cup for instance. It’s hard enough to really understand how this works, but apparently it’s an hierarchical model of sensorial input combined with location information learned through sequential experiences.
Imagine the object. (Put down the cup, close your eyes, and imagine how the cup rotates before you in mid-air). I suppose the model constructed by your brain uses many of the same neural connections as in 1, even though there is no cup.
Imagine some empty space. By focusing on a point (or cluster of points) in mid-air, it seems to me that your brain is using similar displacement cells combined with not visual information, but imagined mental information, just like you imagine the cup in exercice 2.
So in essence, I think your statement is quite correct.
Thank you for the references, they were interesting to read.
I was aware of the story of zero being discovered multiple times throughout history before I made the original post. The word “invented” is hard to work with, I like to think of zero as being “discovered”. Every invention is a result of an HTM modeling higher space through space which means an invention was existing in higher space and the realm of possibilities before HTMs reached and modeled them. This is doesn’t mean zero wasn’t invented also.
He notes that the history of zero is too nebulous to clearly identify a lone progenitor. “In all the references I’ve read, there’s always kind of an assumption that zero is already there,” Seife says. “They’re delving into it a little bit and maybe explaining the properties of this number, but they never claim to say, ‘This is a concept that I’m bringing forth.’”
In order for any HTM to invent or discover something it must a have a representation of that in neural tissue. My question is, how is “nothing in a place” being represented? Is it a location (an object) that has an empty location space (an empty room)? A grid cell location in L6a that has an empty location space in L6b?
A Persian mathematician, Mohammed ibn-Musa al-Khowarizmi, suggested that a little circle should be used in calculations if no number appeared in the tens place. The Arabs called this circle “sifr,” or “empty.”
Practically, understanding how zero is being represented should give us an insight of how mathematics are being performed with orientation, location, movements and spaces in the brain (an empty room is a zero or a variable).
Though people have always understood the concept of nothing or having nothing, the concept of zero is relatively new; it fully developed in India around the fifth century A.D., perhaps a couple of centuries earlier. Before then, mathematicians struggled to perform the simplest arithmetic calculations.
Zero found its way to Europe through the Moorish conquest of Spain and was further developed by Italian mathematician Fibonacci, who used it to do equations without an abacus, then the most prevalent tool for doing arithmetic.
I understand that you are asking about the coding of space but I think that this is closely related. Without special learned mental tricks numeracy seems to depend on perceived size and some concept of grouping. I think that the mental process for concepts involves chunks and relations. The details are not set in stone in my mind and I have gone back and forth on the details as I read different research papers.
The zoo of different representations types (border, head direction, vector & distance, path alignment, place) in the EC/HC seems to grow daily. These are just for the “easy” things you can monitor as a critter moves about. Monkey studies show that relationships of objects on viewed screens seem to call up some sort of representations. I can see that a spatial relationship tied to “air” is a very possible way that this is done. From the links above many animals do know how to code for “nothing.”
If you like those articles you might like the book “The Nothing that Is: A Natural History of Zero” by Robert and Ellen Kaplan I think their names are. Really good book.
Imagine a robot floating inside a pitch-black room without a body. It only has an eye made out of silicon that can move with muscles to sense light in different parts of space.
What would be the input to this system?
There would be no stimuli to the eye, no input to L4 but there would be orientation input from the muscle that moves the eye, from the thalamus to L6a. You will be able to remotely move the eye and sense different locations in the room but there are no features to associate to those locations. How can a location be derived from motor input rather than associated features?
Some time ago I looked into how nothingness (zero) could be stored and came the conclusion that its a two step process using what we can directly perceive. First we think of a thing at a place or inside something that can contain it; then we think about what is at that place or inside the container after the thing is removed. With this reasoning we can say there is “nothing there” (at that place) or the container is “empty”. From there we can generalize to the notion of a void as a spatial place that could contain something.
I think that it is only represented by the presence of its surroundings (e.g. perceivable objects). In other words in a given space there are perceivable things and there are non-perceivable things (nothing) and in this case there is a partial absence of some stimulus but that non-stimulus-triggering space is still partially representable because its surroundings trigger some stimulus.
By example, in an extreme case, “nothing” can’t be represented due to total absence of stimulus (e.g. death). However in this case the term “nothing” truly lives up to its name.
Well how would you know that “nothing” is not an illusion due to the ability to perceive its surroundings? How would you know that nothing is a not a non-predictable thing/event? The act of posting is curiousity IMO much like predicting something that is unpredictable that may cause our brain to build up a more abstract representation of nothingness based on its surroundings however nothing really is perceived or predicted correctly.
This is just my beliefs of course, I would also expect that the brain conserves space/energy and will not or only represent “nothing” as an abstract knowledge.
One should be careful to distinguish between the concept of nothing and the sensory experience of nothing. We can have philosophical and mathematical discussions about the concept of nothing; however, that representation in the brain is certainly distinct from (but possibly linked to) the actual sensory experience of nothing. The sensory experience of nothing is that I do not see any solid or liquid surface or volume inhabiting a particular spatial location, and when I move my hand (or any other sensory patch) through that location, my brain will expect that the incoming sensations will not be substantially different from all of the other times I’ve moved my hand through what appears to be empty space.
This particular example sounds like just a mere misprediction to me just like when a TM mispredicts the next sequence. Except that the sensory input that confirmed the misprediction is un-perceivable or at least partiall/temporarily undetectable. It could be that the brain is representing our misprediction as a knowledge rather than that “nothing”.
How is nothing represented?
Going back to what do we know about the brain - there is a WHAT and WHERE stream. This is well known and widely documented.
As @CollinsEM pointed out we have a concept of location independent from what might be there. We learn this by moving and not encountering anything; we are surrounded by a vast sea of nothing all the time.
I would have to take the default representation of nothing as forming a mental representation of some location (WHERE) without a matching object (WHAT).
I suspect that a better way to think of this is to focus on the concept of object representation as a collection of features. One common collection of features is the default set when no particular object is present to bind to - nothing.