Jacob Bellmund is a postdoc at the Max Planck in Leipzig, studying spatial navigation, cognitive maps, and episodic memory. In this conversation, we talk about his research on deforming cognitive maps, abstract cognitive maps, and the translation of the spatial navigation literature to abstract spaces.
BJKS Podcast is a podcast about neuroscience, psychology, and anything vaguely related, hosted by Benjamin James Kuper-Smith. New episodes every Friday. You can find the podcast on all podcasting platforms (e.g., Spotify, Apple/Google Podcasts, etc.).
Timestamps
00:05: How Jacob started working on cognitive maps
02:05: What are place cells, grid cells, and cognitive maps?
08:49: Discussing Jacob's paper "Deforming the metric of cognitive maps distorts memory"
28:34: Abstract cognitive spaces
41:57: How far do findings from spatial navigation translate to cognitive spaces?
50:40: How many dimensions can grid cells encode?
58:01: What is Jacob going to work on next?
Podcast links
Website: https://bjks.buzzsprout.com/
Twitter: https://twitter.com/BjksPodcast
Jacob's links
Website: https://www.jacobbellmund.com/
Google Scholar: https://scholar.google.de/citations?user=_DRs4ukAAAAJ
Twitter: https://twitter.com/jacobbellmund
Ben's links
Website: www.bjks.page/
Google Scholar: https://scholar.google.co.uk/citations?user=-nWNfvcAAAAJ
Twitter: https://twitter.com/bjks_tweets
References
Auger, ..., & Maguire (2017). Efficacy of navigation may be influenced by retrosplenial cortex-mediated learning of landmark stability. Neuropsychologia.
Bellmund, ..., & Doeller (2016). Grid-cell representations in mental simulation. Elife.
Bellmund, ..., & Doeller (2018). Navigating cognition: Spatial codes for human thinking. Science.
Bellmund, ... , & Doeller (2020). Deforming the metric of cognitive maps distorts memory. Nat Hum Behav.
Jacob wrote a Blog Post about his Nature Human Behaviour article: https://socialsciences.nature.com/posts/55610-distorting-human-memory?channel_id=1745-behind-the-paper
Butler, ..., & Giocomo (2019). Remembered reward locations restructure entorhinal spatial maps. Science.
Constantinescu, ..., & Behrens (2016). Organizing conceptual knowledge in humans with a gridlike code. Science.
Doeller, ..., & Burgess (2010). Evidence for grid cells in a human memory network. Nature.
Hafting, ... , & Moser (2005). Microstructure of a spatial map in the entorhinal cortex. Nature.
Gärdenfors (2004). Conceptual spaces: The geometry of thought. MIT press.
Ginosar, ... , & Ulanovsky (2021). Locally ordered representation of 3D space in the entorhinal cortex. Nature.
Grieves, ... , & Jeffery (2021). Irregular distribution of grid cell firing fields in rats exploring a 3D volumetric space. Nature Neuro.
Kim & Doeller (2021). Adaptive cognitive maps for curved surfaces in the 3D world. bioRxiv. p
Krupic, ... , & O’Keefe (2015). Grid cell symmetry is shaped by environmental geometry. Nature.
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[This is an automated transcript with many errors]
Benjamin James Kuper-Smith: [00:00:00] Actually, so before we start talking about, you know, the two papers of yours that I want to talk about, um, the deforming, the metric of cognitive maps and navigating cognition. Um, I'm just curious, how did you find out about grid cells or play cells or whatever, and how did you end up getting interested in doing this kind of research?
Jacob Bellmund: Uh, that's very interesting. So I, uh, I studied psychology, uh mm-hmm. As my undergrad and I, I got fascinated by memory research mostly. And so I worked with, uh, Sharon Ranana at uc Davis for a few months and then kind of. Was determined to do a PhD in memory research, and I found this position in, in Christian Dell's lab that I signed up for or applied for and was very lucky to get.
And yeah, that's kind of how, how the whole thing started. And in the beginning or so my, my first PhD project was on sort of these. Grid like signals and [00:01:00] imagination and memory recall. So that's sort of the link, uh, between my initial interest in memory and then, um, fitting in the space or the navigation stuff.
Benjamin James Kuper-Smith: But, but you'd heard of grid sales before you applied for the position or,
Jacob Bellmund: yeah. Yeah. I mean, I, I'd heard about a bit about them, but, um, not so much and I, yeah.
Benjamin James Kuper-Smith: Hmm, okay. Was the first one. Is that the, the Eli paper in Donders Town?
Jacob Bellmund: Yeah, exactly. Yeah.
Benjamin James Kuper-Smith: Okay. So you really came through memory. I think that's kind of unusual, right?
I feel like, or I feel like a lot of people who, when they hear about grid cells are play cells. At least for, for me, I heard about it, my masters for the first time, and I was like, and I almost did a research project on this. Um, and for me it was just like this immediate like, oh, this is really cool. I wanna work on this.
And
Jacob Bellmund: yeah, no, I, I definitely had this feeling of being, being fascinated by, uh, by, by really learning about it. Right? But like, I feel, I only, only really learned about it during my PhD. Like before I had some superficial knowledge and I, my, my true [00:02:00] fascination only started when I, um, dug a little bit deeper.
Benjamin James Kuper-Smith: Uh, cool. Okay. So, um, as I mentioned before we started recording, we probably should at least very briefly mention a few keywords. Um, so can you in, I don't know, a minute or two, it doesn't have to be long, say what play sales grid sales are, uh, and maybe what a cognitive map is, I guess.
Jacob Bellmund: Um, maybe I'll, I'll start with the play cells.
Uh, we can go, go in chronological order. Sure. So, uh, play cells were discovered by, uh, John O'Keefe in, in the early seventies. And what, uh, John O'Keefe did is he recorded the activity of, uh, individual neuron. Neurons in the rat hippocampus. And he did that while an animal was moving through space. So, uh, the animal was moving through a little environment, a little box.
And what John O'Keefe noticed was that specific cells were most active when the animal was located at a specific [00:03:00] position, uh, in space. So, for example, the northwest corner of the environment and. So one cell would always fire whenever the animal was at, at that location. And so he termed these cells, place cells.
And the idea is that each cell has a preferred location or, uh, where, where it exhibits a so-called firing field. And together the population of place cells could provide something like, uh, a map of the different locations that are known in the environment. And so in, if we think about, uh, what a cognitive map is, then it's maybe a, like a representation of different locations in space that is somehow true to their, um, relationships.
So, for example, the distances and, uh, directions between positions, uh, in space can be read out from, uh, from this map. And then maybe the, uh, the third component or the third, um, term. We, we, uh, you mentioned are grid cells. And these were, uh, discovered by mire Moser and Adver Moser. And, um, they were discovered in the trinal cortex.
So, uh, one synapse [00:04:00] upstream from the hippocampus. Unlike, uh, a play cell, which is active at one positions have a position in space. Uh, a grid cell is active at many locations in space. And these, um, locations, they're not randomly spread throughout the entire environment, but they're distributed in a very regular pattern where, uh, where the individual firing fields form the vertices of equilateral triangles that tile the entire space.
So you end up with a super regular 60 degree, uh, symmetric firing pattern. And that's actually how, uh, how they got their name.
Benjamin James Kuper-Smith: Yeah. And so maybe if, if, funny thing is, I think explaining play cells is pretty straightforward. Explaining grid cells gets very difficult without visual age. So I think if this is completely new to any listener, just Google grid cell and you'll probably see an image when it becomes pretty clear what, what it is.
But it's, it's always funny, like when I asked, uh, you know, Mattias now did the same thing and he also went this like, God, how do I explain grid cells in a way that's easy to understand, just using words. [00:05:00]
Jacob Bellmund: Yeah, definitely. It, it's very helpful if, uh, if you look at this, uh, this pattern, it's, it's quite striking, but it's quite difficult to describe.
Benjamin James Kuper-Smith: I mean, maybe we could say it's like a chess board, but not with squares, but with hexagonal patterns.
Jacob Bellmund: Yeah, exactly. Or like a coordinate system. Maybe this is, uh, a metaphor that we can, we can use a bit. Right. So it's, it's like a coordinate grid in a way, but, um, they're not, uh, squares, but, uh, hexagons basically.
Benjamin James Kuper-Smith: Okay. And I mean, so these were all found, I mean this all started in animals, right? But then your PhD supervisor, Ola with Neil Boje and Castleberry, they found a way to do this in humans. And I guess this is what I mean, you've only been working in humans, right? With fmri. Yeah, exactly. Yeah. I worked with humans and I guess that's kind of what we'll be talking about.
I don't want to, uh, we'll get to the abstract stuff later. Mm-hmm. Um, but I think maybe it might be important. [00:06:00] Interesting to mention it briefly, that even though all of this was found for special navigation, the, in the last, I don't know, five to 10 years or something, um, that quite a few papers have come out of people showing that this entire system might be used for other dimensions or variables, basically.
So it's not only. The X and Y axis of space, but X and Y can be any axis. But yeah, we'll get to that later. I thought it would be just nice to mention it at least briefly in the beginning.
Jacob Bellmund: Yeah. And maybe, maybe one interesting thing to note there is that this is kind of coming back to, to Edward Toman, who, who coined the term cognitive map, right?
So in, in his work, which was based on navigating rodents, um, no, um, no recordings of neurons, but he discovered that they. We're using something that he referred to as cognitive map and he already speculated that uh, we might have these cognitive maps also for higher level psychological function. And I find it super fascinating that now decades later we're sort of circling back to [00:07:00] these ideas.
Benjamin James Kuper-Smith: Uh, it's funny about this whole thing, right? When you, you feel like there's something that's super new, but then there's a guy in, what was it, 48 or something, writing about this?
Jacob Bellmund: Yeah, yeah. Some cognitive psychologist has done this 40 years ago. Whenever you think of a clever paradigm,
Benjamin James Kuper-Smith: yeah. I mean, I've had that a lot when in my stuff.
Yeah, you think you have a cool idea and then you find like some paper from the seventies or something. I mean, often they didn't. One thing I've at least found is that they then weren't often done quite as well, which is maybe why they weren't, um, the findings unknown as well because of the. The way the experiment worked isn't quite as the, the evidence that maybe isn't quite as good or systematic as you'd like to have it.
But I mean, with Toman it's fairly, uh, I mean, that's well known. Yeah. But actually this is something I, I underlined in your, in your science review, um, did he actually term the, according the term cognitive map? And I always wondered like where it started, or
Jacob Bellmund: I, I think he [00:08:00] was the one who started this. Yeah.
But. Uh, I'm not entirely sure now, but, um, okay. Yeah, I mean, I think he's the one who, who really started using this also for humans. Right. Um, I think the, the 48 paper is called something Cognitive Maps in Mice and Men in something.
Benjamin James Kuper-Smith: Yeah. And I think it's, I mean, it's been like two years or something since I've read that paper.
I think it also gets kind of weird towards the end because it gets really political or something.
Jacob Bellmund: Yeah. It gets quite political and um, it's also. Reflective of the ideas of how human psychology works at that time. Right. It, it's, it's quite different in terms of
Benjamin James Kuper-Smith: Yeah.
Jacob Bellmund: How they, or how he describes the human mind or human psychological function.
Benjamin James Kuper-Smith: Yeah. But, but apart from that, he seems to have been pretty spot on. Yeah. With a lot of stuff. Uh, anyway, so, uh, I guess I'll make a very rough transition here. Um, so I want to talk about, um, your paper de forming the metric. [00:09:00] The metric of cognitive maps, sorry, deforming. The metric of cognitive maps, distorts memory.
Maybe the easiest way is if you introduce it, um, just kind of like what the, or maybe first All these first experiments were usually done in square boxes or round boxes or whatever it, um, so I'm just. Maybe can you intro, can you kind of introduce your paper that way by saying like how the shape of the environment in animal studies has been found to have an effect on this?
Yeah.
Jacob Bellmund: Yeah. So, so this is actually, or, or the, the standard, um, grid cell recording study that is, uh, is done in, in rats are mice is that the animal forges for, for food. The experiment show, uh, throws some cookie crumbs into the environment and the animal, uh, happily runs to pick them up. And this is typically done in, uh, in square boxes that are fairly small.
Maybe a me, uh, one square meter or so. And that, that's where you get these, um, typically, um, [00:10:00] or the, these canonical, uh, grid, uh, grid cell firing patterns. Right. And then I think in, uh, in 2015, a couple of papers came out, one from, um, from John O'Keefe's group and one from the Moser lab about, um, the impact of environmental.
Geometry or environmental boundaries on grid cell firing patterns that sort of suggested that boundaries have an impact of, uh, on grid cell firing and that this can actually lead to distortions. And in particular, it's the study from John O'Keeffe's group, which was led by, uh, Julia Cupid. And, uh, Caswell Berry was, was also part of it where they recorded grid cells in a trapezoidal environment.
As well as in a square. And what they showed is that these typically regular patterns that you get in the square are distorted in the trapezoid. So they became less symmetric and they became sort of expanded in the trapezoid relative to the square. And we were [00:11:00] sort of wondering whether there might be any functional implications, uh, of these, uh, these distortions.
Benjamin James Kuper-Smith: Uh, I haven't mentioned it yet, but I put the references for the papers we mentioned in the description. Uh, so you don't have to look for those. You can just, I guess, look in the description. I mean, one thing that I kind of found funny about your paper is that I, I, I started, I read it and then I think it took me like, I, I got halfway through the results until I realized there wasn't any FMI somehow, I was just so expecting an FM I study because it was about like red cells tion map, and somehow I was like, wait a minute, there isn't any fm.
I, um, so what's that? The. So for you, the, like the behavioral implication was the starting point, or how did it kind of get going?
Jacob Bellmund: Yeah, so, so there are actually two reasons why there's no fm I, um, so, so one is we really wanted, um, to look at behavior, uh, because I think, so everybody sort of assumes that grid cells are very important for navigation and if we think about cognitive maps, then probably we think [00:12:00] they're also important for, for memory somehow.
But actually. This link is not as established as, as we would maybe, like, so for example, typical rodent, uh, recording studies, there's often not really a, a task, right? So there's no memory task. And also in, so there's some evidence that these FMI grid proxy measures might correlate across subjects with, uh, with, with spatial memory performance.
But, uh, within subjects there, there hasn't really been, uh, any investigation. So this is one, one reason why we really wanted to, to focus on behavior. And then the other aspect, um, while we actually couldn't, uh, record any, uh, any brain data here is, uh, that we wanted to use, um, immersive virtual reality.
Reality, sorry. Um, where participants were actually using, um, a head mounted display, so like the Oculus Rift, and they were, they were moving on, uh, on a motion platform. So, uh, this of course, uh, prohibits, uh, [00:13:00] recording, uh, FMI at the same time. And the reason why we really wanted that is that we thought if there's an impact of, um, of boundaries on, on our spatial memory abilities, then probably it's, uh, it's rather subtle.
But, and so we wanted to maximize that impact. So we wanted to be as immersive as, uh, as we could be. That's why we went for this, uh, this behavioral experiment. And there are also some more technical issues with, uh, recording, uh, these, uh, this sex directional grid proxy measure in environments where the sampling is biased because it's an, it's an analysis that's based on evenly sampling, uh, movement directions through space.
And so if you have a trapezoid, then your directional sampling will be, um, will be biased. And this also, it's potentially a solvable problem, but it causes some issues. Yeah.
Benjamin James Kuper-Smith: Yeah. Yeah. Yeah. I mean, it's also, it's not a, a criticism of the paper. It's just somehow, uh, I guess because I know the kind of studies that Cassela does in his lab and because I've, [00:14:00] yeah.
I think like most of the papers in this area I've read have done fmo. So it's, it, it was more like just a com my, like my, my priors were so strong that it took me like quite a lot of words to get that, to, to start questioning that, um, assumption. But. Yeah, can, so one thing I was curious about is, um, so I mean, as far as I understand, in the most of the standard, um, human grid cell studies with fmri, people use, it's kind of like a computer game, right?
You, you press buttons and you move through this kind of arena or whatever.
Jacob Bellmund: Exactly. Yeah.
Benjamin James Kuper-Smith: Um, has anyone actually done a study where they compared weather? Uh, I guess, yeah, the technical limitation is pretty obvious here, but, um, I'm just curious, do you think it's gonna be like, does it make a difference whether people actually move through the space or just watch an avatar kind of move through the space?
'cause in a way that's an assumption you have, right? That's, [00:15:00]
Jacob Bellmund: yeah. So, I mean, I can, I can only speculate here, but mm-hmm. From my personal experience using this VR setup, um, it's much easier to, uh, to navigate, um, because you simply have more cues, right? So you have, um, cues about your body rotation. You, you kind of have, uh, proprioceptive cues about the number of steps that you take.
And these make it a bit easier to. To navigate and to remember different positions. And I, I never formally tested it, but based on my experience with these desktop based computer games, contrasting this to the immersive setup, I felt that participants were better, uh, in the immersive version, in, uh, in learning positions.
Like they were a bit faster to pick it up. Uh, and I guess it's just easier to keep track of your, your, your orientation and then relatedly in, uh, in rodents. There's, um. There's interesting work now that, uh, uh, that, that tries to use VR in, in rodents to [00:16:00] sort of dissociate the, the contribution of different cues like visual cues or self motion cues on the formation of, of grid self firing patterns.
Benjamin James Kuper-Smith: You mean like, because you can manipulate these in vr, but not as easily, at least.
Jacob Bellmund: Exactly. Yeah. So if you use vr, you can disentangle them right by, you know, manipulating how fast you move for a given number of steps.
Benjamin James Kuper-Smith: How do you know much about that? How does that, I mean, I've, I, once, I think one, I saw a very funny image of like a, I think a fruit fly on like some sort of ball with a huge screen in front of it.
So the fruit fly could kind of walk through this virtual space. Is, is it like that or how do you do it with rodents? Do you
Jacob Bellmund: know? Yeah, I think it's, uh, it's a similar setup that you basically have a. Large, like a track ball that the animal runs on. So they had fixed often, or sometimes. So there are also groups that have setups, uh, where the animal can, uh, can turn the head and move around a little bit.
But in essence, the animal walks on, um, like a styrofoam ball and there's a big screen, uh, that surrounds the environment. Yeah. Or surrounds the animal.
Benjamin James Kuper-Smith: Yeah. I [00:17:00] just love the idea of. I don't know, just, it's just inherently funny to me, the idea of these rats being in some sort of vr Yeah.
Jacob Bellmund: And doing it, doing VR and fruit fries.
I mean, that's just amazing.
Benjamin James Kuper-Smith: Yeah. Um, okay, so that's, it's, it's something that kind of seems. Uh, it seems like it might be more, but you, you didn't feel your grid cells firing more or less in all the other
Jacob Bellmund: No, I, I, I, I, I think, uh, some variant of this question is to be asked to mattia stung, right? Because he records signals in freely moving humans.
Benjamin James Kuper-Smith: Oh, that's a good point. Yes.
Jacob Bellmund: So, uh, maybe soon we'll know the answer.
Benjamin James Kuper-Smith: I'll have to ask him that. Yeah. Oh yeah. Because he doesn't have the, the, the FMI limitation, right? Exactly. Yeah. Mm-hmm. Actually write that down because that's sort, it never occurred to me that yeah, this guy will be talking to soon, might actually be the person to ask this question.
Um, anyway, so, okay. So. So, [00:18:00] so how did, yeah, I guess the question's kind of like how you then, how did you decide to do this study? Was it you read this paper, uh, by Kopi at Tower and thought, let's do something with this? Or how did it kind of, or was it already like this question before where you thought like, Hey, I wonder how, whether grid cells actually,
Jacob Bellmund: yeah.
So this was definitely something that I was interested in before. So how, uh, how do grid cells relate to cognitive function? Right. So. How, how could they relate to memory or, um, imagination for example. That's something that I, I worked on before and so I was definitely interested in that. And then the idea was sort of that we could maybe use these distortions as, as a window, um, to look into how, how this relationship might come about.
Right? Of course, whenever I say this, uh, in, in today's conversations, it's with the limit limitation that this is a behavioral experiment, right? And we didn't actually record any, uh, any brain signals.
Benjamin James Kuper-Smith: But I thought it was a very neat [00:19:00] way of, I guess, uh, uh, um, how should we say, sidestepping the technical limitation of not being able to record FMRI in this context.
Yeah. Maybe, um, I guess we've only introduced the paper. Do you wanna say briefly then what you found?
Jacob Bellmund: Yeah, maybe. Yeah. I, I think I haven't even really explained how, what we did, right. So,
Benjamin James Kuper-Smith: yeah, that's, yeah.
Jacob Bellmund: In our experiment. Participants, Navi navigated two environments. So one was a trapezoid and one was a square.
And we'd, we'd match matched them for, uh, for a surface area. And in each of the two environments, they learned the positions of six objects. And then, uh, we probed their spatial memory. So we asked them, um, well, we showed them a queue with an object, um, image. And then the task was to navigate, uh, to the position in the environment where they think the object belonged.
And as I said, we used. This, uh, highly immersive, uh, VR setup. Um, and we also test them afterwards, um, in a simple desktop based experiment. And so for the first part, [00:20:00] what we're interested in was we wanted to look at how precisely they could recall the positions of the individual objects, right? So basically we, we measured the distance between where they think the object belongs and where the object actually belongs.
And what we saw then was, uh, that participant's memory for the object positions was, uh, less precise in the trapezoid than in the square. And we also found evidence for a more fine grain prediction that we had, um, namely that within the trapezoid memory was particularly bad towards the narrow ends, towards the pointy part of the trapezoid.
And this is exactly what, um, Julia Cupid had reported, uh, about the grid cell firing patterns in rats.
Benjamin James Kuper-Smith: One thing that really surprised me reading, uh, this, I mean, I ha I haven't read the paper yet. Um, so I wasn't aware of of them having found that. And it kind of surprised me when I read it in your paper because it seemed kind of counterintuitive to me because I would've somehow imagined if you're closer to borders, it would [00:21:00] be easier to remember this.
But yeah, obviously that's not the case. So. So
Jacob Bellmund: this is, um, definitely an expectation. Um, and it's actually something that we, uh, confirmed that this is the case in the square. There. It seems to work like that, but in the trapezoid, somehow this, uh, this seems to break down. And so it's something that should work against us, right?
So it should be easier to do this in the narrow end because you, you're closer to the boundaries. You have, you, you should actually have more cues about where you are. But somehow, uh, this, this effect could only be seen in, uh, in the square.
Benjamin James Kuper-Smith: Do you have any idea why?
Jacob Bellmund: Well, I, I, I hope to think that it's somehow related to the grid cells.
Um, um, yeah, so, so I mean, typically I think we use boundaries to, to kind of anchor our cognitive maps, right? So to anchor our representations of space, we, we maybe use the corners of a [00:22:00] room and. I don't think so, or quite, quite obviously, our participants weren't lost in the environment. Right? It's still a fairly simple environment, but, uh, precisely locating, um, where something belonged, uh, was more difficult, uh, in, in the trapezoid than the square and more so in the narrow end.
Benjamin James Kuper-Smith: I mean, is it maybe because I don't know, in the square you have both the. So let's assume it works exactly the way it does in rats in humans. So in the square you have both the boundary vector cells and the grid cells. Whereas in the trapezoid, you kind of only have the boundary vector cells because the grid cells kind of break down, or
Jacob Bellmund: Yeah.
I mean, they're not, they don't break down entirely. Right. So the, the regularity of the pattern breaks down. So you, your, your, basically, your memory code might be just less precise.
Benjamin James Kuper-Smith: Yeah, yeah, of course. Yeah. It's not like they just have no idea where they are. Yeah. I think if that was the case, we would've noticed already.
Yeah.
Benjamin James Kuper-Smith: It's an [00:23:00] everyday life. Like as soon as we're not in a square room, we just have no idea where we are.
Jacob Bellmund: Exactly. Yeah.
Benjamin James Kuper-Smith: But it is kind of surprising though, right? That just as I said that it did strike me like this should be something. I don't know. It feels like if, if the, if the, if the shape of the room you're in has such an effect on being able to memorize things that we would kind of know that.
But I've, outside of these basically two studies, I've never heard of the idea that
Jacob Bellmund: mm-hmm.
Benjamin James Kuper-Smith: Um.
Jacob Bellmund: Yeah.
Benjamin James Kuper-Smith: Or is it just like a fairly small effect that, um, yeah, I dunno. Yeah. Do you
Jacob Bellmund: what I mean? I mean, so, so it is a, it is a study, uh, it's, it's a lab study, right? So the situation is, is kind of artificial and generally people were very accurate in remembering these positions, right?
So they, they knew very well what they were doing. Hmm. Maybe anecdotally the. The building at the Donda Institute where I did my PhD. That's a triangle. And that's quite confusing in the beginning when you walk around the corridors and you end up in the same place basically. Sooner than you, [00:24:00] sooner than you thought.
It's, I have
Benjamin James Kuper-Smith: never been in a triangle of building, I don't think.
Jacob Bellmund: Yeah. But I mean, it's a fair point, right? We're we're much more familiar with, uh, rectangular rooms or buildings,
Benjamin James Kuper-Smith: do you think? I'm wondering, are rats more familiar with square rectangular rooms than with Trapezoids? I mean, I guess the ones that grow up in the lab probably are, right?
Jacob Bellmund: I guess they have, uh, like the, the, the home cages are typically rectangular. Yeah.
Benjamin James Kuper-Smith: Yeah. Who knows? Maybe it's just a, yeah.
Jacob Bellmund: But, so one interesting thing about the Cupid papers is that this distortion. Was very, uh, stable over time. So I think they recorded definitely over multiple days. I, I wanna say even two weeks, but, uh, yeah.
Benjamin James Kuper-Smith: Okay. So you'd
Jacob Bellmund: figure
Benjamin James Kuper-Smith: if it was like a learning thing then
Jacob Bellmund: if it was just simple. So, so they are, they're known to be some like transient effect of, uh, of, um, the expansion of, of grid cell firing patterns when you put them into a new environment. Mm-hmm. Then it's a sort of novelty effect. This is something that Kessel Berry, for example, has shown.[00:25:00]
And so it's not that, uh, but it's something that, that seems to persist over time.
Benjamin James Kuper-Smith: Okay, cool. Yeah. Um, one question I wrote down that I think you've kind of already answered in part, but I'll still ask it, is that. I mean, one thing I find kind of interesting about a lot of Ella studies is that it seems a lot of it is a fairly straightforward translation from findings that have been done in animals to see whether we can test it in humans.
Also, my my question was kind of whether your study is a straightforward translation and see in terms of like, is this possible or not? Or whether there's also kind of an extension of it that kind of shows something that we didn't know before? Yeah, I think maybe, it seems like the, the memory aspect might be.
Jacob Bellmund: Yeah, so, so to me the, the new, so had we shown, had we basically done an FMRI experiment and shown that the h directional signal is weaker in the trapezoid than the square, I would say this is like translating that finding. But because our focus here really was the behavior and, uh, or the, uh, and memory, I think [00:26:00] it's, um, yeah, I think we, we we're kind of trying to use the finding in rodents to learn something, uh, about human cognition.
And this is actually one aspect that I really, really liked about, uh, working on this project was that basically we're taking this finding from, from systems neuroscience and we're trying to figure out, uh, if this maybe has a relationship to, to human memory, right? So this kind of high level, uh, human cognitive function.
Benjamin James Kuper-Smith: Yeah. And the, um, I'm assuming the, the paper didn't have this kind of memory aspect to No, I think this was,
Jacob Bellmund: um, a free foraging task.
Benjamin James Kuper-Smith: Okay. Yeah. So, uh, I'd kind of like to leave the, the, um, uh, the, the, wait, what's the word?
Jacob Bellmund: Trapezoid?
Benjamin James Kuper-Smith: Deformed? Yeah, like the deformed spaces. Okay. Kind of on pause for a second, um, because kind of, I want to talk about this in the abstract cognition sense.
Um, so I'll just pause on that for a [00:27:00] second and come back to it later before we go. To the kind of more abstract cognition thing. I was just, one thing I've always been curious about is that, has anyone done a, a grid cell study in non nucle in space? Let's say you have like a rat moving around on a, on a globe or sphere or something like, because the, the kind of basic question is, you know, in a lab we often have, it's always a flat.
Arena. Right. But obviously if you walk up a mountain or something like that, then it's very different. I mean, I've talked to Kate Jeffrey on the podcast about her work in 3D where you have the rats really climbing up and down. But I'm, yeah, just as a kind of curiosity, I'm, I'm not aware of anyone who's, who's looked at when Yeah.
If basically you have a flat, a surface that's not flat in the sense, right.
Jacob Bellmund: Yeah. I'm not sure if anybody has done that in. Rodents. Um, not that I know of at least, uh mm-hmm. And I guess it's, it's kind of hard to do, right? [00:28:00] Yeah. Walking on a sphere is, is quite abstract. There's some work going on in our group.
Actually. There's a recent preprint by, um, MI soon Kim, who's a pre, uh, who's a postdoc in, in our group.
Benjamin James Kuper-Smith: Okay.
Jacob Bellmund: And. She looked at this, uh, she used this basic object position, memory task on a curved surface. So kind of similar to, um, to what you outlined.
Benjamin James Kuper-Smith: Yeah, that sounds
Jacob Bellmund: very similar. Um, this is behavioral work as well, so you, you should definitely check that out.
I'm not gonna spoiler it.
Benjamin James Kuper-Smith: Okay. Yeah, and I'll, if I, if I can find it, I, which I can, I'll put a link in the description. Okay, cool. So. Abstract spaces. I mean, this is the thing that, I mean I, I found the spa navigation stuff really interesting and fascinating and it's really one of the things that kind of got me really interested in neuroscience.
But in a way it's also kind of not that interesting because it's just about moving around. And the thing that's kind of most interesting to me at least, is this, this set of papers that came out in the last few years that show that this is not just about [00:29:00] moving or memory of moving where you are in space, but that this applies.
Well, that's the question, right? I guess your, you in your paper, you say it applies to, you don't exactly say to everything, but it's you, you kind of sit there, say it's a kind of domain, general thing that can, in principle, I guess at least,
Jacob Bellmund: yeah.
Benjamin James Kuper-Smith: Code for any variables. So. Yeah. Can you briefly summarize the kind of Yeah.
The gist of the, of your review paper?
Jacob Bellmund: Yeah. Um, so in this paper we, we kind of tried to bridge, uh, some gaps, right? So we, we worked together with, uh, Edward Moser from, from the physiology side, and, uh, Peter Gaden for who's a philosopher of mind to, to sort of try to apply. Um, what we, we'd known about forming cognitive maps of space and then, uh, these super exciting studies that you refer to that, uh, that sort of came out, uh, in the past couple of years that sort of suggest that these spatially tuned cells, cells like spa, uh, place cells or grid cells also [00:30:00] seem to.
Uh, map more abstract, uh, dimensions. And we, uh, in our paper, we refer to these abstract spaces as cognitive spaces. And, um, we, we tried to summarize the findings that had, uh, had come out from, from different species about how the hippocampus and enteral cortex might build cognitive maps, uh, in tasks. Of different domains.
And then we try to outline how this would be important for, um, for high level cognition. So for example, for concept learning or, uh, or inference and, uh, generalization.
Benjamin James Kuper-Smith: Yeah, I think it's a really nice summary of. Yeah, there's this kind of whole idea because I, I, I was aware of a few papers like the ESCO paper, uh, or uh, one or two others, but I didn't realize just how much had been done in this field already.
And yeah, maybe you, you mentioned that you kind of combined the human work, the electrophysiology, animals, and the [00:31:00] philosophy of mind work, and. I have to admit, I'd never heard of Peter Gaden force. I dunno. Mm-hmm. I know. Yeah. He's Swedish. Yeah. Yeah. Can you, the book sounds super interesting and relevant, but I haven't read it.
Can, uh, what, what kind of book is it? Like, yeah. And what kind of work does he do? Because I'm just not familiar with his work.
Jacob Bellmund: So, um, Peter Gaden force is a, a professor in Lund. Um, and so he works on philosophy of minds and he has this book or his, his, uh, theory actually on conceptual spaces. It's not neuroscience.
So this is really philosophy of mind. It's, uh, it's his key work. There, there is also experimental work, but in, uh, that informs this of course, but, um, it's, uh, it's not really about the brain and. Uh, at some point Christian and I, um, or Christian became aware of this and kind of pointed me towards it and, and I read it and I was kind of fascinated that, um.
Some of these ideas seem to be very [00:32:00] much in line what, uh, with what we were seeing, uh, in, in the hippocampus andal cortex. So the, the general idea of this, uh, conceptual space that Peter Gaden force, uh, put forward or proposes is that. Space is a great representational format to organize knowledge in, right?
So you can, um, you can project knowledge into, uh, into a two dimensional space. And then you can define concepts as, as a region in this space. So, um, one example that, uh, we could maybe use is, say, say we have different animals, right? So we have, we can arrange them based on how they look like, how, uh, how many legs they have, how heavy they are.
Um. Yeah. And so let, let, let's say we have,
Benjamin James Kuper-Smith: that's all the categories we have.
Jacob Bellmund: Hmm. That's all, all, that's everything. We know how fast they can run, whatever, how, how, how large their teeth are. That's probably relevant. Um, and so let's say you, you, you learn that there's this concept of big [00:33:00] cats, right? So these will be animals like lions and tigers and um, maybe a cheetah and.
They will occupy a similar region in this, uh, conceptual space, right? So they, they'll have similar features and so, so they'll be located close by. Now, one important thing is that, um, if you organize. Um, your knowledge about these animals or, yeah, if, if you organize, if you use a spatial representational format, then you can use very naturally similarity between these, um, these entities to generalize, right?
So say you've never seen a tiger, but you know, a cheetah and you know a lion and you know that, uh, you shouldn't come too close because they're pretty dangerous to you, then maybe because the um. Uh, the tiger is similar, you can generalize and also not come to close even if you haven't actually encountered one before.
Uh, and so, um, that's, that's one, uh, one way in which this, uh, spatial representational format is [00:34:00]very powerful.
Benjamin James Kuper-Smith: Mm-hmm. So a kind of, I mean, in some way it's, it's just reasoning by analogy and using. Yeah, whatever variables are most obvious or distinctive or whatever about,
Jacob Bellmund: yeah. I mean, this is, this is then an, an interesting question, right?
What, what are the dimensions that we, uh, that we use to actually, uh, organize something? And in the typical lab experiment, uh, these dimensions are of course. Experimental defined. So they're sort of, well, the experimental decides what the relevant dimensions are, right? So, um, if you, for example, think about the.
Paper from Tim Barron's group by, uh, Alexandra. They have a, have a space of different birds. And the birds, they differ in, uh, how long their neck is and how long their legs are. And so these are the two dimensions that, uh, that sort of span the space. Mm. I think it's very interesting to think about [00:35:00] more naturalistic settings, right?
So, or, uh, or spontaneous grouping, um, in, uh. Of, of stimuli that are not explicitly queued to differ only along two dimensions. Right. But along multiple dimensions. And it could be that these are different depending on, uh, on the context, right?
Benjamin James Kuper-Smith: Yeah.
Jacob Bellmund: So in, in one context, it might be more relevant to know, um, whether the, um, the tiger and the lion are similar in that they will eat me and in, in a different one.
It might be more important to, for example, consider where they live, uh, in which part of the world you can, uh, you can actually find them.
Benjamin James Kuper-Smith: Yeah, and I mean this is kind of where my, um, kind of own interests come fairly close to this because what I'm kind of interested in is. I should say, like if you have a social situation, uh, where you have to make some decision that affects you and someone else, or multiple people, whatever, you always have this like objective outcome that's going to happen.
But people don't make the decision based on this [00:36:00] objective outcome, but rather they have their personal preferences based on whatever context there is, who the other person is, what your history with them is, you know, whatever else is going on in your life or in this situation. And, um, so I'm kind of really interested in how.
Exactly this translation happens. Um, basically how these preferences affect it and specifically how the brain does that kind of how you go from this objective outside world to this kind of in decision via these internal preferences and
Jacob Bellmund: yeah.
Benjamin James Kuper-Smith: Um. One thing that I'm then really curious is about is, for example, yeah, like let's say you have these two dimensions and now they're not space or neck length and leg length, but they are, you know, your payoff and the other person's payoff.
Jacob Bellmund: Mm-hmm.
Benjamin James Kuper-Smith: For example, like how much money do I make if I choose X or Y? How much does the other person make? I guess if you, if you don't mind, shall we speculate a bit on, um, how cognitive abstract [00:37:00] cognitive maps relate to this? Mm-hmm. Um, or specifically, I'll just ask you to speculate more. Um, so I guess the first thing is, so let's say I have one access is my own payoff.
The other is the other person's payoff. And depending on who I'm talking to, there's different. I like the other person more or less. Right. Uhhuh would, do you think that would transform the actual kind of map itself or would you have this kind of objective map and then you would use that information afterwards at a later stage to Yeah, it's kind of like in a way, like if we want to take the grid cell analogy, like would the grid cell pattern be distorted if I like myself more than you or whatever.
Jacob Bellmund: So,
Benjamin James Kuper-Smith: yeah. Or the grids are firing, still be stable. And then at a later stage we would use that information.
Jacob Bellmund: So just so I underst the setup, so you would have two axis of, of space. It's [00:38:00] sort of this, what is it? Is it called the dictator game? The, like this?
Uh,
Benjamin James Kuper-Smith: that's one ex, I mean, there's lots of different games that can manipulate in various ways.
Who gets how much and
Jacob Bellmund: what
Benjamin James Kuper-Smith: options are. Yeah.
Jacob Bellmund: And so your, your idea is that, um, depending on how much you like the other person. That axis is weighted more or less, basically. So,
Benjamin James Kuper-Smith: well, let's just say we have two options, right? Either like I give, uh, oh God, I should have thought of a good example. So let's say you have just a few different options, kind of, you know, you have.
Okay. Let's just be specific. So there's the prisoner S dilemma is the most famous example. We have four outcomes. Mm-hmm. And each of those outcomes gives you some money and me some money. And I mean, we both have to make a decision, but let's just think about like which one I want, which one's my preferred option, this.
So I have four different outcomes with monetary reward for me and you, and. So these four points kind of lie on this two dimensional space. And [00:39:00] I guess the question is kind of like if I'm playing with someone I really like versus with someone I don't like at all, would kind of the space. Still be orthogonal.
Would, would the grid s firing still be regular or would this kind of difference in how much I like the other person just really like shift and deform the space?
Jacob Bellmund: Yeah, that's a super interesting question. Um, I.
Hmm.
Benjamin James Kuper-Smith: By the way, I'll just make this like, uh, uh, you can take as much time as you want and I edit it down to like one second. It looks as if you just immediately came up with the answer.
Jacob Bellmund: I think one idea or one speculation could be that the, the sort of map in the trinal cortex, if you like, um, know all of these different options, um, could remain sort of.
Normal, if you will, or undistorted. And that then the distortion [00:40:00] happens somewhere else. Um.
Benjamin James Kuper-Smith: That would kind of probably be my guess, but I dunno, the special navigation literature that Well, and I wonder whether there's any equivalent study vaguely, you know?
Jacob Bellmund: Yeah. Well, so at least there's, there's some work, uh, in rodents that basically the, the grid pattern is also influenced by locations that are frequently rewarded.
So if you introduce some regularities in the task, actually, then it can happen that, uh, the, the grid pattern already deviates from. From its canonical shape.
Benjamin James Kuper-Smith: I see. Do you know what paper that is?
Jacob Bellmund: Uh, this is work by, uh, Lisa Giacomo, I wanna say.
Benjamin James Kuper-Smith: Oh, okay. She has an interesting looking like review perspective article out that I
Jacob Bellmund: Yeah, exactly.
She also has a recent, uh, recent Nature Reviews, neuroscience, I think it is, right? I haven't, something like that. Yeah. I haven't had time to read it yet, I have to admit. And, uh, actually. What you sort of, uh, described now is that [00:41:00] basically there are two dimensions and it, uh, so, so, or what you described reminds me of a recent paper that came out from the group of Rieman in, uh, in nature Neuroscience.
Yeah. Where they, uh, where they basically have two social hierarchies that form the dimensions of, uh, of a space. Um, and the task of the participant is. Uh, or the cover story is that the participant is an entrepreneur and they have to select the one, uh, that sort of matches or maximizes their, their potential.
And, and actually they report some modulation of the, um, h directional code in FMRI based on, uh, on this, uh, decision value, if I recall correctly.
Benjamin James Kuper-Smith: Mm-hmm.
Jacob Bellmund: Um,
Benjamin James Kuper-Smith: yeah, I still have to read that paper completely. I've only like skimmed it. Yeah, I guess maybe, maybe, uh, uh, my question was a bit, uh, uh. Too, too in too much, uh, too in depth immediately.
So maybe we can like backtrack a little bit and ask kind of Yeah. One, one question that I'm generally [00:42:00] in interested in is kind of like how far the findings from spatial navigation translate to domain general findings, or whether there are things that are specific to navigation that just don't apply to other things.
One, like maybe fairly straightforward question doesn't mean the answer straightforward, but the one question might be like, for example, what is a landmark non-physical space?
Jacob Bellmund: Yeah, exactly. So I, I, I think there are some challenges to, to these ideas, right? So what, what is a landmark? You could say a particular salient object that you know very well is, uh, something like a landmark, right?
Or something like a, the prototype of a given category could be something. Uh, like a reference point, uh, that you use, right? And there's plenty of cognitive psychology work showing that sort of this, um, uh, processing of reference points also in, in, uh, in abstract concepts, kind of biases how we, how we process information.
I think another limitation that's sort [00:43:00] of related that, uh, boundaries that are really essential to, um, to cognitive maps of physical space are much, much harder to, um, come up with in, uh, in an abstract space. Right. Um, because I think what makes a boundary so, um, so influential in, uh. In, in physical space is that you can see it, you can, uh, see it from afar.
You can use it as a reference point, reference points. It gives you distance information. Uh, and these are, uh, things that are not easily implemented in, um, in these sort of abstract spaces. I would say it's, it's much harder. And if you, like, if you follow up on this notion that, uh, a concept is a, is a sort of region in an ab abstract space, then there are.
Boundaries between these, um, these concepts, right? So at some point, um, you go from, from being in concept A towards being in concept B, but maybe in an, in a real world naturalistic settings. Uh, setting these boundaries are [00:44:00] not that sharp. Right? They might be sort of, uh, fuzzy, making them much less suitable to serve as sort of reference points or anchors for your cognitive map, right?
Benjamin James Kuper-Smith: Yeah. Like what you were saying that I, I mean, I was thinking kind of like what actually makes the landmark in these navigation studies. I mean, one thing is that they don't change, right? They kind of fixed points, um, that if you move, you, you can always evaluate your movement relative to this. Um.
Jacob Bellmund: So there, there's some work on, uh, on that by, uh, I think by Eleanor McGuire's group showing basically that, uh, one defining feature of a landmark is that it shouldn't move, uh, necessarily.
Right? And, um, typically we use things as landmarks that don't move, right? So I usually don't use. The car that's parked on the sidewalk as a landmark, uh, because probably when I visit this location next time, it's not gonna be there. Right. Much rather I'll use the bus stop because the bus stop will probably be there.
Benjamin James Kuper-Smith: Yeah.
Jacob Bellmund: Um, but, [00:45:00] so in terms of how this position relative to a landmark is coded, there's, there's some recent work in, uh, in the physiology world about object vector cells. Right. That basically, um, give you your position. Uh, relative to a landmark, these are cells that fire at a given distance and direction to a landmark that's in the environment.
And then if you move that landmark, um, the firing field of that cell, uh, will also shift, uh, by, by a corresponding amount.
Benjamin James Kuper-Smith: Mm-hmm. Yeah. But that, that's all in animal store, right?
Jacob Bellmund: This is an animals, yeah. But, uh, I think it's, uh, it's a great question to also try to tackle this in, uh, in the human brain and maybe in also abstract, uh, sort of dimensions.
Benjamin James Kuper-Smith: Like, one example I'm thinking about right now is maybe, let's say something like one concept might be a person's height, for example. 'cause it's still kind of physical. Um, but, uh, let's maybe use that as an example. I mean, I guess could landmarks be something like, [00:46:00] I don't know, for example, like two meters tall or something as like a a, a kind of or boundary or something like a cutoff point or something where you, or, or something that's like.
Jacob Bellmund: Hmm.
Benjamin James Kuper-Smith: I don't know. Like, I'm trying to think of something that really,
Jacob Bellmund: so I would've speculated that if you think about height, that maybe the height of someone that you're very familiar is, is something like a landmark.
Benjamin James Kuper-Smith: Yeah.
Jacob Bellmund: So maybe the height of your partner, uh, you sort of, uh, it's easy for you to say someone's taller or shorter than that.
Benjamin James Kuper-Smith: Sorry, I just, I just saw the perfect study. So you're gonna use your parents as landmarks and as you grow up, you move close to the boundary or whatever. Right? So now all you have to do is just track lots of children, teenagers, longitudinally. That's brilliant. Yeah. It's, uh, an interesting idea that's completely unfeasible to do.
Um, but something like that, right? I mean, it seems like you, um. Or [00:47:00] Okay. Maybe, or let's say, I dunno what I'm thinking of this example, but like when you, you watch a film or something and you're supposed to rate how good it is, maybe you have like your three favorite films or something that pretty much your, your appreciation of this maybe unchanged or something.
So then you view them as kind of like exemplars of what makes a film or something like that. Yeah.
Jacob Bellmund: Exactly. Yeah. That you, you might have your favorite comedy and your favorite action movie, and you, you compare based on these re reference points, basically, right. That you could use.
Benjamin James Kuper-Smith: Yeah. But it's, it's, it's kind of funny to me how, in a way this.
It seems it should be straightforward, right? Right. You have like, oh yeah, you walk through two dimensions you've got, but then as soon as you, I don't know. It's something that, to me at least, seems like the application should be very straightforward, but it's actually much trickier. Maybe it's just because I don't work on the application, so it just seems easier from the outside because I only see the, the final papers.
But [00:48:00] I mean, yeah, no, I'm not saying that the, you know what I mean? Right. Like I'm not saying this work is easy. I'm still surprised, like how, how difficult I find it to think of the concepts that I'm interested in and kind of fit it into this framework.
Jacob Bellmund: Hmm. Yeah.
Benjamin James Kuper-Smith: Um,
Jacob Bellmund: yeah, so actually to me, one, one of the things that I really like about, um, this is that it sort of merges this very detailed knowledge that we have about how, how the system works in physical space.
Like, we know a lot, we learn so much from these, uh, these studies in rodents and also from the navigation work in humans only. That actually gives us the possibility to think about, uh, think about it in this, uh, level of detail. Like I think that's, that's quite unique. That somewhere pretty deep in the brain, right?
You get this sort of more or less abstract code for positions in space, right? Um, that, um, that is sort of abstracted from other perceptual information and. Hmm. I, I, I feel [00:49:00] there's been amazing work on, on teasing apart how these representations come about. I mean, we still, there's still so much we don't understand, but we actually do know quite a lot and, or, or we, we do know.
Some very cool things about it. And, uh, these only allow us to, um, to ask these questions about how it might work on for, for other, uh, domains, right? And that's why, why I find it so interesting to think about, uh, whether these mechanisms, uh, apply, uh, outside of, uh, the navigation world.
Benjamin James Kuper-Smith: I mean, it's almost like a, a way to jumpstart creativity and having ideas about what you're thinking about because you can just go like, okay, I'm doing this study.
What's a landmark? Or like, in this research area, what's that? What's that? And then you just have
Jacob Bellmund: new ideas. And probably that's, that's taking it or making it way too simple. Right. So probably it's not just gonna mean just for like
Benjamin James Kuper-Smith: generation.
Jacob Bellmund: Exactly. Yeah. You can, you can brainstorm a lot. Right? And you have, have cool ideas, uh, about what you can test.
Yeah.
Benjamin James Kuper-Smith: I mean, it's funny, like [00:50:00] when, whilst you were talking about the, the Kobi paper, I was thinking this. Yeah. We know so much about the navigational system and yet you can, again, I'm oversimplifying completely. You can have a nature paper in 2015 showing like, watch what happens if the box not square. You know?
Yeah. So this was not their only finding. Yeah, yeah, of course. But you know what I mean, right? Like it's. It's, I find it funny how often in, in, in lots of other research areas also, right? You have these like very, um, these findings that are really cool, super well known and everything. And then you ask like some basic thing and it suddenly changes like how you view the other whole thing.
Yeah. Um, anyway, be before we kind of, uh, finish, I, I wanna ask. I guess it's a fairly big question and something that you also address in this, which is how many, how many dimensions can you do with this,
Jacob Bellmund: right? Yeah.
Benjamin James Kuper-Smith: Because that to me seems like a pretty important question.
Jacob Bellmund: I agree. [00:51:00] Um, it's a super important question.
One thing that I'm, so, so there are different aspects to it, right? So on the one hand is if we're really coming from. Or trying to take the physical space analogy far, then we're gonna get in trouble after three dimensions, right? And. There's this super interesting work by Kate Jeffrey, who, who you had on the show and, uh, by KY who studies, uh, flying bats right about play cells and grid cells, um, in, uh, in 3D spaces.
And they do seem to exist. They seem to, uh, at least for the grid cells, they seem to be behaving slightly differently from what we, uh, we, we might've expected.
Benjamin James Kuper-Smith: Yeah.
Jacob Bellmund: I mean, things will break down if we go into higher dimensions. And if you look at, uh, at human cognition or human spatial cognition already, then the third dimension is often encoded, uh, less precisely than, um, than basically, uh, the flat surface, which [00:52:00] might be because we're, it's harder for us to, to, or we, we less frequently navigate, uh, in, in the third dimension.
Right? To
Benjamin James Kuper-Smith: me, humans kind of are two dimensional animals, right? I mean, sure we can. Move, like within, if we raise our arm or whatever we can get, we can go up a ladder or something. But
Jacob Bellmund: basically, yeah. And we walk through buildings basic and, uh, we've got that, have, have stairs and so on. Right. But,
Benjamin James Kuper-Smith: but
Jacob Bellmund: that's
Benjamin James Kuper-Smith: pretty,
Jacob Bellmund: we're we're not that great at 3D and Yeah.
Um, yeah, I don't know. Maybe we should test navigation and divers, uh, something like that to get like volumetric,
Benjamin James Kuper-Smith: wanna do FMI study underwater.
Jacob Bellmund: Exactly. Yeah.
Benjamin James Kuper-Smith: Good luck.
Jacob Bellmund: Someone might drown.
Benjamin James Kuper-Smith: I guess you just need an epileptic patient with the electrodes implanted,
Jacob Bellmund: waterproof.
Benjamin James Kuper-Smith: Exactly. Um, I mean, so there's, it seems to me there's kind of.
Two kind, obvious ways in which you go. Either. It could actually be something that scales for however many dimensions you might want in a [00:53:00] given situation, which. Potentially many, but let's be honest, usually there's only a few that are really relevant. But, so that's kind of one way, right, where it can, can actually contain lots of different dimensions at the same time, or this is the other option that seems kind of obvious to me, is that.
It actually is limited to three or four dimensions and the brain has to kind of figure out beforehand which dimension it feeds into it to deal with the situation. Um, do you have any
Jacob Bellmund: Yeah.
Benjamin James Kuper-Smith: Uh, speculation again about which one would
Jacob Bellmund: be, so, one speculation for me is that we can break down these sort of knowledge kind of problems, two dimensions that we think are relevant at a given time, and probably we cannot handle.
Too many of them at the same time. Uh, I, I, I, I do think, um, and I mean there's lots of work on the use of heuristics, for example, right? So we we're not perfect, uh, at information processing. Actually, actually we're quite far from it. [00:54:00] Um, so, um, I, I think that that's possible. Maybe one thing is that there are also.
Other accounts of how the hippocampus works, that focus sort of more on transitions between different states where defining individual dimensions is maybe not, not as central as to this idea of, um, of conceptual spaces, right? Where you really have to define dimension or where, where you define dimensions based on what the, uh, what the stimulus features are.
So. Um, these could sort of, or maybe they could, uh, yield testable predictions in cases where you go beyond, uh, something that you can, um, uh, you can represent with, uh, 3D Euclidean map.
Benjamin James Kuper-Smith: Yeah. So much to do. It's funny, like, you know, when you first hear about this in, in my case in my masters about spatial n stuff, you're like, wow, they figured this out.
Jacob Bellmund: Yeah.
Benjamin James Kuper-Smith: Like everything's, we know this now. Right? This is stuck. And then, then once you actually do research, you go like, oh, this is just the [00:55:00] beginning. Yeah, this is where it starts, but so does it do, do you think it would,
it seems to me like your, the, the, your review paper is kind of, I mean, you, you address the question that this isn't an important question, but you kind of outline it. Um, how should we say, independent of how many dimensions this can, um, kind of encode for, um, just showing like the general principle and whether it works for three or 10 is maybe another question, but I'm just curious, does it, how, how does it, how would your.
I'm assuming you have also like maybe some slightly bigger theories of like how this all fits together. How would this change, depending on whether the system could only do three dimensions or whether it can do 10 dimensions? Does that Yeah, kinda how, how would that, those two options, let's say, change how you think about how this fits into the bigger picture of, I don't know, memory decision making.[00:56:00]
Jacob Bellmund: I haven't thought about it from this direct angle. So, um, I, I, so to me then. If we figure out that we can only do a certain number of dimensions, um, then I think the, the next obvious question is how do we select the important ones, right? Because that's not always, uh, immediately clear. There, there, there might be situations where, um, where I ask you, I don't know.
How friendly is this person? Then it's, then it's maybe clear. But, uh, if you just ask me, what about x? Um, yes, then I can, uh, judge them on very many, uh, different dimensions. And so to me, this would, um, I, I, I think in both cases it becomes interesting, right? Um, how can we, uh, keep online so many dimensions and combine them and do we maybe weight them equally?
Or if we have to select them, how do [00:57:00] we, uh, how do we pick or do we sort of do some, some implicit dimensionality reduction? Uh, so we end up with, uh, some approximation of a higher dimensional space, right?
Benjamin James Kuper-Smith: Yeah. Yeah. Yeah. And that, yeah. Uh, there's so many links, but I think, uh, um, yeah, I think we'll have to start with here.
Otherwise we're gonna be here forever. Uh, because yeah, I mean, this is, I find this really fascinating and, um, for me, I kind of, I was really interested in the spatial navigation literature then, um, basically fairly random reasons I didn't end up doing research on it and ended up doing other things. And now it's kind of coming back and I'm trying to kind of combine the two and it's just, uh.
Yeah, as I said, it's earlier. Like, I think it's a really cool way also just to have new ideas about what you are doing. Like, not you specifically, but what about what one is doing?
Jacob Bellmund: Yeah.
Benjamin James Kuper-Smith: And what one might do as, as an experiment. Uh, maybe as a last kind of [00:58:00] question, um, what do you plan on doing next? Or what's, what's your kind of current research?
What kind of direction at least?
Jacob Bellmund: Yeah. Um, so at the moment I'm kind of working more on. The representations of, um, relations that occur in episodic sequences. So the idea is that our, uh, our memories kind of consist of different sequences of events. So, um, my memory of our podcast recording, uh, we'll be doing this technical, technical setup then you do, we, we did a little, um, introductory check, uh, and, uh, now we talk and maybe afterwards I'll, I'll have some dinner.
And so I'm interested in, uh, how we represent the temporal relationships between these events. Similarly to positioning them along a dimension in, in an abstract space. And so this is something that I'm currently working on and, um, looking at basically what happens if we have multiple sequences that have, uh, [00:59:00] similar structure.
To, to look at whether we, uh, whether the hippocampus sort of generalizes across, uh, sequences that are sort of similar. So I might have a similar memory if I were invited to a different podcast. And, uh, basically I'm looking at whether, um, what we know from one sequence affects how we represent the other one.
Benjamin James Kuper-Smith: Right?
Jacob Bellmund: Yeah.
Benjamin James Kuper-Smith: Okay.
Jacob Bellmund: So this is, uh, it, it's connected, but it's uh, it's a bit more memory focused. I, I would say.
Benjamin James Kuper-Smith: Yeah. Yeah. It seems like you're going back to, back to the Roots Mutual interest. Exactly. Okay, cool. I, I guess this is gonna maybe be a take a while until that paper's gonna come out, but I'll read it.
Cool.