
The Brain’s “Inner GPS” Creates Conceptual Spaces in the Mind - pseudolus
http://nautil.us/blog/new-evidence-for-the-geometry-of-thought
======
gdubs
The honeycomb lattice mentioned in the article resonated with me.

I’ll go out on a limb and share a personal anecdote: In high school I took
magic mushrooms with my friends, and at one point in the experience the world
disappeared and I saw an undulating fabric in a honeycomb pattern. In the
center of each “hole” in the fabric was a link to a memory, a time and a
place.

It was one of those images that was hard to forget - I can still recall it
many, many years later.

In “Dragons of Eden” Carl Sagan muses that drugs might work in an analogous
way to how night time brings out the stars. The stars are always there, but
daylight masks them.

In a similar way I’ve often wondered if there was something to that geometry I
saw.

Or perhaps it’s just my brain trying too hard to be poetic :P

~~~
ionforce
I've always been under the impression that consciousness is actually a bunch
of brain activity competing for attention and that one thing at a time is
selected/blessed to be the highlight of one's attention.

The addition of drugs sort of pulls back the curtain on what other things may
be just under the mark, lurking beneath your "default" consciousness.

~~~
kadendogthing
>I've always been under the impression that consciousness is actually a bunch
of brain activity competing for attention

This reminds me of one my favorite quotes from Westworld (HBO, 2017)

"There is no threshold that makes us greater than the sum of our parts, no
inflection point at which we become fully alive. We can't define consciousness
because consciousness does not exist. Humans fancy that there's something
special about the way we perceive the world and yet, we live in loops as tight
and as closed as the [robots] do, seldom questioning our choices - content,
for the most part, to be told what to do next." \- Dr. Ford (character)

One of the things I really love about marijuana is that while it mentally
alters your state, it leaves you completely coherent, where you can still be
perceptive and reflective. For me it's like a deep, consistent meditation if I
relax and really focus on how I'm "thinking." Perceptually, at least
personally, it really feels like there are mental facilities that suddenly
become "communicative", a higher (no pun intended) mental state. If I dose
right I often use marijuana to reflect about how I'm living my life, a social
situation that needs attention, a hard problem at work, or sometimes I just
really really love listening to music. And I have to say, if you've never
listened to music while high, you truly are missing out on an experience.

All this is basically to say I totally agree with your statement about
"pulling back the curtain." I personally consider it useful, it's often nice
to have a different perspective on a problem. It's helped me out a lot, I
think.

~~~
saiya-jin
Can attest to those experiences too. Most of my biggest decisions in life were
started as a seed thought in Inception style while high. For this to happen
though, I had to be alone with my thoughts, otherwise others presence would
take all the focus. And they were really good life changing decisions.

What basically happens (among other things) the feed from my subconsciousness
that sometimes suggest ideas out of blue or solves problems becomes much, much
stronger. Sometimes I can't even manage to type all of those ideas/todos into
phone, they come so fast. The only issue is, short term memory impairment also
makes them fade away pretty quickly, so sometime it looks like a race to
record it all.

------
cs702
As it happens, the representations (aka embeddings) learned by deep neural
nets also organize objects geometrically in tensor or vector spaces, such that
similar objects end up near each other in a high-dimensional system of
coordinates. AI researchers nowadays routinely use generative models like,
say, Glow[a] to identify geometric directions in the coordinates of a
representation space that correspond with concepts such as "smiling vs not
smiling," "male vs female," etc.

[a] [https://blog.openai.com/glow/](https://blog.openai.com/glow/)

~~~
jerf
I find myself reading the news backwards; rather than "the brain uses space-
orientation to map other things", it's like "it's interesting how many things
can be represented in a space-like manner that we may not have otherwise
thought they could be".

I think the difference is that rather than "the brain is sort of performing a
hack and reusing something it doesn't seem to have any driving need to re-
use", the news is that many things turn out to fit into that model despite our
intuition that they should have no particular spatialness to them. Metrics are
more fundamental than we may have thought and it's actually neither a surprise
nor a "hack" that the brain exploits this characteristic.

An interesting question comes to mind; do some brains have more dimensionality
than others? Are some people literally one-dimensional thinkers, pervasively?
Could we produce a test to distinguish between 2.1- and 2.5-dimensional
thinkers? Can an increase in dimensionality be trained, or a natural talent
fail to flourish without proper stimulation?

~~~
naasking
> I find myself reading the news backwards; rather than "the brain uses space-
> orientation to map other things", it's like "it's interesting how many
> things can be represented in a space-like manner that we may not have
> otherwise thought they could be".

It could actually be spatially related in the brain too. Neurons are situated
spatially and spatial constraints, ie. they have a limited number of
connections, and the closer two neurons are spatially, the faster they can
signal each other. The neuronal connections also rewire each other based on
reinforcement, which could very well consistent of moving related concepts
closer in your physical brain (at least important ones).

------
Nigredo
I worked on this with Peter Gardenfors in my PhD thesis. If someone is
interested in a mathematical model of conceptual spaces which is not machine-
learning oriented, you can check this out:
[https://arxiv.org/abs/1608.01402](https://arxiv.org/abs/1608.01402)

~~~
j256
Thanks for adding this.

------
rolph
just a quick knee jerk example here, it seems the visual cortex has an
intrinsic noise that is normally filtered out but is shunted through when
psychedelics are in the mix.

[https://en.wikipedia.org/wiki/Form_constant](https://en.wikipedia.org/wiki/Form_constant)

>" Many observers see geometric visual hallucinations after taking
hallucinogens such as LSD, cannabis, mescaline or psilocybin; on viewing
bright ickering lights; on waking up or falling asleep; in “near-death”
experiences; and in many other syndromes. Kl ¨ uver organized the images into
four groups called form constants: (I) tunnels and funnels, (II) spirals,
(III) lattices, including honeycombs and triangles, and (IV) cobwebs. "<

[http://psychedelic-information-theory.com/geometric-
hallucin...](http://psychedelic-information-theory.com/geometric-
hallucinations)

~~~
lphnull
I used to see geometric shapes upon waking up if I woke up abruptly in the
middle of a very visual dream, but only if the first thing I saw was a sudden
bright light (as in having my sleep mask abruptly removed). Hasn't happened to
me in a while, but usually the bright light of the real world looks
"pixelated" in very weird geometric patterns that for me were morphing,
chromatically abberated and animated. These flashes of shapes only lasted 1
second at most but were very trippy to experience.

------
benjaminjackman
>“Cognitive spaces are a way of thinking about how our brain might organize
our knowledge of the world,” Bellmund said. It’s an approach that concerns not
only geographical data, but also relationships between objects and experience.
“We were intrigued by evidence from many different groups that suggested that
the principles of spatial coding in the hippocampus seem to be relevant beyond
the realms of just spatial navigation,” Bellmund said. The hippocampus’ place
and grid cells, in other words, map not only physical space but conceptual
space. It appears that our representation of objects and concepts is very
tightly linked with our representation of space.

That is certainly how I think I think ... I think :) As an experiment two
years ago, I bootstrapped an IDE from an html file with just textarea that
could overwrite it's own source on a webserver (it would restart the server if
the server code was changed) in the browser. Eventually I got it to the point
that it laid out the editors for individual files in an infinite plane of 2d
space (akin to something like placing editor windows in a google maps like
scrollable ui) and saved their locations between refreshes.

I still really miss the spatial sense that the file that controls the editors
is up over there, and the file browser code is right over at that location,
(and they slightly overlap their tests and other supporting files).

I had this vision of this sort of becoming a system wherein everyone could
choose to see all the files in the system being edited in a shared global
space (or perhaps space of workspaces). So if you wanted to see what so and so
was working on you'd just navigate over to area where the files they are
working on are located. By default if you were editing a file in this system
in a public repo, since it was browser based it would be publicly viewable.

Juggling editor tabs and re-opening and reorganizing windows, and not being
able to create workspaces of editor layouts since then has kind of sucked.
It's like having this glimpse of a system that was from some future time but
then having to abandon it.

~~~
jonahx
Something similar to this is discussed and championed in The Humane Interface:

[https://www.amazon.com/Humane-Interface-Directions-
Designing...](https://www.amazon.com/Humane-Interface-Directions-Designing-
Interactive/dp/0201379376/ref=sr_1_fkmr0_1?ie=UTF8&qid=1549949192&sr=8-1-fkmr0&keywords=jeff+raskin+interface)

------
crazygringo
> _“we have reported an unusually precise hexagonal modulation of the fMRI
> signal during nonspatial cognition.”_

The article has an illustration of a hexagonal lattice but makes zero
explanation of what that means in practice, and the sentence above is the only
actual reference.

Can anyone here explain what hexagonal modulation means, and what it means in
the context of an fMRI signal?

~~~
nabla9
Honeycomb structure is the optimal way to cover a region with shapes of the
same area while minimizing the boundary.

You get honeycomb lattices naturally when you try to pack things efficiently
into a surface. For example the same sized soap bubbles on the water surface.

The grid cells are tightly packed to equidistance to each other just like the
bubbles.

------
bakul
I wonder if this explains why the "Method of Loci" or the "Memory Palace"
technique of memorizing and recalling facts work so well.

~~~
justasitsounds
I also wonder what it means for people who have very poor spatial reasoning.
If you have poor navigation skills are you also likely to be bad at
memorisation and recall?

~~~
jacobush
I can navigate quite well, but I need to go to where I must make a choice of
path. I have a hard time visualizing the map, or the overview, so to speak. I
find that I organize my code much the same way. I build patterns that I
recognize and can choose the right way (to modify or use) when I get there. I
guess it must be the same for everyone, but at different levels of scale.

------
onemoresoop
For whoever's interested, there's a Peter Gärdenfors lecture on youtube:

[https://m.youtube.com/watch?v=L0X9mEe9aY0](https://m.youtube.com/watch?v=L0X9mEe9aY0)

------
nl
_In Krakow, Gärdenfors pushed against that prejudice. In his talk, “The
Geometry of Thinking,” he suggested that humans are able to do things that
today’s powerful computers can’t do—like learn language quickly and generalize
from particulars with ease (to see, in other words, without much training,
that lions and tigers are four-legged felines)—because we, unlike our
computers, represent information in geometrical space._

On the contrary, it's pretty common to represent information on computers in
geometrical space. This is what the whole concept of embeddings is, and it
works really well!

------
callesgg
We perceive the world through or conceptual models of it.

So the fact that our analyze of the world is similar to our analyze of our
other conceptual models seams very rational.

