The Representation of Space & Time
A spatiotemporal framework for our inner representation
Two Components of Representation
For our brains to function, “information derived from different sensory sources is merged into a single, immersive, spatiotemporally ordered experience, instead of various disparate experiences.”
There are two key components in the integration process of information. One is space; the other is time.
To think about how space and time is represented in our mind, let's see an interesting example in the book The Brain's Representational Power:
"When we stand in a room with four visually identical windows and corners, our view of any particular window or corner does not tell which of the four windows or corners we are facing. Information on previously traversed paths and body rotations in space is needed to know where our body is situated in space."
This suggests that when visual cues are absent, we can navigate in terms of the alignment between space and time. We memorize traces of our movement, reference ourselves relative to other objects, and keep track of the timing between changes in positions.
Space
In the article “Place cells, navigational accuracy, and the human hippocampus”, the researchers found several interesting properties of place cells:
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Increase in receptive field was NOT Commensurate with the size of the environment increase
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Each place field comprises the summation of two or more Gaussians: distance to a particular wall in a particular direction -->the location of center, amplitude and the width of each Gaussian
Starting from here, they have also observed two notable features in when a rat is put in a square box with identical walls:
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When the animal could not use the walls to differentiate spatial cues, place cells signal the direction in which the animal’s head is pointing in its environment regardless of its location in that environment
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The animal’s distance from the relevant wall might be calculated based on self-motion information, as the firing rate of the cell was a linear function of the speed with which the animal moved through the environment (irrespective of direction).
Based on these findings, we know that there should be an allocentric spatial mapping in an animal's navigation system. This allocentric property gives more stability to our spatial representation and minimizes the influence from environmental factors.
The allocentric spatial system: where mapping is independent of animal’s location in the environment
In an allocentric system, animals are able to move the point of view in the map without actual physical movement in the environment. Moreover, we could incorporate agents (move actively) and non-agents (needs external force to move) into the mapping system. In this case, self is marked as agent, while objects are labeled as non-agent and used as landmarks. With this information in mind, we could further predict the possible kinematic interactions between non-agents or self and non-agents.
However, the interaction between two or more agents is not included due to the high complexity. Further explanation of behavior may require the development of abilities like the theory of mind.
Properties of an absolute spatial system
A spatial system has to be adaptive in order to be absolute. It should still allow us to navigate in certain distortions or featureless spaces. And for it to be adaptive, our navigation should be based on more abstract concepts than simply remembering every detail of a space.
When we predict the interactions between objects in a space, we implicitly assume the objects follow certain physical rules. For example, if a ball is placed on a slope in a room and then released, we could expect the ball to roll down the slope, hit the wall at a certain angle, then bounce back.
Therefore, our perception of the causal interactions between objects may lead to our continuous and adaptive representation of a space. In a sense, our brain’s perceptual and reasoning system constructs our spatial experience.
This absolute spatial system is thought to be located in the hippocampus of our medial temporal lobe.
Time
Time is incorporated into our minds in many different ways. Our approximate sleep cycle is 90 minutes. We have a 24 to 25 hours body lock that guide our alertness and sleepiness. Not following these time spans usually leads to tiredness and a disordered endocrine system. The same thing applies to representational functions of our brain.
With cells acting as harmonic oscillators and aligning to a “master” clock, we can unify our daily experience. One possible mechanism could be oscillatory coupling between distinct brain regions.
Gamma-theta Coupling
Researchers have proposed that theta-gamma coupling might be a potential mechanism for spatial memory retrieval. In a theta-gamma coupling, high frequency gamma-wave (65-85Hz) is modulated by low-frequency theta wave (4-8Hz).
In the experiment done in “Medial Prefrontal Theta Phase Coupling During Spatial Memory Retrieval”, participants were asked to remember the location of six items within a virtual space. Then they were given a cue and asked to identify its location within the space.
When participants were cued to navigate to where the target object was located, an increase is shown in theta power in the mPFC (medial prefrontal cortex) where it:
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is coupled with theta-phase in the MTL (medial temporal lobe, where the hippocampus belong)
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induced gamma wave in the (mPC) medial parietal cortex
It is then concluded that the theta-gamma coupling mechanism is working to temporally regulate our spatial memory retrieval.
Space + Time = Sequence → episodic memory:
Memory can be categorized into semantic and episodic memory, where episodic memory is about recalling previous experience “in terms of time, place, associated emotions.” The hippocampus is closely related to episodic memory. It may also hold the allocentric spatial map and be modulated by mPFC through coupling. This indicates the importance of the alignment between space and time to episodic memory. Moreover, it also revealed the importance of the hippocampus and related structures in providing a spatiotemporal framework of our experience. Such a framework may also incorporate other dimensions of inner representations (such as emotions) in some way.
However, the specific mechanism in which the temporal coupling and spatial information interacts is still quite ambiguous. We do not know how the spatial information is sequenced together through the progress of time. It should be an interesting aspect to look into.
Sources and further readings:
Artem Kirsanov. (2022, October 5). Theta rhythm: A Memory Clock [Video]. YouTube. https://www.youtube.com/watch?v=5CxSoFK5tOQ Eilan, N., & McCarthy, R. A. (1993). Frames of reference: Kant and the sea-horse: An essay in the neurophilosophy of space. In Spatial Representation: Problems in Philosophy and Psychology. Wiley-Blackwell. Kant’s Views on Space and Time (Stanford Encyclopedia of Philosophy). (2022, April 1). https://plato.stanford.edu/entries/kant-spacetime/#:~:text=This%20idea%20comprises%20a%20central,of%20space%20and%20of%20time. Kaplan, R., Bush, D. R., Bonnefond, M., Bandettini, P. A., Barnes, G. R., Doeller, C. F., & Burgess, N. (2014). Medial prefrontal theta phase coupling during spatial memory retrieval. Hippocampus, 24(6), 656–665. https://doi.org/10.1002/hipo.22255 Mumford, S., & Anjum, R. L. (2013). Causation: A Very Short Introduction. Oxford University Press. O’Keefe, J. A., Burgess, N., Donnett, J. G., Jeffery, K. J., & Maguire, E. A. (1998). Place cells, navigational accuracy, and the human hippocampus. Philosophical Transactions of the Royal Society B, 353(1373), 1333–1340. https://doi.org/10.1098/rstb.1998.0287 Pennartz, C. M. (2015). Chapter 8: Requirements for Conscious Representations. In The Brain’s Representational Power: On Consciousness and the Integration of Modalities. MIT Press. ChatGPT is used for grammar correction in some parts
