Analogy and the perceptual reality of concepts

[bnhpct]

This could almost be a topic in the Learning category, but prima facie it has more to do with subjective awareness of the nature of abstract or conceptual perceptions by mathematicians and physicists. It relates to the subjective experience of attention as something like a spotlight or a field of vision within an interior sensorium.

I have postulated that the higher-level perceptions that we call concepts and ‘thinking’ are created and controlled in the same way as configuration perceptions are created and controlled, and by similar neural structures in the cerebellum. (More discussion here.)

In this connection, I remember Einstein’s description of his thought processes involving visual imagery, Feynman’s grounding of abstract discussions in analogs of physical configurations (e.g. Feynman diagrams), studies of the gestures particle physicists make to communicate, and their collaborations with dancers (of which they approved), and so on.

And now I read Kurt Gödel’s understanding of the objects and relations of mathematics in that excellent book, Battle in the mind fields (Goldsmith & Laks 2019), from which I have extracted some quotations:

Reason [presupposes] a sort of eye. There is an organ in the brain to perceive abstract concepts, mathematical objects for example, as the eye perceives objects … [there is] a mathematical eye … linked to cerebral centers of sensory perception and of language (in some fashion attached to both).

— Cassou-Noguès (1997:85).

Some physical organ is necessary to make the handling of abstract impressions possible. Nobody is able to deal effectively with them, except in comparison with or on the occasion of sense impressions. This sensory organ must be closely related to the center for language.

— Gödel, in Wang (1996:233)

We could possess for example a supplementary sense which shows us a space that is completely separate from space and time … and which is so regular that it can be described a finite number of laws. … I think that is the real situation, except that reason is not counted with the senses because its objects are quite different than those of the other senses.

— Gödel (1995:3.353).

We have something like a perception of the objects of the theory of sets. I do not see any reason to have less confidence in this sort of perception, that is to say mathematical intuition, than in sensory perception.

Cassou-Noguès (2007:95), citing Gödel (1995:2.268).

Goldsmith & Laks comment:

Parsons 1995 has an interesting discussion of Gödel’s view in this regard, and he underscores the importance of remembering that in the context of discussions of Kant’s view and Gödel’s views, we need to bear in mind that the term “intuition” is rarely a good translation of the German word “Anschauung.”

Parsons (1995) quotes Gödel:

Concerning my “unadulterated” Platonism, it is no more unadulterated than Russell’s own in 1921 when in the Introduction to Mathematical Philosophy … he said, “Logic is concerned with the real world just as truly as zoology, though with its more abstract and general features.

References

Cassou-Noguès, Pierre. 2007. Les démons de Gödel. Paris: Le Seuil.
Gödel, Kurt. 1995. Collected Works. Edited by S. Feferman. Oxford: Oxford University
Press.

Goldsmith, J. A., & Laks, B. (2019). Battle in the mind fields. The University of Chicago Press.

Parsons, Charles. (1995). Platonism and mathematical intuition in Kurt gödel’s thought.
Bulletin of Symbolic Logic 1.1):44-74.

Wang, Hao. 1996. A Logical Journey: From Gödel to Philosophy. Cambridge, MA:
MIT Press.

[rsmarken]

@bnhpct

I have postulated that the higher-level perceptions that we call concepts and ‘thinking’ are created and controlled in the same way as configuration perceptions are created and controlled,

That’s exactly what Powers postulated.

@bnhpct

and by similar neural structures in the cerebellum. (More discussion here.)

If “higher-level perceptions that we call concepts and ‘thinking’” are created and controlled via neural structures in the cerebellum, then what’s the cerebral cortex for?

@bnhpct

In this connection, I remember Einstein’s description of his thought processes involving visual imagery

This would suggest that a lot of Einstein’s thinking went on in the occipital lobe of the cerebral cortex, which is the part of the brain that handles visual perception.

@bnhpct

And now I read Kurt Gödel’s understanding of the objects and relations of mathematics in that excellent book, Battle in the mind fields (Goldsmith & Laks 2019), from which I have extracted some quotations:

Nice quotes. I particularly like these:

Some physical organ is necessary to make the handling of abstract impressions possible. Nobody is able to deal effectively with them, except in comparison with or on the occasion of sense impressions. This sensory organ must be closely related to the center for language.

— Gödel, in Wang (1996:233)

We have something like a perception of the objects of the theory of sets. I do not see any reason to have less confidence in this sort of perception, that is to say mathematical intuition, than in sensory perception.

Cassou-Noguès (2007:95), citing Gödel (1995:2.268).

[bnhpct]

@bnhpct

I have postulated that the higher-level perceptions that we call concepts and ‘thinking’ are created and controlled in the same way as configuration perceptions are created and controlled, and by similar neural structures in the cerebellum. (More discussion here.)

@rsmarken

If “higher-level perceptions that we call concepts and ‘thinking’” are created and controlled via neural structures in the cerebellum, then what’s the cerebral cortex for?

You are correct, I wrote in too abbreviated a way. The proposal was that the cerebellum handles transformations from one level of the hierarchy to another. Hence, the famous ‘smoothing’ of motor control is due to transforming error at the relationship level to appropriately changing efforts. As you will recall, analysis of neural connections shows that cortical signals take a detour through the cerebellum before passing along either to the brainstem (for motor control) or the thalamus for the return to the cortex.

The diagram refers to transformation of afferent signals, hence PIF, but the proposal also applies to transformation of each efferent error signal to an array of signals in reference input functions (RIF). Note that IO in the diagram means ‘inferior olive’, a large neural nucleus, not the input-output function being suggested for the cerebellum.

[rsmarken]

I guess I just don’t get why you think this happens just in the cerebellum.

[bnhpct]

@rsmarken

@bnhpct

I have postulated that the higher-level perceptions that we call concepts and ‘thinking’ are created and controlled in the same way as configuration perceptions are created and controlled,

That’s exactly what Powers postulated.

Reference?

@rsmarken

@bnhpct

and by similar neural structures in the cerebellum. (More discussion here.)

If “higher-level perceptions that we call concepts and ‘thinking’” are created and controlled via neural structures in the cerebellum, then what’s the cerebral cortex for?

When you find the places where this is “exactly what Powers postulated”, maybe you’ll see context that makes it unnecessary to ask this question. A key word here is “via”.

@rsmarken

@bnhpct

In this connection, I remember Einstein’s description of his thought processes involving visual imagery

This would suggest that a lot of Einstein’s thinking went on in the occipital lobe of the cerebral cortex, which is the part of the brain that handles visual perception.

It seems that the error outputs in controlling the abstract concepts of mathematics were most effective in reference input functions for controlling visual shapes. At least, that was the sensory modality he was most aware of. The concepts themselves are controlled at higher levels by means of varying the references for visual configurations. The thinking involves many levels.

@rsmarken

I guess I just don’t get why you think this happens just in the cerebellum.

What do you think I am proposing happens in the cerebellum?

I did not propose that all the higher-level perceptions that we call concepts and thinking “happens just in the cerebellum.” I proposed that neural functions in the cerebellum abstract invariant relationships so that higher-order signals change only if the lower-level signals on which they are based change in certain ways, and conversely. I took the idea from B:CP 122:

We can define a configuration as an invariant function of a set of sensation vectors, thus implying particular computing properties common to these different input functions: They abstract invariant relationships so that the third-order signals will change only if sensation vectors on which they are based change in certain ways

I proposed that the computing functions that Bill proposed would suffice for the relationship between sensation and configuration levels turns out to be a general-purpose function which suffices for transforming between every pair of levels from there up. This is consistent with available behavioral research and with the evolutionary development of the cerebellum extending the identical remarkable anatomic structures for increasingly abstract levels of perceptual control.

[rsmarken]

@bnhpct

@rsmarken

@bnhpct

I have postulated that the higher-level perceptions that we call concepts and ‘thinking’ are created and controlled in the same way as configuration perceptions are created and controlled,

That’s exactly what Powers postulated.

Reference?

In the chapter on “Higher Levels” in B:CP Bill says “We now pass from classes of perception that can be seen as exterior to ourselves [such as configurations–RM] to those which seem to be inside ourselves [higher level perceptions such as concepts, programs and principles- RM]…This model makes no special distinction between these subdivisions”.(p.154 of first edition). In other words (yours), “higher-level perceptions that we call concepts and ‘thinking’ are created and controlled in the same way as configuration perceptions”.

@bnhpct

I did not propose that all the higher-level perceptions that we call concepts and thinking “happens just in the cerebellum.” I proposed that neural functions in the cerebellum abstract invariant relationships so that higher-order signals change only if the lower-level signals on which they are based change in certain ways, and conversely. I took the idea from B:CP 122:

We can define a configuration as an invariant function of a set of sensation vectors, thus implying particular computing properties common to these different input functions: They abstract invariant relationships so that the third-order signals will change only if sensation vectors on which they are based change in certain ways

I proposed that the computing functions that Bill proposed would suffice for the relationship between sensation and configuration levels turns out to be a general-purpose function which suffices for transforming between every pair of levels from there up. This is consistent with available behavioral research and with the evolutionary development of the cerebellum extending the identical remarkable anatomic structures for increasingly abstract levels of perceptual control.

But that’s exactly what Bill proposed: Every type of perception is an invariant function of lower level perceptions. Invariant functions are perceptual functions that abstract invariant relationships between lower level perceptual inputs in order to produce the perceptual analog of an invariant aspect of sensory input. The perceptual functions that produce configuration perceptions, for example, which are the ones Bill was talking about here, are invariant functions of sensation perceptions that produce a signal that is an analog of some invariant aspect of these sensations, such as “squareness”. But the sensation perceptions are themselves produced by invariant (perceptual) functions of intensity perceptions, resulting in a signal that is an analog of some aspect of these intensities, such as “redness”.

Starting from the top of the hypothetical perceptual control hierarchy, system concept perceptions are invariant functions of principle perceptions, which are invariant functions of program perceptions, which are invariant functions of sequence perceptions, which are invariant functions of transition (event) perceptions, which are invariant functions of configuration perceptions, which are invariant functions of sensation perceptions, which are invariant functions of intensity perceptions which are simply functions (transductions) of the effects of physical variables.

What I think might be a helpful demonstration of how this is all supposed to work (remember, PCT is a theory that still needs to be tested) is available in the form of my spreadsheet hierarchy. The invariant functions in this model (the perceptual functions) are carried out by computer processes. How they are carried out by the brain is (as far as I know) still pretty much a mystery.