Mind is uncountable

I have a vague memory of a dream which had a lasting effect on my concept of personal identity. In the dream, there were two characters who each observed the same event from different perspectives, but were not at the time aware of each other's thoughts. However, when I woke up, I equally remembered "being" each of those characters, even though I also remembered that they were not the same person at the time. This showed me that it's possible for two separate minds to merge into one, and that personal identity is not transitive.

So if you rejected mind-body continuity, you'd have to admit that some non-infinitesimal mental change can have an infinitesimal (practically zero) effect on the physical world. So basically you'd be forced into epiphenomenalism.

I don't think there's a principled distinction here between "infinitesimal" and "non-infinitesimal" values. Imagine we put both physical changes and mental changes on real-valued scales, normalized such that most of the time, a change of x physical units corresponded to a change of approximately x mental units. But then we observe that in certain rare situations, we can find changes of .01 physical units that correspond to 100 mental units. Does this imply epiphenomenalism? What about 10^(-3) -> 10^4? So it feels like the only thing I'm forced to accept when rejecting the continuity postulate is that in the course of running a mind on a brain, while most of the time small changes to the brain will correspond to small changes to the mind, occasionally the subjective experience of the mind changes by more than one would naively expect when looking at the corresponding tiny change to the brain. I am willing to accept that. It's very different from the normal formulation of epiphenomenalism, which roughly states that you can have arbitrary mental computation without any corresponding physical changes, i.e. a mind can magically run without needing the brain. (This version of epiphenomenalism I continue to reject.)

↑ comment by Filip Sondej · 2022-11-02T15:04:48.125Z · LW(p) · GW(p)

Good point. I edited the post to say "near epiphenomenalism", because like you said, it doesn't fit into the strict definition.

If the physical and mental are quantized (and I expect that), then we can't really speak of "infinitesimal" changes, and the situation is as you described. (But if they are not quantized, then I would insist that it should really count as epiphenomenal, though I know it's contentious.)

Still, even if it's only almost epiphenomenal, it feels too absurd to me to accept. In fact you could construct a situation where you create an arbitrarily big mental change (like splitting Jupyter-sized mind in half), by the tiniest possible physical change (like moving one electron by one Planck length). Where would all that mental content "come from"?

Replies from: benjamincosman

↑ comment by benjamincosman · 2022-11-02T16:26:28.608Z · LW(p) · GW(p)

A ball sitting on this surface:

has a direction of travel given by this:

In other words, continuous phenomena can naturally lead to discontinuous phenomena. At the top of that curve, moving the ball by one Planck length causes an infinite divergence in where it ends up. So where does that infinite divergence "come from", and could the same answer apply to your brain example?

Replies from: Filip Sondej

↑ comment by Filip Sondej · 2022-11-02T17:46:16.595Z · LW(p) · GW(p)

Here, to have that discontinuity between input and output (start and end position), we need some mechanism between them - the system of ball, hill, and their dynamics. What's worse it needs to evolve for infinite time (otherwise the end still continuously depends on start position).

So I would say, this discontinuous jump "comes from" this system's (infinite) evolution.

It seems to me, that to have discontinuity between physical and mental, you would also need some new mechanism between them to produce the jump.

Replies from: benjamincosman

↑ comment by benjamincosman · 2022-11-02T20:16:08.528Z · LW(p) · GW(p)

we need some mechanism between them - the system of ball, hill, and their dynamics.

A brain seems to be full of suitable mechanisms? e.g. while we don't have a good model yet for exactly how our mind is produced by individual neurons, we do know that neurons exhibit thresholding behavior ('firing') - remove atoms one at a time and usually nothing significant will happen, until suddenly you've removed the exact number that one neuron no longer fires, and in theory you can get arbitrarily large differences in what happens next.

Replies from: Filip Sondej, Filip Sondej

↑ comment by Filip Sondej · 2022-11-04T14:53:24.367Z · LW(p) · GW(p)

I thought about it some more, and now I think you may be right. I made an oversimplification when I implicitly assumed that a moment of experience corresponds to a physical state in some point in time. In reality, a moment of experience seems to span some duration of physical time. For example, events that happen within 100ms, are experienced as simultaneous.

This gives some time for the physical system to implement these discontinuities (if some critical threshold was passed).

But if this criticality happens, it should be detectable with brain imaging. So now it becomes an empirical question, that we can test.

I still doubt the formulation in IIT, that predicts discontinious jumps in experience, regardless of whether some discontinuity physically happens or not.

(BTW, there is a hypothetical mechanism that may implement this jump, proposed by Andres Gomez Emilsson - topological bifurcation.)

↑ comment by Filip Sondej · 2022-11-02T21:50:05.391Z · LW(p) · GW(p)

Hm, yeah, the smallest relevant physical difference may actually be one neuron firing, not one moved atom.

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What I meant by between them, was that there would need to be some third substrate that is neither physical nor mental, and produces this jump. That's because in that situation discontinuity is between start and end position, so those positions are analogous to physical and mental state.

Any brain mechanism, is still part of the physical. It's true that there are some critical behaviors in the brain (similar to balls rolling down that hill). But the result of this criticality is still a physical state. So we cannot use a critical physical mechanism, to explain the discontinuity between physical and mental.

I'm glad that you identified these two postulates, but I am pretty certain that P1 does not hold in principle. In practice it probably holds most of the time, just because systems that are highly discontinuous almost everywhere are unlikely to be robust enough to function in any universe that has entropy.

Note that continuous physical systems can and frequently do have sharp phase transitions in behaviour from continuous changes in parameters. From a materialistic view of consciousness, those should correspond to sharp changes in mental states, which would refute P1.

Alarmed that with all this talk of anthropics thought experiments and split brains you don't reference Eliezer's Ebborian's Story [LW · GW]. (Similarly, when I wrote my anthropics thought experiment (Mirror Chamber [LW · GW] (as far as I can tell it's orthogonal and complementary to your point)) I don't think I remembered having read the Ebborians story, I'm really not sure I'd heard of it).

It's a very interesting point you make because we normally think of our experience as so fundamentally separate from others. Just to contemplate conjoined twins accessing one anothers' experiences but not have identical experiences really bends the heck out of our normal way of considering mind.

Why is it, do you think, that we have this kind of default way of thinking about mind as Cartesian in the first place? Where did that even come from?

P1 sounds contra the evidences: when an action potential travels a myelinated axon, its precise amplitude does not matter (as long as it’s enough to make sodium channels open at the next Ranvier node). In other words, we could add or substrat a lot of ions at most of the 10^11 Ranvier nodes of the human brain without changing any information in mind.

https://en.m.wikipedia.org/wiki/Saltatory_conduction https://bionumbers.hms.harvard.edu/bionumber.aspx?s=n&v=5&id=100692 https://en.m.wikipedia.org/wiki/Node_of_Ranvier

However I didn’t get how you went from « tiny physical changes should correspond to tiny mental changes » (clearly wrong from above, unless tiny includes zero) to « non-infinitesimal mental change can have an infinitesimal (practically zero) effect on the physical world », so maybe I’m missing your point entirely. Could you rephrase or develop the latter?