I'm not saying that there isn't a "subconscious realm"/"collective subconscious"/whatever. But that doesn't seem to fit with the observations that have been made so far. If this could be demonstrated, then I'd give it due attention, but I worry that your answer to this will simply be that it cannot be demonstrated.
OK, let me try to elaborate my reasoning a bit.
Ultimately, what all science involves is constructing various mathematical models, hypothesizing that portions of the physical World follow those models, and then testing this by seeing whether things that you can deduce from the models turn out to reflect what actually happens in the physical World. That's probably most explicit in physics. In biological sciences (including neuroscience), situations tend to be more complex and as a result the mathematical models are harder to precisely define, so they are more likely to be expressed approximately in English, rather than with formulae - and it may be tempting to think of them as physical rather than mathematical models: But it's still philosophically the same process going on.
So when we talk about physical reality, what we are really talking about is a set of mathematical models. Special relativity is a mathematical model. As is quantum mechanics. As is the theory of evolution. As are the scientific descriptions of the way the various parts of the brain function, or of why - say - a table - behaves the way it does. The materialist claim that the Universe is purely physical is essentially a claim that its behaviour can in principle be entirely explained on the assumption that it conforms to certain models.
Now here's the crucial point: If you only use mathematical models and reasoning, the only thing those will ever lead to is... more mathematical theorems. Comparing the theoretical predictions with experimental result will of course frequently lead to refining the mathematical models (or sometimes, even completely replacing them). That's how science works. But in all cases, the newer theory is just going to be another mathematical model. To the extent that reality conforms to mathematical laws that's fine - and has been proven to be very successful. But it means that if (hypothetically) there is some part of reality that is not mathematical in nature, then you are never going to be able to discover that part of reality using the tools that science uses.
Is there a part of reality that is non-mathematical in nature. Well yes - just look at your senses, your experiences. You gave the example of tasting food.
PaulWeaver has just given the example of blue. From where I'm sitting now I can see a bit of sky. If I look at it I experience the sensation of a rather pleasant region of solid colour. That sensation cannot be described in any mathematical terms. It's something you can only ever experience. And I think PaulWeaver has inadvertently demonstrated exactly that:
For "blue", what it appears to be is that we all have evolved the ability to detect electromagnetic radiation in the 450-500nm range, and when we detect it we term those sensory signals "blue". That detection occurs because cones in our retinas are stimulated by those wavelengths. The stimulation fires electrical signals through nerves to neurons which cause them to behave in a given pattern. The consensus is that we can detect these wavelengths, and we can measure those light waves independently. By looking at blue light, I know that the photons coming from it will be traveling in a wave with a wavelength of about 475nm. That's measurable. The frequency, thanks to a known constant speed of light, is about 630THz, again measurable.
(lots more science snipped)
All great science there. But Paul - do you notice what's missing? You said nothing about the
sensation of blue. Nothing about the
experience of blue. Nothing about
what it's like to see something blue. Why the omission? Could it be because you were giving a scientific description, and there really is no way to account for the sensation itself using any scientific theory. Sure, you can give a detailed account of all the physical phenomena that tend to give rise to the sensation: The photons, the stimulation of the eye receptors, the way each neuron transmits the signal. But that all tells you nothing about the experience itself.
It's the same with anything else that you consciously experience: A sound. The feeling of anger. Or of being at peace. Or any other sensation in life. Including the sensation of tasting food. (I did watch most of the video you linked to by the way. It was interesting, but I felt it didn't say anything relevant to consciousness because it had exactly the same omission as Paul's post did (No bad reflection on the video: That wasn't its purpose anyway)).
Science is increasingly able to give an amazing account of the processes that can usually lead to each sensation happening. And it's very clear from science that very often the sensations are somehow connected with the material world to the extent that they correlate with certain processes in our brains. But being 'connected with' or 'correlated with' doesn't imply 'is the same thing as'! And in the end, science is completely lost when it comes to describing the sensation itself - and that's precisely because science deals exclusively with things that can be expressed as mathematical models. But the sensation is something that you experience: It's not something reducible to a model. In short, science can only deal with empirical things, not experiential things.
If you don't agree with me then try writing down using only words or mathematical symbols a description of 'blue' that is sufficient to allow someone who's never seen anything blue before to know what blue looks like. I'm pretty sure you won't be able to do it. On the other hand, if you merely had to write something that would enable this person to understand the physical processes involved in seeing something that's blue, you'd be able to (An elaboration of PaulWeaver's post that I quoted above should do that nicely!)
Again, it appears to all be physical. And I will again say that, if you are to convince me that consciousness exists outwith our physical world, then you'll have to show me some objective evidence. But please be assured that I will consider the evidence you present. So far, you've only given me a conjecture based on your own beliefs and experiences, and that's not enough to convince me.
Thanks!

And I would argue that this is the evidence: The evidence is in every feeling you experience, every sensation you experience, whether by touch, sight, sound, smell, taste or any other means (Assuming of course that your experience of being alive is comparable to mine!). Science may well eventually be able to tell you precisely in what manner certain parts of your brain are stimulated when you for example, taste a strawberry, but science can never tell you what it is to experience the taste of a strawberry - because science deals only with physical (read: mathematical) models of reality.
You say that there is no evidence that there is a non-physical reality. I put it to you that the reason you have come to that conclusion is that the only evidence you have been prepared to admit is empirical data that reproducibly shows consistency or otherwise of some part of reality with some mathematical model of the physical World. In other words, data that is fundamentally mathematical in nature and which can therefore only ever be used to confirm or deny mathematical models.
Of course, setting up models whose consequences are predictable, and demanding reproducibility, are both hugely important when looking at the physical world, so confining yourself to only that evidence is completely sensible for that purpose. But you also need to bear in mind the restrictions of that kind of data: By only accepting empirical, physical, data, you automatically restrict yourself to analysing phenomena that are empirical in nature. And if you forget that that's a restriction imposed on you by your choice of data, then you'll obviously end up concluding that the World is
entirely physical - irrespective of whether reality really is like that or not. In other words, the fact that you've concluded the world is purely physical really reflects your decision about what kind of data you accept as evidence.
You say you're willing to consider new evidence: I therefore challenge you to also admit the evidence of your senses as data. Admit the
experience of blue or of strawberry-taste or of hot or of cold or of anger as data. Not only the statements about which bits of your brain get stimulated when you eat a strawberry (which is what neuroscience gives you) but the actual experience of strawberry. But this is of course data that can only ever be experienced: It cannot be described by any mathematical model. Those sensations you experience are clearly a part of reality - because you are experiencing them! But if they can't be described by any mathematical model, then they clearly cannot part of the physical world as it's understood in science. Hence there must be some part of reality - some 'realm' that is not part of the physical World.
And my follow-on argument here is: Since the common characteristic of all these experiences that cannot be described mathematically is that they are things that you experience as part of your consciousness, that strongly suggests that the thing that is not part of the physical realm is... consciousness!
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There is by the way one other possible piece of evidence that
may point towards consciousness as being distinct from physical reality, although it's a lot more tentative (and controversial: It has been questioned, and I wouldn't be too surprised if someone comes up with an alternative explanation in the future. Or maybe someone already has and I haven't noticed

). But for what it's worth: In mathematics, Godel's First Incompleteness Theorem tells us (very, very roughly) that there are propositions that are true but unprovable. The physicist Roger Penrose has identified theorems that can be proven to be unprovable either way, but then used human reasoning to show that those theorems must be true. This looks like an example of human reasoning going beyond the limits of mathematics - and that causes problems for any materialist viewpoint, because it seems to contradict the idea that our minds are just machines bound by the laws of physics, which are in turn bound by mathematics. (Penrose thinks the answer may lie somewhere in quantum mechanics, though I personally find that implausible). Certainly, if consciousness existed independently of the physical world, that may provide a resolution to the apparent contradiction. But as I say, that's tentative - I don't yet fully understand the reasoning myself, so for me it's more of an interesting line of thought than any definitive proof.
I mention it though because, to my mind, it does reinforce what I think is a possible problem for materialists: If our minds are machines, and thereby bound by the laws of physics (and mathematics), how do you reconcile that with our apparent ability to mentally create mathematical systems and analyze them (from outside the systems)?
(Yes. Long post. Anyone who's still reading at this point. Congratulations

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