Benevolent physics instructors often give their students exams with "gimme" questions. Often these gimme questions have responses that can be easily ruled out by dimensional analysis: you know it can't be choice (c), because the answer to the question has to be expressed as an intensity, so it will have to be in Watts per square meter, and (c) is in volts.
What's always amazed me, when I've thought about it, is that the whole material universe seems to be describable (at least so far) in terms of just four fundamental dimensions: distance, time, charge, and mass. Quantum physicists may point out other properties, but the point remains that a small number of simple physical dimensions describes our world.
What's also interesting is how some of these units can seem intuitive or counterintuitive to our mammal brains. That things accelerate in terms of distance per time squared I "get". That intensity breaks down to kilograms per seconds cubed makes no sense at all to me. The change over time of the acceleration of mass change? Really?
Of course, we use lots of units that are created out of convenience and that aren't explicitly represented in terms of their basic dimensions. However, this doesn't mean they can't be reduced in principle, just that it's just not normally useful to do so. Temperature is a good one. Although in SI it's considered a basic unit, in reality it's a measurement of molecular motion distributions (mass, time, and distance). Any quick and dirty material unit, even ones in economics, project management, you name it, can be reduced to these basic dimensions.
Things become far more interesting when we look at units measuring subjectively perceived quantities. Scoville units for pepper heat and visual analog scales for pain are two examples. Of course, your internal state can change, and change your subjective "reading" from time to time; I hate IPA beers, particularly Sierra Nevada, but the beer I had at the end of the Big Sur Marathon was one of the best I ever tasted. Taste is a reaction between a substance and your nervous system, and your nervous system can undergo changes - for example, the changes wrought by 26.2 miles of dehydration and depletion of carbohydrates.
But the problem I'm interested in is not the variability in the test almost always found with subjective measurements. Let's return to Scoville units. For the sake of argument let's say you're a brilliant gustatory neurobiologist, and you've devised an equation that, given all the physical data about capsaicin structure and concentration, states of the neurological system it's interacting with (number of nerves on tongue, how they connect to various parts of the brain, emotional state, etc.), you can consistently predict the Scoville assessments that your taster will report. How do you break down perceived heat into these dimensions?
You can't; correlation is not the same as equality. Yes, you can break down into those basic dimensions the chemical process of capsaicin molecules binding to receptors in your mouth. But even if you assume an absolute and inviolable 1:1 correlation between chemical state and sensation - that is to say, an exact correlation between material and experience - the experience still remains an incommunicable property. Consequently the idea of dimensional analysis might give us a new way to worry at the problem of the relation of consciousness to matter.
This last statement is by no means uncontested. The incommunicable components of experience are usually called qualia. Searle draws a hard and fast distinction between third-person measurement and first-person experience but somehow does not brand himself a property dualist. I myself am uncomfortable with the term but have to apply it to myself until I find a way out of it, and find Searle's insistence that he is not one perplexing. Hardcore physicalist/functionalists would say that the heat of a hot pepper is, in fact, an incommunicable property, and therefore not real (technically, this is what Daniel Dennett is telling us). This is problematic for anyone who has eaten a habanero, as I have, because I can tell you for sure that it hurt. It's also problematic for anyone who has not eaten a habanero. You can try to imagine what it might be like, but the fact is (to your profit) you have never felt it firsthand.
This problem has also been phrased as part of Frank Jackson's Mary's Room argument. Let's say you'd lived your whole life in a room that was entirely black and white (including through some devious trick of bioengineering, your own skin, hair, tissues, and fluids). While in that room you train to became a neuroscientist specializing in vision studies, and you learned everything there was to know about color perception, although you'd never actually experienced color. (There are major problems with these "everything there is to know" kinds of suppositions is the often require - I'll address this later in my own response to Searle's Chinese room - but let's go with it for now.) One day the door is opened, and you exit the room, to see blue sky, green trees, and red roses. Do you learn anything? Or (I would argue, a different way of asking the same question) do you experience anything new?
There certainly are cases of people deprived of certain kinds of input earlier in their lives suddenly being given that input. A good deal of our perceptual wiring is biologically driven and will set itself regardless of what stimuli we happen to receive, but a good deal of it is molded in response to experience. For example, there is one case of a man blind until his forties whose vision was restored by an operation. He reports that he cannot tell people apart by faces - which you would think would be hardwired in social animals like humans - and that, having learned to ski while blind, he finds the visual input while skiing to be confusing and keeps his eyes closed.
Consequently you wonder if, after spending your life in this room, you would be able to perceive color at all, or if your senses would have become attuned to shades of gray in such a way as to keep your internal world the same as people who lived in a color world. That is, what the rest of us would call light gray, you experience the same as what we would call lavender.
Where speculation fails us, concrete neurological reality often steps in. And in fact, there are people with us today who are always partly in the black-and-white room: they're colorblind. But we're not about to do eye transplants for philosophical experiments, so hold that thought. Most of us are familiar with the idea of synesthesia, which occurs when sense information crosses channels (e.g. sounds are tasted, colors are heard). Although most people only experience this when using hallucinogens, particularly HT2A agonists, synesthesia exists as a constant condition in some people, perhaps most famously in the writer Vladimir Nabokov. You might ask if people who have been blind since birth see colors when they use LSD, and the answer is yes. And you might also ask whether colorblind people who also happen to be synesthetic experience colors outside the domain of their unfortunately flawed visual apparatus. The answer is yes, and these colorblind synesthetes are fully aware that they have never seen these colors associated with objects in the real world.
Since a colorblind person's isolation from their blind-colors is even more complete than the black-and-white neuroscientist's, it's not a huge leap to expect that you would also experience something new on exiting the black and white room. You could make similar arguments for someone who had never been burned, either by fire, or by capsaicin in their mouths from a habanero.
So we're back to Scovilles as an experiential measure, not able to be reduced to material units. You are still a brilliant gustatory neurologist with your exact 1:1 correlation between capsaicin receptor occupation and neurological state (measurable by mass-charge-time-distance) and Scovilles. So many nanomoles of capsaicin, controlling for temperature, pressure, some measure of how many nerves are in your tongue and how much of your brain is attentive to it - yes, you can predict 100% of the time what the Scoville rating will be when a new subject comes to your lab to taste peppers. But the units are still not the same as your eating a habanero. Per the thought experiment, and the reality of colorblind synasthetes, you still learn something by experiencing the habanero.
Physical quantities can be communicated and replicated without losing anything - they are interchangeable with information. But experience is locked inside your own consciousness, and in fact you can never in principle know whether anyone else actually experiences the world, or are just "zombies" with all the outward appearances of experience. Imagine you stick me in an fMRI and make me eat a habanero. While I'm howling in pain inside the machine, for some masochistic reason you jump into a neat gadget you built which takes my brain activity as input and feeds it to you, so that you experience what I'm experiencing. And suddenly you're howling with my pain of a few hundred thousand Scovilles. Was I feeling that? Or am I just a zombie, and your machine is producing in you, the one conscious being in the world, the sensations that I would be feeling if I were truly conscious?
All this identifies qualia and the world of subjective experience as fundamentally different from and incommensurate with the material world, built as it is of units with convertible dimensions. I am forced to take a dualist position, even if I am assuming (as does David Chalmers) that experience is wholly epiphenomenal.
Panpsychist positions like that developed by Chalmers focus on consciousness as a primitive property of the universe supervening on (epiphenomenal to) matter, and it is to this position that I usually subscribe. Chalmers frequently points out problems with nonpanpsychist assumptions about consciousness that lead us to treat it differently from other phenomena in the universe, for example in its sharp discontinuity and its origination from zero, with no clear demarcations or even the suggestion of how to measure it. I will write more on this later.
One interesting question about reality that panpsychism may begin to answer is in the question about what gives natural laws their "fire" - that is, it is possible to imagine a universe with different fundamental constants. What pins those constants down? What makes the laws of nature what they are, and relate to each other as they do? For example, why aren't there three charges, or another fundamental dimension? It is possible to conceive of countless hypothetical universes, but why are the ones that govern our lives "real" instead of being what-ifs with no power over reality when these laws are just information? I once put these questions to a cosmologist and was offered a modern take on Spinoza's argument for the existence of a supreme being: there is something that has as its nature to exist, and its internal logic has to work out consistently in order to exist. But this still doesn't give us a satisfying answer of why the laws of the material universe - equivalent to mere information as they are - are real and have fire. The answer may be that there is some basic qualium, which I would argue is the pleasure-pain principle, a property of the universe itself, just as mass or charge are. Without pleasure or pain, the other qualia, which otherwise would emerge in structures that become more and more complex, cannot exist at all; this explains why experience would necessarily appear as a part of the life of living things, when there is no clear evolutionary or other story for it. Without pleasure or pain the information of the universe has nothing to mediate it into experience and make it "real".
[Added later: funny cartoon about dimensional analysis here.]