Giving DCP an Intel CPU and a volt meter to reverse engineer the modern PC

[Physics Guy]

Right, the Planck time is not the quantum of time, as far as we know. There could be a quantum of time, and if there is then it is surely some nice mathematical multiple of the Planck time, but we have no reason now to suspect this. The Planck time does represent a frontier in our current knowledge, because according to what we now think, saying exactly what happens with time resolution that high would require an understanding of quantum gravity, which we do not yet have.

The Planck units are not just about time. They are called that because—as I believe Max Planck himself first noticed—by combining Planck's then-new constant of nature "h" with the speed of light "c" and the constant "G" from Newton's Law of Gravitation, one can make a product or ratio that has any kind of units one wants: a length, a time, a mass, an energy—whatever.

In principle we could adopt all these so-called Planck units as our system of measurement, instead of using meters and kilograms or feet and pounds—and instead of using seconds. Then all the laws of nature would be free of constants, in the sense that the speed of light would just be one Planck length per Planck time, and so on. It would be convenient for theoretical physicists, but not so good for anyone else, because the Planck units are all ridiculously tiny compared to the scales that are relevant to humans. The McDonald's quarter-pounder would become a 5000-Plancker with a bit of rounding, which is not actually so bad, but the 3-second rule for picking up dropped food would become a 10^43-Planck rule.

One implication of the Planck units is that there really are no such things as units. Miles are not qualitatively different from hours or pounds, the way we think they are. Everything is just numbers, and our preference for expressing lengths and times and masses in different units is just a psychological quirk of humans, like the British expressing beer volumes in pints while measuring petrol in litres.

So there is a Planck length as well as a Planck time, but space is not discrete any more than time is, as far as we know. It could be so, with a discrete spacing far below our current resolution limits, but we have no such indications as yet. Other things are quantised, in quantum mechanics, but not space and time themselves, except sometimes in models that we imagine. Sometimes models with discrete space or time are serious speculations about how things might really be, but more often the discretization is just a mathematical convenience that we allow ourselves. Sometimes it's even a highly accurate approximation. The physics of solids is really important, and in most solids the atoms are arranged into nearly perfectly regular crystals. The atoms can vibrate around a bit, which is how a solid can be hot, but they don't move far from their evenly spaced spots in the crystal. So if you're studying how electrons can move through a metal or semi-conductor, in an electric current, you can often think of the electrons as hopping from atom to atom, idealising space as a grid. If space actually is discrete like that, though, it's on some far smaller scale than the size of an atom.

So, to come back to consciousness, no, I don't think that consciousness has to be discrete because space or time is discrete, because space and time probably aren't. On the other hand, consciousness probably does have some discrete character, if you zoom in close enough on what the brain is doing, because nerve impulses seem pretty digital. Back on the first hand, however, that probably doesn't matter.

Resolution is one of the big concepts in physics. It turns out that you can consistently describe the world within limited scale ranges. You can do atomic physics in wonderful detail while trivialising nuclear physics to the point of considering any nucleus to be just a charged point. Or you can zoom in on the nucleus, and worry about protons and neutrons and pions, while still ignoring quarks and gluons—and not thinking of atoms at all. Then again you can zoom way back out and think about, say, water waves on the ocean. You don't need to think about molecules at all, to think about surfing. In fact you probably can't think about surfing while thinking of molecules. Your brain does not have the bandwidth, the depth of focus. You need to fade out the molecules to see the waves, forget the trees, see the woods. And as far as the physics of surfing is concerned, water might just as well be continuous water-stuff, the way some ancients imagined it, and not be composed of individual molecules at all.

What would you even add to your understanding of surfing if your brain were big enough to accommodate molecules and meter-scale waves in one view? The laws of continuous hydrodynamics are simply true, on surfing-wave scales. If you could indeed clearly picture the molecules that make up the waves, you would just see that they all conspired to make the pressure and viscosity, and so on, come out to be what they are. If a hydrodynamicist gave a lecture on surfing, in terms of continuous water, and then you stood up to add your giant brain's further insight into surfing, based on your clear view of the molecules, all that you'd be able to say would be, "Yup." You might be able to enlighten the audience greatly about exactly why hydrodynamics works as it does, but concerning surfing itself, you'd have no news to convey.

Nothing in surfing depends on whether water is discrete (on tiny scales) or continuous. Okay, you'd notice the discrete nature of the fluid if you tried to surf on loose gravel, but as long as the individual chunks of fluid are tiny enough, just how tiny they are doesn't matter, for surfing. As far as surfing is concerned, water effectively is continuous.

Whatever consciousness is, it's probably a phenomenon on a much larger scale, in both space and time, than any one nerve impulse, let alone any atom, let alone any Planck unit. I'd say that consciousness is almost certainly continuous in time, even if time itself is indeed discrete, because nothing in consciousness is likely to depend on any temporal discreteness. As far as consciousness is concerned, time may as well be continuous; and for me this is the same as saying that consciousness itself is continuous.