Why the Flow of Time Is an Illusion

> I mean this: a system is deterministic in practice if you can actually predict its outputs based on its inputs with reasonable amount of effort.

You're changing the meaning of determinism and bringing it closer to rationalism. Your introduction of the element of theory to the mix is a violation of Occam's Razor. We already have philosophy and a word that covers what you want it to cover. Theory is a component of rationalism, not of determinism. If you need theory to understand a system, then it already has elements of non-determinism. Theory is what you need to make sense of the non-deterministic. Because theory deals with uncertainty, you wouldn't need any validation of your hypotheses if the system was truly deterministic. One observation would be enough to ascertain the whole thing.

A considered study of history would reveal where you're going wrong here. The Greeks invented empiricism and philosophy and science while the Egyptians never got there despite only being a tiny distance away. They wanted to distance themselves from theological frames. Despite all this, the Egyptians built pyramids. They understood determinism. They could not understand science. Determinism made them good engineers. Engineering is not science.

> A system is deterministic in theory if it's deterministic, but actually predicting its outputs requires absurd amount of computation.

Now you're starting to dip into computational complexity territory. Predicting outputs is the domain that the halting problem puts a backstop to.

To prove to you that a brain is better than a computer, all I have to do is state the obvious, humans make algorithms, not the other way around. Sure, there are programs that will devise algorithms, but humans have to understand the domain before they can make computers do their work for them.

Your examples of Lorenz systems and weather do not change things at all. Humans have a better understanding of weather than computers do. In fact, humans have an entire body of theory that attempts to make sense of why such things have difficult-to-determine causation, chaos theory. Humans devised it, not computers. And they devised it using the tools of epistemology, working out the details of justification of knowledge via seeking rigor, not in the scientific method of dreaming up hypotheses based on empirical analysis and testing them. Chaos theory is more math than science.

In other real ways, humans outclass other mammals, even though we largely share the same macro brain structures. We keep monkeys in cages, monkeys do not keep us in cages.

I'm not sure how much more I have to state the obvious here. You seem to be the one seeking out a special domain in which the rules don't apply, one in which computers are wholly analogous to brains. It may, and this is speculation, be true in degree rather than kind.

But the halting problem itself illustrates a domain in which humans are able to reason past, whereas we cannot possibly program a computer to do it. Computers cannot program themselves to find gradations of the halting problem. Humans have to write algo-generating algos. The pace of comp-sci progress at the moment is fully dictated by human ingenuity, and if you think about it, any change in this means that the singularity is upon us.

I suspect that we'll never be able to get computers to fully take the place of brains. There will always be domains where brains are better than algos. Prove me wrong. Humans are capable of wanting things, even the best machine learning algos at the moment struggle with finding purpose. Finding purpose is something even the most basic virus can achieve. And we can't even determine whether virii are alive or not.

And that's super basic. How much more self-awareness do you think algos can find before running into hard physical limits? The computational and memory concerns are huge. I predict the hard limit of engineered systems will be well below full self-awareness. Instead we'll have to create biological systems to carry on progress. Dogs will get smarter, mice will get smarter, apes will eventually start doing things that humans do now, once we can fit our ethics around it.

>Hand the same input to the same mind and you'll get a different output every single time, unless the mind willed itself to act rationally.

Are you sure? Remember that memory also counts as an input if it's used in a computation; it seems to me that this applies to both humans and computers.

For a harrowing account of what a mind may do when exposed to very nearly the same inputs, you may be interested in one segment from this Radiolab episode: https://www.wnycstudios.org/story/radiolab-loops

It describes a patient with transient global amnesia who has a looping conversation with her daughter. (There's a link to a video of the conversation on that page as well.) Under normal circumstances this wouldn't happen, as once you've had a conversation you also have memories of having that conversation. But if you're unable to form memories...

> I would certainly say consciousness is 'something more', and that this something more has to be something non-material (or at least using 'materials' that have wildly different properties than what we observe using the scientific method).

If you're interested in having that idea challenged, I heartily recommend reading "Godel, Escher, Bach" - the book explains how complexity (perhaps to the point of consciousness) can emerge from "simple" systems.

> de Sitter space is a vacuum solution for Einstein's field equations.

Yes, an exact solution.

> What this means is that the stress-energy tensor is basically canceled out" everywhere by the uniform energy distribution

No, it means that the stress-energy tensor is zero at every point in the whole spacetime. There is no matter to source any curvature; the curvature is specified by the theoretician writing down the vacuum solution.

In Lorentzian 4-dimensional vacuum de Sitter spacetime ("dS" below) there is no useful concept of energy anywhere. The parameter \Lambda is incorporated directly into the Einstein curvature tensor and so is interpreted geometrically. One would have to perturb the dS vacuum in order to have a useful interpretation of \Lambda as a source of gravitational energy.

Vacuum solutions can be useful in understanding physical systems in which gravitation is important. For example, one can add non-zero stress-energy by hand and use perturbation theory to study the consequences rigorously. Alternatively, one can "cut out" parts of a vacuum solution and work with the rest which closely resembles a physical system (such as deep space far from the matter in and around galaxies). As the expansion of the universe dilutes away the matter contributing to a non-zero stress-energy tensor, our universe will resemble the sparser parts of a de Sitter spacetime. However, from our perspective (i.e. with data in our sky) there are much better approximations at various scales than de Sitter spacetime perturbed by matter fields: there is a lot of obviously non-zero stress-energy under our feet, lighting up our sky day and night, and causing heat to flow from one place to another.

> That means no gravity

There can be extremely strong spacetime curvature in de Sitter space!

In general we can time-orient dS: in one direction objects which only interact gravitationally and do not generate significant stress-energy will always converge, in the other they will always diverge, depending on the value of the \Lambda parameter, which is always positive for dS. If \Lambda is large, all such objects leave the others' causal cones much more quickly than they could, even in principle, in flat spacetime.

If we perturb dS with a dense ball of nonrelativistic (i.e., slowly-moving) dust that feels only the gravitational interaction, the dust will tend to collapse if \Lambda is sufficiently small, and will locally approximate a Lemaître-Tolman-Bondi (LTB) collapsing dust metric, which in turn resembles a perturbation of vacuum Schwarzschild or Kerr (which are eternal black hole models; there is no matter to collapse).

A scattering of such collapsing dust-balls with significant gaps between them has been studied by a number of relativists as a family of "swiss-cheese" cosmologies very similar to the one developed by Einstein & Strauss in 1945, who represented the balls of dust as already-collapsed vacuum Schwarzschild solutions, calling them "holes" in the "cheese" of the surrounding expanding spacetime. The Einstein-Strauss-de Sitter model approximated some features of our universe at intermediate ranges, but has since been superseded by the the Friedmann-Lemaître-Robertson-Walker (FLRW) model of the modern standard model of cosmology that among other things has representations of nonzero stress-energy that the vacuum Einstein & Strauss model did not, and which better matches observables in our sky than models that added more realistic matter fields to Einstein & Strauss vacuum.

One feature of Einstein-Strauss-de Sitter style expanding swiss-cheese models is that a small "test" amount of sparse low-mass nonrelativistic dust scattered in the LTB "holes" will stay confined within the hole while the hole separates from everything else. However, an identical test dust scattered in the "cheese" part well outside of holes will never find its way into a hole. Ultimately the former test dust will converge while the latter will diverge.

We can get highly similar results by perturbing the FLRW model. (The observable universe is well approximated by an almost FLRW model in which there are primordial density fluctuations: over-dense areas collapse gravitationally, comparably to the matter in the "holes" of a non-vacuum Einstein-Strauss-de Sitter universe.)

Locally in all these cases, what we have are the tensor fields contributing to the Einstein Field Equations, and general covariance. We can talk about the values of these tensors at any given point (and its neighbourhood), but General Relativity does not lend itself to universal definitions of energy or even energy-density. We can reduce the tensors by using gauge fixing and other techniques, and "demote" the cosmological constant in FLRW or in dS into an energy. (That's really all Dark Energy is in the standard cosmology). In such a gauge we can talk about the work matter interactions (e.g. the electromagnetic interaction) does "against" dark energy. However, the real physics are in the tensors, and applying coordinates and selecting particular observers, while often able to make things much easier to calculate, can be highly misleading too.

The idea that the cosmological constant is "cancelled" out by matter-matter gravitational interactions (and electromagnetic and nuclear interactions) is a statement that the geometrical nature of the cosmological constant is "demoted" into an extremely weak force field, and leads to all sorts of statements that work in that "demotion" context but not generally. Typical statements are that the solar system is expanding, or the galaxy or cluster is expanding, because of the tiny local force on matter by dark energy.

It is better to retreat to "swiss-cheese" and say that the geometry of our solar system is not well-approximated by expanding metrics like dS or expanding Robertson-Walker, and that consequently it is a better fit to observations that in our "hole" (which the matter of our solar system, galaxy and cluster sources) the cosmological constant simply vanishes.

Better still would be to advance to inhomogeneous metrics, but those are a subject of research beyond the scope of this comment.

Finally, your last paragraph can also be read as a request to be directed to the concept of the Jeans Instability in the Expanding Universe. If in the very early universe there was truly uniform and dense distribution of stress-energy, the slightest perturbations would magnify, leading to structure formation. As I wrote above primordial fluctuations of an otherwise FLRW model approximates modern cosmological observations very well. (One could alternatively introduce dissipation, quantum uncertainties, and so forth, as a source of gravitational Jeans Instability causing the collapse or fragmentation of a uniform distribution of stress-energy).

I remember some science show where they said a cup of hot water technically has slightly more mass than a cup of cold water, due to the mass contribution from the (higher/hotter) energy. Are you saying this is not the case? Would a near-absolute-zero cup of water (ice) have the same mass as a cup of boiling water?