But, as you noted, such a world would be completely predestined, and unlike the probabilistic (partly randomized) reality*2 that us humans have to deal with. — Gnomon

That's the deterministic model of the universe, which Laplace's demon ought to easily calculate. Just remind yourself what Laplace is talking about: he is talking about extrapolation, the calculation of the value of a function outside the range of known values. That has nothing to do with randomness or probabilities or statistics. And this is quite possible for Laplace's demon when it isn't participating in the universe. The intellect can really perform then as Laplace asserts. Everything is truly predetermined. The future is what it will be. There is simply no room for choice, chance or randomness.

The negative self-reference refutes this possibility.

Perhaps this would be easier to understand in a game theoretic model. Let's assume a game where there's two paths (A and B) for me to take and I have to pick one and you have to make a correct forecast of what path I take. Might be easy for you and especially easy for Laplace's demon, but the thing is that you have to tell the forecast of what I will do prior of me doing it (as it obviously is a forecast, not just an observation). In order for you to make a correct forecast, you have to name the path that I take.

After you have made your forecast, I will react the following way:

If you forecast I take path A - > I take path B
If you forecast I take path B - > I take path A
If you forecast anything else, or stay silent - > I take path B.

First, is there a correct forecast, a correct model of how the game will play out (what path I will take)? Yes, obviously.

Now do notice here the negative self reference: my decisions are simply based on your forecast itself, or the lack of it. And obviously I do the other thing as you forecast. You cannot deal with this by saying that I will say the path that you won't say (for example B), because then I will do exactly that (say B). Or, if you either start a philosophical lecture or simply just explain the above, it isn't a correct forecast as I defined earlier.

The basic thing in Cantor's diagonalization process is quite similar to that of above, it too is a clever way to have negative self reference and thus show that obviously that real number cannot be in the list (at least one way to make reductio ad absurdum proof.

I suppose our "limitation on modeling" means that, pace Einstein, most of us parts-of-the-whole are not even close to omniscient. — Gnomon

The "limitation" here is simply that you cannot make the correct model.

It's not about omniscience, you could say it's about control. In the above game you could take your favorite shotgun, point it at me and say very threateningly: "SSU WILL CHOOSE PATH A!!!" and I will likely choose path A as I don't want to find out which kind of bullets you have in your shotgun and will you shoot me or not.

Hence we talk about Laplace's demon: if it genuinely makes the correct forecast, then the demon itself controls the whole universe. That's the only way out of the negative self reference: that there simply can't be a negative self reference for the demon. Which, again, I will say that Laplace didn't have in mind when he talked about the intellect.

The random nature of the 'quantum leap' is what caused Einstein to say that he doesn't believe God plays dice. He always maintained that quantum theory must be incomplete, as a consequence of this and other aspects of it, but I think subsequent discoveries have not favoured his objections. — Wayfarer

I think the popular idea is that the elementary particles are lurking in a kind of fuzzy cloud, awaiting measurement; when in reality, they have no definite location, and therefore no definite existence, until they’re measured. Until then there are only degrees of probability, there are not definite particles in the realistic sense generally understood. — Wayfarer

You seem to agree with that idea because you, like others, think that each existence is self-contained or self-supporting. That each unit of reality is in itself responsible for its being. And we know that's not how the universe works. The Schrodinger's thought experiment of a cat in a box with all the other components is a way to convey this idea -- the cat is not just a cat in itself: there is an idea that we're trying to judge. Is it dead or alive? And we can't answer that question by naively saying it's breathing or not breathing. We have to take into consideration whether there is radioactivity, and if there is does it break the flask containing the poison which then kills the cat.

The big bang was not witnessed in itself -- it was theorized.

The expansion of the universe was observed not by actually seeing the edges expanding. But by observing the increasing distance of the other galaxies.

You're just focusing on different aspects of the Uncertainty problem. ↪Benj96
seems to be assuming that the world itself is fundamentally stochastic, while ↪L'éléphant
seems to be saying that the uncertainty is an observer problem. In truth, the answer to the "troubling" emotion caused by the random appearance of quantum phenomena may be to do as the quantum pioneers did : accept the inherent limitations of both observer and object. — Gnomon

That's fair. To me the concept of "random" is similar to the concept of "nothing" if we really want to get to the reality. The nothing was a filler of a gap in our observation. But, as I have said before, there has always been something: when theorists talk about the beginning of the universe, they really don't mean "from nothing".

Everything is truly predetermined. The future is what it will be. There is simply no room for choice, chance or randomness.
The negative self-reference refutes this possibility. — ssu

Some self-reference is necessary to have a self-concept. So I guess you're saying that Laplace's demon is omniscient until it begins to doubt its own abilities : to have a negative bias against itself. However, there may be another interpretation of that negative-self-reflection notion*1.

The Centipede story*2 is an illustration of the psychological effect of too much self-concern, or introspection. Normally, the centipede is able to walk by instinct, without consciously thinking about how to coordinate so many legs. But when her focus is directed from a single goal to the many steps in between, a subconscious process (no need for choice) became a conscious concern (necessity for choosing). I suppose you could say that the complex walking procedure was "predetermined" by instinctive genetics, until it became a rational mechanical design problem.

What would cause the demon's intellect to change her cosmic worldview from A> frozen totally-non-random block-time eternal-isness, to B> dynamic space-time partly-randomized evolution-over-eons? If predestination is switched to free-will, then every step becomes a problem to be solved. Hence, the demon might get distracted from the simple "why?" of the world, to questions of "when & where & how", then confused by so many contradictory options, might fall in the ditch of choice-paralysis*3. :smile:

*1. Negative Self-Reference : "question our assumptions"
https://thenegativepsychologist.com/trap-self-reference/

*2. The Centipede's Dilemma :
The centipede effect occurs when a normally automatic or unconscious activity is disrupted by consciousness of it or reflection on it.
https://en.wikipedia.org/wiki/The_Centipede%27s_Dilemma
A centipede was happy – quite!
Until a toad in fun
Said, "Pray, which leg moves after which?"
This raised her doubts to such a pitch,
She fell exhausted in the ditch
Not knowing how to run.


*3. the paradox of choice suggests that having too many choices actually limits our freedom.
https://thedecisionlab.com/reference-guide/economics/the-paradox-of-choice

So I guess you're saying that Laplace's demon is omniscient until it begins to doubt its own abilities — Gnomon

Oh no, that's not it. I'm just saying that it cannot do what it doesn't do. This is the law of non-contradiction: it states that contradictory propositions cannot both be true in the same sense at the same time.

Hence it cannot simply be omniscient when it interacts with the universe. The only way the demon can be omniscient about an universe is when it's not part of it. And when it's not part of it, it cannot give any information to anybody (interact with it, in general).

Oh no, that's not it. I'm just saying that it cannot do what it doesn't do. This is the law of non-contradiction: it states that contradictory propositions cannot both be true in the same sense at the same time.
Hence it cannot simply be omniscient when it interacts with the universe. The only way the demon can be omniscient about an universe is when it's not part of it. And when it's not part of it, it cannot give any information to anybody (interact with it, in general). — ssu

I'm not sure what the "contradictory propositions" are in this case. Are you talking about A> knowing-Omniscience vs B> acting-Immanence : design & creation of A> perfect self-adjusting evolutionary space-time system vs B> imperfect mechanism requiring occasional adjustments (interactions ; interventions) to physical settings? "A" would leave the creator-demon outside the creation, but "B" would require the demon to stick-around to tweak the dials of Nature to keep it on track.

As I understand Laplace's metaphor of godless purposeless Determinism, it postulates setting Initial Conditions, but not subsequent demonic-intellect "interventions", and would play-out via random physical interactions ; not by divine dial-tweaking. That would be equivalent to the Big Bang Theory, in which the Singularity (the Demon) was a physical state similar to a Black Hole. There was no prior intention or later intervention. That super-dense dot of matter/energy simply exploded. And the happenstance state of the Singularity set the initial conditions for the Bang, which physically determined all future evolutions of matter/energy, which are destined to die in a Big Sigh.

The philosophical problem with the burgeoning*1 Singularity postulation is : C> how did it get into that particular state, and D> what caused the imploded matter to explode? One proposed answer to C & D is that a previous incarnation of a hypothetical Multiverse ended with all matter compacted into a Black Hole, which "bounced" back into a reverse of the implosion motion : an explosion*2.

The Singularity-Demon metaphor could be explained as the intake of knowledge (information) from a previous (precedental) world experiment, which made it effectively omniscient about the new (subsequent) venture in world-making. If the cause & effect are imagined as natural & accidental, then no Creative Intention was necessary to Cause the eruption of an embryonic Cosmos, providentially furnished with DNA/information from a parent world.

Of course, the Mutiverse-Big-Bounce theory is just as unverifiable as a Demonic or Genesis creation story. So, we are arguing about the credibility of a scientific Myth. What's "true" in the metaphor, is not necessarily true in the real world. So, we're back to the OP question of the role of Information and Randomness in our Organic and Entropic world. :nerd:


*1. Burgeoning : beginning to grow or increase rapidly; flourishing.

*2. The Big Bounce hypothesis is a cosmological model for the origin of the known universe. It was originally suggested as a phase of the cyclic model or oscillatory universe interpretation of the Big Bang, where the first cosmological event was the result of the collapse of a previous universe.[1][2][3][4] It receded from serious consideration in the early 1980s after inflation theory emerged as a solution to the horizon problem, which had arisen from advances in observations revealing the large-scale structure of the universe.
https://en.wikipedia.org/wiki/Big_Bounce