What if each instant were independent from the last?

At first sight, this situation, which from now on I will call BLEAK, might seem hopelessly bleak in an epistemological sense. For example: in the real world, a stock quote is probably going to be just a little higher or lower than its previous value, but if BLEAK were true, it would be no more probable that Gamestop remains less valuable than Tesla at the next instant than the contrary. In fact, both companies might not even exist in the next instant. If anyone truly believed that we have no reason to think that BLEAK is false, that one moment affects the next one, he should be paralyzed by uncertainty. But no one is. Therefore, radical sceptics don't even believe what they preach. 

And yet, they probably think they do. They wouldn't all be lying, right? Well, I think they are probably just confused.

However, I intend to show that BLEAK might not be quite as epistemologically bleak as it seems:

Suppose that you throw some dice a huge number of times. You'll notice that they all fall with some number between 1 and 6 face up. Actually that's not a very good example because if you wanted to see what numbers you could get, you would just look around each face of the die. So let's use a black box random number generator instead. Literally just a black box with a screen and a button. When you press the button, a random number between 1 and 6 shows up. So Bob comes across this box and doesn't know what it's for. He messes with it for a bit and notices that a number shows up in the screen every time he presses the button. He becomes obsessed with it and spends whole days and nights pressing it numerous times for the rest of his life. He will soon become used to seeing the same numbers on it. By the end of his life, a seven or an eight will (rightly) seem very unlikely to appear on it.

Now, if BLEAK were true, we could model our experience as this box. Our thoughts, our feelings, our perceptions, (and this is crucial) our memories are what is shown on the screen. So, given that each instant is independent from the next (remember: we are pretending for a second that BLEAK is true), how did we never notice it? Is my whole life just a (very) lucky streak of random feelings and thoughts and perceptions, like seeing the whole Bee Movie appear in the TV static by sheer coincidence?

It could be, but it's very unlikely.

It's more reasonable to infer that the total population of possible experiences from which each instant in my life is a random sample is either only made up of experiences that seem coherent, just like our normal day to day life, or heavily biased toward these experiences, in the same way that if Bob spent his whole life taking samples from our RNG black box, it's reasonable for him to assume that the probability distribution he was sampling from was at least heavily biased towards numbers between 1 and 6, or maybe even consisted entirely of them. 

So, if I suddenly discovered that BLEAK is true, I shouldn't immediately disregard the past observed regularity as a mere lucky streak, just as one might disregard the fact that the last thousand times he threw a die it landed on a six as a huge coincidence, if he knew for a fact that it was a fair die. No. Even if each instant were independent, I should expect that they would probably continue to appear dependent.

But I confess I'm not sure what to make of the past instants. If all the regularity I ever observed is just a general feature of possible experience and the instants themselves are related by no such regularity, then woudn't this make the regularity of the past memories an illusion, and thus the memories themselves illusory? In this case, I would have no right to look upon my past experience as a huge sample of past instants. I would just have the single current instantaneous experience as my only sample, and my memories would just be a feature of it. It would be as if, instead of Bob spending his whole life pressing the button in the black box countless times, he pressed it only once, saw the resulting number on the screen, and had no more data. Now, this would be a really bleak scenario. But I'm not quite sure about this last step of my reasoning.

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If BLEAK really were true, then nothing you do will have any effect on the future in any way whatsoever, so you may as well use the illusion of memory you have in this instant to do whatever seems to follow from those illusions. Not that you have any choice about what to do, since your choices are just as illusory as everything else and you almost certainly won't exist in the next instant anyway (for whatever anemic meaning "next" and "instant" and other time-related concepts have in a universe with no causality whatsoever)

It's even worse than the concept of Boltzmann brains, which at least have the epistemic decency of existing in a lawful universe.

you almost certainly won't exist in the next instant anyway

Maybe I won't exist as Epirito, the guy who is writing this right now, who was born in Lisbon and so on. Or rather I should say, maybe I won't exist as the guy who remembers having been born in Lisbon, since Lisbon and any concept that refers to the external world is illegitimate in BLEAK.

But if the external world is illegitimate, why do you say that "I probably won't exist in the next instant anyway"? When I say that each instant is independent (BLEAK), do you imagine that each instant all the matter in the world is randomly arranged, such that my brain may or may not be generated?

But the whole point of talking about external objects is that they do things and these things sometimes cause you to perceive something (this is the problem with Descartes' purely extended matter, whose definition doesn't talk about sensibility, in opposition to the scholastics' sensible matter. This makes cartesian matter indistinguishable from the merely ideal shapes that e.g. a geometrical treatise might talk about). If the external world consists only in an inanimate snapshot of itself, then there's no sense in talking about an external world at all. There's no sense in talking about brains, or atoms, or Lisbon, or any other object. If you can't shoot with a gun even in principle, if you can't even hold it, is it really a gun?
For this reason, I believe the instants in BLEAK should be understood as pure qualia. And the total population of possible instants, as possible experiences. Now, looking at the neatness of the organization of the first sample, the only one we've got, we might be compelled to expect that this wasn't a coincidence, and the total population of possible experiences is biased towards coherent ones. But this would be like concluding that you must be somehow special for having a very rare disease, when in reality, in a world with so many people, someone or another was bound to get it. In the same way, even if this was a huge coincidence and most instants are pretty uninteresting and nonsensical, why shouldn't another similarly coherent instant appear to me after millennia of me experiencing phenomenological white noise? And, since in these flashes of lucidity I can't remember the white noise, but only (some of) the other coherent moments I experienced (since otherwise that would make the instant that contains the memories of the white noise also partly white noise), what difference does the white noise make?
And that would mean that these perceptions are not so illusory after all. And I should expect to live normally, just as humans naturally expect. If I try to catch a ball, then, after an eternity of phenomenological white noise I won't remember anyway, I will actually catch it and continue my life normally, whereas the Boltzmann brain should expect to have abnormal experiences. He should expect to deteriorate and die in the middle of outer space, instead of continuing his normal functioning.

But if the external world is illegitimate, why do you say that "I probably won't exist in the next instant anyway"?

I never said that the external world is illegitimate. It's just that in the universe as described, any particular features of it are completely transient.

When I say that each instant is independent (BLEAK), do you imagine that each instant all the matter in the world is randomly arranged, such that my brain may or may not be generated?

Yes that is exactly what I imagine, especially given the clarifying examples in the original post like "In fact, both companies might not even exist in the next instant". Was this intended to mean that all the people in the companies exist, and the corporate offices with their logos and so on, but just the people experience different things and no longer believe that they're part of some company?

Also yes, if such a universe covers enough of probability space then you (or someone very like you) may exist again in the future having memories of having experienced something approximating your life to date. In fact, many possible and plenty of impossible variations and continuations of your life to date. The impossible and nonsensical ones (by our standards) will vastly outnumber the possible ones that make sense.