Against skepticism, Epistemology

Against simulation

I want to trash the idea that we are living in a computer simulation. I will specifically examine Bostrom’s argument that either advanced civilizations don’t run simulations, or most civilizations go extinct, or we are living in a simulation. I will show that anyone who believes his argument is forced to believe in the flying spaghetti monster as well, and in any other item of superstitious nonsense that anyone wishes to impose upon the credulous. He reprises Pascal’s wager, misuses the notion of a Bayesian prior, and falls into cardinality pitfalls as old as Zeno. In passing I will slander Hanson’s more limited claim that at least it is not impossible that we are living in a simulation, explain a few philosophy background items for the Matrix, and defend instead a robust form of the Kantian transcendental deduction – we are living in the universe, which is actual and not an illusion; even illusions live in the actual universe.

First the form of Bostrom’s argument. He claims that one of the following is true, he does not decide which –

(B1) the human species is very likely to go extinct before reaching a “posthuman” stage;

(B2) any posthuman civilization is extremely unlikely to run a significant number of simulations of their evolutionary history;

(B3) we are almost certainly living in a computer simulation.

The form he desires for the conclusion of this supposedly necessary triparition is, “It follows that the belief that there is a significant chance that we will one day become posthumans who run ancestor – simulations is false, unless we are currently living in a simulation.”

Notice, on the surface he does not claim to argue independently that any of the three is more plausible than the others, let alone that all three hold. But in fact, he really comes down for B1 or B3, offering the alternatives “we are in a sim or we are all going to die”, and his money is on the “sim” answer.

The idea is either civilizations generally die out, are uninterested in simulation, or we are in one already. The first B1 is meant to be his catastrophe-mongers “out” and a possible resolution of the Fermi paradox (why aren’t the super smart aliens already here? — they are all dead, they routinely destroy themselves as soon as they have the tech to do so). While he is personally quite given to apocalyptic fantasies of this sort, the “very likely” in the phrasing is a give-away that he regards this is less plausible than B3. Some, sure, nearly all, not so much.

The second he actually regards as extremely implausible. On an ordinary understanding of human interests, if we can we probably would, and B2 requires an “extremely” modifying unlikely, as even a tiny chance that a society with the means would also add the desire is sufficient to generate astronomical numbers of sims. B3 is meant to be plausible given a denial of B1. Why? He counts imaginary instances and decides reality is whatever he can imagine more instances, of.

The primary fallacy lies there, and it can be seen by simply imagining a wilder premise and then willfully alleging a bit more cardinality. The flying spaghetti monster universes are much more numerous than the simulations, because the FSM makes a real number of entirely similar universes for each infinitessimal droplet of sauce globbed onto each one of his continuous tentacles. These differ only in what the FSM thinks about each one of them, and they are arranged without partial order of any kind. The sims, on the other hand, are formally computable and therefore denumerable and therefore a set of measure zero in the infinite sea of FSM universes. My infinity is bigger than your infinity. Na nah nana na.

This shows the absurdity of counting imaginaries without prior qualification as to how plausible they are individually. Worse, it shows that we have here just another species of Pascal’s wager, in which a highly implausible premise is said to be supported by a supposedly stupendous but entirely alleged consequence, which is supposed to multiply away any initial implausibility and result in a practical certainly of… of whatever. The argument in no way depends on the content of the allegation – simulation, deity created universe, dreams of Vishnu, droplets of FSM sauce. It is merely a free standing machine for imposing stupendous fantasies on the credulous, entirely agnostic as to the content to be imposed.

As for B1, well we are all going to die. Sorry, welcome to finitude. Doesn’t mean the civilization will, but we aren’t the civilization, we are mortal flies of summer. Theologically speaking it may be a more interesting question whether we stay dead, or whether the Xerox corporation has a miraculous future ahead of it, post human or not, simulated or lifesized. But one can be completely agnostic about that eventual possibility without seeing any evidence for simulation-hood in the actuality around us.

Hanson, a much lesser light, breathlessly insists instead that at least the simulation hypothesis is not impossible. This truly isn’t saying very much. According to the medievals, the position one ends up in denying only the impossible but regarding anything else as equally possible is called Occasionalism. Anything possible can happen and it is entirely up to God, the occasionalists claimed. They denied any natural necessity as limitations on God’s transcendent freedom. Logic and math could be true in all possible worlds, but everything else could change the next instant as the programmer-simulator changed his own rules. This anticipated Hume’s skeptical denial of causality by at least five centuries. The modern forms add nothing to the thesis; I’ll take my al-Ghazali straight, thank you very much.

The immediate philosophical background of these ideas and their recent popularization in the Matrix is the brain in a vat chesnut of sophmore skepticism, and its more illustrious predecessor, Descartes’ consideration in the Meditations whether there is anything he can be certain about. Descartes posits an evil genius deliberately intent on deceiving him about everything, and decides that his understanding of his own existence would survive the procedure. This evil genius has metastasized in the modern forms. As an hypothesis it actually has gnostic roots (caught between a world they despised and a supposedly just omnipotence, they required an unjust near-omnipotence in the way to square their circle), though come to that an occasionalist God would fit Descartes’ idea to a tee. Descartes himself, on the other hand, is quite sure that no intentional deceiver of that sort would deserve the more honorable title.

Why is the evil genius evil? Why is the brain-in-a-vat manager managing brains in vats? Why are the alien simulators studiously absent from their simulations? And why do their make believe realities feature so little of the harps and music and peaceful contemplation of which imaginations of paradise abound, and so much of the decrepitude and banal horror of actual history? No, they don’t need batteries – no civilization capable of such things would have material exploitative motives. One might allow for a set of small measure to discover things; beyond that the sim managers presumably actually have preferences and are fully capable of realizing them. Naturally you should therefore pray to them for a benign attitude toward your own trials and tribulations. The flying spaghetti monster appreciates a fine sauce.

The original Matrix at least kept up the dualism between a technological mask over a theological world and a theological mask over a technological world. The sequels couldn’t maintain it and collapsed into their own action movie absurdities, but the ability in principle to maintain the dualism is a better guide to the argument’s actual tendency. Which is superstition for technopagans.

Against those signs of contemporary intellectual flacidity, a Kant argued on essentially Cartesian grounds that we could arrive at an at least minimalist piece of information about the actual world beyond our interior of experience – that it exists and is real and structures the possibilities of experience. We need not go so far as to accept his characterization of space and time as necessary forms of intuition to see the soundness of this point. Even illusions happen in some real world, and “universe” refers to that ultimate true ground, and not to any given intervening layer of fluff.

Every robust intelligence starts from the actuality of the world, from feet firmly planted on the ground, not airy fantasies between one or another set of ears. The impulse to look everywhere for fantastic possibility instead is a desire for fiction. If you don’t like the truth, make something up. It is a power-fantasy, but shows remarkably little sensitivity to the question what any intelligent being would want to do with power of that sort. The morals of such pictures are a farce, from the gnostics on. But it is enough to notice that the entire subject is a proper subset of historical theology.

Epistemology, Many worlds

Against Many-Worlds

I’ve written in the past about a few of my objections to the many-worlds interpretation of quantum mechanics, for example on the NKS forum, the thread “do many-worlds believers buy lottery tickets?” I want to discuss here my favorite single objection to many-worlds (MW for short) and be specific about where I think it lands, and what it tells us.

The objection is founded on a classic paradox in probability theory called the St. Petersburg paradox. I’ll give the details below. The idea of the paradox is to show that the expectation of a probabilistic process is not the relevant practical guide to behavior toward it, when the sample size is left unspecified. More generally, operations research and optimal stopping problems are full of cases in which the sample size is a critical decision variable, with direct operational consequences for how one should deal with an uncertain outcome.

This is relevant because many worlds advocates frequently claim that their position is operationally neutral – that one would behave the same way if MW is true as if it is false. They essentially argue that the expectation is the right rational guide either way, and that this does not change across views. But the expectation is not a proper rational guide, as examples like St. Petersburg show. MW in effect posits a different value for the sample size, and this has operational consequences if actually believed. Since it does not appear to have such effects on the empirical behavior of MW advocates, one is left with two alternatives – they do not fully understand the consequences of their theory (unsurprising, and charitable), or they do not subjectively believe their own theory (also plausible), and instead advocate it in only a debator’s pose or provocative sense.

First the details of the St. Petersburg paradox. I give the traditional form first and will then reduce it to its essentials. One player offers the outcome of a game to a field of bidders – the highest bidder gets to take the “paid” position in the game, in return for paying the offering player whatever he bid. The paid position earns a chance outcome, determined by repeatedly flipping a fair coin. The payoff for a first flip of “heads” is one cent, and it doubles for each subsequent flip of “heads”, until the first “tails” outcome occurs. With the first “tails” the game ceases and the balance so far is paid to the second, purchasing player. Thus for example if the first flip is tails, player 2 gets nothing, if the first is heads and the second tails, player 2 gets 1 cent, if the first 2 flips are heads and the third tails, player 2 gets 2 cents, for 3 heads he gets 2^2 = 4 cents, and so on.

The expectation for player 2 is the sum of the infinite series of possible payoffs, which is simply equal to the number of terms times half a cent, which formally diverges. In other words the expectation is infinity, and the formal “value” of the game to player 2 is therefore infinity, and if we think a rational rule to adopt toward a probabilistic payoff is to value it at its expectation, then at the bidding stage, a group of supposedly rational players should be willing to outbid any finite bid so far. Notice, however, that all of the payoff is concentrated in the tail of the distribution of outcomes, as the product of an exponentially vanishing probability with an exponentially increasing payout. For any given bid, the probability of a positive result for player 2 can be computed and e.g. for $100, it is less than 1 out of 8000.

Economists typically use the St. Petersburg paradox to argue for adjustments to expectation-centric rules of rational dealing with risk, such as a strictly concave utility function for increments to wealth, that they want anyway for other reasons. But such adjustments don’t really get to the root of the matter. One can simply modify the payoff terms so that the payout rate grows faster than the utility function declines, after some sufficiently lengthy initial period, to insulate player 1 from any likely effect from this change.

Another frequent objection is to the “actual infinity” in the paradox, insisting that player 1 has to actually be able to pay in the astronomically unlikely event of one of the later payoffs. This can deal with the infinite tail aspect and require its truncation. However, if one then makes player 1 a sufficiently large insurance company, that really could pay a terrific amount, the probability of actually paying can still be driven below any practical limit, without recourse to actual infinities. While trivial bids might still be entertained in lottery-ticket fashion, the full expectation won’t be (with sane people using real money and bidding competitively, I mean), especially if it is stipulated that the game will be played only once. Rational men discount very low probability events, below their expectation. It only makes sense to value them at their full expectation if one is implicitly or explicitly assuming that the trial can be repeated, thus eventually reaching the expectation in a multiple-trial limit.

So just imposing a utility function with fall-off or just truncating the series will not eliminate the paradox. (The latter comes closer to doing so than the former, to be sure). The root of the matter is that the utility of improbable events is lower than the product of their value and their probability, when the sample size imposed on us is radically smaller than required to make the event even plausibly likely, in our own lifetimes. In similar fashion, rational men do not worry about getting struck by lightning or meteors; superstitious men might. It is in fact a characteristic sign of a robust practical rationality, that events below some threshold of total possibility over all the trials that will ever be made of them, are dropped outright from consideration.

Now, if MW is true, this would be irrational rather than rational. All the low probability events would occur somewhere in the multiverse that one’s consciousness might traverse and experience. Effectively MW posits the reality of a space of independent trials of every probabilistic outcome, that is unbounded, raising every unlikely outcome to the same practical status as certain ones. Certainly a MW-er may distinguish cases that occur in all possible worlds from those that branch across them, and he may practically wish to overweight those that have better outcomes in a space of larger probability measure. But he will still bid higher in the St. Petersburg game. He should buy lottery tickets, as I put it elsewhere – or at a minimum, lottery tickets that have rolled over to positive expected value (or have been engineered to have one from the start). Non-MWers, on the other hand, willingly “write” such risks – who rationally cares about the magnitude of a downside that is 100 billion to 1 against, to ever happen?

Peirce defined belief as the willingness to stake much upon a proposition. By that definition, I submit that MWers do not believe their own theory. In fact it has all the marks of a theory-saving patch, held to avoid some set of imagined possible criticisms of a valuable physical theory. I think it is superfluous for that – QM can stand on its own feet without it. I consider a more honest assessment of QM to be, that it simply underspecifies the world, or does not attempt to tell us what will actually happen, or that the determinism of wave function evolution is a conventional holdover from classical Laplacean physics. We can take this position without accepting any of the outright silliness of subjectivist interpretations of QM.

The principle noticed in this criticism, stated positively, is that the sample size posited by a theory is just as important a parameter as its expectation. Positing sample sizes that do not really occur will lead to errors in prediction and implication just as real as getting a magnetic moment wrong. And the actual, instantiated universe is sample size one – its first syllable says as much. When we refer to larger sample sizes, we are always talking about proper subsets that really are formal duplicates of each other, or we are talking about unknowns whose variation we are trying to characterize. Attempts to replace actualization with a probability measure will work if and only if the actual sample size truly involved suffices for the two to be practically close substitutes, and this is emphatically not guaranteed in general. Wherever the actual sample size is small, a probability measure view will underspecify the world and not fully characterize its practical reality, for us. And the deviation between the two widens, as the absolute probability of the events involved, falls.


Against skepticism

Or, a requirement of any theory of knowledge

Independent of my interest in NKS, I have philosophic objections to skepticism. I tell students that I break most of my lances against it; it is the particular philosophic position I wind up railing against. At bottom I consider skepticism a debator’s position, a dodge and evasion, and morally speaking a piece of arrogance masked as “humility for export”. (Being humble oneself may be a virtue, telling others to be humble can itself be far from humble). If the classic Socratic thesis of skepticism is that the only thing we know is that we know nothing, I claim we know no such thing.

NKS is useful for me in such discussions first because it finds a variety and complexity usually associated with empiricals, within purely formal systems. Pure NKS stands on the same ground as mathematical conjecture or long unsolved mathematical puzzles – we get pieces of pure logic that refuse to become simple “just because” they are “only” logic. Easy dicotomies that trace all epistemic difficulties to getting our formal ideas to correspond to “external” or empirical matters don’t really have a place to put such things.

This shows that the habit of equating the logical or formal with the simple is a selection bias and little else. Our past formal ideas have deliberately stayed simple enough we could noodle them out in (typically) four or five steps. In computational matters we counted “one, two, three, many”. The reality is any elaborate enough piece of pure logic, (even a strictly finite, always terminating block of it), isn’t simple at all. And a conclusion being “already entailed” by the premises won’t make it simple. This means deductive work meaningfully adds information. Hintikka is one contemporary philosopher who has noticed and tried to explore that intuitive fact, incidentally.

But against extreme skepticism about such things, they can have answers and we can find them. Not all large, involved pieces of logic are created equal. Those that inherently involve many possible cancellations or useful substitutions can be reduced by clever reasoning, or sometimes cracked completely with a piece of math. (For example, there is a simple formula operating on just the initial condition that will tell you the value of a cell later on in a rule 90 pattern, without requiring computation of all the intervening steps). Others inherently resist such methods and remain involved; only a huge amount of direct computational work can work them out. This is a phenomenal given of NKS, and before it of some sorts of math (e.g. number theory).

The philosophic issue is how well various stances about the problem of knowledge handle this phenomenal given.

Remarkably poorly, I claim. Empirical epistemology lumps everything formal into a “shouldn’t be any problem” bin, where the hard cases don’t fit. More extreme forms of skepticism lump all the formal cases into its only bin, “can’t be known”, and thus effectively predicts the simple and reducible ones won’t be readily solvable, when they obviously are. Popperian fallibilism wants there to be new information only where something can eventually prove to be wrong (traced say to a possible-worlds variability), but once actually solved any such formal puzzle is as certain as the simplest syllogism and true everywhere and always. Logical positivism largely continues to think of anything reduced to logic as solved, and glosses over everything interesting with an “in principle”. (I’ve read a book on the logic of game theory that explains in the first chapter that Go is finite, so backward induction could be used and it is therefore solved “in principle”).

But the patent fact is that some pieces of even pure math or logic can be known completely, others yield only to great computational effort, and still others won’t be solved in the lifetime of the universe. The problem of knowledge in its full variety is already present inside just one of the usual stances’ dicotomy boxes, and that the most formal.

Now, you don’ t solve a problem by evading it or denying its existence. You can’t explain how something like knowledge arises or works or can happen in the first place, by pretending it doesn’t. We hit kilometer wide windows at Mars after years in space. If a skeptic doesn’t want to call that knowledge I can play term games and call it thizzle, but thizzle still exists and needs to be explained. I’ll still be able to have thizzle about the center column of a simple CA like rule 250 (which makes a checkerboard pattern) but not about the center column of a CA out of the same rule-space, just as formal and involving just as many elements, but inherently generating complexity, like rule 30. A skeptic won’t take even very low odds on a bet against my thizzle about the former, but anyone will take them about the second, on terms indistinguisable from guessing about the purest randomness. The difference is real and operational, and whatever doubt-brackets anyone else puts around their epistemic claims, they see the same thizzle-relations as me or anyone else who understands the two systems.

The value of NKS on this subject is to focus the point of disagreement, and to clear away scores of side issues. Sensitivity analysis on the problem of knowledge rejects numerous popular theses about it. On the principle that an effect should cease when its cause ceases, we can reject various claims about how the problem of knowable vs. unknowable arises, because they predict a uniformity of knowability-status within a formal domain, where we can see there is no such uniformity. Any adequate theory of knowledge must conform to the operationally real distinctions among “readily known, reducible”, “knowable only with significant computational effort”, and “intractable”, already present in purely formal problems. If its categories aren’t fine enough to do so, then it is simply wrong.


Knowledge in CAs

I like the way NKS turns some existing ideas about knowables sideways.  The relevant distinctions aren’t inside or outside, model or nature, historical or natural, formal-mathematical or empirical etc.  Instead it is rule to behavior and simple or complex.  Meaning, simplicity is readily knowable whatever domain it occurs in, but complexity is hard to know about, again regardless of the domain.  This tracks our experience better than the usual epistemological puzzles, which always prove too much, and pretend we don’t know things we obviously do.

You can’t know the behavior of a simple program doing complicated things until you’ve done an awful lot of irreducible logical work, stepping through its actual behavior one to one and onto.  But you can know the behavior of a simple rule doing a simple thing, with a short cut equation, in seconds.  Some things are knowable, others are not, in precisely the same domain.  Theories of limits of knowledge that depend on domain categories would put rule 30 and rule 250 in the same box – but in fact their knowability is not the same.  The same theories put Popper’s clocks and clouds into the same category and get their knowability difference wrong, too, in an exactly parallel manner.

There may still be additional hurdles to line up formal theories to externals, to be sure.  But there are obviously knowable pockets of simplicity in both external reality and mathematics – and complex obscurities in both, as well.  The real distinction isn’t between the domains, but cuts right through all of them.  Simples are knowable and complexities are hard.