Tuesday, February 19, 2013

Empirical Evidence That the World Was Not Created Five Minutes Ago

Bertrand Russell writes:

There is no logical impossibility in the hypothesis that the world sprang into existence five minutes ago, exactly as it then was, with a population that "remembered" a wholly unreal past. There is no logically necessary connection between events at different times; therefore nothing that is happening now or will happen in the future can disprove the hypothesis that the world began five minutes ago.... I am not here suggesting that the non-existence of the past should be entertained as a serious hypothesis. Like all sceptical hypotheses, it is logically tenable but uninteresting (The Analysis of Mind, 1921, p. 159-160).
Wait... what?! We can't prove that the world has existed for more than five minutes, but who cares, bo-ring?

I'd think rather the opposite: We can prove that the world has existed for more than five minutes. And if I didn't think I could prove that fact, I wouldn't say ho-hum, whatevs, maybe everything I thought really happened is just an illusion, *yawn*.

Okay, well, "prove" is too strong. Logical certainty of the 2+2=4 variety, I can't provide. But I think I can provide, at least to myself, some good empirical evidence that the past existed five minutes ago. I can begin by opening up the New York Times. It tells me that Larry Kwong was the Jeremy Lin of his day. Therefore, the past exists.

Now hold on, you'll say. I've begged the question against Russell. For Russell is asking us to consider the possibility that the world was created five minutes ago with everything exactly as it then was, including the New York Times website. I can't disconfirm that hypothesis by going to the New York Times website! The young-world hypothesis and the old-world hypothesis make exactly the same prediction about what I will find, and therefore the evidence does not distinguish between them.

Here I need to think carefully about the form of the young-world hypothesis and the reasons I might entertain it. For example, I should consider what reason I have to prefer the hypothesis that a planet-sized external world was created five minutes ago vs. the hypothesis that just I and my immediate environment were created five minutes ago. Is there reason to regard the first hypothesis as more likely than the second hypothesis? I think not. And similarly for temporal extent: There's nothing privileged about 5 minutes ago vs. 7.22 minutes ago vs. 27 hours ago, vs. 10 seconds ago, etc. (perhaps up to the bound of the "specious present").

So if I'm in a skeptical enough mood to take young-world hypotheses seriously, I should have a fairly broad range of young-world hypotheses in mind as live options. Right?

In the spirit of skeptical indifference, let's say that I go ahead and assign a 50% probability to a standard non-skeptical old-world hypothesis and a 50% probability to a young-world hypothesis based on my subjective experience of a seeming-external-world right now. Conditional on the young-world hypothesis, I then further distribute my probabilities, say, 50-50% between the I-and-my-immediate-environment hypothesis and the whole-planet hypothesis. The exact probabilities don't matter, and clearly there will be many other possibilities; this is just to show the form of the argument. So, right now, my probabilities are 50% old-world, 25% young-small-world, and 25% young-large-world.

Now, if the world is young and small, then all should be void, or chaos, beyond the walls of this room. (In a certain sense such a world might be large, but the Earthly stuff in my vicinity is small.) In particular, the New York Times web servers should not exist. So if I try to visit the New York Times' webpage, based on my entirely false seeming-memories of how the world works, New York Times content which is not currently on my computer should not then appear on my computer. After all the hypothesis is that the world was created five minutes ago as it then was, and my computer did not have the newest NYT content at that time. But, I check the site and new content appears! Alternatively, I open my office door and behold, there's a hallway! So now, I reduce the probability of the young-small-world hypothesis to zero. (Zero makes the case simple, but the argument doesn't depend on that.) Distributing that probability back onto the remaining two hypotheses, the old-world hypothesis is now 67% and young-large-world is 33%. Thus, by looking at the New York Times website, I've given myself empirical evidence that the world is more than five minutes old.

Admittedly, I'd hope for better than 67% probability that the world is old, so the result is a little disappointing. If I could justify the proposition that if the world is young, then it is probably small enough not to contain the New York Times web servers, then I can get final probabilities higher. And maybe I can justify that proposition. Maybe the likeliest young-world scenario is a spontaneous congealment scenario (i.e., a Boltzmann brain scenario) or a scenario in which this world is a small-scale computer simulation (see my earlier posts on Bostrom's simulation argument). For example, if the initial probabilities are 50% old, 45% young-small, 5% young-large, then after ruling out young-small, the old-world hypothesis rises above 90% -- an almost-publishable p value! And maybe the probability of the old-world hypothesis continues to rise as I find that the world continues to exist in a stable configuration, since I might reasonably think that if the world is only 5 minutes old or 12 minutes old, it stands a fair chance of collapsing soon -- a possibility that seems less likely on the standard non-skeptical old-world hypothesis. (However, there is the worry that after a minute or so, I will need to restart my anti-skeptical argument again due to the possibility that I only falsely remember having checked the New York Times site. Such are the bitters of trying to refute skepticism.)

You might object that the most likely young-small-world hypothesis is one on which there is an outside agent who will feed me the seeming-New York Times website on demand, purposely to trick me. But I'm not sure that's so. And in any case, with that move we're starting to drift toward something like Cartesian demon doubt, which deserves separate treatment.

[Slightly edited 6:33 pm in light of helpful clarificatory questions from Jonathan Weisberg.]

29 comments:

Leon Leontyev said...

"...I should consider what reason I have to prefer the hypothesis that a planet-sized external world was created five minutes ago vs. the hypothesis that just I and my immediate environment were created five minutes ago. Is there reason to regard the first hypothesis as more likely than the second hypothesis? I think not."

How come this indifference doesn't extend to the old-world hypothesis? In other words, why does old-world get 50%, whereas the other two get 25% each, rather than all three getting 33%? And as you expand the number of hypotheses that are worthy of consideration (from a skeptical point of view) the old-world hypotheses should get less and less credence. If the old-world hypothesis gets the same initial value as the young-large-world hypothesis (which is what a skeptic ought to say), then no amount of empirical discovery will ever drive one's credence in the old-world hypothesis above 50%.

Leon Leontyev said...

Sorry, my comment didn't really address your second last paragraph, in particular this claim:

"If I could justify the proposition that if the world is young, then it is probably small enough not to contain the New York Times web servers, then I can get final probabilities higher."

I guess my thoughts are, if you can justify that if the world is young, then it is probably small, then you should be able to justify your way out of just about any sceptical hypothesis.

Eric Schwitzgebel said...

Maybe so, Leon! But it would have to be pretty small to lack the demon, yes?

Eric Schwitzgebel said...

In any case, I'm happy enough with the conditional. I assume you're dubious about my hope of making a small-world hypothesis a more likely skeptical hypothesis than a large-world hypothesis. I agree that I don't argue for that in the post, and it's only a hope. I think it's not a wholly forlorn hope, though, e.g., in light of the seeming probability of smaller Boltzmann brains compared to larger and smaller simulations compared to larger, etc.

Anonymous said...

I think the probability of a young-world is actually much higher than the probability of an old-world.

A low entropy state is more likely than a high entropy state. As the total entropy of the universe is always (or practically always) increasing, it's more likely that the universe just started in this relatively high entropy state than it is that it began long ago with that extremely low entropy state that supposedly preceded the big bang.

Another way of looking at it is, it is much more likely for 3 things (X, Y, and Z) to pop into existence than it is for 100 things (3 of which are, or are just like, X, Y, and Z) to pop into existence. As a universe with no past would contain less things/events, it is more likely than a similar universe with a past.

I don't understand how you get this claim: "Now, if the world is young and small, then all should be void, or chaos, beyond the walls of this room." Suppose the young-world contains the exact same objects as this universe, including all of the distant galaxies and whatnot, and that the only difference is that it does not contain any of the events that supposedly preceded the old-world. That state is still much, much more likely than an old-world that contains these events, as well as all the events that preceded them. This after all is the point of the Boltzmann brain thought experiment. N.B., just because you may be able to disprove the existence of the smallest world (by, e.g., looking out your window) does not mean that you have disproved the existence of larger small worlds, e.g., worlds in which the universe contains all of the objects it now does, except, no past. And there are a practically infinite number of smaller worlds, whereas there is only one this-(supposedly-old)-world, and, to make matters worse, each one of those smaller worlds are more likely than this old-world (by virtue of being smaller).

In short, you are not justified in assuming that an old-world is even 50% as likely as a young-world. In fact,
even the claim that the old-world is 1% as likely as the young-world would be too generous to the old-world hypothesis.

Of course, I believe the old-world hypothesis, but I cannot say that I have a good empirical reason to believe it.

Anonymous said...

Oh looks like I jumped the gun. I had only skimmed your post: I see what you were getting at with the small-and-young world claim. But I think my point still stands: the smallest and/or youngest possible world is always more likely than this big old world; and that you can empirically disprove some of the smallest/youngest worlds does little to put this big old world anywhere near 50% likely, because if even one smaller and/or younger world remains, then it is more likely than this world (and surely there's more than one that would remain even after all the available empirical facts are in).

dietl said...

I'm with Russell on this one. Randomly attributing propabilities isn't really good evidence in my opinion. The hypothesis is metaphysical, it can't be falsified.

Eric Schwitzgebel said...

Anon: Thanks for the thoughtful comments!

I agree that if you take a BB-type cosmology as a given, then the odds of a small Earth-like environment are vastly greater than the odds of a large Earth-like environment. But if the BB cosmology isn't taken as a given, the razor cuts the other way. Suppose you're 90% on a BB cosmology and 10% on some other cosmology that favors a large Earth. And suppose that a straight BB cosmology predicts a 99% likelihood that there is no hallway outside my room (given my current state of evidence), while the other cosmology predicts 99% that there is the hallway. When I open up the door, see the hallway, and do the Bayesian update, the probability of the BB cosmology falls drastically.

Eric Schwitzgebel said...

Dietl: Oh well! I suppose you don't live by following maxim: "Distribute your priors arbitrarily but not too near 1 and 0, and then just keep updating." I've become keener on metaphysics since I've started to see what I take to be empirical angles into it.

dietl said...

Eric: How can one "keep updating" if nothing really counts as evidence for or against a hypothesis?
Or do you disagree with this:
"...nothing that is happening now or will happen in the future can disprove the hypothesis that the world began five minutes ago"?

The same method could be applied to the question if there is a god. But just like your Argument this is no empirical matter.

Your post is called
"Empirical Evidence That the World Was Not Created Five Minutes Ago" but you could also have called it
"Empirical Evidence That the World Was Created Five Minutes Ago"
for you could easily create a similar argument that comes to the opposite conclusion using the same method.

Jorge A. said...

Let's get meta. Let's say you read Eric's post, and now, every once in a while you think to yourself, "let's try to falsify the young world hypothesis".

You go like this for several years, and then one day, you're falsifying the young world hypothesis when you ask yourself a weird question:

"Does the fact that I have a ton of (potentially false) memories regarding my hypothesis checks on young-world, actually render young-world less likely? What kind of insane trickster god also puts in the memory of me trying to refute his trickery?"

Let's get meta meta. Let's say I read this post, and think to myself: "Well, every once in a while I should think about the kind of meta entity that might trcik me into thinking I've done hypothesis checking." You go like this for severall years until you think to yoruself:

"Wow, what if the universe came into being 5 minutes ago and I have memories implanted of doing hypothesis checks AND also of thinking about the potential trickster godlike agencies that create such complicated logics?"

Let's get meta meta meta. Now I'm thinking of the infinite regress implied by all my former meta analyses which may or may not be false, and I think to myself truly what kind of Cantorian nightmare I've gotten myself into...

dietl said...

"
You go like this for several years, and then one day, you're falsifying the young world hypothesis when you ask yourself a weird question:

"[1] Does the fact that I have a ton of (potentially false) memories regarding my hypothesis checks on young-world, actually render young-world less likely? [2] What kind of insane trickster god also puts in the memory of me trying to refute his trickery?"
"

But that "weird question" doesn't falsify anything. Besides, my answers would be: 1. No. 2. A clever one.

"
I think to myself truly what kind of Cantorian nightmare I've gotten myself into...
"

Welcome to reality :-P

Eric Schwitzgebel said...

Jorge, you have described one feature of my philosophical phenomenology on the issue of radical skepticism -- at least, that's what I seem now to be recalling about the phenomenology of my philosophical reflections about skepticism!

Eric Schwitzgebel said...

I agree with dietl's emoticon. I think.

Eric Schwitzgebel said...

Dietl: I do disagree with:
"...nothing that is happening now or will happen in the future can disprove the hypothesis that the world began five minutes ago". I was hoping that my post would be seen as an argument against that claim of Russell's, but based on the number of people who seem to have been confused by the post (both here and on Facebook), I think I must have failed to be clear.

dietl said...

One thing I have a problem with is, like I said, your attributing of propabilities.
To make it clear:
P(A v non-A) = 1
So:
The propability of the old-world hypothesis being true (P(old-world)) and the propability of the old-world hypothesis being false (P (non-old-world)) must be 100%.
If you now assign 50% to the old-world hypothesis you can't assign 50% to the small-world hypothesis, because the small-world hypothesis is not equal to non-old-world.

I hope this is not too confusing and I didn't make any mistakes, but if one of this is the case I happily refer to Mr. Emoticon :-P

Eric Schwitzgebel said...

Right. I don't disagree with P(A v non-A) = 1. To simplify the argument, I treated the case as though there were only the three possibilities, but the basic reasoning is similar if we carve up the probability space into finer slices.

dietl said...

I think this would have been less of a problem if those possibilities were equal. But what you showed in your argument is that the small-young-world hypothesis is falsifiable, in contrast to the other hypotheses.

"Distributing that probability back onto the remaining two hypotheses, the old-world hypothesis is now 67% and young-large-world is 33%."

When distibuting back. why not to 50%-50%? And why start with 50%-25%-25% and not 33%-33%-34%? I know this has already been mentioned in previous posts. It seems to me that you try to force the conclusion more than come to it through logical steps.

Simon Bee said...

"Empirical evidence that I'am not a human being"

Let's suppose there is someone who has never heard about animal species before. He doesn't know that he is a human, he even doesn't know what is the difference between humans and dogs. But he is provided with some data. He knows some estimations: there are about 3 x 10^33 living creatures in the world [suppose the data are true] he knows that there are 400 billions of mammals and that 7 billions of them are human beings. So his initial estimation is that there is nearly 0 probability that he is a mammal (not to mention human). But now let's suppose he learns some facts about mammals and he comes to conclusion that he is in fact a mammal [ he has empirical evidences ], he can now exclude the probability that he is not a mammal. What should he now respond if we ask him if he thinks that he is a human? He simply calculates the probability : p = 7/400, so there is a 1,75% chance that he is a human. He will answer with certainty: 'I am not a human being' (because he assumes that the value of not-p is publishable). There is no error in his reasoning but he is simply wrong. Probability is only a guide it doesn't tell us what is true. It doesn't matter how unlikely it was for myself to become a human if in fact I am. If accidentally the world did come to existence 5 minutes ago it doesn't matter how unlikely it was...

Eric Schwitzgebel said...

Dietl: I don't think the argument hinges on the exact probabilities. As long as you do standard Bayesian updating and the right conditional probabilities hold (specifically a very high chance of there being a hallway if the world is old, and only a moderate chance if it is young), then you get an increase in the old-world hypothesis after opening the hall door. So at least there's some confirming evidence, if not proof or a publishable p-value at the end.

Simon: Your "someone" sounds pretty reasonable to me, just ignorant. One issue would be whether that person is blamelessly ignorant.

Simon Bee said...

It was only an example, it can be tailored to suit the "blemelessness demand". More important problem in my opinion is how we use probability. It is good tool to study statistical data but hopeless to tell something about particular cases. It can be true that the probability that I will win a lottery is desperately low, but if I hold a winning ticket - it doesn't change that fact, if the probability that I will die in an air crash is relatively small it won't save my if my aircraft in 10 minutes will crash into the ocean. That's one thing. Second is that probability can be well applied to cases in which we know or have good estimations on probability distribution (in my example with the "the someone" I believe it is the case, but he simply doesn't have enough information to derive the right conclusion) In your reasoning there are no good grounds for probability distribution estimations, that's why the indifference principle is applied, but it is only a heuristic; it gives good outcomes when we apply it to dice or coins, but if no information or statistics are provides it can be very misleading. Example: Some savage don't know what is the probability that he will die after consuming a meal and drinking a drink in a foreign country. He is going to eat a meal and have a drink in this country. He use "the indifference principle" and concludes: the probability that I will die after the meal is 1/2, after the drink 1/2 so the probability that I will die after the diner is 75% (disregarding other possibilities of dying during that diner). What I am trying to say here is that the subjective probability is no more than a heuristic and should be applied with great care because the possibility of error is higher than we usually imagine. That's why I think arguments like Russell's can't be undermined by arguments from subjective probability.

Simon Bee said...

Last but not least there is the problem of how you use the probability. It was criticised in earlier posts but I will add a word. The most problematic are changes in probability distribution that you make for instance in these lines:
"So now, I reduce the probability of the young-small-world hypothesis to zero. (Zero makes the case simple, but the argument doesn't depend on that.) Distributing that probability back onto the remaining two hypotheses, the old-world hypothesis is now 67% and young-large-world is 33%."
You can't just raise the probability of the old-world hypothesis if initially you have ascribed it probability 1/2. I think again an example will easily show that this strategy is faulty. If there is an urn and I am told that are tennis balls and ping-pong balls. Using the indifference principle (which probably shouldn't be used here but if we use it in Russell's hypothesis I assume I can also use it here) I assume that there is 1/2 probability that if I take a ball from the urn it will be tennis ball. Ok, but some of the tennis balls can be red and some can be yellow ( I estimate 50/50 chance ). Now someone tells me that it is the case that there are no red tennis balls in the urn. Do I have any reason to conclude that now the probability that I will take out a ping-pong ball will rise? Only if I have applied the indifference principle to the three possibilities (red-tennis, yellow-tennis, ping-pong) at the outset, but I didn't!

Eric Schwitzgebel said...

But Simon, what can we do other than take our best guess with the probabilities? I see no other way. I agree that taking specific numbers overly seriously is a problem. But your foreign traveler implicitly thinks the probability of death is lower when he eats the food he is given than if he were to eat molten lava; otherwise, he'd make a different choice.

On your urn example: I agree the indifference principle creates all kinds of puzzles and problems, and it's difficult to see how to apply it rigorously. And it's difficult to know what the conditional priors are or should be in your urn case. It seems natural to treat the denial that there are any red tennis balls in the urn as not influencing the probability. And maybe that's right. But now suppose I start with the view that tennis balls can be any color and that I'm not told for sure that there are both tennis balls and ping pong balls in the urn but only that there might be either or both. I also hear, "And there are no blue tennis balls". "And there are no green tennis balls". "And there are no black tennis balls". Etc. At some point I might reasonably start to lower my credence that I will draw a tennis ball, and maybe even doubt that there are any tennis in the urn at all.

All this is just to admit that the whole business is a mess. But I don't think the way to deal with the mess is to cast aside probability and updating!

Simon Bee said...

I think we both agree that deciding on priors is both crucial and uncertain at the same time in such cases, but I cannot agree that we can change priors in these examples. Maybe my example wasn't clear, but the probability is conditional only when there is an intersection between events sets. --> p(A|B)= p(A^B)/P(B). if not, the events are independent. It also concerns your example with urns - you shouldn't use conditional probabilities. let's assume for simplicity that there are 30 possible colours of the tennis balls. if your prior for tennis was 1/2 and 1/30 for each colour (and eg. 29/30 for not-blue) after announcement: "there are no blue tennis", you update: 1/2 for not-blue tennis ball, 0 for blue tennis, 1/29 for each not-blue tennis colour, but still 1/2 for ping-pong, not as it is in your example 31/60 for ping-pong. Only after you have exclude all colours you can conclude that the probability for ping-pong is 1. Otherwise your change in priors is rather arbitrary - it is ok to say that your subjective probability has changed but your grounds are not justified by probability calculus. The same thing concerns your argument on small/large-world uncertainty. Some one has noted that the argument could as well prove the contrary and I completely agree with that. There are many possibilities about large-world: there is a possibility that there are other intelligent creatures in the universe, that gravitons exist, that there is some worldwide conspiracy.. We can estimate our subjective probability on these matters but if it will be possible to exclude some of the alternatives it doesn't follow that it is more and more probable that the small-world hypothesis is true, or at least that is my intuition.

Simon Bee said...

it should be of course "(1/29)*(1/2) for each not-blue tennis colour" - I have omitted the prior prob.

Eric Schwitzgebel said...

As long as I don't decide to mess around with my priors and I do decide to update in the usual way (and sometimes I think one does want to violate these maxims), then doesn't Bayes rule plus conditional updating plus the existence of the hall being very likely in an old world scenario vs. somewhat dodgy in a new world scenario get me the probability increase I want after I peek into the hall?

Callan S. said...

In the spirit of skeptical indifference, let's say that I go ahead and assign a 50% probability to a standard non-skeptical old-world hypothesis and a 50% probability to a young-world hypothesis based on my subjective experience of a seeming-external-world right now. Conditional on the young-world hypothesis, I then further distribute my probabilities, say, 50-50% between the I-and-my-immediate-environment hypothesis and the whole-planet hypothesis. The exact probabilities don't matter, and clearly there will be many other possibilities; this is just to show the form of the argument. So, right now, my probabilities are 50% old-world, 25% young-small-world, and 25% young-large-world.

Aww no, man! This is what religious folk sometimes use to try and prove the existance of (their) god, by divying up percentages in their favour.

Also if the world is new and small? Where did the small qualifier come from? Why would whatever it is render only part of the world? How'd that get added in?

I'd look at the process for rendering such a world - if the world is all consistant in regards to causality, then really the only way to render the world is to have, in some way shape or form, have run that causality program. Now okay, that might be a virtual world (that semi exists on some sort of god computers micro chips), but it is a past that causally occured before the universe was 'printed out' into a hard copy. You always have a history.

The only problem is is if godly computer rendered all that history in five minutes.

On the other hand, from a perspectival level, its five minutes might be our five billion years (or whatever time period).

Simon Bee said...

You are right, if one accepts your assumptions the conditional probability would be as you have written. One may argue that the small/large world distinction is highly controversial. Given our estimations about the size of the universe a galaxy-size world seems rather small-world scenario and any galaxy-size world can include New York Times and hallways, so why we should think that my environment-world hypothesis is equally or even more probable than the universe-size-world if there is a continuous scale between these extremes?

John Jones said...

The essay contains a mistake, as do all transcendentally real theses on Time:

What is "five minutes ago"? This refers to the hands of a clock, let's say. But there is no fact that makes this fact, or any other, more temporally substantive than any other event.

Bite the transcendentally ideal bullet. Events don't happen temporally. They happen associatively.