It’s one of those questions again–“oh my gosh, all the gas molecules could gather on the other side of the room, and I’d suffocate”–but in a larger question, prompted by another thread where someone wrote, with much pith, “science isn’t into the whole 100% thing.” [if anyone knows, please give cite.]
So, statisticians/physicists: besides saying “this is a group of questions answerable by saying ‘vanishingly small’ and ‘stop wasting my time,’” is there some formal/discussed way this inquiry is limited in the science[s] or by the philosophers of science? Without the whole quantum reality thing… There must be.
Unless someone has a third answer than those two, which would be interesting as well.
For this question, let there be “real tomorrow,” based on whenever you are reading or answering this thread, and up to 5 billion years of “tomorrows.” (Wiki timeline for the prudent here.) Narrowness of error bounds is part of the general question.
There a lot of reasons the sun might not rise tomorrow. Phrased in such a broad way, we don’t even know how small the odds are because some of the mechanisms for it not rising may be based on things we don’t even know exist. (i.e. let’s say that dark matter travels around in super-dense invisible blobs that haven’t even theorized about, but that there’s a chance these could destroy the sun at any given moment). There are some other things we might have theories for (like vacuum instability), but we might be missing a lot of the information that would be necessary to get any useful calculations about that.
On the quantum issue… we can do that calculation, but the idea of fuzzy particle location happens at such a small scale (small both in terms of mass and distance) that the sun spontaneously moving to another location is basically just 0. Maybe it’s actually one in a googol googols, but that’s pretty much 0.
Like too many of my OPs, the hed has a local grabber of an instance, but the meat is in the text. I don’t want to bug the mod for a change.
First off, the hed posits the “proof” of a negative. So that’s dumb to begin with (not faulting dracoi, who answered patiently).
Yes, I’d like to bat that around, that, or the “all the gas could move away” question. Or better ones of your choosing.
My interest here is on the ontological status of the vanishingly small.
I have a sense that the statistical stance–pre quantum–in physics has dealt with this since gas laws were being first poked around with, and I wondered how that was dealt with as a fact of judgement–the shock of dealing with chances. Or am I off–way off–on my history of science?
There is a qualitative difference between “This thing has a ridiculously small probability of happening” and “I have no information with which to estimate the probability of this thing happening.” Are you after that distinction? For the former, there’s nothing too ontologically surprising: a low probability means just that, and it behaves the same as any other probability. For the latter, one has to step careful to ensure that questions about the probabilities are well-posed. We had a thread recently that went this way (“urn problem” by Frylock), but I don’t get the impression that this is what you’re after.
There is no known mechanism by which the sun could suddenly vanish, so there is no way to compute the odds for such a thing happening.
To say that the odds are zero, or vanishingly small or even “unknown,” is to imply that such odds exist in some form and there is no reason to believe they do.
One can imagine that monkeys will fly out of one’s butt. One cannot figure the odds for such an event.
FYI, there is actually a small probability that a pot of water placed on a lit burner will freeze instead of boil. I have read what this probability was, but don’t remember the numbers. I do remember that there were a whole lotta zero’s between the decimal point and the first non-zero digit.
When you’ve had N observations and the event of interest has not been seen, a rough rule of thumb is that the ‘true’ probability of the event happening is less than 3/N.
So, if you’ve made 10 observations and the event hasn’t been observed, you can be 95% sure that its true probability is less than 3/10 ~ 0.33
Regarding five billion years of sun rising, you get:
3/(5,000,000,000 X 365) = 1.643835616 × 10[sup]-12[/sup] (i.e. less than one chance in 1.643835616 x 10[sup]-12[/sup] that it won’t rise).
At the moment I’m still following up KarlGauss, ca. 2002. The .pdf link is bogus now, and the Wiki link was acting up, so I’ll look at it–whatever it is–later. Do you have a new cite for the .pdf?
Chances are good (:)–it just came out that way) I will find out my beef is with probability as a whole, but as suggested above I need to get clear on what’s bugging me.
I’m thinking the probability is much lower than the number KarlGauss came up with. We have an understanding of angular momentum, which the Earth has and which leads to the Sun rising. We understand the physics of the Sun very well. Both of these understandings are backed up by observations of, well, the whole universe.
The probability of the Sun going out, or for the Earth to stop spinning, is incredibly small barring something like large massive body from outside the solar system coming in and colliding with the Earth. And again, we have observations of not just our Sun, but of the entire universe, and we don’t see many of these sorts of collisions. We also have a handle on how many bodies that might collide with the Earth and prevent the Sun from rising are out there.
I think the key is that not only have we had five billion years of the Sun continuing to shine, but we’ve also had a great deal of time each for a great many other stars, which appear to be similar to the Sun to varying degrees. If all we knew about stellar evolution came from observation of the Sun, then we probably couldn’t do any better than KarlGauss’s estimate.
[QUOTE=a Senior Common Room Betting Book at Oxford University]
“… The subwarden bets Professor Hardy his fortune till death to one halfpenny that the sun will rise tomorrow (7th Feb 1923).”
[A couple of days later Hardy took the same bet again, but the odds had shortened significantly – for reasons at which we can only guess. This time it was only half his fortune till death, against one whole penny.]
[/QUOTE]
If I haven’t made some mathematically unsound assumptions from the description in the wikipedia article on the rule of three that KarlGauss links to, 99.99% sure would give a rule of ninety-two. With N trials without the event you can be 99.99% sure that the probability is less than 92/N.
Depends on whether you define “tomorrow” astronomically or horologically. 0001 referenced to your local time zone will occur whether or not the Sun or Earth exists at that moment. There’s also an element of confusion between dawn and midnight in your assertion.
Yes, I recognize you’re sort of joking & I’m sort of falling for a whoosh.
So, we’re postulating an observation station set up on a point on the surface of the earth? Given plate tectonics, and depending on the starting point, I’m guessing the odds that it ends up lying within either the arctic or antarctic circle at some point in the next five billion years are significant.
For a definition of tomorrow using a calendar (i.e., within the next no more than 24 hours), and for an observation station located at the north pole right now, I’d give odds of the sun not rising tomorrow at very near 100%.
I guarantee the sun is not going to rise tomorrow. You may have heard of a new theory called heliocentrism. It’s still controversial I guess, but as difficult as it may be to believe, the sun does not rise each day. It must be some kind of optical illusion or something.
It’s really counter-intuitive. Among other things, it predicts that an observer in one place could see the sun rise, while an observer in another place could see it set at the same time! Mind-blowing, huh?