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Probability (part one)

Probability is false. Imagine the following scenario:

You and Dominique Jones are great friends in 2nd grade. Then, twenty years later, Dominique moves to Venezuela and loans a Noam Chomsky book to Hugo Chavez. Then, you become a custodian for a small high school. Then, you win the lottery – without even buying a ticket. Then, you travel to the Congo. In Congo, you run into Dominique. Dominique says, “Oh gosh! What are the chances?”

Most people would respond with something ignorant such as “Yeah I know!” or “Pretty low!” According to my research, however, the proper response is 100%. But why?

Because if this scenario happens, the chances of it happening are of course 100%. The key terms in my analysis are “if,” “happens,” and “of course.” If it didn’t happen, then the chances of it happening were always 0%. Some people would argue that this commits me to hard determinism, but it does not. A la carte Peter van Inwagen free will exists. What it commits me to is the world of facts. If you are pro-fact, then you will abandon all probabilities between 0 and 100%.

45 thoughts on “Probability (part one)”

  1. Pingback: A defeat worth watching « Sophismata

  3. So if I toss a coin, the odds of it coming up heads are . . . 100%? 0%?

    Funny, if I toss that coin a bunch of times, it’ll come up heads about 50% of the time. You should try that for an experiment. You might be surprised to learn that the odds of a coin toss coming up heads are neither 0% or 100%.

    I can’t believe I actually had to say that to someone . . .

  4. He’s a Troll. But, to answer the point, you are misinterpreting the expression “what are the chances”. If it means, “what are the chances that the event happened in the past” then you’re right, 100%.

    I think the claim is “before the event happened, what would have been the chances that this event occurred as opposed to any other”

    Here, probabilistic interpretation is meaningful.

  5. Oh Christ, and this from the person who said that semantics has been disproven. This is semantics.

    If you can perfectly measure every single factor that might contribute to these two meeting, then sure, the probability is 100%.

    But probability is based precisely on not having perfect measurements. If we know that 30% of people buy Fords, then the probability of any one random person having bought a Ford is 30%, but the more we know about that person: their gender, income, nationality, proximity to a Ford dealership, etc., the better our prediction can become. We can never have perfect measurements of ALL such factors (which could include just about ANYTHING: fetal androgen levels, which shade of yellow he likes best, his high school girlfriend’s middle name). Probability is about making predictions on the available evidence.

  6. Dear WTF:

    Funny, if I toss that coin a bunch of times, it’ll come up heads about 50% of the time. You should try that for an experiment. You might be surprised to learn that the odds of a coin toss coming up heads are neither 0% or 100%.

    Congratulations on not understanding anything I wrote. In each of those cases, the probability of the result will be 100%. This is actually verifiable by doing it.

    NS

  7. Dear Kerry,

    I think the claim is “before the event happened, what would have been the chances that this event occurred as opposed to any other”

    It is unclear what the “chances” are beforehand, mainly because it is IMPOSSIBLE TO TIME TRAVEL.

    NS

  8. Dear Patrick:

    If you can perfectly measure every single factor that might contribute to these two meeting, then sure, the probability is 100%.

    With this admission, I could rest my case. You admit that once you know the maximal facts about the world, you learn that the only possible probabilities were 0 or 100%. This is exactly my point. Probability is ignorance, not knowledge. Orwell would have a field day.

    Out of pure sport I choose not to rest my case there.

    If we know that 30% of people buy Fords, then the probability of any one random person having bought a Ford is 30%. … Probability is about making predictions on the available evidence.

    In the first part you use a semantic trick by grouping the people, which is less accurate than considering them individually. Individually the probability is 0 or 100% that a Ford will be purchased (probably 0%, given the current auto crisis). Moreover, even considering groups, the probability is either 0 or 100% that the group will purchase X number of Fords, where X stands for the Real Percentage of Fords bought. Now the second part of your silly argument is just plain fortune-telling. This confirms my belief that many scientists and mathematicians have sympathies with what should properly be called witchcraft.

    NS

  9. I am either incredibly amused by your brilliant satire or horrifically frustrated at your logic. The probability of either possibility is exactly equal to either 0% or 100%.

  10. If you think of probability as describing the uncertainty in our knowledge of nature rather than a statement about nature itself, many of the paradoxes go away.

  11. “If you are pro-fact, then you will abandon all probabilities between 0 and 100%.”
    Genius. Absolute genius. How does the 0%/100% thing work for predicting things yet to occur? Are they all 100%, all 0% or a mixture of the two? Or are all predictions in the box marked “ignorance”? Should we refrain from predictions because they aren’t fact? Don’t you think that in some cases predictions can be useful?

    I’m fascinated by this site and, frankly, shocked by those querying the serious nature of your blog. This is clearly deep philosophical thought – and in no way satirical.

  14. Dear JDC,

    Thanks for the questions.

    It is an open question whether or not we want to predict future events. I’m against it, primarily on religious/spiritual/philosophical grounds. But it’s up to each person whether they want to say that an event either will or will not happen.

    NS

  15. Seriously?

    You have completely defeated the purpose of probability. You use probabilities BEFORE something occurs, to see IF it will, not AFTER and WHEN it occurs.

    This seems to be fairly simple logic. Seems to be, anyway.

  17. You know, I’ve come across this as well and I was actually surfing around to see if anyone agree with me on the matter.

    I’m required to take a probability and statistics class for my major here at UT-Tyler (Electrical Engineering) and I’ve always had a logical mind set. I thoroughly believe that nothing can be predicted.

    Prediction is a term that I relate to gypsies and palm readers.

    You can look at it in one of two ways

    1.) Everything is predetermined by a God of some kind.

    You flip a coin, it lands on heads. There is no other alternate universe in which that coin would have turned up tails. So the probability of that event occurring would have always been 100%, or 0% for tails.

    2.) Nothing is predetermined.

    We are always in the present, never in the future, never in the past. You flip a coin, it lands on heads. What happened? Nothing. Nothing mystical happened, it just landed on heads.

    Now the question becomes, can’t I predict this happening by using probability theory? I put it to you that you can’t. There are two sides, you guess you’re either right or wrong. There is no mathematical influence behind it, it is just something that happens.

    While I may not be a great thinker, or have a PhD or something of that nature I can understand the concept of probability:

    Well, this is the likelihood that this will happen. Sure, that’s fine and all, but what purpose does it serve? In the end it will happen or not.

    I think in the end I have to reach this conclusion about probability.

    In all reality and in all events occurring anywhere in the universe an event will either take place or not. Which begs another question, what is the probability of the universe itself? Well, silly me, it’s 100% because it’s here. So what about before it was here? What was the probability before that? was it 70%, 14%,0% or 100%? Well, we can rule out 0% because here we sit. Then we can rule out 70% and 14%. Why? Because here we sit.

    (I so wish I could explain myself better)

    What I’m trying to say is, look at it in reverse. You flip a coin, it lands on heads. Now go back in time and flip it again, will it still land on heads or will it land on tails? It’s too late it’s already happened. Every action since the dawn of time has lead up to that single conclusion. That coin was always going to land on heads, it was never going to land on tails. I think that the only true way that probability of any significance can exist is in a universe where there is a god, but only cares some of the time.

    It’s all a bunch of voodoo to me.

  18. The Greeks didn’t have probability for the same reason; the events that happened were supposed to happen according to the will of the gods, and chance did not exist.

  19. Dear Nickel,

    An excellent example, worthy of the annals of the history of science and math being defeated. The Greeks provide in this case, as in so many other cases, an example of unjustified true belief.

    Compare for example early beliefs that the earth was round (which contra Copernicus, it is). They thought it was round because they thought symmetry was nice. True conclusion, but the justification is (only slightly) off the mark.

    Thanks for the comment. Please notify all of your friends, families, and teachers about the existence of my groundbreaking blog. A chain email would suffice.

    Cheers,
    NS

  20. I will say that I agree with the many people who have already expressed similar impressions: this post, and all of the posts I’ve read from this blog so far, are of poor quality and certainly useless. It does get people reading though!

  21. Let me just say one more thing. The author seems to miss the point entirely of what probability is used for. It is used to measure the reliability of a prediction in mathematical terms. It has nothing to do with “truth” – whatever that might mean to him. His point seems to be…what? That probability misrepresents reality because it makes us believe that things which are inevitable are actually unlikely? If that is his point, it is not communicated clearly. His point certainly can’t be that probability should be abandoned. Why does the author construct such articles?

    I, too, have read the Aristotle quote that says, “It is likely that unlikely things should happen.” (I believe it was Aristotle).

  22. Dear Crank Refutation:

    You vomit,

    You have completely defeated the purpose of probability. You use probabilities BEFORE something occurs, to see IF it will, not AFTER and WHEN it occurs.

    What you are describing is prophecy, not probability analysis. Ergo, probability is ipso facto a descriptive claim, having nothing to do with normativity of future judgments. Have I made my case? I have made my case.

    NS

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  26. “if this scenario happens, the chances of it happening are of course 100%”

    In other words, P(A|A)=1.

    When someone asks, “What are the chances” – that doesn’t mean “What are the chances of this happening, given that it happened”.

  27. “Dear Patrick:

    If you can perfectly measure every single factor that might contribute to these two meeting, then sure, the probability is 100%.

    With this admission, I could rest my case. You admit that once you know the maximal facts about the world, you learn that the only possible probabilities were 0 or 100%. This is exactly my point. Probability is ignorance, not knowledge. Orwell would have a field day.

    [snip]

    NS”

    Do you know anything about information theory? Look up Laplace’s cosmic intelligence; such total knowledge isn’t possible. We can extrapolate on our limited information, but factors that we can’t know or account for will still effect the results. And probability is certainly not ignorance. It is, if anything, an extension of knowledge, because it gives us more information than a mere empirical trial would result in.

  28. Crank refu… was correct. How ever, what they discribes is not prophesy, but the standard definition of probablity. For example, before I flip a coin, what are the odds that it will come up heads?

  30. When someone asks, “What are the chances” – that doesn’t mean “What are the chances of this happening, given that it happened”.

    I am aware of this, but thank you for making sure. This does nothing to refute my point, as you know.

    Cheers,
    NS

  31. Mr. Mister Cow,

    Information theory is bunk, as demonstrated by a reduction ad absurdum that shows it helps William Dembski. As for Laplace, this is easily dispatched: Laplace’s demon is a thought experiment to show what would be involved in a deterministic system. But my arguments does NOT, I repeat, arguments DOES NOT, assume that the universe is deterministic. Even in a NON-deterministic universe, what happens… happens!

    Cheers,
    NS

  33. Have you ever heard of the Monty Hall problem? there is your answer, dear noted scholar.

    Thanks,
    CS

  34. My dear chap,
    Of course the odds of an event happening shall be 1/1…
    IF you nominate said odds after the occurrence and observation of the actual event.
    Odds are calculated before the event of which the odds we are trying to nominate occurs.
    With your logic, PaddyPower should be offering bets on yesterday’s matches with, say, 11/12 odds for the team that (we know) won and 1/10 odds for the losing team and still profit. Dearie me, I cannot believe my own goblin bins.

  35. Excuse me, brain fart:
    Winning team odds:anything above 1/inf^-1
    Losing team odds:anything below inf/1
    Bets on match: 1 or more
    ???
    PROFIT!!!

    I couldn’t resist.

  36. If this is true, then how can you or I determine what the outcome of an event is before it occurs?

  37. “But to answer your point, it is unclear what the “chances” are beforehand, mainly because it is IMPOSSIBLE TO TIME TRAVEL” Really? So I’m NOT traveling forward at 1 s/s? (s/s or seconds per second is the standard metric unit for time travel)

  38. Sorry to post on such an old thread, but I just need to state that usually I disagree with the things on this website, but this one I agree with completely. The reason for this is simple: probability in an actual sense applies only to quantum mechanics, the rest is just a lack of knowledge about a system. So, if I flip a coin, given all the knowledge about wind speed, the coin’s exact shape, the exact force that I exert on it, I could accurately predict its result every single time.

    Thanks, notedscholar for pointing out something that I think people should actually be aware of.

  39. Yeah… Here’s the thing, Rational Skeptic. It is literally impossible to account for all of that in flipping a coin, rolling dice, etc. In particular, we can’t control how much force we use, and even a fraction of a millimeter difference of where the coin starts, or a small change in drag, have a significant effect. That’s why we have probability. It allows us to figure out how likely it is for an event to happen that hasn’t occurred yet. You mentioned it has it’s uses in quantum mechanics, which refutes your point anyway, and it is also used in other areas, such as actuarial science.
    You’re also missing NotedScholar’s point: the chances of something happening are either 0% or 100%, because it can’t only partially happen; it either does or doesn’t. That said, this seems to be the converse of the anthropic fallacy used by creationists to “disprove” evolution, where they argue that the chances of us having evolved through random mutation are miniscule. This is a fallacy because, as has been repeatedly pointed out on this page, the chances of an event happening given that it happened is always exactly 100%. All mathematicians, as well as most logicians and scientists, have always known this. However, none of that makes probability as a whole less useful or less correct. Probability is a measure of likelihood under uncertain conditions. It is very useful in many areas of research, and attempting to disprove it is an insult to human ingenuity.

  40. I never claimed that probability wasn’t useful. It can and certainly is used as a nice approximation. That being said, probability as it is commonly used, as in the flipping of a coin, does not exist as it is commonly imagined.
    You are also completely right that quantum mechanics do invalidate my point, so let me restate myself more accurately: probability as it is commonly percieved does not exist.
    Were someone to take some quantum random event, and base a macroscopic change around that result, then yes, that would be random.
    Also, we seem to agree that the probability of an event happening given that it happened is 100%, yet here’s an interesting thought that I haven’t considered fully: does quantum mechanics disprove this statement?

  41. Pingback: Fighting the moderately good fight on probability | Science and Math Defeated

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