Lord Antares

This is where you show that you don't understand it.

While you are correct in saying this, I doubt that's the reason why more women don't get into physics. If you are a woman and very interested in physics, I seriously doubt you would dismiss your chance based on the fact that there might be a higher chance of you being harrassed than in some other discipline. To me, it is clear that it's just that women aren't as interested in physics as men are. I have noticed, based on a large enough sample of people, that women are generally more into ''life'', than secondary hobbies. Think about almost any hobby there is: In chess, there are substantially more men than women even though both have equal opportunity. In fact, women have MORE opportunity there than men do, yet they are still far less interested. In video games, there are many more men than women. In some competitive (meaning, professional) scenes, there are NO women at all, even though they have equal opportunity. Same with physics. You would think that with equal interest, we would have 50% of women here, but we clearly don't. Especially with a non-investive thing like a forum, this CLEARLY shows that women have a lesser interest in it than men do. Now as to why this is the case is another matter. You might argue that women are naturally wired to be focused more on their children and future as a protector and rational thinker as a way to ensure theirs and their children's survival. This is a wild guess but it might be so. Also, I agree with DrKrettin that it is not an issue. If they have a lesser interest, let them have a lesser interest. You might even argue that prompting them to want to join studying physics would be a form of pressuring, even though this is far-fetched.

I think the answer is as smiple as: they are not interested in it as much as men are. There is no other logical explanation. Also, linking is disabled for you, a new member, as a form of spam protection. It is usually required that a discussion takes place on the forum itself.

Why would they? For a black hole, density is key, rather than just mass. A black hole with the mass of the earth could exist, given that it was dense, i.e. small enough. An object having relatively high mass or energy has nothing to do with it becoming a black hole; it needs to be condensed. Also, there are different sized black holes. An object most definitely could, in theory, exert more force than a black hole. I think the earth condensed into a black hole would exert the same amount of force as the earth itself does, because it contains the same amount of mass.

Well, that is what I'm asking you. But look at this. Take two different examples 1) We are on meter 1 and we must find the probability that we return to 0 with infinite flips 2) We are on meter 700 and we must find the probability that we return to 0 with infinite flips Although mathematically, we might find that the probability of both instances is 1, isn't it technically more likely that instance 1 will bring us back to 0, given the almost surely clause? I draw a parallel to wtf's earlier example: Let us say that we must pick one number in the set of natural numbers (or any set), the probability that we guess which one gets picked randomly is 0, since we have a 1/infinity chance of guessing it right. However, let us say that we must pick two numbers and we must guess one of them. The probability would be 2/infinity. Although the probability in both instances is 0, is the latter, or is it not, technically more probable? This may not make sense, but in my opinion, it is a very interesting question. By the same logic, if the must pick a number in the set of real numbers, rather than naturals, does the probability decrease, even though it is still 0? I think that the answer to this has bearing on our infinite ruler example. This is a very important question to me, answers are most appreciated.

Comparing the infinite ruler to the simple coin flips example (never flipping tails), in the latter, the situation resets every time you flip a new coin. The tosses are independent. When you flip heads, the chance of flipping tails on the next turn doesn't decrease or increase. I understand how the probability of that happening is zero, but it doesn't absolutely mean that it won't happen. It makes sense to me. However, on the infinite ruler example, the probability of getting to zero changes based on previous tosses. So, if you flipped heads 699 times in a row, you would be at 700, making it less likely that you would eventually return to zero. This is all fine and dandy, however, infinity complicates the issue. I am not sure if the probability is 1 (the opposite of the previous example's 0), or if it is somehow changed based on the fact that previous tosses impact the result. It makes sense to me that it would be, but it also makes sense that it wouldn't. I am not certain.

Thank you for your input. I didn't realize it was a somewhat complicated issue. I will have to look up what you recommended. I have run into this 95% certainty thing before in statistics. I have read that a 95% certainty in statistics is considered to be statistically sound and likewise, a 5% certainty unsound. What is the significance of these numbers? Surely, this is just an arbitrary, generally agreed upon limit. There is no other significance of the number, right?

Yes, but the numbers don't make sense to me. I don't know how you arrived at a few of them and at the estimate of time. It doesn't seem obvious to me. Some of it is correct, but I'm not sure about the whole equation. Maybe I'm missing something.

There is a typo here somewhere. And concerning the rest of the post, don't you mean that it will almost certainly happen, rather than almost never happen? Then you do not understand infinity. Given infinite time, everything will certainly happen (or almost certainly as pointed out by wtf). You did a quick google search and misunderstood the text. Quote from wikipedia. Note that the last part deals with finite number of monkeys and finite amount of time, which is what you may have read somewhere in that article. For example, an infinite amount of monkeys would produce Hamlet in simply the time it takes one of them to write Hamlet. This is not a myth. I propose you think twice or at least read up on it.

This makes me think that you don't understand probability. The monkey, given an infinite amount of time will certainly (or almost certainly, as was correctly noted in another thread) produce every literary work ever made. We are trying to calculate the expected amount of time it would take. Please do not post if you have nothing of value to contribute. Sorry, crosspost. I will check your calculation, Raider.

I know that coin flips are not random. We even had a long talk about it in another thread. Basically, they are AS GOOD as random to us, because we do not posses the brainpower to predict their force, spin, velocity etc. They are not random at all. As for the thread, I will now attempt to calculate it. Do make sure it is correct. If you have any further comments on this philosophy of probability, do comment. Alright, back on topic. You may be misunderstanding something here. There were two questions. One was how long it is expected for the monkey to type out Hamlet and another was what are the odds that it would type it out on the first attempt. You figure of 1 in 26^130 000 answered the latter correctly (assuming that punctuation, spacing etc. wasn't needed and that the monkey only had access to the letters of the alphabet and not the other keyboard keys). There was no need to equate that to 100%, whatever that means. It answered the question. I just tried to do it and I realized I can't, which is a shame. I'm not sure how you factor time into the equation and get the expected time of the monkey's success. It is the same as asking ''What is the expected amount of time it would take you to flip 5 heads in a row?'' only with higher figures. It seems simple, but I realize that I don't know how to solve it. Note that time refers to physical time and not the number of coin flips.

Ah, I replied before the edit, so I wasn't sure what you were getting at. Of course. The point that you're trying to make is that probability changes based on whether the ''pool of possibilities'' diminishes or not after each attempt, right? So, even a finite number of coin flips always has the unchanged probability of 0.5 for either heads or tails (assuming that the coin is purely mathematical and random, of course). When you take these chocolates out, the probability for any one being taken out diminishes by 1 each time. So, 1/10 on the first draw, 1/9 on the second...eventually arriving at 1/1. So yes, there are different kinds of probability. It is similar with lotto numbers as drawing one ball eliminates the chance of it being drawn again, diminishing the ''pool of possibilities'', so the odds change after each draw. Btw, side question: are the terms ''probability'', ''odds'' and ''chance'' synonimous? I'm not a native English speaker.

Now that you mention it, yes, I have thought about this. It reminds me of Creationists saying ''what are the odds that the Earth was formed exactly the way it was?'' This question is moot, because all the other possibilities of how it could have been formed are equiprobable. So, let's say that you must throw a die 1000 times in a row and record the results. Upon witnessing the results, you then exclaim ''what were the odds that I would get this exact same sequence?'' It makes no sense, because all other results yielded the same probability of 6^1000 and one of them had to happen. Of course, another question is how well earth would have worked out were it formed in a different way and is it possible that we, or the same ''we'' would exist on it, but this is a completely different matter alltogether. The same logic applies for questions like ''what were the odds that you would have these exact personality traits'' or ''have this exact name and do this specific thing at this time'' etc. Surely, the statement ''it's unlikely that you exist'' is clumsy linguistics. It may or may not have been unlikely that he would exist prior to his existance, but it is certain once it has happened. It is, as you mentioned, a posterior probability once it has happened. No, I don't want to say that. The thread was merely meant to deal with basic mathematical probability. Saying that it was likely or unlikely that Shakespear would have written Hamlet is difficult as you have to account for his mental traits and age of when you want to say this for. I don't feel like giving probability (other than 1) for posterior cases makes sense. In other words, saying that something that happened is unlikely is a clumsier and less precise way of saying that it WAS unlikely prior to it happening. But you could argue they are the same thing. It was offtopic, but sure, I welcome it.

I'm thinking there is a deeper point to your post. Surely, 10th selection when isolated is not random. Or, if viewed from the standpoint of probability, it always has the probability of 1. I'm not sure if the question was directed to wtf or me.

Correct. On the first attempt, mind you. That is not counting other characters such as punctuation, spaces and especially capitalization. But the rest of your post is baffling. For example, What do you mean by this? It is 1 in 27^130 000. I don't know what kind of equalization with 100% you're talking about. The rest of the math is puzzling to me. It is a straightforward calculation. I don't know why you think it's impossible to calculate. It assumes that the monkey types with regular speed. X letters per minute, constantly. This is of course, hypothetical. It doesn't need to sleep, eat, etc. You just need to factor time into the equation. Try it. Don't mock him. He is very good at math, but I don't know what kind of point he was trying to make with his post. Let's say that it was a joke.

Are you joking? Clearly, you understand that I mean that the monkey needs to write it independently of Shakespeare and it has nothing to do with posterior probability. You're just pulling my leg.

Aha, I get it. I just expressed myself wrongly. So, 0 = almost never, rather than almost 0 = almost never. The latter is an invalid term, right? I confused my terminology. That's alright. I found the input interesting and learned something knew, as I didn't think about it.

I am not sure what you mean by that, but I wish that we make the calculations for ourselves. All we need is the number of characters in Hamlet (or letters, if we want to simplify) and we can agree upon the other variables as we can make them up according to what is most appropriate and it should be easy from there.

Thank you, this helped me understand it. I am going through the linked article, but I am illiterate in the mathematical language so it will take time until I've understood the whole of it. But basically this is because we're dealing with infinity. We have an infinite sample of real numbers, and therefore picking any number will yield a probability of 1/infinity, which is 0. That is a good point and it makes sense to me. But is this diffferent from my problem? Flipping a coin for an infinite amount of tosses and never getting tails has ''almost zero'' chance, as you said, but I am thinking it should be a different probability than for my infinite ruler. So, is the probability of getting to 0 on an infinite ruler ''almost one'', or something else?

So, given enough time, a monkey typing random words on a keyboard will eventually type out Hamlet word for word. Let us calculate the expected time it would take the monkey to do that. In my intuitive (but limited) understand of probability, I think we only need to know: 1) The number of letters in Hamlet (or characters if you want it to include spacing, punctuation etc., but excluding capitalization) 2) The average time it takes someone to type one letter, or in other words, words per minute. We must be given some leeway here because we must agree upon whether the monkey is frantically mashing the button with its fingers (not whole hands, because then the probability would always be 0) or it is typing at a rate of an average human. 3) The number of accepted buttons we will give the monkey (or words in the alphabet, depending on what we want to do) I think given these variables, the calculation should be easy. Of course, this assumes that all keys/letters have an equal probability of being hit Another thing we can do is calculate the probability of the monkey writing Hamlet on the first attempt. This has one less variable (2 is excluded) so it is an even easier calculation. I'm sure I could find the answer out by googling, but it is more fun this way. So, does anyone care to add the necessary information?

Concerning our talk about coin flips and infinite tosses, it seems that we were both right for different reasons. You said that the probability of reaching 0 in an infinite number of tosses is 1. Today I found out that, while this seems to be correct, it doesn't mean what I thought it does. Wikipedia states that it is possible that it never reaches zero (the article specifically talked about tails never being flipped in an infinite amount of tosses), which I was thinking might be correct! Since you can always get further on each flip, it is technically possible that we never reach 0 on the ruler, even with an infinite number of flips, which is strange to think about, as infinity is supposed to cover all possible situations and conditions. Still, it makes sense to me that this can be true, even though it's a bit tricky to think about. Here is the article: https://en.wikipedia.org/wiki/Almost_surely And here is the quote specifically concerning coin flips: So basically, the article states that the probability of 1 doesn't necessarily mean that the event MUST happen, which makes no sense to me. It cannot possibly be mathematically correct to say that p = 1 is an almost certain event. Is this another approach to probability, which I am not aware of? It makes no sense to me so it might be a more subjective (hence, less mathematical?) approach. Input on this would be greatly appreciated. EDIT: But wait just a minute. If, mathematically speaking, the probability of never flipping tails in an infinite amount of coing flips is technically not 100% (but rather, unfathomably close to it), isn't the probability for my problem around 0.5, rather than 1?

In other words, questions about what you don't know are always welcome here, however simple and basic. Claims and theories that you know something that others don't without proper evidence is what's uncwelcome. You can ask about anything, the site exists to educate people with lesser knowledge. You will do fine.

The correct answer is that no one knows. Some scientists think the universe is finite, while others say it's infinite. It's irrelevant because it's just a guess at this point anyway.

You have got a thought experiment. Others have done actual experiments. Do you at least care to elaborate why it has got to be this way? Not that it matters, because the experiment shows that it is wrong. What do you mean by the cloud of possibility spinning? Is there more to it or is this all that is included in your ''thought experiment''? I also don't understand the reasoning behind your predictions. You should elaborate on these things when posting, because you are going to get asked anyway.

I would say that it is impolite to ignore them and pretend you didn't see them. I would be slightly offended, at least. Why not just greet them, or the regular ''What's up, how are you doing? Where are you heading? Ok great, see ya.''?