A Discussion of Probabilities

[anobserver]

Is 10 consecutive heads when flipping a coin really a sign of the universe coming apart at the seams?

My understanding of this is pretty basic, so bear with me, and if need be, correct me/clarify/etc.

When flipping a (fair) coin, the probability of getting heads is 1 out of 2. Since each flip is an independent event, the fact that you have already gotten 9 consecutive heads doesn't change the the fact that the probability of getting heads is still 1 out of 2.

If you flip a coin 10 times, there is a fixed number of possible outcomes. Which means the probability of getting 10 straight heads would be 1 out of (total number of possibilites). Basically, it would be just as likely as any other combination of results.

Have I gone wrong somewhere?:confused0006: If anyone has a really good understanding of probabilities, would you please comment on the accuracy of Walter's statement/my analysis? Thanks.

[blindmansleeps]

Well, I'm not a probability 'expert', but I think the possible reference is the law of large numbers, which says that any +/- random sequence will eventually reach a fairly equal distributions. It says that if I were to flip a coin 100 times, the results would eventually average up to a fairly equal distribution: roughly 50 heads and 50 tails. (This law is actually one of the ones that I find pretty BS in probabilities--even worse when inferences about a population are drawn from similar laws.)

That being said, 10 heads in a row isn't enough to qualify under the 'large number' rule. But, the concept remains the same. On any flip, there is a 50/50 chance of getting heads or tails. That being said, in a series of 10 flips, anything over 7-8 flips would be considered rare.

While it may not make sense to my head completely, I trust Walter. Haha.

[MYOB]

It's been a long, long time, but if I remember correctly, when you calculate the probability of two separate events (x AND y) occurring, you multiply the separate probabilities. To calculate the probability of either occurring (x OR y), you add the separate probabilities.

Given an infinite number of sets of 10 coin tosses, the odds of heads for all ten tosses is 1:1024. The odds of all heads OR all tails is 1:512. It comes up the same sometimes, and you can't predict when, but when people are also falling through concrete balconies, I'd go with Walter's gut feeling. :haha:

[tricked]

I think the coin toss thing, is a reference to quantum entanglement. When discussing the nature of entanglement, a coin being cut in half is a common analogy as well as using the name "Alice" as a sort of "John Doe" generic name. Alice is used, because it begins with A. Likewise, Bob is used because it begins with B. So, Alice and Bob and coins are commonly used analogous symbols to explain things in physics.

The show mentions entanglement directly, as well as the character Alice, and the coin ... Walter quotes Einstein "spooky action at a distance" ... so on and so forth. So I think the coin is just referencing that. It came up ten times the same, because in an entangled universe ... had he done the same thing there, it would come up ten times the opposite. The key, is the soft spot ... where you would notice the entanglement. If there was no soft spot, you could flip the coin and get heads or tails either one. But since there was a soft spot, and they were "close to the entangled universe" so to speak ... the coin toss thing was to drive home the point that they could only do one KIND of thing in that spot ... a deterministic thing, of which, the opposite was taking place IN THAT SAME SPOT and they were "closer" to it because the veil was so thin, yada yada. Does that make sense?

[andrewk512]

If you flip a coin 10 times, there is a fixed number of possible outcomes. Which means the probability of getting 10 straight heads would be 1 out of (total number of possibilites). Basically, it would be just as likely as any other combination of results.

To get heads 10 times out of 10 would be .098%, so yes, it's extremely rare. While I understand what you mean, Walter's point was more so that he got 10/10 heads compared to the 99.9% chance of a different result. The degradation of the universe presumably altered the coin's 50/50 probability. It's kinda contrived. I thought it would've been cool if they linked the coin's improbability to the death of Alice's husband (something like he always picked heads or something.)

[lolsusl]

I think it's the early hit that one the other side Alice died.
Because the one coin toss caused it all.
Like Olivia said "it's not about physics, but about people".

On the blue side: Derek chooses heads, coin toss result: heads, ergo he dies.
On the red side : Derek chooses heads, coin toss result: tails, ergo Alice dies.

Alice and Altderek know that it all just happend because the coin fell the way it did and that's why they are holding on the fact that the coin showed heads/tail and that causing the coins to show only heads on the blue side and I guess only tails on the red side.


And why the coin showing heads 10 times is highly unlikely can be explained with a binomial distribution (http://en.wikipedia.org/wiki/Binomial_distribution) where the success probability of each trial is p=0,5.

[Conrad]

Derren Brown did a trick in his "The System" UK television special, where he flipped a coin heads 10 times in a row. Here's a link to it on youtube http://www.youtube.com/watch?v=X1uJD1O3L08 (http://www.youtube.com/watch?v=X1uJD1O3L08)

Later in the show he explains how he did it. He started filming in the morning and flipping the coin, and every time he flipped tails, he'd start all over. He just kept doing this until he got heads 10 times in a row. It took him nine hours to get it.

[Joe Curwen]

Is 10 consecutive heads when flipping a coin really a sign of the universe coming apart at the seams?



I'll take a stab at answering this part.

As others have mentioned the odds of getting 10 heads in a row is roughly one in a thousand. Would such an improbable event signal that the universe was coming apart at the seams?

In the real world, no, it wouldn't. We'd need a lot more proof than that. An extraordinary amount, even.

But in the fringeverse, because they know that the universe is liable to come apart, they've flipped the null hypothesis around so that extraordinary proof is no longer required. You can do simple tests like flipping a coin 10 times or seeing if a coin floats on water and that's enough to know if something is wrong.

--
Joe

[jay_eilthabhae]

I think the coin toss thing, is a reference to quantum entanglement. When discussing the nature of entanglement, a coin being cut in half is a common analogy as well as using the name "Alice" as a sort of "John Doe" generic name. Alice is used, because it begins with A. Likewise, Bob is used because it begins with B. So, Alice and Bob and coins are commonly used analogous symbols to explain things in physics.

The show mentions entanglement directly, as well as the character Alice, and the coin ... Walter quotes Einstein "spooky action at a distance" ... so on and so forth. So I think the coin is just referencing that. It came up ten times the same, because in an entangled universe ... had he done the same thing there, it would come up ten times the opposite. The key, is the soft spot ... where you would notice the entanglement. If there was no soft spot, you could flip the coin and get heads or tails either one. But since there was a soft spot, and they were "close to the entangled universe" so to speak ... the coin toss thing was to drive home the point that they could only do one KIND of thing in that spot ... a deterministic thing, of which, the opposite was taking place IN THAT SAME SPOT and they were "closer" to it because the veil was so thin, yada yada. Does that make sense?

The best explanation so far....very nicely explained and that explains the coin reference in alice and derek's case as well...



I'll take a stab at answering this part.

As others have mentioned the odds of getting 10 heads in a row is roughly one in a thousand. Would such an improbable event signal that the universe was coming apart at the seams?

In the real world, no, it wouldn't. We'd need a lot more proof than that. An extraordinary amount, even.

But in the fringeverse, because they know that the universe is liable to come apart, they've flipped the null hypothesis around so that extraordinary proof is no longer required. You can do simple tests like flipping a coin 10 times or seeing if a coin floats on water and that's enough to know if something is wrong.

--
Joe

Yeah...true, I mean I don't think walter would have freaked out if he wasn't already facing fringe events for a living.....so with everything else that happened, the coin toss was a good enough quick check to make sure that something's wrong.........It's like when you know your computer is already giving you a lot of problems, and hangs up everytime, then you know that everytime your numlock key stops responding or your mouse is stuck, its a quick check to know that the computer has hung again....

[ramparts]

Is 10 consecutive heads when flipping a coin really a sign of the universe coming apart at the seams?

My understanding of this is pretty basic, so bear with me, and if need be, correct me/clarify/etc.

When flipping a (fair) coin, the probability of getting heads is 1 out of 2. Since each flip is an independent event, the fact that you have already gotten 9 consecutive heads doesn't change the the fact that the probability of getting heads is still 1 out of 2.

If you flip a coin 10 times, there is a fixed number of possible outcomes. Which means the probability of getting 10 straight heads would be 1 out of (total number of possibilites). Basically, it would be just as likely as any other combination of results.

Have I gone wrong somewhere?:confused0006: If anyone has a really good understanding of probabilities, would you please comment on the accuracy of Walter's statement/my analysis? Thanks.

Are you familiar with the concept of entropy? It's a bit of a detour from coins (which I'll get to in the next paragraph!) but it's relevant. Consider a large collection of gas molecules randomly distributed in a room at some temperature. Now, it's just as likely to have all those molecules in a particular configuration bunched up in one corner as it is to have them in a particular configuration evenly spaced around the room, but if you saw all the molecules bunched up in a corner you would immediately think it's really unlikely. The reason is that there are so many more possible configurations which look like evenly distributed gas than there are configurations that look like gas bunched up in the corner. Entropy measures the number of possible microscopic configurations you can have which look the same at macroscopic scales - so the room with all the gas bunched up in one corner has very low entropy, while the room with gas evenly spread has very high entropy. You're much more likely to find a room with high entropy, even though strictly speaking any room will have a very unlikely configuration of molecules.

The same principle applies here. If I flip a coin 10 times, there's a 1/2^10, or about 0.1%, chance of any particular configuration happening. However, there's only one configuration in which I get heads (or tails) every time, so there's a 0.1% chance of Walter's outcome.

Similarly, there's a 0.1% chance of getting (in order) HTHTHTHTHT, and a 0.1% chance of getting THTHTHTHTH, and of getting HHHHHTTTTT, etc., but in the end all of those look like "5 heads and 5 tails", so we count them together. I'm a little rusty on this but I believe for 10 coin flips, there are 10!/(n!(10-n)!) possible ways to get n heads (! is factorial), so there are 10!/(5!5!)=252 ways to get 5 heads, and the total probability of getting 5 heads (in any order) is 252/2^10 is just under 25%.

So any individual way of getting 5 heads is as (un)likely as getting 10 heads, but simply getting 5 heads in 10 tries regardless of the order is 250 times more likely!

(That said, looking at this from a physics standpoint - which is where what little training I have is - it's not very plausible that a degrading of physical law would lead to an effect as macroscopic as coin flips coming out the same... at least not without some more serious side effects that would likely lead to some dead characters! But then most of Fringe has only tenuous relations to real physics, and we watch anyway :) )

[tricked]

Derren Brown did a trick in his "The System" UK television special, where he flipped a coin heads 10 times in a row. Here's a link to it on youtube http://www.youtube.com/watch?v=X1uJD1O3L08 (http://www.youtube.com/watch?v=X1uJD1O3L08)

Later in the show he explains how he did it. He started filming in the morning and flipping the coin, and every time he flipped tails, he'd start all over. He just kept doing this until he got heads 10 times in a row. It took him nine hours to get it. Holy #$%#$% !!!


.........It's like when you know your computer is already giving you a lot of problems, and hangs up everytime, then you know that everytime your numlock key stops responding or your mouse is stuck, its a quick check to know that the computer has hung again.... Dude, get a Mac ... lol :)


Are you familiar with the concept of entropy? It's a bit of a detour from coins (which I'll get to in the next paragraph!) but it's relevant. Consider a large collection of gas molecules randomly distributed in a room at some temperature. Now, it's just as likely to have all those molecules in a particular configuration bunched up in one corner as it is to have them in a particular configuration evenly spaced around the room, but if you saw all the molecules bunched up in a corner you would immediately think it's really unlikely. The reason is that there are so many more possible configurations which look like evenly distributed gas than there are configurations that look like gas bunched up in the corner. Entropy measures the number of possible microscopic configurations you can have which look the same at macroscopic scales - so the room with all the gas bunched up in one corner has very low entropy, while the room with gas evenly spread has very high entropy. You're much more likely to find a room with high entropy, even though strictly speaking any room will have a very unlikely configuration of molecules.

The same principle applies here. If I flip a coin 10 times, there's a 1/2^10, or about 0.1%, chance of any particular configuration happening. However, there's only one configuration in which I get heads (or tails) every time, so there's a 0.1% chance of Walter's outcome.

Similarly, there's a 0.1% chance of getting (in order) HTHTHTHTHT, and a 0.1% chance of getting THTHTHTHTH, and of getting HHHHHTTTTT, etc., but in the end all of those look like "5 heads and 5 tails", so we count them together. I'm a little rusty on this but I believe for 10 coin flips, there are 10!/(n!(10-n)!) possible ways to get n heads (! is factorial), so there are 10!/(5!5!)=252 ways to get 5 heads, and the total probability of getting 5 heads (in any order) is 252/2^10 is just under 25%.

So any individual way of getting 5 heads is as (un)likely as getting 10 heads, but simply getting 5 heads in 10 tries regardless of the order is 250 times more likely!

(That said, looking at this from a physics standpoint - which is where what little training I have is - it's not very plausible that a degrading of physical law would lead to an effect as macroscopic as coin flips coming out the same... at least not without some more serious side effects that would likely lead to some dead characters! But then most of Fringe has only tenuous relations to real physics, and we watch anyway :) ) Great entropy analogy ! :happy15: