One In A Googol vs One In A Googolplex

[David Sklansky]

I've often toyed with having a bit of fun with these two numbers as it applies to probability questions especially since it was my father's math professor who coined those words. A googol is ten to the hundredth power. In other words one followed by one hundred zeroes. A googolplex is ten to the googleth power. One followed by a googol zeroes.

I am going to periodically start a thread asking about the probability of extremely unlikely events. In each case I will ask which of three categories the answer is:

A. More common than one/googol.

B. Rarer than one in a googol but more common than one in a googolplex.

C. Rarer than one/googolplex.

THESE QUESTIONS ARE ONLY DIRECTED TOWARD THOSE WHO ARE NOT GOOD AT MATH. If you are, you will spoil the fun by answering them. In fact it won't be fun if even the math challenged try to calculate the answer. Better they just give their gut feelings.

A, B, or C?

1. The chances that you will win the next 100 lotteries in a row.

2. The chances that a specific player will hit 500 homeruns this year, assuming everything is random and he normally hits 10.

3. Your 90 year old grandmother's next 50 bowling games are 300.

4. Every single time a poker machine is played for the next million years it will deal a pat Royal Flush.

5. Your pet parrot, who has been taught to randomly speak every individual sound in the English language, randomly recites Hamlet.

6. All players who are capable of reaching the cup from outside the green always sink their chip or drive and never have to put again for the next 50 years.

I mean for all these questions to be pure probability questions regarding multiple independent events with no funny business or divine intervention going on. I think even the most ardent atheist would admit that if any of these things happened it would more likely be the work of a designer than a miniscule underdog coming in randomly. But for the purpose of these questions we assume that isn't happenning.

[SNOWBALL]

[ QUOTE ]
1. The chances that you will win the next 100 lotteries in a row.



[/ QUOTE ]

b


[ QUOTE ]
2. The chances that a specific player will hit 300 homeruns this year, assuming everything is random and he normally hits 10



[/ QUOTE ]

A

[ QUOTE ]
3. Your 90 year old grandmother's next 50 bowling games are 300.


[/ QUOTE ]

B

[ QUOTE ]
4. Every single time a poker machine is played for the next million years it will deal a pat Royal Flush.


[/ QUOTE ]

C

[ QUOTE ]
5. Your pet parrot, who has been taught to randomly speak every individual sound in the English language, randomly recites Hamlet.

[/ QUOTE ]

C

[ QUOTE ]
6. All players who are capable of reaching the cup from outside the green always sink their chip or drive and never have to put again for the next 50 years.


[/ QUOTE ]

C

[yNnOs]

1. B
2. A
3. A
4. C.
5. B.
6. B.

I hope you were only expecting answers and not explanations. Though I'm good at math, I'm not the best with probability.

[soon2bepro]

Alright, gut only. And I'm not good at math. I already have a hard time imagining these numbers in my head.

[ QUOTE ]

1. The chances that you will win the next 100 lotteries in a row.

[/ QUOTE ]

B

[ QUOTE ]

2. The chances that a specific player will hit 300 homeruns this year, assuming everything is random and he normally hits 10

[/ QUOTE ]

A

[ QUOTE ]

3. Your 90 year old grandmother's next 50 bowling games are 300.

[/ QUOTE ]

That would depend on her physical ability and experience in bowling, but I'd say A

[ QUOTE ]

4. Every single time a poker machine is played for the next million years it will deal a pat Royal Flush.


[/ QUOTE ]

definitely C, unless it's not in constant use, which is really not the point here I presume

[ QUOTE ]

5. Your pet parrot, who has been taught to randomly speak every individual sound in the English language, randomly recites Hamlet.


[/ QUOTE ]

C

[ QUOTE ]
I think even the most ardent atheist would admit that if any of these things happened it would more likely be the work of a designer than a miniscule underdog coming in randomly.

[/ QUOTE ]

Not at all. If you could predict it somehow, then we could discuss the matter, but up front, just because an extremely unlikely event happens doesn't mean anything.

[Sephus]

seems like people are overusing C.

[PairTheBoard]

[ QUOTE ]
I think even the most ardent atheist would admit that if any of these things happened it would more likely be the work of a designer than a miniscule underdog coming in randomly. But for the purpose of these questions we assume that isn't happenning.


[/ QUOTE ]

I scientist would begin work looking for yet to be discovered laws of physics to explain the anomaly.

PairTheBoard

[RocketManJames]

Here are my answers.

1. 100 lotteries in a row. Answer: B

2. 500 homeruns. Answer: A

3. Grandmother bowls 50 300's. Answer: B, assuming chance of strike isn't 0. Edited this one, I mistyped my answer.

4. All poker machines deal pat Royal Flush for next million years. Answer: C.

5. Pet parrot randomly recites Hamlet. Answer: B.

6. Golfers never having to putt again for 50 years. Answer: C.

-RMJ

[ski]

[ QUOTE ]
Here are my answers.

1. 100 lotteries in a row. Answer: B

2. 500 homeruns. Answer: A

3. Grandmother bowls 50 300's. Answer: C, shes dead

4. All poker machines deal pat Royal Flush for next million years. Answer: C.

5. Pet parrot randomly recites Hamlet. Answer: B.

6. Golfers never having to putt again for 50 years. Answer: C.

-RMJ

[/ QUOTE ]

what constitutes a golfer? If people like me are included in the definition it reduces the chance quite a bit. If its only professionals then B probably.

[soon2bepro]

[ QUOTE ]
seems like people are overusing C.

[/ QUOTE ]

really?

<font color="white">

According to Wikipedia, Hamlet consists of 29,551 words, and the bird can't screw up in one. How many different words are in the english language anyway? I just googled these up:

"The Second Edition of the Oxford English Dictionary contains full entries for 171,476 words in current use, and 47,156 obsolete words. To this may be added around 9,500 derivative words included as subentries"

"But estimates of Shakespeare’s vocabulary vary from about 18,000 to 25,000 in various books, because writers have different views about what constitutes a distinct word."

And David didn't even say the parrot knew all the words, but all the sounds, which makes it extremely more unlikely.

I don't know how many tries the parrot gets, but even in a lifetime of tries, C seems extremely optimistic. There's just no way it'll get it right.

A pat royal is like, what, one in 500,000 or something? (quick google didn't help, too many promotions and bragging) In my original reply I thought it was just one particular machine, now I saw it's every video poker machine?... Get out of here!`

</font>

[Prodigy54321]

1 c
2 a
3 a
4 b
5 a
6 a

I'm probably not even close if I only considered each question with respect to the others...

holla

[Metric]

I'd like to add a question:

If you had to randomly pick the initial conditions of the universe (including all the matter inside it, as well as the universe itself), what are the odds that your random pick would lead to a universe that looks anything at all like ours? A, B, or C?

If the answer was C, would this quote still apply?
[ QUOTE ]
I think even the most ardent atheist would admit that if any of these things happened it would more likely be the work of a designer than a miniscule underdog coming in randomly.

[/ QUOTE ]

[Prodigy54321]

[ QUOTE ]
I'd like to add a question:

If you had to randomly pick the initial conditions of the universe (including all the matter inside it, as well as the universe itself), what are the odds that your random pick would lead to a universe that looks anything at all like ours? A, B, or C?

If the answer was C, would this quote still apply?
[ QUOTE ]
I think even the most ardent atheist would admit that if any of these things happened it would more likely be the work of a designer than a miniscule underdog coming in randomly.

[/ QUOTE ]

[/ QUOTE ]

I don't think it would if we can't record the negative outcomes...and there may be an insane number of universes...

but, even if there were just one universe...and one shot...the fact that conditions are are met against these odds still wouldn't allow us to come to the conclusion that randomness is unlikely to be the cause...again, simply because we can't record negative outcomes...

*that's just middle of the night rambling...basically pulled out of my ass. /images/graemlins/laugh.gif..I know nothing about how this stuff works.

am I right though there are implications when we record successes, but don't record losses..that has to do something that screws up an analysis based on that data (what I referred to as successes and losses)...right?

[godBoy]

[ QUOTE ]
1. The chances that you will win the next 100 lotteries in a row.

[/ QUOTE ]
B

[ QUOTE ]
2. The chances that a specific player will hit 500 homeruns this year, assuming everything is random and he normally hits 10.

[/ QUOTE ]
A

[ QUOTE ]
3. Your 90 year old grandmother's next 50 bowling games are 300.

[/ QUOTE ]
B

[ QUOTE ]
4. Every single time a poker machine is played for the next million years it will deal a pat Royal Flush.

[/ QUOTE ]
C
[ QUOTE ]
5. Your pet parrot, who has been taught to randomly speak every individual sound in the English language, randomly recites Hamlet.

[/ QUOTE ]
B
[ QUOTE ]
6. All players who are capable of reaching the cup from outside the green always sink their chip or drive and never have to put again for the next 50 years.

[/ QUOTE ]
C

[soon2bepro]

[ QUOTE ]
I'd like to add a question:

If you had to randomly pick the initial conditions of the universe (including all the matter inside it, as well as the universe itself), what are the odds that your random pick would lead to a universe that looks anything at all like ours? A, B, or C?

If the answer was C, would this quote still apply?



[/ QUOTE ]

MWI (http://en.wikipedia.org/wiki/Many-worlds_interpretation) aside, answer is definitely C (though I have trouble understanding what you mean by randomly picking it, as in, random between what? position? Anyway, doesn't matter much).

The quote didn't apply (was invalid) in the first place, but your argument is just an example of why that is, not the sole reason.

[Piers]

[ QUOTE ]
I think even the most ardent atheist would admit that if any of these things happened it would more likely be the work of a designer than a miniscule underdog coming in randomly.

[/ QUOTE ]

Clearly false, in that I am sure there are many ardent atheists who would think no such thing.

Your statement is slightly tricky in that whether it’s the result of a designer or random is fairly irrelevant as the third possibility, ‘due to some process we don’t yet understand’, is so much more likely. Although admittedly you can be extremely flexible about what you mean by ‘due to a designer’.

[bottomset]

MLB players only get around 650plate appearances in a season, hitting a homerun 75% of the time when the alltime best is in the 8-11% range and thats from players that don't qualify for this(they normally hit way more than 10)

I think this is less likely than people are giving it credit for, it may be A if you were only talking about Barry Bonds playing his 2001 season over and over again with his early 90's legs and the leap from 73 to 500 is massive

[Metric]

[ QUOTE ]
MWI aside, answer is definitely C (though I have trouble understanding what you mean by randomly picking it, as in, random between what? position? Anyway, doesn't matter much).

[/ QUOTE ]
Just a random point in phase space. I.E. if the phase space is represented as a darboard of initial conditions, what is your chance of throwing a dart (with an infinitely fine point) from across the room and hitting it precisely in the region in which galaxies arise and dominate the universe, etc? And yes, it's C.

[andyfox]

C on all. That is, basically as close to impossible as can be.

[Sephus]

[ QUOTE ]
[ QUOTE ]
seems like people are overusing C.

[/ QUOTE ]

really?

<font color="white">

According to Wikipedia, Hamlet consists of 29,551 words, and the bird can't screw up in one. How many different words are in the english language anyway? I just googled these up:

"The Second Edition of the Oxford English Dictionary contains full entries for 171,476 words in current use, and 47,156 obsolete words. To this may be added around 9,500 derivative words included as subentries"

"But estimates of Shakespeare’s vocabulary vary from about 18,000 to 25,000 in various books, because writers have different views about what constitutes a distinct word."

And David didn't even say the parrot knew all the words, but all the sounds, which makes it extremely more unlikely.

I don't know how many tries the parrot gets, but even in a lifetime of tries, C seems extremely optimistic. There's just no way it'll get it right.

A pat royal is like, what, one in 500,000 or something? (quick google didn't help, too many promotions and bragging) In my original reply I thought it was just one particular machine, now I saw it's every video poker machine?... Get out of here!`

</font>

[/ QUOTE ]

calculationish stuff in white <font color="white">

you can do the halmet problem by assuming (conservatively) 100 different english sounds and 300,000 sounds in the play. seems like slam dunk to me.

if a pat royal is even one in a million and you need it to be dealt a quintillion times in a row (a trillion times a year for a million years), don't you end up with like 6 quintillion zeros? you don't even get close to C.
</font>

[SBR]

I'm just going to say that at first glance C isn't ever a correct answer.

[Sephus]

[ QUOTE ]
C on all. That is, basically as close to impossible as can be.

[/ QUOTE ]

i thought the same thing but i'd go with B on all.

[RJT]

Sorry to go off on a tangent, like I seem always to do with your posts. But a question and a comment. Do you know how he came up with the name googol - just curious?

Wouldn’t it have been nice if he had copyrighted the name? Big time money with Google search engine. I think copyrights expire after 17 (19?) years anyway. Oh well, such is life.

[Justin A]

[ QUOTE ]
C on all. That is, basically as close to impossible as can be.

[/ QUOTE ]

This was my thought as well. Time to do some calculations.

Edit/ After doing the lottery calculation, I feel I have seriously underestimated how large a googleplex is. Basically to the point that it's embarrassing.

[Justin A]

[ QUOTE ]
[ QUOTE ]
C on all. That is, basically as close to impossible as can be.

[/ QUOTE ]

i thought the same thing but i'd go with B on all.

[/ QUOTE ]

That's what I'm going with as well now.

Very interesting exercise, my gut feelings were way off.

[Siegmund]

So, the lesson here is pretty much that a googolplex is a really big number.

After going back through the list, I was forced to change several Cs to Bs. (And after researching numbers of at-bats, I was forced to change my answer to 2 from C to B - since I had guessed, wrongly, that 500 at-bats was too many to fit in one season.)

Does anyone have an example of an event that is definitely possible, but has a probability of less than 1/googolplex of happening?

Seems pretty much the only things in category C are things that are mathematical impossibilities...

[thylacine]

[ QUOTE ]
I'd like to add a question:

If you had to randomly pick the initial conditions of the universe (including all the matter inside it, as well as the universe itself), what are the odds that your random pick would lead to a universe that looks anything at all like ours? A, B, or C?

If the answer was C, would this quote still apply?
[ QUOTE ]
I think even the most ardent atheist would admit that if any of these things happened it would more likely be the work of a designer than a miniscule underdog coming in randomly.

[/ QUOTE ]

[/ QUOTE ]

[ QUOTE ]
[ QUOTE ]
MWI aside, answer is definitely C (though I have trouble understanding what you mean by randomly picking it, as in, random between what? position? Anyway, doesn't matter much).

[/ QUOTE ]
Just a random point in phase space. I.E. if the phase space is represented as a darboard of initial conditions, what is your chance of throwing a dart (with an infinitely fine point) from across the room and hitting it precisely in the region in which galaxies arise and dominate the universe, etc? And yes, it's C.

[/ QUOTE ]

This is the only thing in this thread for which you could entertain the idea of it being as improbable as C. But since the universe has actually been observed, then of course it is more reasonable (as Metric knows) that there is some missing explanation yet to be found, and that once we understand it, we will realize that it wasn't really so improbable after all. Also DS's "...ardent atheist..." does not apply since that replaces an improbable effect with an even more improbable cause that requires even more explanation. And saying that it really is that improbable, but that there have been sufficiently many trials that it was bound to happen, is unsatisfactory since there is no evidence, or reason to believe, that such trials occur. The Intelligent Design hypothesis is the dumbest idea. The Anthropic Principle is the second dumbest idea. Some physicist argue that since the second dumbest idea compares favorably to the dumbest idea, that therefore the second dumbest idea is actually true. One even wrote a book. Right, Metric? /images/graemlins/wink.gif

None of the things in DS's OP are remotely improbable enough to be C. On the other hand, they have never been observed, so there is no compelling reason to seek any explanation for such hypothetical events.

[PairTheBoard]

[ QUOTE ]
I think even the most ardent atheist would admit that if any of these things happened it would more likely be the work of a designer than a miniscule underdog coming in randomly.

[/ QUOTE ]

Notice David does not give you a choice here between a "Deisgner" and "Yet to be discovered laws of Physics". His choice is between a Designer and Random Chance. In reality those aren't your only choices. All these Events are examples of the Principle I gave in another Thread which I think is a fundamental observation for those who demand miracles from God before they can believe in him.

If "God" were tinkering with the universe, his magical tricks would be indistinguishable from natural events for which there are shortfalls in scientific explanation.

A corollary to this principle is, if your paradigm for reality has you always look for yet to be discovered laws of physics to explain anomaly Events rather than attributing them to either a Designer or Divine Intervention, then there is no reason why one of these Sklansky Events should change that paradigm for you.

Hint for the Probability Estimates: (In white)
<font color="white">(10^x)^y is much different than 10^(x^y). That's because, (10^x)^y = 10^(x*y). The probability for a sequence of events looks more like (10^x)^y </font>

PairTheBoard

[chillrob]

I think the baseball one would definately be as close to impossible as anything - don't you think every pitcher would start intentionally walking the batter after, say, he hit 100 homers in a row?

[vhawk01]

[ QUOTE ]
I think the baseball one would definately be as close to impossible as anything - don't you think every pitcher would start intentionally walking the batter after, say, he hit 100 homers in a row?

[/ QUOTE ]

More likely they'd cancel the baseball season or suspend him or something.

[David Sklansky]

[ QUOTE ]
Sorry to go off on a tangent, like I seem always to do with your posts. But a question and a comment. Do you know how he came up with the name googol - just curious?

Wouldn’t it have been nice if he had copyrighted the name? Big time money with Google search engine. I think copyrights expire after 17 (19?) years anyway. Oh well, such is life.

[/ QUOTE ]

He asked his five year old nephew to tell him the biggest number he could think of. True story.

[NLSoldier]

ditto to both of justin's posts.

[tshort]

Better they just give their gut feelings:

1. The chances that you will win the next 100 lotteries in a row.

B (close to C)

2. The chances that a specific player will hit 500 homeruns this year, assuming everything is random and he normally hits 10.

B

3. Your 90 year old grandmother's next 50 bowling games are 300.

B

4. Every single time a poker machine is played for the next million years it will deal a pat Royal Flush.

C

5. Your pet parrot, who has been taught to randomly speak every individual sound in the English language, randomly recites Hamlet.

B

6. All players who are capable of reaching the cup from outside the green always sink their chip or drive and never have to put again for the next 50 years.

C

[Metric]

[ QUOTE ]
[ QUOTE ]
I'd like to add a question:

If you had to randomly pick the initial conditions of the universe (including all the matter inside it, as well as the universe itself), what are the odds that your random pick would lead to a universe that looks anything at all like ours? A, B, or C?

If the answer was C, would this quote still apply?
[ QUOTE ]
I think even the most ardent atheist would admit that if any of these things happened it would more likely be the work of a designer than a miniscule underdog coming in randomly.

[/ QUOTE ]

[/ QUOTE ]

[ QUOTE ]
[ QUOTE ]
MWI aside, answer is definitely C (though I have trouble understanding what you mean by randomly picking it, as in, random between what? position? Anyway, doesn't matter much).

[/ QUOTE ]
Just a random point in phase space. I.E. if the phase space is represented as a darboard of initial conditions, what is your chance of throwing a dart (with an infinitely fine point) from across the room and hitting it precisely in the region in which galaxies arise and dominate the universe, etc? And yes, it's C.

[/ QUOTE ]

This is the only thing in this thread for which you could entertain the idea of it being as improbable as C. But since the universe has actually been observed, then of course it is more reasonable (as Metric knows) that there is some missing explanation yet to be found, and that once we understand it, we will realize that it wasn't really so improbable after all. Also DS's "...ardent atheist..." does not apply since that replaces an improbable effect with an even more improbable cause that requires even more explanation. And saying that it really is that improbable, but that there have been sufficiently many trials that it was bound to happen, is unsatisfactory since there is no evidence, or reason to believe, that such trials occur. The Intelligent Design hypothesis is the dumbest idea. The Anthropic Principle is the second dumbest idea. Some physicist argue that since the second dumbest idea compares favorably to the dumbest idea, that therefore the second dumbest idea is actually true. One even wrote a book. Right, Metric? /images/graemlins/wink.gif

[/ QUOTE ]
Another way to say this is that, yes, randomly picking a "nice" point in our phase space really is this improbable. So the universe probably isn't random. Exactly how it isn't random is the puzzle (since the assumption of randomness works extremely well for every other application of stat-mech). A designer would be one way to invoke non-randomness, but of course its not a scientifically clean idea -- it carries a lot of other baggage that people would rather not have to deal with in the pristine realm of physical theory. So maybe there is a cleaner way to think about it. Anthropic reasoning is an attempt at this -- it's clean, but it simply doesn't get the job done.

[Neuge]

[ QUOTE ]
MLB players only get around 650plate appearances in a season, hitting a homerun 75% of the time when the alltime best is in the 8-11% range and thats from players that don't qualify for this(they normally hit way more than 10)

I think this is less likely than people are giving it credit for, it may be A if you were only talking about Barry Bonds playing his 2001 season over and over again with his early 90's legs and the leap from 73 to 500 is massive

[/ QUOTE ]
This is true. What are the odds a random variable is 50 or more standard deviations from the average?

Interesting blog about the statistical improbability of Barry Bonds' 73 homeruns (http://kermittheblog.wordpress.com/2007/05/10/beisbol-been-barry-barry-good-to-uh-barry/)

[Neuge]

[ QUOTE ]
Better they just give their gut feelings:

1. The chances that you will win the next 100 lotteries in a row.

B (close to C)

[/ QUOTE ]
FYI for everyone

White text- <font color="white"> This is nowhere near C. It's much closer to being A than C. </font>

[chillrob]

[ QUOTE ]
[ QUOTE ]
Better they just give their gut feelings:

1. The chances that you will win the next 100 lotteries in a row.

B (close to C)

[/ QUOTE ]
FYI for everyone

White text- <font color="white"> This is nowhere near C. It's much closer to being A than C. </font>

[/ QUOTE ]

Sorry, I know this is absolutely impossible, because I haven't even bought any lottery tickets and have no plans to do so.

[Sephus]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Better they just give their gut feelings:

1. The chances that you will win the next 100 lotteries in a row.

B (close to C)

[/ QUOTE ]
FYI for everyone

White text- <font color="white"> This is nowhere near C. It's much closer to being A than C. </font>

[/ QUOTE ]

Sorry, I know this is absolutely impossible, because I haven't even bought any lottery tickets and have no plans to do so.

[/ QUOTE ]

the chances that you have a change of heart/go completely crazy/aliens take over your body are high enough to dismiss this point.

[bottomset]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Better they just give their gut feelings:

1. The chances that you will win the next 100 lotteries in a row.

B (close to C)

[/ QUOTE ]
FYI for everyone

White text- <font color="white"> This is nowhere near C. It's much closer to being A than C. </font>

[/ QUOTE ]

Sorry, I know this is absolutely impossible, because I haven't even bought any lottery tickets and have no plans to do so.

[/ QUOTE ]

the chances that you have a change of heart/go completely crazy/aliens take over your body are high enough to dismiss this point.

[/ QUOTE ]

well powerball is 146million and change to 1 against, so hitting that 100times + the extra factor of not playing the lottery in the first place(barring those extremely rare cases) should make this really small

megamillions is 175.7million to 1

estimate on the lottery one for powerball

2.7e816

[arahant]

[ QUOTE ]
MLB players only get around 650plate appearances in a season, hitting a homerun 75% of the time when the alltime best is in the 8-11% range and thats from players that don't qualify for this(they normally hit way more than 10)

I think this is less likely than people are giving it credit for, it may be A if you were only talking about Barry Bonds playing his 2001 season over and over again with his early 90's legs and the leap from 73 to 500 is massive

[/ QUOTE ]

I know we aren't supposed to mess with 'trickiness', but it's obviously flat-out zero. When Barry was on a heater and smacking one every 5ab's or something, he got 3-4 walks a game.
Basically, we need to add in the probability that the pitchouts come close enough to the hitter for him to swing.
Although, if that got high, you'd start seeing pitchers rolling the ball in, catchers on third base, etc...

[vhawk01]

[ QUOTE ]
[ QUOTE ]
MLB players only get around 650plate appearances in a season, hitting a homerun 75% of the time when the alltime best is in the 8-11% range and thats from players that don't qualify for this(they normally hit way more than 10)

I think this is less likely than people are giving it credit for, it may be A if you were only talking about Barry Bonds playing his 2001 season over and over again with his early 90's legs and the leap from 73 to 500 is massive

[/ QUOTE ]

I know we aren't supposed to mess with 'trickiness', but it's obviously flat-out zero. When Barry was on a heater and smacking one every 5ab's or something, he got 3-4 walks a game.
Basically, we need to add in the probability that the pitchouts come close enough to the hitter for him to swing.
Although, if that got high, you'd start seeing pitchers rolling the ball in, catchers on third base, etc...

[/ QUOTE ]

So, what are the odds that the commissioner steps in and changes the rules of baseball to make this illegal, and to force people to pitch to Bonds? 1 in a billion? Ok, no sweat.

[arahant]

[ QUOTE ]
[ QUOTE ]
MLB players only get around 650plate appearances in a season, hitting a homerun 75% of the time when the alltime best is in the 8-11% range and thats from players that don't qualify for this(they normally hit way more than 10)

I think this is less likely than people are giving it credit for, it may be A if you were only talking about Barry Bonds playing his 2001 season over and over again with his early 90's legs and the leap from 73 to 500 is massive

[/ QUOTE ]
This is true. What are the odds a random variable is 50 or more standard deviations from the average?

Interesting blog about the statistical improbability of Barry Bonds' 73 homeruns (http://kermittheblog.wordpress.com/2007/05/10/beisbol-been-barry-barry-good-to-uh-barry/)

[/ QUOTE ]

This article is a gross abuse of statistics, the worst 3 errors (but not the only ones) being:
1) Failure to perform the statistical analysis across all players. It's not like Bonds had to be the one to hit 73.
2) Failure of IID, in almost every part of the analysis.
3) Method of establishing the underlying distribution was flawed.

Bah.
Frankly, the mere fact that it happened is pretty damn fine evidence that there is something wrong with the analysis. And if you did the same analysis on the HR leader every year, I bet you'd get 3+SD's for every one.

[tshort]

[ QUOTE ]
[ QUOTE ]
Better they just give their gut feelings:

1. The chances that you will win the next 100 lotteries in a row.

B (close to C)

[/ QUOTE ]
FYI for everyone

White text- <font color="white"> This is nowhere near C. It's much closer to being A than C. </font>

[/ QUOTE ]

Can you use your vast knowledge to explain why your text needs to be in white?

It must be close to:

<font color="white"> ((1/15^8)^100) &gt; Googol</font>

[soon2bepro]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
seems like people are overusing C.

[/ QUOTE ]

really?

<font color="white">

According to Wikipedia, Hamlet consists of 29,551 words, and the bird can't screw up in one. How many different words are in the english language anyway? I just googled these up:

"The Second Edition of the Oxford English Dictionary contains full entries for 171,476 words in current use, and 47,156 obsolete words. To this may be added around 9,500 derivative words included as subentries"

"But estimates of Shakespeare’s vocabulary vary from about 18,000 to 25,000 in various books, because writers have different views about what constitutes a distinct word."

And David didn't even say the parrot knew all the words, but all the sounds, which makes it extremely more unlikely.

I don't know how many tries the parrot gets, but even in a lifetime of tries, C seems extremely optimistic. There's just no way it'll get it right.

A pat royal is like, what, one in 500,000 or something? (quick google didn't help, too many promotions and bragging) In my original reply I thought it was just one particular machine, now I saw it's every video poker machine?... Get out of here!`

</font>

[/ QUOTE ]

calculationish stuff in white <font color="white">

you can do the halmet problem by assuming (conservatively) 100 different english sounds and 300,000 sounds in the play. seems like slam dunk to me.

if a pat royal is even one in a million and you need it to be dealt a quintillion times in a row (a trillion times a year for a million years), don't you end up with like 6 quintillion zeros? you don't even get close to C.
</font>

[/ QUOTE ]

<font color="white"> Wait, how can it be easier to get all the sounds right than all the words right? Since there are so many sound combinations that don't make a real word, it ought to be easier if the parrot just knew all the words.

And as I said I'm not good at math, but it seems like you're making a mistake in your pat royal calculations? Someone please confirm

</font>

[PairTheBoard]

[ QUOTE ]
calculationish stuff in white

<font color="white"> you can do the halmet problem by assuming (conservatively) 100 different english sounds and 300,000 sounds in the play. seems like slam dunk to me. </font>


[/ QUOTE ]

White:
<font color="white">

(100)^300,000 = (10^2)^300,000 = 10^600,000 &lt; 10^1,000,000

That's 10^(1 followed by 6 zeros)

Compare to C

</font>

PairTheBoard

[Neuge]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Better they just give their gut feelings:

1. The chances that you will win the next 100 lotteries in a row.

B (close to C)

[/ QUOTE ]
FYI for everyone

White text- <font color="white"> This is nowhere near C. It's much closer to being A than C. </font>

[/ QUOTE ]

Can you use your vast knowledge to explain why your text needs to be in white?

It must be close to:

<font color="white"> ((1/15^8)^100) &gt; Googol</font>

[/ QUOTE ]
The theme of this thread has mostly been to put technical solution talk in white so as not to disrupt Sklansky's "gut feeling" request.

White text- <font color="white"> Yes, the lottery question odds are about 10^800 which is obviously much greater than a Googol. But, it's much, much less than 10^(Googol), which is what I originally said. </font>

[spaceman Bryce]

I stink at math, so
I read this and thought it was interesting and I had no idea what a google plex meant so I wrote a google down on paper basically it takes up half the page and still didnt understand what you meant by google plex. Then after thinking about it for about 5 minutes I got it and realized thats a really really really big number but i need more reallys and i dont own enough pages to fill all those zeros on. It really blew my mind when i figured it out. It was scary and really creepy amd icky and now im going to have nightmares about zeros.

[gimmickthistime]

[ QUOTE ]
asked his five year old nephew

[/ QUOTE ]wired mickeymouse for answer he says wtf googolplex is biggern people think infact cant writeit within know universe and the nephew was nine

[jogger08152]

[ QUOTE ]
I've often toyed with having a bit of fun with these two numbers as it applies to probability questions especially since it was my father's math professor who coined those words. A googol is ten to the hundredth power. In other words one followed by one hundred zeroes. A googolplex is ten to the googleth power. One followed by a googol zeroes.

I am going to periodically start a thread asking about the probability of extremely unlikely events. In each case I will ask which of three categories the answer is:

A. More common than one/googol.

B. Rarer than one in a googol but more common than one in a googolplex.

C. Rarer than one/googolplex.

THESE QUESTIONS ARE ONLY DIRECTED TOWARD THOSE WHO ARE NOT GOOD AT MATH. If you are, you will spoil the fun by answering them. In fact it won't be fun if even the math challenged try to calculate the answer. Better they just give their gut feelings.

A, B, or C?

[/ QUOTE ]

I'm decent at math, but I'll restrict myself to 10-second, back-of-the-envelope estimates only.

[ QUOTE ]
1. The chances that you will win the next 100 lotteries in a row.

[/ QUOTE ]
B

[ QUOTE ]
2. The chances that a specific player will hit 500 homeruns this year, assuming everything is random and he normally hits 10.

[/ QUOTE ]
NFC

[ QUOTE ]
3. Your 90 year old grandmother's next 50 bowling games are 300.

[/ QUOTE ]
NFC

[ QUOTE ]
4. Every single time a poker machine is played for the next million years it will deal a pat Royal Flush.

[/ QUOTE ]
Assuming it's played frequently, B.

[ QUOTE ]
5. Your pet parrot, who has been taught to randomly speak every individual sound in the English language, randomly recites Hamlet.

[/ QUOTE ]
Easy C. I think. /images/graemlins/wink.gif

[ QUOTE ]
6. All players who are capable of reaching the cup from outside the green always sink their chip or drive and never have to put again for the next 50 years.

[/ QUOTE ]
B. (Pure guess.)

[vhawk01]

NFC? I hope that doesn't mean no....chance.

[jogger08152]

[ QUOTE ]
NFC? I hope that doesn't mean no....chance.

[/ QUOTE ]
No, means no [censored] clue: I don't understand the activity well enough to hazard even a wild guess.

[ungar2000]

B to all
not even close to using C

[Zeno]

[ QUOTE ]
A googol is ten to the hundredth power. In other words one followed by one hundred zeroes.

[/ QUOTE ]


Just to give a gut feel to the size of this lowly number titled a googol, rough estimates as to the number of atoms in the universe are much less than a googol. Estimates usually range near 10^80.

A copy and paste of one such estimate is below just for fun:

Atoms in the Universe

Estimates the the number of atoms in our galaxy to be in the area of 10^68 and, if dark and exotic matter are considered, then their numbers are possibly close to 10^69.

It is stated that there is a wide range of estimates given for the number of galaxies in the universe. Some put the number in the very low 100 billions, others bring it much closer to the one trillion mark.

The size of other galaxies range from one million to hundreds of billions of stars. The mass of some of the largest galaxies is trillions of times the mass of our sun. Again, it is supposed that much of this mass consists of dark and exotic matter.

If we consider our galaxy to be of average size, and use the highest estimates for both the number of atoms in our galaxy and the total number of galaxies, then the universe would contain about one trillion times the number of atoms as our galaxy. Since our galaxy probably has no more than 10^69 atoms, this would mean that at most the universe contains 10^69 x 10^12 atoms in all. This works out to be just under 10^81.

If we use lower estimates for the number of atoms in our galaxy and total number of galaxies, then the total number of atoms would be as much as 20 times less, or within the area of 10^79.

Hence, "atoms in the universe" belongs on this page which spans from 10^78 to just under 10^81.

__________________________________________________ _

Most calculations are based on the above assumptions with slighty different numbers given but the above is a reasonable representation of the process.

Here is web page of interest:

Is there a googol of anything (http://fuse.pha.jhu.edu/~bianchi/kit1/googol.html)

-Zeno

[Zeno]

For the math inclined on the forum, here are 236 papes of interesting stuff related, I think, to this thread.

Algorithmic Information Theory (http://www.cs.auckland.ac.nz/CDMTCS/chaitin/cup.pdf)

-Zeno

[tomb8663]

I am not good at math but if you ask me the probability of any of these events happening are 0%. Since C is the closest to 0% I would pick C for all.

[Eihli]

1. C
2. C
3. C
4. C
5. C
6. C

[ill rich]

what is the chance of winning a googolplex digit lottery 100 times in a row?

[T_Nasty]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
C on all. That is, basically as close to impossible as can be.

[/ QUOTE ]

i thought the same thing but i'd go with B on all.

[/ QUOTE ]


That's what I'm going with as well now.

Very interesting exercise, my gut feelings were way off.

[/ QUOTE ]
I did the same thing. I cant quite wrap my mind around how big there numbers are.

Is there any event that would be a C? Obviously you can just do some simple number crunching and find how many times in a row you'd have to win the lottery for it to be a C.

Besides stringing together a chain of events, Is there any one single event that could be considered a C?

Here are some of the most unlikely events I could think of. It's difficult to put numbers on these, but would you consider any of them C's?

New born ostrich solves some unsolved math problem, energy crisis, etc...

Infant runs a mile in &lt;1 second.

Man jumps from the earth to the sun.

The universe disappears on on January 27, 2009 at 12:59 AM EST.

[rebuyboy]

question: is there anything with a probability of happening less than 1/graham's number.

http://en.wikipedia.org/wiki/Graham's_number

[BillNye]

Disclaimer: I'd be happy to get 2/5

1. The chances that you will win the next 100 lotteries in a row.

C

2. The chances that a specific player will hit 500 homeruns this year, assuming everything is random and he normally hits 10.

B (dont follow Baseball that much tho)

3. Your 90 year old grandmother's next 50 bowling games are 300.

A


4. Every single time a poker machine is played for the next million years it will deal a pat Royal Flush.

C (if by poker machine, u mean handheld pkr, online pkr, etc). not sure what you mean tho

5. Your pet parrot, who has been taught to randomly speak every individual sound in the English language, randomly recites Hamlet.

A

6. All players who are capable of reaching the cup from outside the green always sink their chip or drive and never have to put again for the next 50 years.

Really no clue on this one, I'll guess B.


Edit: After thinking about it I'd guess there are no C's. Where are the results?

Btw: instead we should rank these most likely, to least likely, would be very interesting.

[livin_a_lie]

[ QUOTE ]
question: is there anything with a probability of happening less than 1/graham's number.

http://en.wikipedia.org/wiki/Graham's_number

[/ QUOTE ]

That's insane.

this is a good page for those of that are math challenged (http://www-users.cs.york.ac.uk/susan/cyc/g/graham.htm)

[ungar2000]

ranking the events:
1, 3, 2, 6, 4, 5

just an educated guess

[vhawk01]

I love this thread.

And I vote B for all of them except maybe the baseball one, which would be A, but I think its kind of close.

[vhawk01]

David, do you mind if I steal this and use it on some other people? I will even give you credit, or change your examples, whatever you are more comfortable with. Otherwise, I'll have to steal it anyway, but modify it enough so it isn't copying, and I really, really like the way you asked it.

[hasugopher]

I don't claim to be a math expert by any means, but none of these answers should be 'c' and it shouldn't even be close.

[hasugopher]

googol = 10^100, such a massive number it's beyond comprehension.

googolplex = 10^googol = not really sure how to describe it. Just say infinite instead its the same thing basically.

[vhawk01]

[ QUOTE ]
googol = 10^100, such a massive number it's beyond comprehension.

googolplex = 10^googol = not really sure how to describe it. Just say infinite instead its the same thing basically.

[/ QUOTE ]

In reading about evolution, and more importantly, evolution-denial, you tend to come upon things described as "more unlikely that 1 in 'all the atoms in the universe'" quite often. That probably biases me to put things in category B that might actually be in category A, simply because I have some intuitive concept of a googol, and I can imagine something being more unlikely than that (barely). Agreed that none of these are C, and I have a sneaking suspicion none of them are even B...thats what makes this a good thread, to DS. I still stand by my (likely way off) guesses above, though.

[Insp. Clue!So?]

A
B
B
B
B
A

C = probability a famous Swedish Rock group would name itself after an American candy bar.

[CallMeIshmael]

B sounds good for all of them

[ungar2000]

chance of winning lotto:

say for some reason it is 1/10 each trial, being extremely, extremely conservative. (really more like 1/over 1,000,000)

Well, 1/10 to the 100th power is the likelyhood, then, of winning 100 lottos in a row. 10^100 is a googel, so A cannot be right. This is probably that one of the most likely one occurs (probably the baseball one is most likely), but anyway, it stands that A cannot hold for any case, so it is B for all of them. C is ridiculously big, just forget about that.

when are the answers to this coming???

[Tom1975]

I imagine it would be difficult to construct a scenario where the answer would be C without actually using the numbers googol or googolplex in the scenario.

[PairTheBoard]

[ QUOTE ]
I imagine it would be difficult to construct a scenario where the answer would be C without actually using the numbers googol or googolplex in the scenario.

[/ QUOTE ]

Suppose that for any atom, there is 1 chance in 10 billion that in the next second it will behave radioactively and decay away a little subparticle of nuclear energy. Now, consider the Event where every atom in the Universe gives off one of these Freak particles every single second for the next 1,000 years.

PairTheBoard

[Sephus]

[ QUOTE ]
[ QUOTE ]
I imagine it would be difficult to construct a scenario where the answer would be C without actually using the numbers googol or googolplex in the scenario.

[/ QUOTE ]

Suppose that for any atom, there is 1 chance in 10 billion that in the next second it will behave radioactively and decay away a little subparticle of nuclear energy. Now, consider the Event where every atom in the Universe gives off one of these Freak particles every single second for the next 1,000 years.

PairTheBoard

[/ QUOTE ]

it's not immediately clear to me that this would be C.

[chillrob]

[ QUOTE ]
I love this thread.

And I vote B for all of them except maybe the baseball one, which would be A, but I think its kind of close.

[/ QUOTE ]

I would think 3 would be the most likely by far. Rolling a strike 600 times in a row doesn't seem that unbelievable, even for a grandma. This is the only one that, if I heard reported as fact, wouldn't be immediately certain was untrue.

[CallMeIshmael]

[ QUOTE ]
[ QUOTE ]
I imagine it would be difficult to construct a scenario where the answer would be C without actually using the numbers googol or googolplex in the scenario.

[/ QUOTE ]

Suppose that for any atom, there is 1 chance in 10 billion that in the next second it will behave radioactively and decay away a little subparticle of nuclear energy. Now, consider the Event where every atom in the Universe gives off one of these Freak particles every single second for the next 1,000 years.

PairTheBoard

[/ QUOTE ]

This is still in the B range, at least by my calcs

[PairTheBoard]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
I imagine it would be difficult to construct a scenario where the answer would be C without actually using the numbers googol or googolplex in the scenario.

[/ QUOTE ]

Suppose that for any atom, there is 1 chance in 10 billion that in the next second it will behave radioactively and decay away a little subparticle of nuclear energy. Now, consider the Event where every atom in the Universe gives off one of these Freak particles every single second for the next 1,000 years.

PairTheBoard

[/ QUOTE ]

it's not immediately clear to me that this would be C.

[/ QUOTE ]

White:
<font color="white">
Check my math.

1 chance in 10^10 for one atom in the next second. Assuming 10^80 atoms in the Universe, the chance it happens for every single one in the next second would then be,

1 in (10^10)^(10^80) = 10^(10*10^80) = 10^(10^81)

There are over 10^10 seconds in 1000 years so the chance this happens every single seconds for 1000 years is less than,

1 in [10^(10^81)]^(10^10) = 10^(10^91)

So doesn't quite get there. I was thinking there were 10^20 seconds in 1000 years. But if you replace "second" with "millisecond" and "1000 years" with "1 billion years" in the setup, it looks like it just makes it.

</font>

PairTheBoard

[AlexM]

[ QUOTE ]
I love this thread.

And I vote B for all of them except maybe the baseball one, which would be A, but I think its kind of close.

[/ QUOTE ]

I'm pretty sure the baseball one is actually the least likely.

[vhawk01]

[ QUOTE ]
[ QUOTE ]
I love this thread.

And I vote B for all of them except maybe the baseball one, which would be A, but I think its kind of close.

[/ QUOTE ]

I'm pretty sure the baseball one is actually the least likely.

[/ QUOTE ]

Really? Why? I can see someone hitting 100 HR within the actual realm of possibility...500 is a LOT more than that, but enough tobe &gt; winning the lottery 100 times in a row?

[vhawk01]

[ QUOTE ]
David, do you mind if I steal this and use it on some other people? I will even give you credit, or change your examples, whatever you are more comfortable with. Otherwise, I'll have to steal it anyway, but modify it enough so it isn't copying, and I really, really like the way you asked it.

[/ QUOTE ]

Its too late, I already stole it, though I did quote you and attribute it to you. I'm much more interested to see the results from the people I'm testing than a bunch of poker players. /images/graemlins/grin.gif

[Benholio]

I think a lot of people are underestimating the baseball problem. I see it easily qualifying for a 'B'. If we simplify the season to about 550 AB's, we have the following:

The player normally hits 1 HR per 55 AB's.
The player would need to hit 500 homers in 550 AB's.
This is on the same order as drawing the Ace of Spades out of a randomized deck 500 times in 550 tries.

[bottomset]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
I love this thread.

And I vote B for all of them except maybe the baseball one, which would be A, but I think its kind of close.

[/ QUOTE ]

I'm pretty sure the baseball one is actually the least likely.

[/ QUOTE ]

Really? Why? I can see someone hitting 100 HR within the actual realm of possibility...500 is a LOT more than that, but enough tobe &gt; winning the lottery 100 times in a row?

[/ QUOTE ]

its not Barry Bonds, Babe Ruth or any other alltime great hitting, its a weak hitter who likely isn't much better than replacement level or plays Catcher, Shortstop and his value comes from defense

the record for plate appearances is 773, so at best he can succeed with 66% HR rate, Barry Bonds in a top5 season alltime hit a HR 11% of his PA

the player has to hit more HRs than Bonds did in the whole season every single month of the year, and basically can't walk or hit doubles(Bonds walked 177times in 01)

then again a googol is so huge it could still be A if you force pitchers to attempt to get the player out

[vhawk01]

[ QUOTE ]
I think a lot of people are underestimating the baseball problem. I see it easily qualifying for a 'B'. If we simplify the season to about 550 AB's, we have the following:

The player normally hits 1 HR per 55 AB's.
The player would need to hit 500 homers in 550 AB's.
This is on the same order as drawing the Ace of Spades out of a randomized deck 500 times in 550 tries.

[/ QUOTE ]

I think 550 ABs is a really bad simplification for this problem, because when a guy is hitting this many homeruns, he's going to be getting up a whole lot. Think how many outs a normal player makes: thats how many extra games this guy gets to play, at a minimum, assuming his production has no positive effect on the rest of his team (which it will). He is going to get 7-800 PAs, IMO, which changes the probability a whole lot. 500 HR in 500 AB is a lot different than 500 HR in 800 AB.

But of course there are lots of problems. Why in God's name is anyone pitching to this guy? They never would. So, are we allowed to build in to our probability the likelihood of MLB changing the rules and forcing them to never walk Captain Awesome? If so, we have to worry about 500 HR in 800 AB. If not, we have to worry about 500 HR in 150 AB.

[LA_Price]

They are all C except 2 and 3. 3 has probability 0

1 could be finite if you gave a specific lottery on a specific date played through 100 times but since you didn't it's infinite. Basically there could exist a single lottery that you play where the chance of winning it would be bigger than a googelplex

2 not infinite because you said "this year" in which the number of players and at bats will be finite so I think it would be A.

3 is 0 because I don't have a 90 year old grandmother and I couldn't possibly ever have one, although people who have a 90 year old grandmother would give a different answer.

4 theres no way to possibly know how many times the poker machine will be played in the next million years so it's infinite

5 is infinite because new words are created all the time and since you didn't give a static date of language there would always be more possibilities being added as the parrot recited

6. I think is bigger than a googelplex because you don't know how many people are going to play golf and have have the ability to reach the cup from outside the green. Although I could be persuaded this one is B because it has a finite period of time to occur.

[Neuge]

[ QUOTE ]
[ QUOTE ]
I think a lot of people are underestimating the baseball problem. I see it easily qualifying for a 'B'. If we simplify the season to about 550 AB's, we have the following:

The player normally hits 1 HR per 55 AB's.
The player would need to hit 500 homers in 550 AB's.
This is on the same order as drawing the Ace of Spades out of a randomized deck 500 times in 550 tries.

[/ QUOTE ]

I think 550 ABs is a really bad simplification for this problem, because when a guy is hitting this many homeruns, he's going to be getting up a whole lot. Think how many outs a normal player makes: thats how many extra games this guy gets to play, at a minimum, assuming his production has no positive effect on the rest of his team (which it will). He is going to get 7-800 PAs, IMO, which changes the probability a whole lot. 500 HR in 500 AB is a lot different than 500 HR in 800 AB.

But of course there are lots of problems. Why in God's name is anyone pitching to this guy? They never would. So, are we allowed to build in to our probability the likelihood of MLB changing the rules and forcing them to never walk Captain Awesome? If so, we have to worry about 500 HR in 800 AB. If not, we have to worry about 500 HR in 150 AB.

[/ QUOTE ]
A 1 in 55 shot 500 out of 800 times is still well within B, ~10^(674). Hell, a 1 in 6.5 shot (what Bonds hit in '01) 500 out of 800 times is ~10^(200). And the "pitch-to" rule would have to be implemented. Bonds only had 473 at bats in '01 because of his 177 walks, anyone shattering that record beyond comprehension would be walking far more often.

Crap, I was just getting ready to hit submit. These are both exactly 500 out of 800, obviously anything &gt;=500 would still qualify. But, I don't have time to do the rest of the cases and can't automate it. I had to waste enough doing some of the calcs by hand to (just barely) prevent stack overflows. I can't imagine it'd change the answer hundreds of orders of magnitude.

[vhawk01]

Ok, so its definitely B with any sort of assumptions...it would take crazy assumptions to get it down to A.

[btmagnetw]

[ QUOTE ]
3 is 0 because I don't have a 90 year old grandmother and I couldn't possibly ever have one, although people who have a 90 year old grandmother would give a different answer.

[/ QUOTE ]...oook then

edit: i only read your answer to 3 before submitting this but after having read all of them.. you must be the least interesting guy to have any conversation with, ever.

[Jshuttlesworth]

i was thinking C for every one

[JAD]

Guessing A for all simply because I can't wrap my head around even a googol let alone anything larger. PS: I suck at math.

[thylacine]

[ QUOTE ]
[ QUOTE ]
A googol is ten to the hundredth power. In other words one followed by one hundred zeroes.

[/ QUOTE ]


Just to give a gut feel to the size of this lowly number titled a googol, rough estimates as to the number of atoms in the universe are much less than a googol. Estimates usually range near 10^80.

A copy and paste of one such estimate is below just for fun:

Atoms in the Universe

Estimates the the number of atoms in our galaxy to be in the area of 10^68 and, if dark and exotic matter are considered, then their numbers are possibly close to 10^69.

It is stated that there is a wide range of estimates given for the number of galaxies in the universe. Some put the number in the very low 100 billions, others bring it much closer to the one trillion mark.

The size of other galaxies range from one million to hundreds of billions of stars. The mass of some of the largest galaxies is trillions of times the mass of our sun. Again, it is supposed that much of this mass consists of dark and exotic matter.

If we consider our galaxy to be of average size, and use the highest estimates for both the number of atoms in our galaxy and the total number of galaxies, then the universe would contain about one trillion times the number of atoms as our galaxy. Since our galaxy probably has no more than 10^69 atoms, this would mean that at most the universe contains 10^69 x 10^12 atoms in all. This works out to be just under 10^81.

If we use lower estimates for the number of atoms in our galaxy and total number of galaxies, then the total number of atoms would be as much as 20 times less, or within the area of 10^79.

Hence, "atoms in the universe" belongs on this page which spans from 10^78 to just under 10^81.

__________________________________________________ _

Most calculations are based on the above assumptions with slighty different numbers given but the above is a reasonable representation of the process.

Here is web page of interest:

Is there a googol of anything (http://fuse.pha.jhu.edu/~bianchi/kit1/googol.html)

-Zeno

[/ QUOTE ]

There are about one googol of Planck volumes in a cubic centimeter.

If you accept the idea that space is discrete at the Planck scale, then the number of seperate discrete actual physical entities in a cubic centimeter is about one googol.

[Neuge]

[ QUOTE ]
Ok, so its definitely B with any sort of assumptions...it would take crazy assumptions to get it down to A.

[/ QUOTE ]For the 800 at bat season, it would take roughly 1 home run in every 3.75 at bats to make it into category A. That's about 3 times the all-time career best AB/HR average. I'd say that's more than outrageous for a 10 HR/year batter.

[rebuyboy]

what do you people estimate how many home runs he would have to hit to make his chance in category C.. 1000? 10000?

[Neuge]

[ QUOTE ]
what do you people estimate how many home runs he would have to hit to make his chance in category C.. 1000? 10000?

[/ QUOTE ]
It's not possible at all though, the all-time single season record for at bats is 705.

If as many at bats as necessary were possible, for a 10 HR/yr hitter hitting .650 (all home runs), I'd estimate it'd be roughly 10^(1000000000000000000) home runs. That's not a calculation, just an (quasi-)guesstimate, and probably too low.

[FortunaMaximus]

[ QUOTE ]
[ QUOTE ]
what do you people estimate how many home runs he would have to hit to make his chance in category C.. 1000? 10000?

[/ QUOTE ]
It's not possible at all though, the all-time single season record for at bats is 705.

If as many at bats as necessary were possible, for a 10 HR/yr hitter hitting .650 (all home runs), I'd estimate it'd be roughly 10^(1000000000000000000) home runs. That's not a calculation, just an (quasi-)guesstimate, and probably too low.

[/ QUOTE ]

Odd. I went to check that stat out too.

This isn't being pedantic. Just that the specific number of homers isn't the relevant element here. It's a ridiculously improbable event, and you may as well say 300 instead of 500.

IMHO, #1 and #4 are static and independent events and unless I'm missing something here, they're A.

The others don't have probabilistic answers, just a general sense of a vast improbability. Mainly because of the human elements necessary to carry out these tasks.

IMHO, the ability of an individual human being to not stray from a non-existent margin of error actually approaches infinity. It takes a long while in a linear fashion to approach a googol or googolplex, so, yeah.

I'm somewhat of a melted crayon when it comes to articulating concepts that seem obvious to me though, so I don't know how better to describe that.

[Neuge]

[ QUOTE ]
This isn't being pedantic. Just that the specific number of homers isn't the relevant element here. It's a ridiculously improbable event, and you may as well say 300 instead of 500.

[/ QUOTE ]
That was the whole point of the exercise, to determine if an event was a certain extent of "ridiculously improbable." There's a hugely significant difference between something at 1e80 and 1e100, even though both have a practical probability of zero. We've already shown conclusively in this thread that at least two of the scenarios are B, and the rest seem intuitively to be roughly the same (I'm not quite convinced of the bowling one though). Basically, if you don't think there's a difference between 300 and 500 home runs, you're missing the whole point of the thread.

[FortunaMaximus]

[ QUOTE ]
Basically, if you don't think there's a difference between 300 and 500 home runs, you're missing the whole point of the thread.

[/ QUOTE ]

Exactly.

[samsonite2100]

[ QUOTE ]
[ QUOTE ]
Basically, if you don't think there's a difference between 300 and 500 home runs, you're missing the whole point of the thread.

[/ QUOTE ]

Exactly.

[/ QUOTE ]

OK, clearly there's a probabilistic difference between hitting 300 and 500 HRs. Is there a meaningful difference, though? If either one happened, it would be the most mind-blowingly miraculous event in all of human history, and by several orders of magnitude. It seems like this thread is more about people underestimating the size of a googolplex.

[bottomset]

[ QUOTE ]
Basically, if you don't think there's a difference between 300 and 500 home runs, you're missing the whole point of the thread.

[/ QUOTE ]

300hrs might get Bonds01 into A range, but the 10hr guy will still be in the B range, even tying the record PA and not being walked

[CallMeIshmael]

[ QUOTE ]
[ QUOTE ]
Basically, if you don't think there's a difference between 300 and 500 home runs, you're missing the whole point of the thread.

[/ QUOTE ]

Exactly.

[/ QUOTE ]


No, he's not.

Both are hundreds of orders of magnitudes less than 1 in a googol and many many orders more likely than 1 in a gp. This is exaclty the point of the thread.

[FortunaMaximus]

[ QUOTE ]
This isn't being pedantic. Just that the specific number of homers isn't the relevant element here. It's a ridiculously improbable event, and you may as well say 300 instead of 500 as an arbitary value.

[/ QUOTE ]

I was trying to show that trying to find an artificial probability in an event that has 0 chance of happening, somebody hitting 1k or 10k homers in a season has no relevance to the thread.

The probability of hitting 300 is going to be higher than the probability of hitting 500. As CMI said,
it's a matter of difference of orders.

#6 struck a chord with a family member who golfs, that I posed the OP's question to. "Golf balls think." and "There's theory and there's reality." Which I suppose is how most people would see it.

[jackaaron]

[ QUOTE ]

1. The chances that you will win the next 100 lotteries in a row.
C.

2. The chances that a specific player will hit 500 homeruns this year, assuming everything is random and he normally hits 10.
A.

3. Your 90 year old grandmother's next 50 bowling games are 300.

B.

4. Every single time a poker machine is played for the next million years it will deal a pat Royal Flush.

C.

5. Your pet parrot, who has been taught to randomly speak every individual sound in the English language, randomly recites Hamlet.

B.

6. All players who are capable of reaching the cup from outside the green always sink their chip or drive and never have to put again for the next 50 years.

C.



[/ QUOTE ]

[jstnrgrs]

I remember seeing a calculation of the probability that all of the air molocules in a (air tight) room randomly move to the same half of the room (so that hlaf the room has all the air and half the room had no air). I don't remember the answer, but I think it was on the order of 1 in a googleplex.

[hasugopher]

[ QUOTE ]
They are all C except 2 and 3. 3 has probability 0

1 could be finite if you gave a specific lottery on a specific date played through 100 times but since you didn't it's infinite. Basically there could exist a single lottery that you play where the chance of winning it would be bigger than a googelplex

2 not infinite because you said "this year" in which the number of players and at bats will be finite so I think it would be A.

3 is 0 because I don't have a 90 year old grandmother and I couldn't possibly ever have one, although people who have a 90 year old grandmother would give a different answer.

4 theres no way to possibly know how many times the poker machine will be played in the next million years so it's infinite

5 is infinite because new words are created all the time and since you didn't give a static date of language there would always be more possibilities being added as the parrot recited

6. I think is bigger than a googelplex because you don't know how many people are going to play golf and have have the ability to reach the cup from outside the green. Although I could be persuaded this one is B because it has a finite period of time to occur.

[/ QUOTE ]
no (to most of what is written)

I just cashed a check from pokerstars for $10,000. That's a nice $10^4 payday (true).

Last I heard, sbrugby had a solid $million in his FTP account. $10^6.

The US National debt? About $10^13 (10 trillion)

approximate number of atoms in my body? 10^28

in the universe? 10^80

now, a googol is 1.0*10^100, so that right there puts us about 20 orders of magnitude more than number of atoms in the universe.

We could just say # of atoms in universe = googol*sextillion (which is 10^21, a number most people cant even appreciate).

Now to go back to the point, a googolplex is 1^googol. A googol orders of magnitude! It's not something that's supposed to be used to relate 'extremely unlikely' events to. In all actuality, despite what one might seem to think they 'know', all of these events are extraordinarily LIKELY in relation to 1/googolplex.

none are infinitely unlikely nor mathematically close.

[thylacine]

[ QUOTE ]
I remember seeing a calculation of the probability that all of the air molocules in a (air tight) room randomly move to the same half of the room (so that hlaf the room has all the air and half the room had no air). I don't remember the answer, but I think it was on the order of 1 in a googleplex.

[/ QUOTE ]

I'm going to guess that's about 1 in 10^(10^(25)) which is extremely more unlikely than anything in the OP, but still nowhere near 1 in 10^(10^(100)).

[LA_Price]

[ QUOTE ]
no (to most of what is written)

I just cashed a check from pokerstars for $10,000. That's a nice $10^4 payday (true).

Last I heard, sbrugby had a solid $million in his FTP account. $10^6.

The US National debt? About $10^13 (10 trillion)

approximate number of atoms in my body? 10^28

in the universe? 10^80

now, a googol is 1.0*10^100, so that right there puts us about 20 orders of magnitude more than number of atoms in the universe.

We could just say # of atoms in universe = googol*sextillion (which is 10^21, a number most people cant even appreciate).

Now to go back to the point, a googolplex is 1^googol. A googol orders of magnitude! It's not something that's supposed to be used to relate 'extremely unlikely' events to. In all actuality, despite what one might seem to think they 'know', all of these events are extraordinarily LIKELY in relation to 1/googolplex.

none are infinitely unlikely nor mathematically close.

[/ QUOTE ]

I don't know what this response really means but whenever you are talking about infinity(which would be response C) the language and grammer with which you ask the question is vitally important. You can't just consider the questions based on their mathematical element. Any number no matter how large, whether its a google, a googleplex, or whatever is infinetely far from infinity. The questions I answered and said were infinite all contained what could be interpreted from the language in which they were asked, an unbounded or infinite element, making the whole question infinite.

I just noticed I misread question five and noticed David said "every sound" in the english language, and since there are a finite number of sounds I think it would be B.

[hasugopher]

[ QUOTE ]
[ QUOTE ]
no (to most of what is written)

I just cashed a check from pokerstars for $10,000. That's a nice $10^4 payday (true).

Last I heard, sbrugby had a solid $million in his FTP account. $10^6.

The US National debt? About $10^13 (10 trillion)

approximate number of atoms in my body? 10^28

in the universe? 10^80

now, a googol is 1.0*10^100, so that right there puts us about 20 orders of magnitude more than number of atoms in the universe.

We could just say # of atoms in universe = googol*sextillion (which is 10^21, a number most people cant even appreciate).

Now to go back to the point, a googolplex is 1^googol. A googol orders of magnitude! It's not something that's supposed to be used to relate 'extremely unlikely' events to. In all actuality, despite what one might seem to think they 'know', all of these events are extraordinarily LIKELY in relation to 1/googolplex.

none are infinitely unlikely nor mathematically close.

[/ QUOTE ]

I don't know what this response really means but whenever you are talking about infinity(which would be response C) the language and grammer with which you ask the question is vitally important. You can't just consider the questions based on their mathematical element. Any number no matter how large, whether its a google, a googleplex, or whatever is infinetely far from infinity. The questions I answered and said were infinite all contained what could be interpreted from the language in which they were asked, an unbounded or infinite element, making the whole question infinite.

I just noticed I misread question five and noticed David said "every sound" in the english language, and since there are a finite number of sounds I think it would be B.

[/ QUOTE ]
I'm actually glad you posted this because what I ended up trying to convey (the vastness of the numbers involved) was different then what I started the post with (quoting and disagreeing with what you said).

Good point about the infinite aspect. However, my contention (that I never got around to making) is that none of these, even in the words in which they were asked, contain an infinite element. Let me try to give an example, and keep your imagination open.

Let's talk about our grandmother's bowling game. What are the chances that she rolls a strike? One in 10,000? One in a billion? One in a quadrillion (lol)? Obviously it doesn't matter. Even 600 times in a row. We have a googol orders of magnitude to work with.

More importantly, I assume you don't have a 90 year old grandma, hence the infinite element. How sure are you though? 1,000,000,000:1? 1,000,000,000,000:1? Think about the wildest possible imagination where what you think could turn out to be completely wrong. Say your mother was delivered to the wrong mother, or you have a yet to be discovered mental illness that screws with your memory. There are countless other things that could be imagined. Even combined, what is the probability of all this? Obviously extraordinarily low. But how low? Would you be comfortable in saying 10^10:1 against? 10^100:1 against? What about 10^1000:1 against? If you honestly and genuinely said yes to all three of those, then you really are crazy. /images/graemlins/smile.gif

If anything I'm trying to argue doesn't make any sense, just let me know. It's pretty late for me over here. In all seriousness though, this is far from what Sklansky intended for this thread to be (I think?) so I'll just leave it alone from here on out.

[hasugopher]

I just reread my post and it's pretty clear that it isn't the angle sklansky or anybody else was looking for. I do think it's somewhat interesting though and technically correct. It's amazing what a few beers and being extremely tired can do to you. /images/graemlins/smile.gif

[jogger08152]

Hey Dave,

You mind answering these also?

Thanks,
Jogger

[hasugopher]

[ QUOTE ]
Hey Dave,

You mind answering these also?

Thanks,
Jogger

[/ QUOTE ]
I don't want to steal david's thunder, but most of these are pretty easy to figure out and should be very clear which category they fall in. For example, question number 1 can be written as 50,000,000^100, assuming the probability of winning the lottery = 1 in 50 million. Obviously more than 10^100, but still approximately 0% to one/googolplex, so the answer is B.

[jogger08152]

[ QUOTE ]
[ QUOTE ]
Hey Dave,

You mind answering these also?

Thanks,
Jogger

[/ QUOTE ]
I don't want to steal david's thunder, but most of these are pretty easy to figure out and should be very clear which category they fall in. For example, question number 1 can be written as 50,000,000^100, assuming the probability of winning the lottery = 1 in 50 million. Obviously more than 10^100, but still approximately 0% to one/googolplex, so the answer is B.

[/ QUOTE ]
What are the answers to 2, 4 (include your assumption for play frequency) and 5-6?

[hasugopher]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Hey Dave,

You mind answering these also?

Thanks,
Jogger

[/ QUOTE ]
I don't want to steal david's thunder, but most of these are pretty easy to figure out and should be very clear which category they fall in. For example, question number 1 can be written as 50,000,000^100, assuming the probability of winning the lottery = 1 in 50 million. Obviously more than 10^100, but still approximately 0% to one/googolplex, so the answer is B.

[/ QUOTE ]
What are the answers to 2, 4 (include your assumption for play frequency) and 5-6?

[/ QUOTE ]
going on the assumption that these are all unrelated, independent events, white: <font color="white">

2. Let's say the guy gets 500 AB a year, which is obviously a low estimate for an everyday MLB player. It also makes things conveniently simple for me.

2% chance of a HR/at-bat, so 1 in 50^500, B.

4. I think this question was specifically asked because this is largely a poker forum and the answers would heavily be swayed towards C. Same thing would happen if say, you posted a 'basketball miracle' on an NBA forum. An english or literary major would almost certainly feel the same way about #5.

Anyway, the probability of hitting a pat royal flush on any given deal is 1 in 649,740. Let's just say 1 in a million. Let's say it's played a billion times.

1,000,000^1,000,000,000

clearly more than 10^100. Still about 0% to 10^googol. So B. It's really hard to explain the difference between googol and 10^googol. Like, you take 10^100 and get a googol (more than the number of atoms in the universe with about 20 orders of magnitude to spare). So you take 10^googol, crazy stuff.

5. hmmmm, taking a (educated) guess, it should most certainly be B. I don't claim to be an english or shakespeare? master, but say there are 100 sounds in our language and 10,000 words in hamlet. Say each word has 5 individual sounds. 100^50,000, so B.

6. Golf question. This is far from correct, but take any reasonable X^Y and you will get B. X = chance of making long shot; Y = number of occurances. Take any not-so-reasonable X^Y and you still get B.

Hope this helps and you enjoyed it /images/graemlins/smile.gif

sorry david


</font>

[Raydain]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Hey Dave,

You mind answering these also?

Thanks,
Jogger

[/ QUOTE ]
I don't want to steal david's thunder, but most of these are pretty easy to figure out and should be very clear which category they fall in. For example, question number 1 can be written as 50,000,000^100, assuming the probability of winning the lottery = 1 in 50 million. Obviously more than 10^100, but still approximately 0% to one/googolplex, so the answer is B.

[/ QUOTE ]
What are the answers to 2, 4 (include your assumption for play frequency) and 5-6?

[/ QUOTE ]
going on the assumption that these are all unrelated, independent events, white: <font color="white">

2. Let's say the guy gets 500 AB a year, which is obviously a low estimate for an everyday MLB player. It also makes things conveniently simple for me.

2% chance of a HR/at-bat, so 1 in 50^500, B.

4. I think this question was specifically asked because this is largely a poker forum and the answers would heavily be swayed towards C. Same thing would happen if say, you posted a 'basketball miracle' on an NBA forum. An english or literary major would almost certainly feel the same way about #5.

Anyway, the probability of hitting a pat royal flush on any given deal is 1 in 649,740. Let's just say 1 in a million. Let's say it's played a billion times.

1,000,000^1,000,000,000

clearly more than 10^100. Still about 0% to 10^googol. So B. It's really hard to explain the difference between googol and 10^googol. Like, you take 10^100 and get a googol (more than the number of atoms in the universe with about 20 orders of magnitude to spare). So you take 10^googol, crazy stuff.

5. hmmmm, taking a (educated) guess, it should most certainly be B. I don't claim to be an english or shakespeare? master, but say there are 100 sounds in our language and 10,000 words in hamlet. Say each word has 5 individual sounds. 100^50,000, so B.

6. Golf question. This is far from correct, but take any reasonable X^Y and you will get B. X = chance of making long shot; Y = number of occurances. Take any not-so-reasonable X^Y and you still get B.

Hope this helps and you enjoyed it /images/graemlins/smile.gif

sorry david


</font>

[/ QUOTE ]

Way to steal David's thunder jackass. Who would've known someone else could solve the answers using mathecamatics.

[Fight Club]

thinking about a googolplex makes my head explode

my first thought is that C isn't used, with just As and Bs.

[hasugopher]

[ QUOTE ]
Way to steal David's thunder jackass. Who would've known someone else could solve the answers using mathecamatics.

[/ QUOTE ]
some things you may want to consider before you go around calling people a 'jackass':

1. The thread has been dead for pretty much a week.

2. There was actually a LOT of math work done in this thread before I ever even posted here. Scroll up, look in white in particular.

3. It's a subject that appealed to me, somebody was asking for help, and I felt the best thing to do would be to try to help them. It is the science, MATH, and philosophy forum, you know. /images/graemlins/smile.gif

cheers

[Double Down]

Sorry, quick question about a googolplex.

It is googol X googol, so mathematically speaking, it's a 1 with 200 zeroes behind it, yes?

[Double Down]

nevermind. Just researched it. A one with a googol zeroes. Got it. LOL yeah, none of those examples are remotely C. Especially since my grandmother is an awesome bowler, and she didn't even hit her stride till her late 80's.

[jogger08152]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Hey Dave,

You mind answering these also?

Thanks,
Jogger

[/ QUOTE ]
I don't want to steal david's thunder, but most of these are pretty easy to figure out and should be very clear which category they fall in. For example, question number 1 can be written as 50,000,000^100, assuming the probability of winning the lottery = 1 in 50 million. Obviously more than 10^100, but still approximately 0% to one/googolplex, so the answer is B.

[/ QUOTE ]
What are the answers to 2, 4 (include your assumption for play frequency) and 5-6?

[/ QUOTE ]
going on the assumption that these are all unrelated, independent events, white: <font color="white">

2. Let's say the guy gets 500 AB a year, which is obviously a low estimate for an everyday MLB player. It also makes things conveniently simple for me.

2% chance of a HR/at-bat, so 1 in 50^500, B.

4. I think this question was specifically asked because this is largely a poker forum and the answers would heavily be swayed towards C. Same thing would happen if say, you posted a 'basketball miracle' on an NBA forum. An english or literary major would almost certainly feel the same way about #5.

Anyway, the probability of hitting a pat royal flush on any given deal is 1 in 649,740. Let's just say 1 in a million. Let's say it's played a billion times.

1,000,000^1,000,000,000

clearly more than 10^100. Still about 0% to 10^googol. So B. It's really hard to explain the difference between googol and 10^googol. Like, you take 10^100 and get a googol (more than the number of atoms in the universe with about 20 orders of magnitude to spare). So you take 10^googol, crazy stuff.

5. hmmmm, taking a (educated) guess, it should most certainly be B. I don't claim to be an english or shakespeare? master, but say there are 100 sounds in our language and 10,000 words in hamlet. Say each word has 5 individual sounds. 100^50,000, so B.

6. Golf question. This is far from correct, but take any reasonable X^Y and you will get B. X = chance of making long shot; Y = number of occurances. Take any not-so-reasonable X^Y and you still get B.

Hope this helps and you enjoyed it /images/graemlins/smile.gif

sorry david


</font>

[/ QUOTE ]

I did! Thanks for the reply! /images/graemlins/smile.gif

[askrak]

[ QUOTE ]
googol = 10^100, such a massive number it's beyond comprehension.

googolplex = 10^googol = not really sure how to describe it. Just say infinite instead its the same thing basically.

[/ QUOTE ]

1 is as close to infinity as a googleplex so that makes no sense

[ QUOTE ]

thinking about a googolplex makes my head explode

my first thought is that C isn't used, with just As and Bs.

[/ QUOTE ]
agree to quote carl sagan in cosmos(greates science documentary ever) "A piece of paper large enough to contain all the zeroes in a googleplex could'nt be stuffed into the known universe"

[vhawk01]

[ QUOTE ]
[ QUOTE ]
googol = 10^100, such a massive number it's beyond comprehension.

googolplex = 10^googol = not really sure how to describe it. Just say infinite instead its the same thing basically.

[/ QUOTE ]

1 is as close to infinity as a googleplex so that makes no sense

[ QUOTE ]

thinking about a googolplex makes my head explode

my first thought is that C isn't used, with just As and Bs.

[/ QUOTE ]
agree to quote carl sagan in cosmos(greates science documentary ever) "A piece of paper large enough to contain all the zeroes in a googleplex could'nt be stuffed into the known universe"

[/ QUOTE ]

What font size? 'Cause, like, sure if its 12 point Arial double-spaced or something but...

[PairTheBoard]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
googol = 10^100, such a massive number it's beyond comprehension.

googolplex = 10^googol = not really sure how to describe it. Just say infinite instead its the same thing basically.

[/ QUOTE ]

1 is as close to infinity as a googleplex so that makes no sense

[ QUOTE ]

thinking about a googolplex makes my head explode

my first thought is that C isn't used, with just As and Bs.

[/ QUOTE ]
agree to quote carl sagan in cosmos(greates science documentary ever) "A piece of paper large enough to contain all the zeroes in a googleplex could'nt be stuffed into the known universe"

[/ QUOTE ]

What font size? 'Cause, like, sure if its 12 point Arial double-spaced or something but...

[/ QUOTE ]

If they were the size of an atom they might fit ok. Taking the Diameter of an atom to be 10^(-8) cm, you could fit 10^24 zeros of that size in a cubic centimeter. With 10^80 atoms in the Universe you could do it if you have 1 cubic centemeter of open space in the Universe for every atom in the universe, which seems likely to me. I'm not sure where you would get paper as thin as an atom though. What would you make it out of?

Of course that's just the zeros in a googolplex. There's only a googol of those.

PairTheBoard

[hasugopher]

[ QUOTE ]
[ QUOTE ]
googol = 10^100, such a massive number it's beyond comprehension.

googolplex = 10^googol = not really sure how to describe it. Just say infinite instead its the same thing basically.

[/ QUOTE ]

1 is as close to infinity as a googleplex so that makes no sense

[ QUOTE ]

thinking about a googolplex makes my head explode

my first thought is that C isn't used, with just As and Bs.

[/ QUOTE ]
agree to quote carl sagan in cosmos(greates science documentary ever) "A piece of paper large enough to contain all the zeroes in a googleplex could'nt be stuffed into the known universe"

[/ QUOTE ]
probably a poor choice of words by me, but I hope others got the gist of what I was trying to say.

[Hawklet]

I don't think any of these can possibly be C.

C requries a seemingly infinitly possible event occuring over an infinately big distance for an infinite number of times.

I.e. the chances of every electron in the world forming a line in the molocule parallel to every other electron line in the universe.