From: David Clounch <david.clounch@gmail.com>

Date: Sun Jun 21 2009 - 17:01:49 EDT

Date: Sun Jun 21 2009 - 17:01:49 EDT

Lets start with a simpler example. I asked my son this question over the

weekend:

D: "Suppose the room we are in contains 100 rubber balls, all identical

except for color. I state that the probability of the balls being blue is

0.97 and the probability of them being red is 0.03."

J: "ok"

D: "How many of the balls are red?"

J: 3

D: "Thats right! The probability is the fraction of red balls divided by

the whole set. So, do we know which are red?"

J: "No."

D: "Correct. Now, suppose I tell you the probability of being red is

0.0000000001. Now how many red balls are in the room?"

J: "Zero."

D: "That is correct. But Why?"

J: "Because you can't have a fraction of a ball and still have it be a

ball. To have one red ball you would need a sample size of 10000000000

balls. To have three red balls you would need a sample space of

30000000000."

D: "And how confident are you that you are correct?"

J: "very confident."

J later pointed out that this meaning of probability (probability is a

fraction of existing states being populated) is different than the common

sense of probability most people use. The latter is more like "there is a 30

percent chance it will rain today, meaning it might or might not happen."

At this point we had an argument. I stated that the 30% chance really means

its is raining over 30% of the area - but that we cannot know if we are at

one of those spots until it happens. In fact we cannot know if anybody is

going to be at a rainy spot just like we cannot know which 3 balls in the

room are red. But we do know that 3 balls are red (without even looking).

But we couldnt agree as to why the weatherman's meaning is different than

the meaning in physics. J proposed the weatherman is predicting a future

event that may or may not take place, not a fraction of states that exist

right now. I pointed out that is more like wishful thinking or guessing

than computing a fraction based on knowledge and laws.

And he then said something very much like what Jim said ---- "any very

unlikely event can still take place - for example, I might tunnel to New

York City any moment now because there's a tiny probability this could

take place."

I then asked him if he carries subway tokens in his pockets just in case.

His answer was "no - nobody expects such an event to really happen".

To which I pointed out that if he were to expect such an event, and take

it seriously, then to me he would be acting as if he believes in the flying

spaghetti monster. He looked at me a bit puzzled. I told him,

D: "Look at it this way J. Suppose you are standing on the edge of Lake

Michigan in Chicago on August 15th and its 95 in the shade. We both agree

there is a tiny probability all the kinetic energy in the water could

spontaneously tunnel to the north end of the lake, leaving the lake near

Chicago to freeze solid. Right? "

J: "Right."

D: "So, do we wear our coats, caps, and mittens to the beach?"

J: "ha ha."

D: The expectation value is so low nobody believes it will really happen.

Right."

J: Nods his head.

D: "Thats why John Wheeler wrote that events that have a probability of less

that 1x10^-50 don't exist. Don't actually happen."

J: "OK, but whats the point?"

D: "the point is some people I know are trying to tell me that events less

likely that Wheelers number take place not once, not twice, but billions

of times in a row. Even though the expectation is so low nobody believes

even one event will ever happen anywhere in the universe. Its like our

cousin Vinny who thinks he can win the lottery 1000 times in a row. "

J: Looks at me kinda funny.

D: "J, when someone tells me those events are taking place many times in a

row, I think what what they are really saying, if they are rational, is

the expectation value is way higher than is commonly believed."

J: "Yeah, and why couldn't it be way higher?".

D: "I'm not saying it couldn't. This is where the flying spaghetti monster

part comes in. They don't try to show there is a higher expectation value.

Instead they claim events with a probability 0f 10^-2000 (for example)

actually happen many times a day. Thats the flying spaghetti monster

part. To me its a kind of magical belief. I just cannot believe in it."

Well, it was obvious at this point J didnt like me invoking language about

the flying spaghetti monster.

He then started to tell me about muon decay and why it is all neutrinos in

the universe are all left handed even though no known law of nature says

they should be. His point was it is purely statistical. I told him its

because the mechanism has a partition function that says every surviving

neutrino is likely to be left handed - thus producing the statistics.

And the key is *always* finding the partition function.

Which brings me back to Jim Armstrong and the helium example. The partition

function gives the probability of a helium atom being excited. If you want

to change the probability you raise the temperature. But that detail was

for another posting.

On Thu, Jun 18, 2009 at 11:44 AM, David Clounch <david.clounch@gmail.com>wrote:

*>
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*>
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*> On Thu, Jun 18, 2009 at 10:46 AM, Jim Armstrong <jarmstro@qwest.net>wrote:
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*>
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*>> I think extraordinarily improbable events DO take place every day.
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*>>
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*>
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*> Jim,
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*>
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*> One needs to quantify what "improbable" means.
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*>
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*> So, let me ask this. Lets assume we have a very large box containing
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*> helium gas. Pick any size box you want, lets say its solar system sized.
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*> The temperature is 300K and the pressure is 1 atmosphere.
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*>
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*> How many helium atoms are excited above ground level to the next higher
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*> level?
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*>
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*> Best Regards,
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*> -Dave
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*>
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*>
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*>
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*>
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Received on Sun Jun 21 17:02:23 2009

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