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Arguments from improbable events

RoyLatham
Posts: 4,488
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2/21/2011 4:13:34 AM
Posted: 5 years ago
Suppose an event has one chance in 10^66 of occurring. Do you think you will see such an event?

To put his into perspective, there have been about 5 x 10^17 seconds in the life of the universe. If events of the improbable sort might occur every nanosecond, that would still be only 5 x 10^26 rolls of the dice, as it were. 10^44 lifetimes-of-the-universe would be required before the event occurred, on average.

The event is dealing a specific hand of bridge in a particular order. There are 52 choices for the first card, 51 for the second ... or 52! ways of dealing the deck. 52! is about 8 x 10^67. Yet despite the utterly negligible probability, every time the deck is dealt, one of the events appears.

Related errors in computing probabilities are common in claims about the probability of a universe supporting life, life occurring on earth, or the probability of humans evolving.
Puck
Posts: 6,457
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2/21/2011 4:33:38 AM
Posted: 5 years ago
At 2/21/2011 4:13:34 AM, RoyLatham wrote:
Related errors in computing probabilities are common in claims about the probability of a universe supporting life, life occurring on earth, or the probability of humans evolving.

Such arguments also tend to treat probability as an abstraction and ignore causality. A coin toss for example we apply a 50/50 probability. It's simply shorthand for saying 'we don't have the physics for the coin toss worked out' - the result of the toss is deterministic, not 50/50 - we just don't have access to that in most cases and so apply the probability.
Thaddeus
Posts: 6,985
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2/21/2011 4:53:36 AM
Posted: 5 years ago
At 2/21/2011 4:13:34 AM, RoyLatham wrote:
Suppose an event has one chance in 10^66 of occurring. Do you think you will see such an event?

To put his into perspective, there have been about 5 x 10^17 seconds in the life of the universe. If events of the improbable sort might occur every nanosecond, that would still be only 5 x 10^26 rolls of the dice, as it were. 10^44 lifetimes-of-the-universe would be required before the event occurred, on average.

The event is dealing a specific hand of bridge in a particular order. There are 52 choices for the first card, 51 for the second ... or 52! ways of dealing the deck. 52! is about 8 x 10^67. Yet despite the utterly negligible probability, every time the deck is dealt, one of the events appears.

Related errors in computing probabilities are common in claims about the probability of a universe supporting life, life occurring on earth, or the probability of humans evolving.

Also with the life thing; we can't see how many times that particular "deck" was not dealt because of the observer bias of life having had to have formed before we can observe it.
Cerebral_Narcissist
Posts: 10,806
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2/21/2011 9:16:58 AM
Posted: 5 years ago
If you do not know how many times the die was rolled etc etc. Probability argumens are the recourse of lesser minds.
I am voting for Innomen because of his intelligence, common sense, humility and the fact that Juggle appears to listen to him. Any other Presidential style would have a large sub-section of the site up in arms. If I was President I would destroy the site though elitism, others would let it run riot. Innomen represents a middle way that works, neither draconian nor anarchic and that is the only way things can work. Plus he does it all without ego trips.
CosmicAlfonzo
Posts: 5,955
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2/21/2011 9:46:12 AM
Posted: 5 years ago
At 2/21/2011 4:33:38 AM, Puck wrote:
Such arguments also tend to treat probability as an abstraction and ignore causality. A coin toss for example we apply a 50/50 probability. It's simply shorthand for saying 'we don't have the physics for the coin toss worked out' - the result of the toss is deterministic, not 50/50 - we just don't have access to that in most cases and so apply the probability.
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RoyLatham
Posts: 4,488
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2/23/2011 8:51:36 AM
Posted: 5 years ago
At 2/21/2011 4:33:38 AM, Puck wrote:

Such arguments also tend to treat probability as an abstraction and ignore causality. A coin toss for example we apply a 50/50 probability. It's simply shorthand for saying 'we don't have the physics for the coin toss worked out' - the result of the toss is deterministic, not 50/50 - we just don't have access to that in most cases and so apply the probability.

In the case of shuffling and dealing cards, the deterministic causes are clear, but it is still way more convenient to deal with the probabilities. Point is that an ability to predict the individual outcomes wouldn't have much effect on how the events are treated.

Modern physics claims that some events are truly random and unpredictable at any level of understanding. These include Heisenburg uncertainty, quantum fluctuations, and individual particle decay events. If there were no such genuinely unpredictable events the universe could not function as it does. So perhaps such events come into play in such things as shuffling cards. I dunno.
Thaddeus
Posts: 6,985
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2/23/2011 8:56:21 AM
Posted: 5 years ago
At 2/23/2011 8:51:36 AM, RoyLatham wrote:
At 2/21/2011 4:33:38 AM, Puck wrote:

Such arguments also tend to treat probability as an abstraction and ignore causality. A coin toss for example we apply a 50/50 probability. It's simply shorthand for saying 'we don't have the physics for the coin toss worked out' - the result of the toss is deterministic, not 50/50 - we just don't have access to that in most cases and so apply the probability.

In the case of shuffling and dealing cards, the deterministic causes are clear, but it is still way more convenient to deal with the probabilities. Point is that an ability to predict the individual outcomes wouldn't have much effect on how the events are treated.

Modern physics claims that some events are truly random and unpredictable at any level of understanding. These include Heisenburg uncertainty, quantum fluctuations, and individual particle decay events. If there were no such genuinely unpredictable events the universe could not function as it does. So perhaps such events come into play in such things as shuffling cards. I dunno.

Unpredictable, yes. Random, not necessarily.
RoyLatham
Posts: 4,488
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2/23/2011 12:11:51 PM
Posted: 5 years ago
At 2/23/2011 8:56:21 AM, Thaddeus wrote:

Unpredictable, yes. Random, not necessarily.

No, they are genuinely random, and they have to be random for the universe to function. For example, it's not that an electron has a position that cannot be measured, it is that the electron's position only exists as a probability distribution.

I think this poses a problem for the philosophical debate on free will vs. determinism. Determinism cannot exist according to the laws of nature. That means it cannot be postulated to exist and be consistent with nature as it is. That poses a challenge to defining "determinism" in a philosophical debate.
Puck
Posts: 6,457
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2/24/2011 1:06:31 AM
Posted: 5 years ago
At 2/23/2011 8:51:36 AM, RoyLatham wrote:
In the case of shuffling and dealing cards, the deterministic causes are clear, but it is still way more convenient to deal with the probabilities. Point is that an ability to predict the individual outcomes wouldn't have much effect on how the events are treated.

Yeah, it was more in relation to the types of arguments made from probability, in that they treat the probability itself as a 'thing' devoid of context, context being in most cases for these arguments, natural processes which includes causality etc.

Modern physics claims that some events are truly random and unpredictable at any level of understanding. These include Heisenburg uncertainty, quantum fluctuations, and individual particle decay events. If there were no such genuinely unpredictable events the universe could not function as it does. So perhaps such events come into play in such things as shuffling cards. I dunno.

This article: http://www.science20.com...
discusses what I think your point is (determinism vs. non in quantum systems), interesting to read nonetheless.
Cliff.Stamp
Posts: 2,169
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2/24/2011 9:29:14 AM
Posted: 5 years ago
At 2/21/2011 4:13:34 AM, RoyLatham wrote:

Suppose an event has one chance in 10^66 of occurring. Do you think you will see such an event?

Yes, and for events which are much lower than that as well. Everyone sees them every day, you are seeing them right now all around you. You can reduce the probability of any observable event down to an infinitismal amount simply by adding more constraints and describing the event in more detail.
PervRat
Posts: 963
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3/9/2011 12:04:37 AM
Posted: 5 years ago
At 2/21/2011 4:13:34 AM, RoyLatham wrote:
Suppose an event has one chance in 10^66 of occurring. Do you think you will see such an event?

To put his into perspective, there have been about 5 x 10^17 seconds in the life of the universe. If events of the improbable sort might occur every nanosecond, that would still be only 5 x 10^26 rolls of the dice, as it were. 10^44 lifetimes-of-the-universe would be required before the event occurred, on average.

The event is dealing a specific hand of bridge in a particular order. There are 52 choices for the first card, 51 for the second ... or 52! ways of dealing the deck. 52! is about 8 x 10^67. Yet despite the utterly negligible probability, every time the deck is dealt, one of the events appears.

Related errors in computing probabilities are common in claims about the probability of a universe supporting life, life occurring on earth, or the probability of humans evolving.

A lot of it depends on context. Supernovae are exceptionally rare events, in that the chance that a star will go supernova at a certain time (or even within a human lifetime, say 80 years) is exceptionally rare. However, the chance of being able to see and witness a supernova in your life is actually not so exceptionally rare, because there is such an enormous number of stars, and a supernova in particular is so very powerful and puts out so much light, it can be visible to the naked eye even in galaxies so distant that the human eye cannot distinguish individual stars in the galaxy.

The context for supernova is different in terms of whether you can expect to witness one in your lifetime primarily because of how visible a supernova event is. An even that is not so visible from so far away that has an equal probability to a supernova, chances are much lower that you'd get to witness one since you would have to be much closer to such an event (given its lower visibility) to witness it.
Illegalcombatant
Posts: 4,008
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4/12/2011 6:29:27 AM
Posted: 5 years ago
Here is another way of looking at probabilities, they mean nothing. Either something happens or it doesn't.

When something happens, does it check with the statistical theory, oh hang on, I am a very unlikely event, so I had better not happen.

I'm sure there is some implication here, I just don't know what that is.
"Seems like another attempt to insert God into areas our knowledge has yet to penetrate. You figure God would be bigger than the gaps of our ignorance." Drafterman 19/5/12