Probability of nature coming up with Beethoven's 'Fate' by chance?

siti said:

The probability of an event that has already happened is 1 - it makes no difference how you attempt to explain it - blind chance, reductive materialism or divine intent...

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We are not talking of conditional probability.

... you want us to imagine ourselves back at the moment of the Big Bang ....

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Of course no. We have a model beginning at Big Bang, characterised by non-sentience, evolving naturally to a stage where there are beings who create stupendously and there are beings who can relish such creations.

atanu said:

We are not talking of conditional probability.

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Oh I see! And that changes the probability of an event that has happened how exactly?

atanu said:

We have a model beginning at Big Bang, characterised by non-sentience, evolving naturally to a stage where there are beings who create stupendously and there are beings who can relish such creations.

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Yes we do indeed have such a model. And this changes the probability of an event that has happened how exactly?

siti said:

Oh I see! And that changes the probability of an event that has happened how exactly?
Yes we do indeed have such a model. And this changes the probability of an event that has happened how exactly?

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Because you a got ‘Tail’ does not change the probability of getting ‘Tail’ to 1.

atanu said:

Because you a got ‘Tail’ does not change the probability of getting ‘Tail’ to 1.

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Yes it does - and that has nothing to do with conditional probability.

siti said:

Yes it does - and that has nothing to do with conditional probability.

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Please explain.

atanu said:

Please explain.

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Conditional probability is about calculating the probability of an event given that another event has already happened.

Suppose I want to calculate the probability of getting at least 2 tails in 3 coin tosses...

The unconditional probability is 0.5 because there are 4 ways of getting 2 or more tails: TTT, TTH, THT, HTT; and four ways of getting less than 2 tails: HHH, HHT, HTH, THH so 4/8 = 0.5

But the conditional probability of getting two or more tails in 3 tosses GIVEN that at least one turns up tails is 0.75 because there 3 ways of getting at least 1 tail on the two remaining tosses: TH, HT and TT as opposed to only 1 way of getting no tails: HH.

We could write that P(A|B) where event A would be getting at least two out of three tails and B would be the condition that at least one toss turns out tails

But to write P(A|A) - apart from making no sense - would express the probability of event A occurring given that event A occurs - or in the coin toss thing - getting at least two tails given that we get at least two tails...and that can only ever be exactly 1.

Unless you are asking us to place ourselves prior to the composition of Beethoven's symphony and (pretending that we do not know that this is a universe that has produced Beethoven's symphony) calculate the odds from that perspective (which of course we couldn't possibly), what you are asking is for us to calculate the odds of a universe that has produced Beethoven's symphony (being as it is the only universe we know about) producing Beethoven's symphony given that it is a universe that has produced Beethoven's symphony.

The answer is still 1 - I'm sure of that - but I still don't understand the question!

siti said:

- but I still don't understand the question!

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I think I will leave at that.

blü 2 said:

We know the probability is 1.00.

Beethoven's brain had no other source than nature, after all, and it was chance that put him in a musical culture in the right time and place.

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These are crap answers, presuming miracle.

bharti said:

These are crap answers, presuming miracle.

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No, that's exactly what they don't presume.

The chance of something happening once it's already happened is 1.00.

There is nothing magical about the occurrence of people with particular kinds of genius, whether for music, maths or chess (some say the three are related), for painting or sculpture, for technical design and esthetic design, for various kinds of organizing and leadership ─ and so on.

Beethoven was a product of a time, a place and a culture that clicked with his genius. If he'd been brought up in a culture from Africa, India, the Arabic world, China, and so on, it would be extremely likely we'd never have heard of him.

The chances of having drunk a glass of water with the specific water molecules as the one you just drank are exactly as vanishingly small as the chances of drinking one in the future with some specific combination.

Yet we do it all the time without thinking about it.

atanu said:

What is the probability?

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Please do not bring in the subject of intelligent design -- pro or against. Let us please stick to actual statistical calculations only.

Or just enjoy the stupendous creation.

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Since there is no natural process that produces musical compositions by any means - random or otherwise - , the probability is zero.

*That is, assuming that Beethoven (a naturally evolved being) producing it, doesn't count as "nature doing it".

atanu said:

What is the probability?


Please do not bring in the subject of intelligent design -- pro or against. Let us please stick to actual statistical calculations only.

Or just enjoy the stupendous creation.

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You are asking the question as if you are at the universe in it's pre-big bang state and in a spaceship (that can exist in non-spacetime) and have a recording of this Beethoven piece. And saying "if this compressed ball of super quantum energy expands and grows into a universe, what are the odds this piece will be composed by life?"

But this universe happened to form stable solar systems and one at least one planet life formed which eventually became intelligent. So we ended up with all kinds of things that are remarkable next to a compressed ball of quantum energy.
All kinds of music, art, science and so on.
There are also many hypothetical pieces that were never written.
Life creating art is clearly something nature can produce. But Beethoven just happened to hear that music in his head on that day. So he wrote it down. What is the probability that a high level musician/composer wrote a great piece?
The Brandenburg Concertos are even more epic. But Bach was super skilled and it seems reasonable that he wrote those.

There is probably far superior music that was never written because humans have limits on how god-like their talents can be.
Before that piece existed there was a high probability that something of that caliber would be written by that composer. And there it is.

I don't understand the significance of a small probability. Any time you have a support of infinite or effectively infinite possible outcomes then the probability of a single event occurring is effectively zero. Something had to occur and if that event is swimming in a sea of events where each event has an infinitesimal probability of occurring then the probability of something occurring with an infinitesimal chance of occurring is highly likely and should be expected.

ReluctantMathematician said:

I don't understand the significance of a small probability. Any time you have a support of infinite or effectively infinite possible outcomes then the probability of a single event occurring is effectively zero. Something had to occur and if that event is swimming in a sea of events where each event has an infinitesimal probability of occurring then the probability of something occurring with an infinitesimal chance of occurring is highly likely and should be expected.

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In which case, you shift from the probability of an event to the probability distribution, integration of which gives the probability for a range of events.

It is clear that this situation deals with a tail of some probability distribution with the whole tail being something with low probability.

Polymath257 said:

In which case, you shift from the probability of an event to the probability distribution, integration of which gives the probability for a range of events.

It is clear that this situation deals with a tail of some probability distribution with the whole tail being something with low probability.

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Even something as simple as a roll of a 6-sided die or a coin flip has a probability distribution, we are always on a probability distribution when talking probability.


Having an infinite number of possible outcomes simply means that we have a continuous distribution rather than a discreet distribution. As far as the shape of the distribution, that is only something we can wildly speculate on, but we really have no information to assess the shape of that distribution. Also, tail ends do not necessarily mean lower density under the curve, consider the exponential distribution or the uniformed distribution for example.


Furthermore, what we view as a low probability due to our arbitrary interpretation of what a small number should look like may actually be high when considering the long-term relative frequency of the entire distribution. We don't actually have the needed information to even interpret what a small probability is in these considerations.


The truth of the matter is that this is not even a question probability could answer, as we would not be looking at one probability distribution, but rather an uncountable multiples of distributions to such a scale, it would be impossible to calculate or even understand.

atanu said:

What is the probability?

...

Please do not bring in the subject of intelligent design -- pro or against. Let us please stick to actual statistical calculations only.

Or just enjoy the stupendous creation.

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100%.

The odds of something happening once it's happened are 100%.

9-10ths_Penguin said:

100%.

The odds of something happening once it's happened are 100%.

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If something is being considered a unique event then the probability of it occurring given that it occurred is 0. It already happened, so unless you are talking about the probability of it happening again, then it has a 0% chance of happening. I believe the OP is talking about the chances of it happening in the first place.

ReluctantMathematician said:

If something is being considered a unique event then the probability of it occurring given that it occurred is 0. It already happened, so unless you are talking about the probability of it happening again, then it has a 0% chance of happening. I believe the OP is talking about the chances of it happening in the first place.

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Funny - I missed where the OP used the words "happening again."

9-10ths_Penguin said:

Funny - I missed where the OP used the words "happening again."

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So, did I. You are the one that said. . .

9-10ths_Penguin said:

100%.

The odds of something happening once it's happened are 100%.

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Which would explain why I quoted you. Also, you are not using the term odds correctly.

9-10ths_Penguin said:

100%.

The odds of something happening once it's happened are 100%.

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That is wrong on many different levels.

One, probabilities don't change simply because an event happened. The probability of a coin landing on heads is still 1/2 even if some particular coin lands on heads some particular time.

Two, we are clearly talking about a conditional probability here. What is the probability of something happening given certain initial conditions?

This does NOT assume it 'already happened'.

The question is better stated as 'what is the probability of Beethoven writing his music given the condition of the universe 10 billion years ago'?

Although we might want to generalize this a bit to:

What is the probability of some intelligent creature producing audio based art that emotionally moves its listeners in the way that Beethoven's music moves people'?

And, the fact of the matter is that there is no way to even start to determine that probability.