Probability....

DeVore

Biffa Bacon originally proposed this:

Well the statement I made was 100% correct so it seems you’re the one who doesn’t understand probability. Let me explain. Let’s say we have a bag with four black balls and six white balls in it. What is the probability that a ball drawn at random will be black? Two-fifths right? Now let’s say I draw one ball at random and hide it in my hand. What is the probability that it is black? This time it is either one, if it is black, or zero if it is white. It’s a minor point really and I don’t know why you highlighted it and ignored the rest of my post.

quote:

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Originally posted by amp
Yeah! All that Quantum mechanics codology! Next thing you know people will be saying the world is round! And that the Earth revolves around the sun! And that Australia exists!

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Sigh.

I referred to it as "codology" not because I doubt its veracity but because I think its application to the example I gave is just being a bit pedantic. Please forgive me.

ok, let me hear your thinking on this:

The ball isnt chosen by your hand in the normal sense.

There are two bags of balls. The balls are chosen on the chances of a radioactive isotope decaying. That triggers the selection of a white or black ball. ie:

If the isotope decays within one minute the ball chosen will come from the black bag. If it doesnt decay in time it will come from the white bag. The ball is placed in your hand but you cant see it or the bag from which it came.

The probability of the isotope decaying in time is 2 times in every 5.

When you have a ball in your hand but you have not yet looked at it, what is the probability (in your opinion) that it is black?


DeV.

Keeks

From what i remember from probability, it goes somethning like this:

No. of favourable outcomes/ no of possible outcomes

Although it is more complicated than that. (i'm sure some1 will correct me).

Now let’s say I draw one ball at random and hide it in my hand. What is the probability that it is black?

its still 2/5. U might think 50/50 (0/1) but it has to fit into the formula.

If you came up to someone and said

I'm after pick a ball from a bag. It in my hand. Its either black or white.
What is the probability that it is black?

based on that info it would be 50/50 (0/1). The accuracy of the probability is based on the amount of information include in the probability statement.

A lot of what I've just said is prbably wrong, as it is ages since I've done probability in college. I'd have to go back and look it up, and I'm doing that any time soon (although i will have to). But thats how I remember it.

/me is think that if his maths leacturer sees this he will come after him with a cleaver!

bonkey

Originally posted by Keeks
[]If you came up to someone and said

I'm after pick a ball from a bag. It in my hand. Its either black or white.
What is the probability that it is black?

based on that info it would be 50/50 (0/1). The accuracy of the probability is based on the amount of information include in the probability statement.

Yes and no. If someone made that statement to me, I would have to ask about how many balls of each colour were in the bag in order to give a probability. Without that information, the best I can do is make an assumption about that information, and thus arrive at a "presumed probability", rather than the actual probability.

So, given that you have a ball in your hand, who's colour is a direct representation of the outcome of a random event with probability of .4, and it is stated that you have no direct knowledge of the ball's colour, nor of the bag it came from, then the odds of the ball being black must be .4.

The original statement from Biffa contained some inaccuracies which are misleading :

Now let’s say I draw one ball at random and hide it in my hand. What is the probability that it is black? This time it is either one, if it is black, or zero if it is white

This is nonsensical. Probability to who? Someone who knows the colour (you) or someone who doesnt know the colour (e.g. me). Probability is based on available information, and you have more information than I do on the issue. Therefore, for Biffa, there is certainty - there is no probability at all. However, unless he divulges the information as to what is hidden in his hand, then for the rest of us, this information doesnt exist, and we are left with a probability of .4 for black again.

jc

Keeks

Originally posted by bonkey


Yes and no. If someone made that statement to me, I would have to ask about how many balls of each colour were in the bag in order to give a probability. Without that information, the best I can do is make an assumption about that information, and thus arrive at a "presumed probability", rather than the actual probability.

Thats the point I was making, or at least trying to. The "accuracy" of the probability increases with the amount of information (variables) that is available. (This isn't aslways true).

I realise my example is flawed. I haven't used probabilty in a long while (only for gambling )

Now let’s say I draw one ball at random and hide it in my hand. What is the probability that it is black? This time it is either one, if it is black, or zero if it is white

Actually the more I look at this, I'm begining to wonder where the 1 or 0 come in?

Biffa Bacon

The point that the probability is either 0 or 1 was made to me by my mathematics lecturer in college so that's why I consider it to be correct. But DeVore probably knows more about it than me so I will bow to his superior knowledge on the subject.

The reasoning though is that if I have chosen the ball from the bag then it is either black or white. The probability of it being black is 1 if it is black and 0 if it is white. Probability only comes into it before the selection is made, since the selected ball does not yet exist. Of course, you would still use probability to formulate a best guess as to what colour the ball is before you observe it, but not to describe the true state, black or white, of the ball.

I guess this is not true though if you take quantum mechanics into account, i.e. the ball only becomes "real" when it is observed. I thought it was pedantic to bring it up because I thought it was only applicable on the sub-atomic level, not in "real" life.

Biffa Bacon

Thanks DeVore for hiding my shame btw .

DeVore

I thought it was pedantic to bring it up because I thought it was only applicable on the sub-atomic level, not in "real" life.

But you see now (and this was Shroedengers (?) great break through), that what happens at the sub atomic level can easily be translated to the macro level.

However, I hate the thought that someone is "bowing to my superior knowledge, when there is a doubt in my head (which there is but I cant define it yet) so I'm going to research this.

DeV.

bonkey

The reasoning though is that if I have chosen the ball from the bag then it is either black or white. The probability of it being black is 1 if it is black and 0 if it is white.

Ah - now I see what you're driving at.

I guess its a question of semantics.

Technically, what your lecturer is saying is indeed correct. The ball has a fixed colour - so there is no probability (only certainty). When we ask "what is the probability that the ball is black", then you can completely pedantic and say "1 or 0, depending on whether or not the ball is black". You are technically answering the exact question.

However, the intention of probability is to assign a level of certainty to a given scenario. In otherwords, the 40% figure is answering a slightly different (albeit more useful) question - "with what certainty can you say the ball is black" (or something to that effect).

Now, all that remains is to ask what the question was - the actual colour of the ball, or the "predictors" statement of what colour it is - which are two different things.

Also, using Schroedinger's quantum logic, we can state factually that we cannot know whether the ball is black or white until we look at it. Therefore, we must say that until we look at it (or at what remains in the bags, if possible) it is both black and white - with the percentages of each being linked to the probability of having drawn that colour.

jc

Keeks

That actually makes a lot of sense bonkey...even to me

DeVore

Hmm, I dont think thats true bonkey.

The ball is not 40% certain black or 60% certain white. The wave function is in whats called a "super position" of both states which collapses to one state when observed. Totally annoying and I hated it in college but there you go. Its both until its observed...
The temptation to say that it doesnt apply to anyone but Tefal-heads is strong but remember that Quantum uncertainty is useful for a number of possible computer related things. Encryption and decryption for one, logical gates that can be in both states at the same time for another... theoretical afaik but interesting propositions.

I'm still researching this because I want to know exactly *when* the observation occurs...

Meanwhile, this link has a good explanation of the experiment (you even get to make cat go splat!), while at the same time keeping it kinda funny.
http://users.ox.ac.uk/~jsw/Schroedinger.html

DeV.

bonkey

Originally posted by DeVore
Hmm, I dont think thats true bonkey.

The ball is not 40% certain black or 60% certain white. The wave function is in whats called a "super position" of both states which collapses to one state when observed. Totally annoying and I hated it in college but there you go. Its both until its observed...

I may be mistaken, but is it not true that this has only been verified at a quantum level with experiments such as quantum interference.

We can extrapolate and apply the same logic to the macro scale, but there is no evidence to say that this is what is actually happening - whereas we can definitively show that it does appear to happen at the quantum level.

If you apply quantum reasoning at a macro level, it is still a valid model for extrapolation, but only at a theoretical level. Now, arguably thats all mathematics is - a theoretical level - but it is equally valid to apply other reasoning which cannot be shown to be incorrect, such as the allegation that super-position of states cannot be shown to exist at the macro scale.

Which is why it boils back down to semantics - its a matter of which model you choose to apply. At a quantum scale, only one is valid, but at a macro scale, both appear to be true in terms of what is verifiable.

The temptation to say that it doesnt apply to anyone but Tefal-heads is strong but remember that Quantum uncertainty is useful for a number of possible computer related things. Encryption and decryption for one, logical gates that can be in both states at the same time for another... theoretical afaik but interesting propositions.

More than theoretical - those mad tefal-heads actually have quantum computers working at a limited scale (7 qbits to date, IIRC). However, the computer-related applications all work at a quantum-scale to achieve this - it actually works at a scale where quantum super-position is known to occur.

However, dont let this stop your research....and let me know if you find a good answer

jc

Bob the Unlucky Octopus

Here's a case in point of how the macro scale can indeed be applied. Consider this thought experiment- I catch a butterfly in my hands in front of you, it was clearly alive at the time that I caught it...then I turn to you, a passive neutral observer, with the butterfly concealed in my hands, and ask you: Is the butterfly alive or dead?. Now if you reply that it is alive (its last observed state), I simply squash it with an imperceptible move of my lower digitalis muscles in my fingers. If you say it is dead I just let it go, and off it flies. It's state cannot be pronounced upon until it is observed- which it can't be unless I open my hand. The macromodel has limitations as does the quantum model, in other words, exact states cannot be observed. The difficulty that most encounter with this concept is that in macromodels, states are usually easy to observe, and that is usually crucial to a macromodel's assessment. This is a special case of probability states I guess.

Returning to the original topic of what Biffa was discussing- equating the existence of God with a probability state- well both states have to be observable and known to be possible for probability to even enter the equation! Let me explain- we know that the butterfly is either alive (biological observation gives us the knowledge that things are alive, and that one of these things is that particular member of the insect kingdom)- and the same observational and biochemical science tells us that it is possible for that creature to be dead. Both states are observable, and therefore possible- ie, one might be more probable than the other. In the case of God- neither state is observable, therefore the question of God can't be scientifically considered- no observation possible, so we must presume that from a scientific point of view God is null and void- existence is an irrelevant question. Quantum events mean that even the most unlikely occurences can be modeled to some extent, game theory and chaos theory are the discrete and continuous branches of math that allow us to focus on improbable events.

So, to cut a long story short, the concept of God may once have been needed, but no longer.

Occy

Biffa Bacon

In the case of God- neither state is observable, therefore the question of God can't be scientifically considered- no observation possible, so we must presume that from a scientific point of view God is null and void- existence is an irrelevant question...So, to cut a long story short, the concept of God may once have been needed, but no longer.

I don't follow your reasoning there Bob, but perhaps we should continue that discussion in the other thread.

DeVore

Bonkey, I think you are incorrect about thinking super positions only occur at the sub atomic level.

Think about this:

If a qbit is in one state the ball is black, if in the other state it is white. Now, since the qbit is in a super position of states my understanding is that since the colour of the ball is *directly* dependant on the state of the qbit it is also in a super position of states.

In fact I'm also pretty sure that thats exactly what Schroedinger was demonstrating with the infamous Cat experiment...
The cat is both dead and alive...

Bob, I dont think your butterfly idea works as you know the butterfly is alive and you are simply killing it to show him wrong. The butterfly is observed (by you) and its wave funtion couldnt be in a super position (even if it was, you're observation of it would collapse it into a single state... alive).

I talked to a few physics lecturer mates of mine and they initially agreed that the moment of observation was when the ball is withdrawn from the bag, but then realised that if you simply put the ball BACK in the bag its wave function would intermingle with the other 9 balls again.
IE: if we look at the ball we change the probability of the next ball being drawn and the distribution of the balls in the bag. but if we DONT look at the ball then we can only go on previous data as nothing has really changed.

So the answer is that the ball must be observed before the quantum wave function collapses to a specfic state and that that observation is NOT just the selection of the ball.

DeV.

Bob the Unlucky Octopus

As with all probability tests, mine was conducted from the point of view of an unknowing observer. Creating an analogy- if you looked into the bag while drawing the ball out (so you could see what you were taking out before you drew it), the probability state would collapse. Not looking/knowing the color of the ball before you draw it out leads to a probability experiment. Just as if it wasn't me the butterfly experiment was conducted on. From the point of view of the person I'm demonstrating the butterfly experiment to, I'm convinced it holds up.

Occy

bonkey

Originally posted by DeVore
Bonkey, I think you are incorrect about thinking super positions only occur at the sub atomic level.

Think about this:

Your example fits very well with what I said :

If you apply quantum reasoning at a macro level, it is still a valid model for extrapolation, but only at a theoretical level

We can indirectly observe quantum super-position at work with experiments such as quantum interference with photons. This shows that the superposition theory is valid - that there is a superposition of states, because of our ability to indirectly observe that the photon must have passed through both gates in order to interfere with itself.

At the macro level, we cannot do any such indirect observation. Therefore, while the superposition model theoretically matches what we can see, we cannot say for certain that superposition actually occurs.

Going back to the bag and the balls, what this means is to me is that the model which says "the ball is both black and white until you observe it" is a valid model, but does not necessarily reflect what is actually happening. It may reflect what is happening, but we cannot determine that for sure, which we can do at a quantum level.

This is why I said it is down to semantics. Is the ball actually black and white, or do we just consider it to be black and white? Given that we cannot observe it directly or indirectly, either is surely valid, depending on which theoretical model we choose to represent the system with.

If the quantum theory holds true, then doesnt it have some interesting implications. For example, what counts as "observation". If I take a photo of the ball I drew out, has the superposition collapsed? If so, what if I then destroy the film without ever having looked at it? We still have never seen what colour the ball is, so was it black or white?

If on the other hand, simply taking the picture isnt enough, then looking at the photo presumably does. What if one looks at it some days later - does suddenly cause the superposition to collapse - and if so, at what point in time has the superposition collapsed? At the time of observation, or at the time the photo was taken?

At a quantum level, "observation" requires interference, and this interference is what actually causes the collapse of the state superposition, if memory serves correct. Again, this is interpretative. If you set up a quantum interference experiment, and set the process running which determines which gate the photon passes through, then you will not see quantum interference, even if you never look at the data telling you which gate the path ran through.

At a macro level, does this hold true? If you take a photo of the ball, without you looking at either, has the superposition been resolved? No answer that I can see makes logical, consistent sense.

Maybe one of them does, but I cant see why.

Some food for thought, perhaps.

jc