How “random” is “randomness”?

[shemp]

How “random” is “randomness”?

Let’s start here, with the page that got me to start thinking about this question:

Schrödinger's cat

Schrödinger wrote:

One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.

It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a "blurred model" for representing reality. In itself it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.

The idea, of course, is to tie the existence of the cat to a “random” 50/50 probability. In the Wikipedia article, four interpretations are given: The Copenhagen interpretation, in which a superposition of states collapses when observed; Everett’s many-worlds interpretation, in which the universe splits into two, one where the cat is alive and the other where the cat is dead; the Ensemble interpretation, which denies that the concept of “wave function” exists in the real world and is merely an abstract mathematical concept; and the Objective collapse theories, which state that wave function collapse occurs not when an observer intervenes, but occurs either randomly or when some arbitrary physical threshold is reached.

I wonder if the real problem with interpretations of the Schrödinger's cat thought experiment is with the concept of “randomness”. Just how “random” is “randomness”?

Take, for example, the game of Craps. In theory, if the dice are not “loaded”, the chance of the dice coming up with the values 2-12 is:

2: 1/36
3: 2/36
4: 3/36
5: 4/36
6: 5/36
7: 6/36
8: 5/36
9: 4/36
10: 3/36
11: 2/36
12: 1/36

Since on any given throw, we don’t know in advance which of these values the dice will add up to, we say that the result is random. However, I say that the result is not random. Instead, I say that the result is predetermined by the conditions of the throw (such as the position of the dice in the thrower’s hand, the speed of the throw, the spin placed on the dice by the throw, the quality of the felt on the table, the hardness of the table, the hardness of the rail at the end of the table, the temperature of the dice, various qualities of the surrounding air [such as temperature, humidity, and air movement], along with other possible intangibles). The throw only appears to be random to the observer because he does not have all of this information and the capability to process it to determine the outcome of the throw.

We can make similar arguments for games such as, for example, roulette or tossing a coin. We can calculate probabilities for these games, but there is really nothing random about them. The outcomes are predetermined by the physical conditions, but nobody has the ability to calculate the information to determine the outcome. Perhaps, given enough information, time and computing power, one could determine the outcome of a coin toss or a roulette spin in advance.

So is there really no randomness in the non-quantum world? I think there is not. I think that every action at this level is predetermined by the physical conditions preceding it. This would mean that non-quantum randomness is merely an interpretation that we use to explain these actions. Of course, this brings free will into question. If there is no randomness at this level, is there no free will? Is our consciousness only a product of the physical conditions within our brains?

Then, of course, we can ask ourselves, “Is there any randomness even at the quantum level?” Or is quantum-level randomness just a perception caused by a lack of information and computing power? I’m sure this question has been addressed many times, but I’m not a professional in this area, and I’m sure there are compelling arguments pro and con.

OK, let’s cut to the chase, sum things up, and pose the questions I’d like some answers to (or at least debate on, if there are no clear-cut answers):

1. Is there really randomness in the macro, non-quantum world, or is it just an illusion and a lack of information and computing power?

2. Similarly, is there really randomness in the quantum world?

3. If the answers to questions 1 and 2 are different, where can we draw the line separating the two?

4. Is the question of the existence of “free will” related to these questions, or not? Can free will exist without randomness?

 

[DanishDynamite]

1. Is there really randomness in the macro, non-quantum world, or is it just an illusion and a lack of information and computing power?

In the macro-world there is no true randomness with 99.9999999999999999999999 and some % probability.

2. Similarly, is there really randomness in the quantum world?

To the best of our knowledge, yes. Hence, the reason the above number is not 100%.

3. If the answers to questions 1 and 2 are different, where can we draw the line separating the two?

Philosophically, nowhere. In practice, somewhere above molecular size.

4. Is the question of the existence of “free will” related to these questions, or not? Can free will exist without randomness?

Depends what you mean by "free will".

 

[shemp]

Depends what you mean by "free will".

When confronted with two or more choices, do I have the "free will" to make the choice, or is my decision controlled by physical circumstances in my brain?

 

[SirPhilip]

In the macro-world there is no true randomness with 99.9999999999999999999999 and some % probability.

Curious. Does that apply beyond the event horizon of black holes?

 

[rcronk]

In English, the definitions of random and arbitrary seem to have mushed into meaning pretty much the same thing.

In cryptography and computing, for example, randomness means that each option appears equally, like picking 1000 numbers from 1 to 10 and each of the 10 options come up statistically the same number of times. In computing, pseudo-random number generators use previously generated numbers as input to the next number that's generated.

Arbitrariness means that each number picked does not have any connection with previous numbers. So if I were to pick 1000 numbers from 1 to 10, we couldn't say anything about the distribution of the numbers because they aren't derived from anything.

Computers can't create an arbitrary number because the number has to come from somewhere. The only attempt to create "real" arbitrary numbers in computing was to hang an antenna out of the box and have it pick up "random" noise from the universe and use that - but that's not random or arbitrary, it's created from sources that are just too complicated to track down. I guess it could be called pseudo-arbitrary.

A funny result of the above definitions is that 1,2,3,4,5,6,7,8,9,10 is a random list because each item appears statistically the same number of times. Most people seem to think that random means mixed up or shuffled in such a way that it seems arbitrary. The number PI is actually statistically random as all numbers appear in it statistically the same number of times for a given set (like the first billion digits, for example).

I think this all might have something to do with "free will" if you mean that free will is a decision that a person makes that's not based on anything but what the person "wants" to do at that moment - coming from somewhere within them that isn't deterministic or dependent upon anything else. It would seem that people's decisions are in fact affected by their experiences up to that point, but who knows if there's something inside a person that affects that decision that doesn't have anything to do with their experiences up to that point.

This is also something I've been struggling with lately and I'm not sure where to take the logic of it from here. The paradox I'm faced with is that I believe in an omniscient God but I also believe in free will, or the ability for me to do whatever I want to do. I don't believe in predetermination (that I'm following a predetermined script) but I do believe that God knows what's going to happen with my choices in the future.

Any ideas people here have would be very helpful to me. And please don't bash me for believing in God, I'm really just looking for some more ideas about how to resolve this apparent paradox and get a little closer to the truth of reality. Thanks.

 

[blobru]

1. Is there really randomness in the macro, non-quantum world, or is it just an illusion and a lack of information and computing power?

Regular dice behave statistically because no one is skillful enough to account for all the intangibles you list -- a lot of crap artists out there, but no one's that good! -- so they 'cancel out' in any large sample.

2. Similarly, is there really randomness in the quantum world?

For quantum craps, there don't seem to be any intangibles* in play. The "dice" are purely statistical. (*not sure about the "Objective collapse" interpretation though)

3. If the answers to questions 1 and 2 are different, where can we draw the line separating the two?

Philosophically, I would just draw the distinction between observed randomness (craps) and theoretical randomness (quanta).

4. Is the question of the existence of “free will” related to these questions, or not? Can free will exist without randomness?

Don't think there's a necessary connection. A random will isn't any more "free" than a determinist will really. Its actions are just harder to predict.

Determinist will: brain state A --> action z always (100% of the time).
Random will: brain state A --> action z (40% of the time), y (30%), x (20%), w (10%); for example.

But "free" will I think means something like...
Free will: brain state A --> (???) --> action z,y,x,w... (question: can the observed actions of a "free will" follow a statistical pattern?)

In other words, (???) = some intermediate unknown state that doesn't obey macro-physical (deterministic) or micro-physical (probabilistic) laws.
I've seen some philosophers argue that "free" will is an emergent property of the complex physical system that is our brain and body, in other words that (???) = 'emergent property', but I can't say I understand them too well. It seems to me that for authentic "free" will you'd really need something like a self-governed source that transcends physics, causa sui, i.e., a "soul"(?)

 

[Schneibster]

please don't bash me for believing in God, I'm really just looking for some more ideas about how to resolve this apparent paradox and get a little closer to the truth of reality.

Well, no promises I won't tell you things that will challenge your faith, perhaps more than a bit- but at least I'll try to be civil, and I won't attack it deliberately; it's just that I don't see much way to talk about this from a standpoint that includes the possibility of the existence of an omniscient individual. So if you can be tolerant of that, I can at least try to remain civil. Full disclosure: I am an atheist, and I have been most of my life- I tried religion once in my early adulthood, and just couldn't handle how much it made me feel like a hypocrite. If that doesn't scare you off, read on.

In English, the definitions of random and arbitrary seem to have mushed into meaning pretty much the same thing.

From the standpoint of casual language, you may be correct, though I'm not as sure about it as you seem to be. These concepts can be amazingly slippery when discussed with someone not aware of the formal definitions.

From a formal standpoint, they are very different. "Random" means a value that cannot be predicted by what has come before; it may (and in most cases does) indicate a value that is the outcome of a stochastic process, that is, a process that has a probability distribution among the possible results. Such a process, if repeated a large number of times, will show a limited number of possible outcomes that occur at various probabilities. "Arbitrary," on the other hand, means a value that need not be connected to what has come before, but might or might not be. While this may only appear to be a shade of difference, in formal usage, one would talk about how a function would behave given an arbitrary input value if one were discussing the function pedantically, and how it would behave given a random input value if one were discussing the conclusions that can be derived from that function if it describes the consequences of a random process.

In cryptography and computing, for example, randomness means that each option appears equally, like picking 1000 numbers from 1 to 10 and each of the 10 options come up statistically the same number of times. In computing, pseudo-random number generators use previously generated numbers as input to the next number that's generated.

Arbitrariness means that each number picked does not have any connection with previous numbers. So if I were to pick 1000 numbers from 1 to 10, we couldn't say anything about the distribution of the numbers because they aren't derived from anything.

Having done a fair bit of cryptographic coding, I note that you have confused a test for randomness with randomness itself. Also, your definition of arbitrariness seems a little more like a definition of how to get randomness, not what randomness actually is; if you, for example, hit a paintbrush against your hand in front of a crowd, and ask everyone who did not get paint on them to pick a number from one to ten, the numbers they picked would be both random and arbitrary; the people chosen would be arbitrarily chosen, upon random criteria. (Assuming they did not all jump up and beat the tar out of you. )

Randomness can be tested by checking that the occurrence of outcomes conforms to the expected probability distribution. That is, if the statistical universe is 1,000 picks of a number from 1 to 10, one should find equal numbers of each; whereas if the statistical universe is 1,000 decays of a photon of 1.02MeV energy into two particles, one should find almost all of the decays have resulted in the pair production of an electron and a positron, but just a few have come out as an electron neutrino and electron antineutrino. The probability distribution of arbitrary picks over a range of numbers should yield equal probability for each number; however, the probability distribution of photon decays does not yield equal probabilities of each outcome. A process, therefore, that conforms to the test of its probability distribution is a random process; but it is not the test that determines the randomness, it is the character or nature of the process that determines it.

It is a common misconception that "random" means "equal probability of all outcomes;" actually, it does not. They might have unequal probabilities, as any gambler can tell you, but still be random.

It is a further misconception that anything that is random cannot be deterministic. In fact, processes whose outcomes conform to a probability distribution are completely deterministic. One will not, after all, see the gamma ray photon decay into a nitrogen nucleus; that has zero probability, since it would violate conservation of mass-energy. The gamma ray photon can only decay in a certain limited number of ways, and it is certain (i.e. predetermined) that it will choose one of them every single time. Equally, if one asks that a number between 1 and 20 be picked, and discards every choice that is not between 1 and 20, then all the numbers picked and not discarded will be between 1 and 20, and this too is predetermined.

It is the individual photon decay, or the individual choice of a number, that is random. Note, however, that the individual photon decay is, as far as we can tell, truly random; whereas the individual number choices may or may not be truly random; for example, some people may have a favorite number (whatever that might mean) that is within the range, and if given the choice will always pick that number; the choice, for them, then, would be deterministic, but still arbitrary from the point of view of a person asking for number selections from their arbitrary choice of people to ask.

Computers can't create an arbitrary number because the number has to come from somewhere. The only attempt to create "real" arbitrary numbers in computing was to hang an antenna out of the box and have it pick up "random" noise from the universe and use that - but that's not random or arbitrary, it's created from sources that are just too complicated to track down. I guess it could be called pseudo-arbitrary.

Actually, you can buy devices that use "Johnson thermal semiconductor shot noise" to generate random numbers. These devices use the occurrence or non-occurrence of a random quantum event within a set period to determine whether the next bit output is a one or a zero. With judicious choice of the parameters of the junction, and the bit clock, one gets equal numbers of ones and zeros over the long haul, with no chance of predicting whether any particular bit is going to be a zero or a one. (I have vastly oversimplified the design of such devices, but I have, I think, captured the principles of their operation sufficiently for clear understanding.)

A funny result of the above definitions is that 1,2,3,4,5,6,7,8,9,10 is a random list because each item appears statistically the same number of times.

No, sorry, this is wrong. That list would be a legitimate single occurrence of output from a random process, but for the process to be adjudged random, it would have to occur on average no more than one time in ten billion (the number of permutations of ten numbers taken ten at a time). The other nine billion, nine hundred and ninety-nine million, nine hundred and ninety-nine thousand, nine hundred and ninety-nine times, on average, it would have to be different. (I am of course using American numbering- the British use "billion" to denote a million million, not a thousand million.) It might still be within the expected deviation if you saw it a few times- but the more times you see it, the less likely it is that the process is random, and that probability declines abruptly after just a few repetitions within a trial of ten billion.

Most people seem to think that random means mixed up or shuffled in such a way that it seems arbitrary. The number PI is actually statistically random as all numbers appear in it statistically the same number of times for a given set (like the first billion digits, for example).

Well, at least the second part is true. I hesitate to agree with statements about what "most people think."

I think this all might have something to do with "free will" if you mean that free will is a decision that a person makes that's not based on anything but what the person "wants" to do at that moment - coming from somewhere within them that isn't deterministic or dependent upon anything else. It would seem that people's decisions are in fact affected by their experiences up to that point, but who knows if there's something inside a person that affects that decision that doesn't have anything to do with their experiences up to that point.

I tend toward the view that we cannot show that we do not have free will, and therefore the question is meaningless. It is also true that we are constrained by physical law; for example, due to the symmetry of physics over rotations, it is unlikely in the extreme that any of us will ever turn a corner and "turn into" a penguin. Do we therefore lack "free will?" Obviously, this example cannot answer the given question; my contention is, there is no example that can answer it. Certainly we lack free will in many situations; however, it appears that we have free will in many others. But now we're straying into philosophy on the Science forum.

This is also something I've been struggling with lately and I'm not sure where to take the logic of it from here. The paradox I'm faced with is that I believe in an omniscient God but I also believe in free will, or the ability for me to do whatever I want to do. I don't believe in predetermination (that I'm following a predetermined script) but I do believe that God knows what's going to happen with my choices in the future.

If you're going there, perhaps you should consider whether it is possible for God to both be omniscient and have free will. I think the answer is an obvious "no," and offer this as some inducement to think outside the box you are currently inhabiting, in my view; you are of course free to ignore my advice.

Any ideas people here have would be very helpful to me. Thanks.

Perhaps my meager ideas may help you; perhaps they are useless. Either way, you are welcome to them.

 

[Schneibster]

Since on any given throw, we don’t know in advance which of these values the dice will add up to, we say that the result is random. However, I say that the result is not random. Instead, I say that the result is predetermined by the conditions of the throw (such as the position of the dice in the thrower’s hand, the speed of the throw, the spin placed on the dice by the throw, the quality of the felt on the table, the hardness of the table, the hardness of the rail at the end of the table, the temperature of the dice, various qualities of the surrounding air [such as temperature, humidity, and air movement], along with other possible intangibles). The throw only appears to be random to the observer because he does not have all of this information and the capability to process it to determine the outcome of the throw.

I disagree, and most physicists would, too. Ultimately, the outcome of the throw is based not only upon random quantum phenomena, but upon values that are in principle unmeasurable; that is, not merely we cannot measure them, but they do not in principle have a determined value. The values of variables that depend upon them, therefore, are stochastic probability distributions, whose individual outcomes cannot be predicted from any prior knowledge of the state of the system, no matter how detailed. At any of numerous critical moments during the throw, the outcome of the dice roll can be influenced by a single quantum event, which is in principle truly random.

One might constrain particular throws; for example, it is possible that a sufficiently skilled thrower could alter the probability to favor some outcomes over others. Or the dice can be loaded, increasing the probability of certain outcomes. One will never, however, no matter how fine the control, absolutely determine the outcome. It is in principle impossible to do so under the laws of physics our universe operates on.

So is there really no randomness in the non-quantum world? I think there is not. I think that every action at this level is predetermined by the physical conditions preceding it. This would mean that non-quantum randomness is merely an interpretation that we use to explain these actions.

We have shown (to a certainty of over two hundred standard deviations, a truly astounding level of certainty) by experiment that indeterminate (uncertain in the sense of Heisenberg's Uncertainty Principle) quantum values are not merely unmeasurable, but in fact cannot have a definite value. The experiment is called the Aspect Experiment; you can find a discussion of this experiment on this forum by searching on that term. It is therefore incorrect, even if you do maintain that every quantum action is predetermined by physical conditions, to state that the outcome is determinate; that is impossible, since the physical conditions are not merely unmeasurable but nonexistent.

1. Is there really randomness in the macro, non-quantum world, or is it just an illusion and a lack of information and computing power?

According to the outcome of experiments, there really is randomness in the non-quantum world, and it springs from:

2. Similarly, is there really randomness in the quantum world?

Yes, again, according to the outcome of experiments.

3. If the answers to questions 1 and 2 are different, where can we draw the line separating the two?

It is not a sharp line, but there are areas that are definitely on one side or definitely on the other. As has been stated, the line is somewhere above the size of a molecule. The proof of this is an experiment that appears to contradict the Second Law of Thermodynamics, but confirms a derivation of that Law known as the Fluctuation Theorem. Details are available upon request; I'll have to google it up, and if you just want to argue philosophy, it's not worth my while. If you're interested in the hard evidence, I can provide it.

4. Is the question of the existence of “free will” related to these questions, or not? Can free will exist without randomness?

On that, I have an opinion, but it is not grounded in the previous questions. I'll therefore answer (out of order) that I don't know whether it can, and I don't know if it is.

 

[rcronk]

Excellent comments everyone. Thanks! I'm going to go do some more research on the topics brought up here.

 

[fls]

At any of numerous critical moments during the throw, the outcome of the dice roll can be influenced by a single quantum event, which is in principle truly random.

How do we know this (other than by reference to basic principles)?

And is there a discussion somewhere as to the extent that single quantum events influence outcomes in everyday life, as in speculative essays or articles from someone who is knowledgeable in the field? (Much as I appreciate your essays, they must take considerable effort on your part and I don't wish to put you out - I'm willing to do my own legwork if you can point me in a particular direction).

Linda

 

[Rolfe]

The paradox I'm faced with is that I believe in an omniscient God but I also believe in free will, or the ability for me to do whatever I want to do. I don't believe in predetermination (that I'm following a predetermined script) but I do believe that God knows what's going to happen with my choices in the future.

Any ideas people here have would be very helpful to me. And please don't bash me for believing in God, I'm really just looking for some more ideas about how to resolve this apparent paradox and get a little closer to the truth of reality. Thanks.

Have you considered the aspect that you are living in a linear, two-dimensional time stream (or at least it appears to you that you are), but God is not confined to that time stream?

Rolfe.

 

[Ivor the Engineer]

I disagree, and most physicists would, too. Ultimately, the outcome of the throw is based not only upon random quantum phenomena, but upon values that are in principle unmeasurable; that is, not merely we cannot measure them, but they do not in principle have a determined value. The values of variables that depend upon them, therefore, are stochastic probability distributions, whose individual outcomes cannot be predicted from any prior knowledge of the state of the system, no matter how detailed. At any of numerous critical moments during the throw, the outcome of the dice roll can be influenced by a single quantum event, which is in principle truly random.

One might constrain particular throws; for example, it is possible that a sufficiently skilled thrower could alter the probability to favor some outcomes over others. Or the dice can be loaded, increasing the probability of certain outcomes. One will never, however, no matter how fine the control, absolutely determine the outcome. It is in principle impossible to do so under the laws of physics our universe operates on.

We have shown (to a certainty of over two hundred standard deviations, a truly astounding level of certainty) by experiment that indeterminate (uncertain in the sense of Heisenberg's Uncertainty Principle) quantum values are not merely unmeasurable, but in fact cannot have a definite value. The experiment is called the Aspect Experiment; you can find a discussion of this experiment on this forum by searching on that term. It is therefore incorrect, even if you do maintain that every quantum action is predetermined by physical conditions, to state that the outcome is determinate; that is impossible, since the physical conditions are not merely unmeasurable but nonexistent.

According to the outcome of experiments, there really is randomness in the non-quantum world, and it springs from:

Yes, again, according to the outcome of experiments.

It is not a sharp line, but there are areas that are definitely on one side or definitely on the other. As has been stated, the line is somewhere above the size of a molecule. The proof of this is an experiment that appears to contradict the Second Law of Thermodynamics, but confirms a derivation of that Law known as the Fluctuation Theorem. Details are available upon request; I'll have to google it up, and if you just want to argue philosophy, it's not worth my while. If you're interested in the hard evidence, I can provide it.

On that, I have an opinion, but it is not grounded in the previous questions. I'll therefore answer (out of order) that I don't know whether it can, and I don't know if it is.

How does the Many Worlds interpretation of QM affect the randomness?

ETA: And Bell Test loopholes?

 

[Harpoon]

...It is a common misconception that "random" means "equal probability of all outcomes;" actually, it does not. They might have unequal probabilities, as any gambler can tell you, but still be random.

That misconception may result from statistics. In order to conduct a scientific, random survey of a group or community, each member must have an equal opportunity to be included in the survey. Random is not at all haphazard.

 

[andyandy]

ok, how does infinity effect considerations of randomness?

If we accept that by random we mean that which can not be predicted from the preceeding event, then situations can be constructed through infinity to remove randomness from a probalistic framework....

Working within an infinite set encompassing all that which can occur and will occur, if we have an event A then regardless of the probability we assign to it for its occurance, as long as it is greater than zero, the fact that it belongs to our set means that it occurs with 100% certainty an infinite number of times - all probabilities, whether 0.01 or 0.9999 are subsumed into 1, and all occur with the same infinite frequency....

...and then we're no longer dealing with that which is random, but that which is determined and independent of probability.

 

[rcronk]

Have you considered the aspect that you are living in a linear, two-dimensional time stream (or at least it appears to you that you are), but God is not confined to that time stream?

Rolfe.

Yes - as I thought about this discussion, the time issue came to mind. In many places it says that everything is an eternal present to him and that time as we know it doesn't exist. There are many references to infinite and eternal things and that God exists in that context where we are in a different context of finite time and beginnings and endings, etc. I'm still churning it around in my head and I'm looking to read up on the topics brought up here too. Thanks.

 

[Folly]

ok, how does infinity effect considerations of randomness?

Poorly?

If we accept that by random we mean that which can not be predicted from the preceeding event, then situations can be constructed through infinity to remove randomness from a probalistic framework....

Working within an infinite set encompassing all that which can occur and will occur, if we have an event A then regardless of the probability we assign to it for its occurance, as long as it is greater than zero, the fact that it belongs to our set means that it occurs with 100% certainty an infinite number of times - all probabilities, whether 0.01 or 0.9999 are subsumed into 1, and all occur with the same infinite frequency....

...and then we're no longer dealing with that which is random, but that which is determined and independent of probability.

With infinite samples, you can have things occurring which have zero probability. Random samples from distributions over intervals of real numbers are all zero probability events. Even worse in the latter case, I strongly believe (but can't remember for sure) that the reasoning of "infinite samples -> surety of outcome" breaks down.

So I think instead you're stuck saying "if I make a set of all things that will occurr, anything that will occurr is in the set with probability 1" which is not so interesting.

 

[andyandy]

With infinite samples, you can have things occurring which have zero probability. Random samples from distributions over intervals of real numbers are all zero probability events. Even worse in the latter case, I strongly believe (but can't remember for sure) that the reasoning of "infinite samples -> surety of outcome" breaks down.

So I think instead you're stuck saying "if I make a set of all things that will occurr, anything that will occurr is in the set with probability 1" which is not so interesting.

Ah, true, with a random sample from the real numbers (say), the probability of any particular choice is [latex]$$ lim_{x \to \infty}\frac{1}{x}= 0 $$ [/latex]

well that buggers things up even more

I've seen the infinity of samples, surety of outcome espoused in certain physical interpretations of cosmology - many worlds, bubble universes....but whether or not the interpretation is mathematically valid, I don't know....it seems pretty counter-intuitive in some respects - I started a short thread on this not too long back....this was my op, based on an argument in Chown's The Never Ending Days of being Dead -

first we take the premise of a bubble universe [BU] which is formed as a result of utterly random quantum contortions in the primoridal vacuum - which means that everything within the observable universe is ultimately the result of random processes that occured in the first split second of the universe's existence. So what is true of our observable universe must be true of all other regions the size of the observable universe in our BU. This means that all possible arrangements of protons in an area the size of our observable universe will occur in other regions of the BU. The way in which protons can be arranged within the observable universe is finite, and so because the BU is infinite it follows that every possible arrangement must occur somewhere - indeed every possible arrangement must occur an infinite number of times in an infinite number of places

it starts by asserting that the number of protons which could fit in the observable universe is about 10^118

and that in each one of these 10^118 locations can either have a proton or no proton, and as such if there are n possible locations for protons, and so there are 2n different universes possible. In our universe where n=10^118 then there are 2^(10^118) possible ways to arrange the protons which is approx equal to 10^(10^118)

Applying this method to finding the distance one would have to travel to find an exact replica of oneself, the figure of 10^28 is used for the number of particles in one's body, which means there are 10^(10^28) possible arrangements of the protons within the body, and therefore this means that one's nearest double is just approximately 10^(10^28) metres away.

The chapter concludes that the existence of your double is extremely difficult to take, but an unavoidable consequence of the standard theory of the universe incorporating both QM and inflation - so if it is not true, then either QM or inflation is incorrect.

otherwise Elvis lives.

http://www.internationalskeptics.com/forums/archive/index.php/t-83314.html

 

[andyandy]

double post double post double post

 

[Rolfe]

Yes - as I thought about this discussion, the time issue came to mind. In many places it says that everything is an eternal present to him and that time as we know it doesn't exist. There are many references to infinite and eternal things and that God exists in that context where we are in a different context of finite time and beginnings and endings, etc. I'm still churning it around in my head and I'm looking to read up on the topics brought up here too. Thanks.

C. S. Lewis has some musings on this, though I don't think they're especially profound. I suppose you could say that while you had free will to chose to type that post or not, now we all know you typed it and the deed is done, does that mean you didn't have free will at all?

Lewis talks about an author writing a book and going off and thinking about things then returning, while only seconds may have passed in the time scale of the narrative. I'm not sure that's terribly helpful though, because the characters in a novel don't have free will as I'd understand it.

I'm not sure that "eternal present" is a very good analogy either, because the whole concept of "present" is so tied up to the linear time stream we experience. Being "outside" of time as we know it, as we are "outside" the page of the book we are reading or writing might be a better analogy.

Rolfe.

 

[steenkh]

Have you considered the aspect that you are living in a linear, two-dimensional time stream (or at least it appears to you that you are), but God is not confined to that time stream?

But in this case, you are effectively trying to find an explanation for something for which there is no evidence, or God is magic, and anything goes - including a number of paradoxes.