Freethought & Rationalism Archive

Malaclypse the Younger · 02-25-2002, 08:47 AM

HRG

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1. It is by no means clear that the space of all possible combination of constants is bounded (compact in the mathematical sense). I'd rather regard it as an open subset of some higher-dimensional Euclidean space.

I don't know enough physics to evaluate this statement. If true, it seems that one could not apply the FTA at all, since one could not compute a numerical probability even of P(E). However, since the FTA fails even if it is stipulated that the space of all possible constants is compact, it is useful at least for an exploration of probability mathematics.

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2. The "volume" of this set is not defined, since we could exchange our "old" constants for "new" ones, as long as there is a (differentiable) one-to-one connection between each "old" and each "new" connections. The famous constants of nature are actually constants of our particular description of nature; if we everywhere replaced the fine-structure constant by its logarithm, physics would not change (only its formulas).

It seems clear that the volume of constant spaces depends on accepting prior to the argument some definite, specific formulation of the laws of physics, even if that formulation is arbitrary. It doesn't seem particularly difficult to obtain agreement on this point at least for the sake of argument.

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3. Thus all probability distributions on the set of all possible combinations are to some degree arbitrary. Dividing it into equal volumes E1 ... En is thus undefined since the notion of "equal volume" depends on the choice of constants, as in 2.

Again, that formulation depends on (admittedly arbitrary) points already stipulated to construct the FTA in the first place.

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More specifically, I can rewrite physics in such a way that the tiny speck of constants which allegedly *) is necessary for life as we know it makes up 99% of the total space.

This is an interesting claim. Perhaps you might start a thread to explore it in more detail?

JB01 · 02-25-2002, 11:01 AM

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Originally posted by HRG:

1. It is by no means clear that the space of all possible combination of constants is bounded (compact in the mathematical sense). I'd rather regard it as an open subset of some higher-dimensional Euclidean space.

I would go further and claim that it is not possible at present even to guess at the number of dimensions of this space. Physicists are still gamely trying to devise a "theory of everything", which would reduce the dimensionality to zero, implying P(E|C)=1. It's a possibility that can't yet be ruled out.

Other assumptions of the fine-tuning argument that can reasonably be challenged as lacking evidence are

1. That equally-sized "volumes" of configuration space represent a priori equally likely outcomes in the chance creation of universes.

2. That the amount of allowable variation in the constants that is consistent with the existence of life as we know it represents only a tiny fraction of the total amount of allowable variation.

3. That there is, in fact, only one universe, i.e., just one toss of the dice.

While the last of these is, applying Occam's razor, a reasonable assumption for day-to-day reasoning, it cannot simply be assumed for purposes of this argument.

Malaclypse the Younger · 02-25-2002, 11:21 AM

JB01

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I would go further and claim that it is not possible at present even to guess at the number of dimensions of this space.

Well, it is always possible to guess.

But you have an obviously compelling point. The fundamental stipulations necessary to even formulate the FTA are in sufficient doubt that any conclusion one can draw from it are not substantively persuasive.

Still, as a thought experiment, it is at least somewhat instructive as to the formulation of evidential arguments generally and probabilistic arguments specifically.

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While the last of these is, applying Occam's razor, a reasonable assumption for day-to-day reasoning, it cannot simply be assumed for purposes of this argument.

Well, one can assume most anything for the purposes of argument, but one must then recognize that the argument is (at best) truthful only relative to those assumptions.

HRG · 02-25-2002, 11:29 AM

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Originally posted by JB01:
[QB]

I would go further and claim that it is not possible at present even to guess at the number of dimensions of this space.

I agree with you. It may be infinite-dimensional or consist of a single point.

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Physicists are still gamely trying to devise a "theory of everything", which would reduce the dimensionality to zero, implying P(E|C)=1. It's a possibility that can't yet be ruled out.

Other assumptions of the fine-tuning argument that can reasonably be challenged as lacking evidence are

1. That equally-sized "volumes" of configuration space represent a priori equally likely outcomes in the chance creation of universes.

That's exactly what I meant when I said that there is no non-arbitrary probability distribution on the set of all possible universes, so that we can speak about dividing it into equally probable pieces.

Regards,
HRG.

2

HRG · 02-25-2002, 11:42 AM

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Originally posted by Malaclypse the Younger:


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More specifically, I can rewrite physics in such a way that the tiny speck of constants which allegedly *) is necessary for life as we know it makes up 99% of the total space.
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This is an interesting claim. Perhaps you might start a thread to explore it in more detail?

No need for a new thread. It is rather trivial if you think like a topologist (those guys which cannot distinguish between a teacup and a donut).

Let L be a contractible *) region of N physical constants such that every combination in L is compatible with life (fine-tuners tell us that L is tiny).

Let U be the unit cube in N dimensions.
Map L one-to-one onto a cube C within U which has 99% of the volume of U, and all other combinations of constants onto the rest of U. Rewrite all physical equations in terms of the new constants.

Suddenly 99% of all possible universes (those described by points in C) are compatible with life!

Regards,
HRG.

*) i.e. topologically trivial

Malaclypse the Younger · 02-25-2002, 01:06 PM

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Originally posted by HRG:
Let L be a contractible *) region of N physical constants such that every combination in L is compatible with life (fine-tuners tell us that L is tiny).

Let U be the unit cube in N dimensions.
Map L one-to-one onto a cube C within U which has 99% of the volume of U, and all other combinations of constants onto the rest of U. Rewrite all physical equations in terms of the new constants.

Suddenly 99% of all possible universes (those described by points in C) are compatible with life!

*) i.e. topologically trivial

We are assuming the Axiom of Choice, are we not?

tw1tch · 02-25-2002, 01:25 PM

Malaclypse the Younger

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Originally posted by Malaclypse the Younger:
The analogy can be further extended by assuming the anthropic principle.

I am an experimenter. I have a box known to be a fair random number generator with a range of 1 to 10^12. I have another box known to be fixed to always produce a certain number; I know also that that number is the range 1 to 10^12. I also know which box is which, but I don't know what number the fixed box is preset to produce, nor do I know (by definition) which number the fair box will produce. I also have a coin known to be fair.

Why don't you know what number the fixed box is fixed to? Isn't this like saying you don't know the probabality that God would create the universe life friendly? Please exlain.

Tercel · 02-25-2002, 04:37 PM

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Originally posted by Wizardry:
This seems to be a very simple problem. All we are doing is comparing the values

P(E|C)*P(C) and P(E|D)*P(D)

which isn't really all that difficult considering that P(E|D) and P(C) can both be shown to be trivially close to one. For the purposes of this argument, P(C) is assumed to be equal to the value 1-P(D). Since P(D) is generally assigned a small a priori value, the value of P(C) becomes nearly 1, which makes the first term to be approximately equal to P(E|C).

Yup, I agree completely.

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P(E|D) can be considered to also be trivially close to 1 because the designer in question is defined to prefer a life-sustaining universe to a non-life-sustaining universe. This reduces the second term to approximately P(D).

You could do that. However it seems simpler to me to split P(E|D) and P(D), such that P(D) is the probability that the universe is the creation of an intelligent being, and P(E|D) the probability that an intelligent being who was creating a universe would create one sustaining life as opposed to one which does not.

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There are a few objections that can be raised with assigning such a high value to P(E|D). Knowing nothing else about a designer, other than the fact that he is a designer does not necessarily imply that he prefers life to non-life.

Agreed. However, in my experience an intelligent being usually finds other intelligent beings far more interesting than non-intelligence. All the argument needs though is that P(E|D) be not too low. Just how low it can be for the argument to still work of course depends on the values assigned to the other probabilities: But I would suggest that, in general, a P(E|D) = one in 10^10 or anything greater than that would be completely adequate for the argument.
But I think that is a ludicrously low probability anyway: Is an intelligent being ten billion more times likely to decide to create a universe incapable of sustaining life than they are of creating one capable of sustaining life?
If you asked me, I'd say the odds are about even or even significantly greater: That is to say, I don't see any reason to think an intelligent being would be more interested in making a universe without intelligent life than they would be in making a universe with intelligent life.

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So arguing from an anonymous designer stand point, the only motivation we have for arguing that P(E|D) is higher than P(E|C) is that E is somehow a preferred condition for a designer.

Not exactly. The difference is in the number of combinations they have to choose from.
An example:
Say there are a trillion different possible settings of constants - one of which allows intelligent life to form while the rest for some reason or another prevent life forming.
If the physical constants are taking their values by chance then the chance of them taking values allowing life are 1 in one trillion. ie P(E|C) = 1 in one trillion.
But this is different if an intelligent being is designing things. An intelligent being will not randomly select a constant combination, but rather it will have a purpose and a goal. It will make the basic decision of whether it wishes to allow intelligent life in the universe it's creating. Then it will select an appropriate combination of contants which will fulfill that design decision. Chance had a trillion options to choose from: The designer had two.
This is the whole key to the Fine-Tuning argument. The designing intelligent since it can have goals and purposes doesn't have the one in a trillion chance-level probability of selecting the life-allowing constants. Rather the designer will make the design to allow life or not -a two way decision- and select the physical constants accordingly.
Thus if we know nothing about the designer other than the being can make such a decision, then given two choices the probability of them choosing a given one is 0.5. ie P(E|D) = 0.5
While chance has a trillion choices to choose from giving P(E|C) = 0.000000001
The important point is that because the designer is intelligent it only makes a two-way decision instead of a trillion way one.

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The problem with that is that we are not fully aware of the special phenomena existing in other possible combinations of physical constants, which might also be unique and interesting to a designer.

There might be and they might be.
However for the argument it is usful to limit the discussion to our sort of life and physical constants moderately close to ours.
It doesn't do any damage to the argument though I don't think. Look at it this way: The range of physical constants near ours is our sample-space. Within our sample-space we find only a tiny proportion of combinations of the constants allow life. If ours is the only universe that exists, then the chance hypothesis would predict that our sample space contains a reasonable number of life-allowing combinations. While the design hypothesis makes no prediction on the matter. Thus the data serves to disconfirm the chance hypothesis to the degree suggested by Bayes' Theorem in the Fine-Tuning argument.

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To better illustrate my point, I am going to refer to the RNG example from the beginning of this thread. An analogous situation to the fine-tuning argument would be to argue that the generated number is a special number, say a prime number or a sum of squares or a product of cubes or a triangular number or some other mathematical anomaly, which receives special attention. Due to this unusual result, it might be concluded by some that the RNG wasn't truly random because the odds of getting such a special number is so low that there must be some intelligent force which prefers special numbers and contrived to output such a special number. However, the problem with this is that depending on how you look at it, any number might be interesting.

I agree that different people might find any number interesting certainly. However I objectt to the analogy of course. Your complaint with the analogy is that you find "interesting numbers" difficult to distinguish from "non-interesting numbers", is it not? The analogous complaint with the Fine-Tuning argument would seem to be that you find intelligent life difficult to distinguish from no intelligent life. Or possibly that an intelligent designer wouldn�t be interested at all in whether its created universe contained intelligent life or not. Do you really?

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For the sake of argument, I will concede a anthropomorphic designer and a value of 1 for P(E|D). Ultimately, this leaves us comparing the values P(E|C) and P(D).

I�m not arguing for a value of 1 for P(E|D) so you don�t need to �concede� it. I suggest 0.5 as I described above.

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I will first confront the less complicated issue: P(D). This term has the potential of rendering the argument to be rather unconvincing because a convinced theist could assign P(D) a very high value, making the entire argument little more than a confirmatory exercise. Likewise, a staunch atheist could assign P(D) an incredibly low value and render the argument similarly useless. That being said, I find it very difficult, if not impossible, to formulate a reasonable guess for P(D) that would not be pulled from my ass. I couldn�t possibly argue why the value should be 10^-54.32564 rather than 10^-43.89385.

I mostly agree. It�s a subjective thing, and it�s impossible to assign it an exact value. Certainly an extreme atheist might go so far as to say P(D) = 0 end of story and an extreme theist P(D) = 1 and likewise. However we can argue about what we think is reasonable and what we think isn�t, until we�re about agreed or at least certain of what we each think the values should be.
Personally I would say that the idea of some sort of intelligent designer is not inherently extremely improbable. What that translates into in terms of statistics is somewhat hard to say, although I think I would stick it at about 1 in ten. Certainly I would not be impressed by anyone who decided it was less than 1 in a million million million or so.

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Finally we have P(E|C). I really don�t see how we can reasonably determine a value for this. To my knowledge, we have no evidence concerning possible ranges for these values which would correspond directly to how probable or improbable it was. Sure, life as we know it would be non-existent in a universe where Newton�s constant of gravitation was 30 orders of magnitude greater than its current value, but is that a possible configuration? If experience has taught us anything in science and mathematics, it is that lucky accidents are not really accidents, there is most likely a simpler phenomenon which explains the amazing coincidences. I can not rationally justify assigning any kind of value to P(E|C), even a relative one, because it would be out of ignorance. I don�t even think that modern science has anywhere near the level of sophistication necessary to give us an idea. All they can say is basically �If the constants were different, the universe would be different from the one we observe and would have different phenomena, one of which is probably not life that we are familiar with�, which was obvious already.

I think modern science has sufficient sophistication to model small differences in the constants. I doubt there would be much trouble modelling anything up to a 10% difference and analysing the results. But we don�t even need that: Being able to accurately model a 0.00001 % difference in the constants is perfectly adequate. It gives us our statistical sample space and we can adequately derive the required data and numbers.

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The fine-tuning argument seems to boil down to determining which value is greater: P(D) or P(E|C). At this point in time, the answer seems inconclusive, forcing us to rely on other evidence in order to answer the salient question here.

I would say that at this point the evidence from the Fine Tuning argument looks very conclusive. Fifty or so orders of magnitude sort of conclusive.
Just curious, but if I was to convince you the Fine Tuning argument succeeded, which explanation would you opt for out of: Necessity, Many-many universes, and a Designer?

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I think we all know which way that evidence points.

Yip.

Tercel

02-25-2002, 05:43 PM

The argument from fine tuning shows only that any process that is conducive to the creation of life is a priori (as if we were really in a situation where we had no data with which to support our hypotheses) more likely to create life than a totally random processes. The question of whether a being is more likely to HAVE created life is a different issue for then we also have to factor in information that we do not have.

SOMMS,

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Note: At this point, the classic atheistic position is to ask 'But how can you KNOW that God would probably make a life-friendly universe?'

However, this is simply an argument from ignorance and can easily be countered simply asking 'How do you KNOW that God would NOT make a life-friendly universe?'

I have no idea that God would not make a life-friendly universe and that is the important point. By placing the value of the likelihood that God would produce life at 1.0 you are simply making the uninformative assertion that �If a god-who-creates-life exists, then he will create life�. You know what? You�re absolutely right, if the cosmic-sperm-of-an-ant-which-creates-life existed, the probability of life would also be 1.0. Therefore the cosmic-sperm-of-an-ant-which-creates-life is on equal footing, by this argument, as the God-who-creates-life hypothesis. (Although both are more likely to produce life than the universe-in-which-stable-entities-tend-to-persist possibility, I find this last theory a bit more plausible and is a good non-random alternative to God or The Ant.)

As anyone can see, there are an infinite number of X-which-produces-universes-which-support-self-replicating-processes hypotheses trivially supportable by the fine tuning argument. This is not a �God-who-creates-life vs. The Random Universe Generation Machine� debate.

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God is infinitely complex. If you have an infinite number of features (tuning constants, so to speak) we are left with, well, a rather large number of possible Gods. They could be nice, bad, totally evil, really nice or omnibenevolent. They could be physically embodied, they could a trinity(or any number of persons) male, female, both or any sort of entity (None of which are detectable or fathomable, of course!). Naturally, these qualities are independent. For example, whether God is hermaphroditic or homosexual has no bearing on his goodness or malevolence.

The fact that our God has the attributes that he does is so incredibly unlikely that we are forced to find some explanation for God:

1) A priori, the precise configuration of the God that we have is extraordinarily unlikely due to the infinite combinations of qualities a deity might have.
2)A meta-god-who-would-create-the-kind-of-god-we-have would increase the probability of God�s existence to 1.
3)God exists.

Therefore, by Bayes theorem (I don�t know if anyone cares to work out the calculations to glean that thin veneer of mathematical certainty that the FT argument enjoys.)

4)It is more likely that a Meta-God created God than our Deity coming about by random chance.

We simply don�t know how likely our universe is, we don�t know all possible mechanisms by which universes could come about and we don�t know the respective likelihood of said mechanisms. For this reason the anthropic fine-tuning argument for God fails and for this reason the theopic argument for Meta-God fails.

Regards,
Synaesthesia

Satan Oscillate My Metallic Sonatas · 02-25-2002, 06:46 PM

Synaesthesia,
A few points:

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Originally posted by Synaesthesia:

I have no idea that God would not make a life-friendly universe and that is the important point. By placing the value of the likelihood that God would produce life at 1.0 you are simply making the uninformative assertion

Not true. There is evidence to support that it is 1. Why should I conclude the contrary (that God wouldn't likely create life) when there is absolutely NO evidence to support such a premise???
An unbiased thinker would not come to such a conclusion.

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Originally posted by Synaesthesia:

You�re absolutely right, if the cosmic-sperm-of-an-ant-which-creates-life existed, the probability of life would also be 1.0.

Your absolutely right. However, there is no evidence to support 'cosmic-sperm-of-an-ant'. There has been no revelation of 'cosmic-sperm-of-an-ant'. Mankinds history has not been affected
by 'cosmic-sperm-of-an-ant'. Mankinds eternal ponderance of God has these things. In short,
'cosmic-sperm-of-ant' is not a credible threat whereas God is (at the very least) a meaningful, cohesive idea(l).

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Originally posted by Synaesthesia:

As anyone can see, there are an infinite number of X-which-produces-universes-which-support-self-replicating-processes hypotheses trivially supportable by the fine tuning argument. This is not a �God-who-creates-life vs. The Random Universe Generation Machine� debate.

Also not true. It is not as trivial as you say. Notice in EVERY case of 'X-produces-life-friendly-universe' X MUST exhibit the following attributes:
A-An unlimited amount knowledge to design such a mechanism (the universe and everything in it)
B-An unlimited amount of power to pull it off
C-A will to do so.
D-An essence distinct from and transcendant of the actual creation.

Know what? If 'cosmic-sperm-of-ant' exhibited these properties I would definitely regard 'cosmic-sperm-of-ant' as God.

The specific syntax we use to refer to 'life-friendly-universe-creator' isn't important. The attributes are.

Thoughts and comments welcomed,

Satan Oscillate My Metallic Sonatas

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