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Author
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Topic: Universal probability bound?
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Melvin H. Fox
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posted 02. November 2005 14:28
I am new and ask your patience if this matter has already been settled. I have read Dembski’s book Intelligent Design. I have also followed closely the thread on the 2nd and 4th laws of thermodynamics. Is there a consensus on the existence of a universal probability bound? There seems to be no challenge to the idea of a non-zero lower limit to the probability of an event occurring by chance. If accepted then doesn’t chance immediately become impotent as an agent of change at least in the realm of evolutionary processes? Chance being castrated; are we not left with a designer as the only plausible explanation of the universe and life in it?
[ 11. November 2005, 06:57: Message edited by: Moderator ]
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Evan
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posted 02. November 2005 21:56
The question is how do you determine the probability of an event happening, because no real-world event happens by pure chance: all events are caused by a sequence and confluence of other events that are largely caused by natural laws in conjunction with some contingent and chance factors.
So the idea of whether there is a UPB, and what is it, is fairly empty without a way of realistically calculating the probability of events that we in fact do know happen without the intervention of a designer.
[ 02. November 2005, 22:22: Message edited by: Evan ]
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John A. Davison
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posted 02. November 2005 23:11
Einstein remained a convinced determinist:
"Everything is determined... by forces over which we have no control."
I agree. It is fundamental to the Prescribed Evolutionary Hypothesis and is antithetical to neoDarwinism. Leo Berg, referring to both ontogeny and phylogeny put it this way:
"Neither in the one nor in the other is there room for chance."
Nomogenesis, page 134
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kyle7
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posted 03. November 2005 03:45
Melvin,
I think your answer is yes -- the whole theory of evolution does become suspect if Naturalists accept the design inference, where the upper probability bound is used to discern complex specified information. This is why, I think, there is such opposition to ID.
The critics of ID would accept some upper bound, but they question whether we can realy know with accuracy this probability -- it is so small if it approaches the upper bound. Their fear is that it would be too easy to challenge NeoDarwinism, and the potential exists to inaccurately calculate this probability. For example, ignoring some of the "side information" could lead to significant differences in the results. Many within the scientific community view those within the ID community as shysters, so they fear this assault on NeoDarwinism could lead to manipulation and distortion.
I think the fear of miscalculating the probability is groundless. As in any scientific endever, the process and methods should be clearly stated in the paper describing the work. Others will then be able to challenge the assumptions made within the work and put forth new work to show why they think the first work was wrong. The benefit that ID affords science, is that it will force scientists to address the weak points of NeoDarwinism. If NeoDarwinism is true it will only strengthen the theory. If it is wrong, ID will begin to grow in strength as more and more areas of evolution are challenged and questioned.
An example will help show some of the difficulties. Let us say that we found some markings in a sandy desert and we wanted to decide using ID if these were natural or made from some form of intelligence. How would we go about examining this? One method would be to take random photographs of "natural" sand within the desert and see the different formations we would expect to find. We could develop an ID program to compare the picture of the markings to the picture of the odd sand formations. If we took enough samples we could determine whether or not the markings are designed. But a noticeable problem is evident: taking enough samples to approach the upper probability bound would be prohibitively long. So does this limitation make ID useless? No. You just have to examine a number of parameters and not just one. For example, with the sand marking you may have to divide the markings up into sub-markings. You find the probability of each sub-marking developing naturally in the environment and then attempt to find the probability of the combined total markings. You also could try examining different wavelengths of light in taking the pictures. You could develop a fluids model to examine the effects of wind on sand. The big challenge would be to incorporate all the individual probabilities together. As ID progresses, I think you will begin to see this area explode with research. Probability and statistics will be pushed forward by ID.
While, I am on the subject, let me point out some difficult areas.
1) If we confine our search of desert sands too narrowly, then you could see erroneous results. For example, if we took samples in the wrong desert than our results on the probability may be way off.
2) The fluids results would be highly influenced by the initial conditions. Possibly our lack of understanding the initial conditions would skew our probability results.
3) We may have failed to account for some physical phenomenon. For example, we may have only used gases in the fluids analysis when actually the sand formation was due to water. We may have overlooked lightning resulting in a probability totally off basis.
4) The method of combining the probabilities may be wrong. For example, the existence of one sand formation may mean that the probability of the other sand formation existing together may be much higher than what we assumed.
5) Even if we had a number of parameters to use in the calculation of the probabilities, reaching the upper probability bound would be difficult. As ID advances, I think the notion of only one upper probability bound will change. Some problems may find the use of an upper probability bound less stringent than that proposed by Dr. Dembski. I think that over time we will develop standards on what to base the upper probability bound based upon the different types of problems and fields of ID. Initially, ID will use little physics, but I think over time the amount of physics will increase.
[ 10. November 2005, 02:29: Message edited by: kyle7 ]
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Melvin H. Fox
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posted 04. November 2005 13:32
Thanks to all who replied. Kyle, your sand example does show some of the difficulties in calculating probabilities. But a discovery of an object like the pyramids in the middle of a desert would require no calculation; they could not have formed by chance. Perhaps in a simpler example the role of chance will become clearer. Suppose we take a fair six sided die, gently shake it back and forth in a cup for 3 seconds and release it ten centimeters above a one km2 hard flat surface. Some of the forces in this experiment we have limited control over and some we have no control over. We can make predictions about what will happen to the die upon release with varying degrees of certainty. Under normal initial conditions the die will come to rest on the surface. Of this we are sure and chance has clearly nothing to do with it.
Let’s say that of the six faces we have a favorite. Call this face “three”. We are convinced that it is possible that the die could come to rest with “three” face up. Because of the extremely limited control and the symmetry of the fair die, our favorite face is no more likely to be face up than any of the other five faces. Which of the faces that ends up face up is then normally attributed to chance. Let’s remember not to give chance too much credit here. After all, the position of the die throughout the experiment is completely determined by the forces acting on it and the laws of motion. Chance is only at play in our predictions of what will occur.
What if we predict that the die will come to rest on one of the eight corners? Is this event even possible? To my knowledge, there is no account of such an outcome. On the other hand, having witnessed a man stack eight bowling balls one on top of the other, I am sure someone with a steady enough hand could place the die on the surface so that it would rest on one corner. Is the argument then: The event the die will land on one of its corners by chance (without specific control) is possible because it is possible for the die to be placed (with specific control) in that position? Intuition is definitely in opposition to this argument. If we were to witness someone role a corner, we would immediately attribute the result to some sort of outside interference.
In general, if the complexity of an individual outcome reaches a certain level, we internally decide that it could not occur by chance. Some known or unknown force must have caused it or controlled the other forces at work. The problem for ID is to show that this intuitive conclusion is empirically or at least theoretically true. I am not an expert in information theory. Is the choice Dembski makes for the universal probability bound arbitrary or derived from sound theory?
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kyle7
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posted 10. November 2005 03:58
Some probability calculations would have to be done even if you did discover pyramids. Possibly the pyramids could be due to crystalization. For ID to be scientific you couldn't just say, "Oh that pattern must be designed because my gut tells me it is." You would have to show your analysis.
The initial conditions in the die example can be used to predict the outcome of the throw, but the outcome will still be a probability and not a concrete answer. At the molecular level, everything is based on probabilities, due to quantum mechanics. For one throw, the molecular vibrations may cause the die to fall one way and another throw with the exact same initial conditions, assuming we could get the exact same initial conditions, the die may fall another.
If the die landed on its edge, then it would be unstable. It would tend to fall toward one direction or another. The molecular vibrations would play a part in this. Now if we did see a die stay on the edge for an extended period of time, this could suggest that some dynamic force is causing this effect. Some force is cancelling out the normal molecular vibrations and other forces tending the die to fall.
Behe has championed the irreducibly complex biological systems in ID. Dembski has championed complex specified information (CSI) in ID. Others have championed the fine tuning found in nature. So, I think this notion of complex dynamic systems is another field of ID. Essentially, this field is very similar to Dembski's CSI, but rather than dealing with information we are dealing with mechanics and physics of dynamical systems. I bring this subject up because you seem to touch on this in your post.
The universal probability bound given by Dembski is based on the maximum possible number of atomic collisions that could have occurred throughout time based on what scientists believe the Universe to be (off the top of my head I think this is what Dembski bases it on). My books are in storage so maybe someone could verify that my memory is correct. So Dembski's use of this stringent probability bound does have merit in keeping the critics of ID at bay.
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Christopher D. Beling
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posted 10. November 2005 19:17
Hi Melvin,
Let me add some comments that might clarify the correct scientific perspective on the UPB and provide some of those details mentioned by Kyle.
Take a look at the following diagram - This shows the probability P(m) of "having thrown a 6 at least once in m trials".
This distribution is known as the Cumulative Geometric Distribution in probability theory - more details can be found Dr. Dembski's book "The Design Inference" (DI) p 176. It is the correct distribution for understanding small probabilities. We can derive this curve as follows:
Prob of 6 of 1st throw = (1/6)
Prob of 6 not on 1st but on 2nd = (5/6)x(1/6)
Prob of 6 not on 1st/2nd but on 3rd = (5/6)^2x(1/6)
Prob of 6 not on 1st/2nd/3rd but on 4th = (5/6)^3x(1/6)
Prob of 6 not on prior m-1 but on mth = (5/6)^m-1x(1/6)
So the cumulative probability of having thrown at least one 6 within "m" throws is the sum of the above:
P(m)=(1/6)*[1+(5/6)+(5/6)^2+(5/6)^3 + . . . (5/6)^(m-1)]
=1-(5/6)^m
where we have summed the geometric series using the standard formula - however the result is also seen in the sense that (5/6)^m is the prob of throwing any thing that is not a 6 m-times.
This result is easily extendable - if we are dealing with a small probability "p" of an event happening by chance in one throw then the chances of it happening in "m" throws is:
P(m)=1-(1-p)^m
Going back to the dice example - where the (1/6) is not really that small a probability - how many throws do you need to have a 50:50 chance of getting a 6 - the answer is ln(0.5)/ln(5/6)=3.8 throws. If we extend this to the case where probability "p" is very small and ask how many trials m* are required to give a 50:50 chance (i.e. just as likely as not) then we find the neat result (DI,page 203):
m*=ln(2)/p ~ 1/p
Well where is all this leading us. Basically to this - that in order to see a low probability event one must normally expect to wait for ~(1/p) trials .
Lets take an example from physics:- The neutral pion particle decays normally into two gamma photons:
pion -> photon + photon (p~0.99)
but very occasionally it can also decay into a positron electron pair
pion -> electron + positron (p~10^-7)
How many pion decays must the physicist expect to look at before he/she sees this rare decay? - the answer is ~ 1/p=10^7=10,000,000. Indeed we can say that if the physicist saw this rare decay occuring as the first event after switching on the detectors he/she would be very surprised indeed - because the probability is of this happening is so very low. If he/she did see such a thing - they would say "thats such a complete fluke" - (luck similar to winning a national lottery and impossible). He/she would not believe it was a real detection and would check the apparatus and then repeat. Then what if exactly the same thing happened (after checking) and after switching on the detectors? Well then the physicist would know there was something most decidedly strange going on and that this did not happen by chance. But the major point I am making is that the physicist knows that in order to "see" a rare event of the order of (1/p) attempts must be made.
Universal Probability Bound : This is defined based on the above sort of reasoning: In order for an event (small probability p) to occur with any liklihood we must have the possibility of (1/p) attempts. But such possibility is limited physically by the number of fundamental particles in the universe and the maximum number of times they could have changed state. Quoting Dr. Dembski (DI page 209):
quote:
Specifically, within the known physical universe there are estimated to be no more than 10^80 elementary particles. Moreover, the properties of matter are such that transitions from one state to another cannot occur at a rate faster that 10^45 times per second. Finally, the universe itself is about a billion times younger than 10^25 seconds (assuming the universe is around 10 to 20 billion years old). ....these cosmological constraints imply that the total number of specified events throughout cosmic history cannot exceed
10^80 x 10^45 x 10^25 = 10^150
With this 10^150 being the largest number of trials that the universe is capable of making - With this being the absolute maximum "throwing" capability that the universe can muster it can be asserted that any possible event having a probability of less than 10^-150 is not going to occur with any reasonable liklihood. Corollary: if such an event is observed to have occured then chance is not the best inference. [Note also Dr. Dembski has already over-estimated the "throwing" capability by writing the time as 10^25 sec - this is ~10^9 times longer than the time since the Big Bang! - this gives a large safety margin and the UPB should really be more like 10^-141]
- Chris
[ 11. November 2005, 06:20: Message edited by: Christopher D. Beling ]
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Zachriel
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posted 11. November 2005 16:12
Christopher D. Beling: "With this 10^150 being the largest number of trials that the universe is capable of making - With this being the absolute maximum "throwing" capability that the universe can muster it can be asserted that any possible event having a probability of less than 10^-150 is not going to occur with any reasonable liklihood."
Hmm. I shuffled two ordinary playing decks of cards together. I then examined the order of the cards. I note that they are arranged in a specific pattern the probability of which exceeds the "Universal Probability Bound".
http://www.google.com/search?hl=en&q=104%21
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Christopher D. Beling
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posted 11. November 2005 20:15
Hi Zachriel,
The number of ways of getting any single combination of the 104 cards (produced by putting both packs together) is indeed 1.03x10^166. The probability of your getting the hand you have drawn by chance is indeed 0.97x10^-166 which exceeds (or should we say more correctly is below) the UPB. Agreed - but the problem here is that you have post-specified . The fact is that you said only after having shuffled and distributed - "thats my specific pattern". You could have said this about any outcome - and if all outcomes can be "specific patterns" at the will of the observer then it follows that the probability of getting a "specific pattern" could be as high as 1. No - try pre-specifying. For example if you had said my pre-specification is that all the cards must come out in the order:
[Pre-Spec#1>=Clubs 1-10,J,K,Q,Clubs 1-10,J,K,Q, Spades 1-10,J,K,Q, Spades 1-10,J,K,Q, Hearts 1-10,J,K,Q, Hearts 1-10, J,K,Q, Diamonds 1-10,J,K,Q, Diamonds 1-10,J,K,Q
then the probability would be 10^-166x10^31=10^-135.
I can fairly well guarantee that based on probability you are not going to realize your pre-spec configuration. Moreover, if you do realize [pre-spec#1> then it would not have been by chance. It is true that 10^-135 is a larger probability than the UPB, but in terms of the local "throwing" resources you have (i.e. the LPB=Local Probability Bound - i.e. your throwing rate would probably be only 1 every 10 sec) it is still so unlikely that one would not expect it to happen by chance.
The need to pre-specify is very important - especially when considering biological systems - it is not up to any human observer in such cases to dictate what DNA coding specifications are going to be functional (specified) [i.e. "that DNA configuration looks nice - or no I will choose this one"]. What works with the DNA configuration will be determined solely by physico-chemical laws and the environment (physical and ecological). i.e. we are not at leasure to post-specify.
- Chris
[ 11. November 2005, 20:43: Message edited by: Christopher D. Beling ]
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kyle7
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posted 13. November 2005 03:28
The critics of ID often make this mistake. In his book, Dembski goes into significant detail on this subject. We are not just looking for an improbable event, we are looking for an intelligent pattern. For example, a signal form space that sequentially transmitted the first hundred prime numbers would be such a pattern. A pattern in the sand that was written out "I am here" would also suggest intelligence. The probability of seeing such an event occuring naturally would suggest that the writing was from some intelligent being -- it is so improbable and the writing shows that we are not just cherry picking what we want to see.
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RBH
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posted 13. November 2005 23:05
Christopher wrote quote:
Going back to the dice example - where the (1/6) is not really that small a probability - how many throws do you need to have a 50:50 chance of getting a 6 - the answer is ln(0.5)/ln(5/6)=3.8 throws. If we extend this to the case where probability "p" is very small and ask how many trials m* are required to give a 50:50 chance (i.e. just as likely as not) then we find the neat result (DI,page 203):
m*=ln(2)/p ~ 1/p
Well where is all this leading us. Basically to this - that in order to see a low probability event one must normally expect to wait for ~(1/p) trials .
There are one or two assumptions underlying that equation that you folks might want to take into consideration. For example, it assumes that the trials over which the probability is estimated are independently and identically distributed (i.i.d.). Ask yourself how useful that assumption is for calculating the probability of assembly of a chemical system of interconnected mutually catalyzing reactions, or any system in which trials are not independent, rather than in tossing dice and flipping coins.
RBH
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Zachriel
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posted 14. November 2005 08:29
Christopher D. Beling: "Agreed - but the problem here is that you have post-specified."
Funny then, how some try to apply postdiction (and UPB) to the origin of life, not knowing the exact deck, the method of shuffling, or even how many cards are in the deck. How likely is it that trillions of atoms will line up in perfect formations? So unlikely, that ancients had to invoke the Intelligent Designer, Vulcan, to explain crystals.
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Christopher D. Beling
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posted 14. November 2005 20:16
Hi, RBH
I would really like to understand your point to see if we fundamentally we agree. Not being a chemist I may need some correction, but I will proceed anyway (in trepidation) to try and make progress and clarify issues. My understanding is that you are proposing that the following sort of system presents a problem for the law of small probabilities (i.e. the UPB).
Here I draw only 6 enzymes Xi (i=1-6) that are mutually interacting. Something like:
and the system would be characterized by certain reaction rates to the nth enzyme Lamda(Ci,Cj,Ck;n), Ci Cj and Ck being the concentrations (or perhaps probabilities of finding at a location) enzymes Xi,Xj and Xk. Although complex, the system can be characterized at any time "t" by a concentration "vector"
[C;t>={Ci}=(C1,C2,C3,C4,C5,C6).
The time evolution of the vector [C;t> will no doubt be very complex and dependent on the initial state [C0;t=0>, but I think it is true (correct me if I am wrong) that the system will tend towards some equilibrium state [C0*>. It is probably also true that given a different initial state [C1;t=0> that a different final equilibrium state [C1*> may be obtained. However, I think (and again correct me if I am wrong) that there are not an infinity of final states to this system - that the system will "relax" into only a finite set of final states - say [Cm*>, m=1 thru M.
If what I have said so far is true, in general outline, then it follows that we can define probabilities p(m) of getting any of these M final system states? But here it must be understood that this probability is obtained by averaging over ALL POSSIBLE INITIAL STATES [CN;t=0>. This is true only if we know nothing about how the system was initiated - only that some chemist has had access to these 6 enzymes and has been able to "throw" them together in different initial proportions.
Note here I have assumed that all the probabilities p(m) are computable. Although the equations are awesome - I suspect there may indeed be analytical solutions - but even if there are not then numerical solutions can be assumed and found if all the reaction rates are known.
In this system of enzymes I think it unlikely that any of the probabilities will be that small. Say if there were 10 possible final states one might expect that the system might land in, then I would be very surprised if the probabilities where very much less than 1/10. [Of course the sum of all probabilities must be unity]. But in principle I guess it may be possible for one of the final states to have a p-value less than the UPB - say 10^-160. Should this be the case then by the law of small probabilities we would conclude that if this state was observed then it is very unlikely to have resulted from a chemist randomly throwing together different enzyme solutions . Perhaps it is more likely, though, that the probabilities of the final states are more ~10^-1 in which case we can infer that they did come about by a combination of chemical law and chance.
quote:
Ask yourself how useful that assumption is for calculating the probability of assembly of a chemical system of interconnected mutually catalyzing reactions
In the above example I have described the probability calculations were assumed tractable. In my understanding the "calculating the probability" problem is a separate issue to whether one can use probabilities to infer chance or not.
It is interesting to reflect on the fact that if we had not started the above system with some of the basic enzymes, but rather we had just thrown together in a reaction chamber all the separated O,C,H and N atoms that comprized the make-up of the 6 enzymes and asked for the final state probabilities p(m) then we would have gotten a very different set of p(m). Indeed I would hazard a guess that in this case the p(m) would have been much much less than the UPB - perhaps of order 10^-10,000 (as some of the calculations to produce the compounded probability of producing a single functional protein by chance are of this order of magnitude). Likewise if I was to "throw" all the separated constituent protons, neutrons and electrons into the reaction chamber at time zero I would get an even smaller probability (perhaps akin to getting a pyramid built by chance?). In short I agree that the final state probabilities p(m) do depend heavily on the initial conditions - i.e. what is it that we are "throwing"?
quote:
it assumes that the trials over which the probability is estimated are independently and identically distributed (i.i.d.).
I dont think that in the enzyme case discussed the outcomes were identical (all final probabilities were assumed different) - however I believe that all trials were independent. Our hypothetical chemist was "throwing" different enzyme solutions if you like at random - and hopefully taking no thought for the previous solutions (and their outcomes) that he had concocted. Am I understanding what you mean by independently and identically distributed (i.i.d.)?
Hoping this will stimulate more discussion
-Chris
[ 14. November 2005, 22:45: Message edited by: Christopher D. Beling ]
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RBH
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posted 15. November 2005 02:48
I am pressed for time these days. Here's a brief reference for i.i.d. The "identically" doesn't refer to outcomes, but to distributions -- the PDFs.
Given that we know that carbon-based compounds are common in (non-biological) terrestrial and extra-terrestrial environments, the initial conditions were almost certainly not aggregations of bare atoms of C,O,H, N, etc.
As I said, I do not have a whole lot of time, but as I do, I'll re-read the relevant parts of Kauffman's Origins of Order. Though it's been some years since I read it, as I recall he spends some time on the topic.
RBH
[ 15. November 2005, 02:50: Message edited by: RBH ]
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kyle7
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posted 15. November 2005 02:51
RBH,
Could you not take the probability that is most favorable for evolution/abiogenesis and use this initial guess in calculating the probability? An accurate probability is not needed -- just the worst case probability. Specifically, you can take the probability that is most favorable for evolution/abiogenesis. Everyone should see that if we assume probabilities most favorable for evolution/abiogenesis and the results shows that it cannot happen, then this analysis is a strong indicator that life did not arise naturally. We don't even require a normal distribution. Each distribution could be completely different.
So, why do you make this an issue, when it is not even a problem for ID?
The cell is not just a few amino acids thrown together. Extreme precision is observed within the cell. Rather, the cell is like a nanomachine that has extreme complexity. Now that science has been able to identify the building blocks at the molecular level, it should be evident that we lack a lot of information about life.
Regards
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