Universal Probabilty Bound?

[inocente]

Maybe at least one difference from the snowflake is there there are so many of them that it is not surprising when many possible combinations occur.

Another difference from here: (the notion of a “tidy” explanation.
…]
Read more: reasonablefaith.org/fine-tuning-argument#ixzz1syZvIVwX

To me the “tidy explanation” business feels like special pleading. I mean, “God done it” is for some a very tidy explanation, and for others no explanation at all.

I’ll put forward the Mandelbrot set. It’s infinitely complex, 100% probable, yet based on iterating around the simplest of rules (for anyone new to it, here’s a zoom into one area).

If we didn’t know how that pattern is generated then it’s so complex we might well believe it’s intelligently designed. A central flaw in Dembski’s work is that every candidate he finds could as easily be the result of a dumb process which no one has yet worked out.

I guess you could argue that even simple rules must themselves be intelligently designed, but that would seem to make Dembski’s upb and specified complexity pointless.

 

[yppop]

I will do better than that. I will teach you how to do it, and then next time you don’t have to ask, you can simply do it.

The function is F(x) = ax[sup]5[/sup] + bx[sup]4[/sup] + cx[sup]3[/sup] + dx[sup]2[/sup] + ex + f
where a, b, c, d, e and f need to be resolved. We know that
F(1) = 7
F(2) = 23
F(3) = 11
F(4) = 42
F(5) = 3
because that is what you wanted. Now, substitute 1 into x and you will get
a + b + c + d + e + f = 7
Now substitute 2 into x and you will get
32a + 16b + 8c + 4d + 2e + f = 23
… keep on substituting the values of 3, 4 and 5. You will get 5 linear equations with 6 variables, so you will get infinitely many solutions. Easy as a breeze. Finish it at your leisure. I hope you can solve a set of linear equations. If you cannot, get an HP calculator to do it.

Serious
Thank you for your answer; but I am still missing something that apparently is a simple task for both you and Gorgias, so I ask: what is the simple method for finding the values of the 6 variables a, b, c, d, e and f with only 5 linear equations? I know how to solve for variables in equations by elimination and substitution, but I thought that (n+1) variables in equations is unsolvable. You seem to imply that the situation of (n+1)V in E results in and infinite number of solutions. I thought that the opposite V in (n+1)E yields an infinite number of solutions. So where am I wrong?

I know that what I am asking has nothing to do with the point you are making (order does not mean design?) and even though I am 78 years old I am still learning and would appreciate a “simple” answer.
Yppop

 

[danserr]

To me the “tidy explanation” business feels like special pleading. I mean, “God done it” is for some a very tidy explanation, and for others no explanation at all.
…

I guess you could argue that even simple rules must themselves be intelligently designed, but that would seem to make Dembski’s upb and specified complexity pointless.

But by “tidy explanation” we don’t mean “emotionally satisfying.” It’s a technical term (as the article indicates) that refers to something that while it explains a phenomenon also reveals that there is something to be explained.

It’s not special pleading that applies to God alone, the examples given in support are totally secular.

Leslie gives a great many charming examples of tidy explanations. For instance, you are shopping in the bazaar, and the silk merchant is displaying for you a drape of silk. His thumb just happens to be covering the moth hole in the cloth. Now of course his thumb has to be somewhere, and any location on the drape is equally improbable; nevertheless—! That he is hoodwinking you provides a tidy explanation of why his thumb happens to be where it is. Or again, Bob, who was born on August 23, 1982, receives a car for his birthday from his wife with the license plate BOB 82382. That this plate number is the result of intelligent design is a tidy explanation of it. In light of the fact that it is Bob’s birthday which is being celebrated, one is not being “Bob chauvinistic” in singling out his name and birth date as a significant pattern crying out for explanation

Read more: reasonablefaith.org/fine-tuning-argument#ixzz1t3ZQ4XKh

 

[buffalo]

The link in the OP cites the definition at iscid.org/encyclopedia/Universal_Probability_Bound - the “about” page on that site lists Dembski as its Executive Director.

Notice the word - specified

A degree of improbability below which a specified event of that probability cannot reasonably be attributed to chance regardless of whatever probabilitistic resources from the known universe are factored in. Universal probability bounds have been estimated anywhere between 10^–50 (Emile Borel) and 10^–150 (William Dembski).

 

[buffalo]

I guess you could argue that even simple rules must themselves be intelligently designed, but that would seem to make Dembski’s upb and specified complexity pointless.

You make a point that rossum and I have posted about. That may be because we are inside the design frame itself.

 

[Alberti_Devoveo]

Yppop asked the same question, and I presented the method how to do it. And, no it does not have to be in ascending order and it does not have to be integer either. See the post directly above. It does not have to be just 5 numbers. It could be 10 numbers or a 100, or 10million. It does not matter. Of course the calculation would be very tedious, but elementary.

I do not quite believe it; having an infinite number of solutions is not a solution.

No. The numbers were created by a random number generator (not an easy task, but can be done). When we get the result, we “cheat” and create a formula, which would give the same result. But we can do this only AFTER we recieved the result, and “design” would demand that we do it BEFORE the result is presented.

I hate to inform you, but RNG’s are not actually random. There is a prescribed formula to the values pulled out to make it appear random, but it is not really random; hence they are often called pseudo-random number generators.

 

[Gorgias]

Serious
Thank you for your answer; but I am still missing something that apparently is a simple task for both you and Gorgias, so I ask: what is the simple method for finding the values of the 6 variables a, b, c, d, e and f with only 5 linear equations? I know how to solve for variables in equations by elimination and substitution, but I thought that (n+1) variables in equations is unsolvable.

I just looked back and saw Serious’ solution. I’m with you on this one: as you can see from my example, I was picking two points and forming a line; in other words, I was suggesting that a solution from a series of points (n, F) should be of the form:

c[sub]1[/sub]x[sup]n-1[/sup] + … + c[sub]n-1[/sub]x + c[sub]n[/sub] = F

In other words: n equations in n unknowns (i.e., an (n-1)[sup]th[/sup] degree polynomial).

 

[inocente]

But by “tidy explanation” we don’t mean “emotionally satisfying.” It’s a technical term (as the article indicates) that refers to something that while it explains a phenomenon also reveals that there is something to be explained.

It’s not special pleading that applies to God alone, the examples given in support are totally secular.

I beg to differ. The examples given involve human agencies, the pleading is that we should ascribe motives to events. Here’s the horse’s mouth, John Leslie himself:

5.31 We must tread carefully here because, I repeat, the availability of a tidy explanation does not mean that other explanations are wrong. The tidiness of an explanation can confirm only that some explanation or other is needed. Competing explanations may be even more tidy. So we might on reflection prefer to believe that our universe, and any others which actually exist, had to be life-containing since God wanted to produce living beings. I am saying only that it would be wrong to reject all explanations in this area, deciding that there was nothing to be explained. - books.google.es/books?id=K71RVWGn0EwC&pg=PA125&lpg=PA125&dq=tidy+explanation&source=bl&ots=76yqceUtvg&sig=OK1yCGZ2buAzFF2hTCKxxyjNZGw&hl=es&sa=X&ei=4QSYT5WKAoOHhQflhNSHBg&ved=0CGUQ6AEwCQ#v=onepage&q=tidy%20explanation&f=false

He doesn’t really seem to be saying much except that maybe the universe is fine-tuned, so maybe there’s a fine-tuner, and maybe the fine-tuner is a powerful personal agent, maybe with a motive, and maybe the motive is to produce living beings such as John Leslie. Few too many maybes.

 

[inocente]

Notice the word - specified

I did but the whole idea sounds daft to me. For instance, look here at a supposed calculation of specified complexity - I can’t take any of it seriously (the article suggests that few others can either, one summary being * ‘A study by Wesley Elsberry and Jeffrey Shallit states that "Dembski’s work is riddled with inconsistencies, equivocation, flawed use of mathematics, poor scholarship, and misrepresentation of others’ results"’*).

 

[buffalo]

I did but the whole idea sounds daft to me. For instance, look here at a supposed calculation of specified complexity - I can’t take any of it seriously (the article suggests that few others can either, one summary being * ‘A study by Wesley Elsberry and Jeffrey Shallit states that "Dembski’s work is riddled with inconsistencies, equivocation, flawed use of mathematics, poor scholarship, and misrepresentation of others’ results"’*).

Not unusual for skeptics…what do you expect them to say. They would just like for him to go away.

 

[inocente]

You make a point that rossum and I have posted about. That may be because we are inside the design frame itself.

Not sure I understand, could you please expand on it a little.

 

[inocente]

Not unusual for skeptics…what do you expect them to say. They would just like for him to go away.

Do you mean like being at a party and hoping the bore doesn’t spot you?

 

[buffalo]

Not sure I understand, could you please expand on it a little.

rossum and I had a few go arounds on how design can be proven. It may be that because we actually live inside the design frame of reference that we cannot differentiate design. In other words, we would have to be outside this frame of reference to actually see design. Being in the frame itself everything looks designed to us, but that could be that the entire frame is designed therefore everything in it.

 

[buffalo]

Do you mean like being at a party and hoping the bore doesn’t spot you?

no - more like the guy who is going to crash it.

 

[danserr]

I beg to differ. The examples given involve human agencies, the pleading is that we should ascribe motives to events. Here’s the horse’s mouth, John Leslie himself:

5.31 We must tread carefully here because, I repeat, the availability of a tidy explanation does not mean that other explanations are wrong. The tidiness of an explanation can confirm only that some explanation or other is needed. Competing explanations may be even more tidy. So we might on reflection prefer to believe that our universe, and any others which actually exist, had to be life-containing since God wanted to produce living beings. I am saying only that it would be wrong to reject all explanations in this area, deciding that there was nothing to be explained. - books.google.es/books?id=K71RVWGn0EwC&pg=PA125&lpg=PA125&dq=tidy+explanation&source=bl&ots=76yqceUtvg&sig=OK1yCGZ2buAzFF2hTCKxxyjNZGw&hl=es&sa=X&ei=4QSYT5WKAoOHhQflhNSHBg&ved=0CGUQ6AEwCQ#v=onepage&q=tidy%20explanation&f=false

He doesn’t really seem to be saying much except that maybe the universe is fine-tuned, so maybe there’s a fine-tuner, and maybe the fine-tuner is a powerful personal agent, maybe with a motive, and maybe the motive is to produce living beings such as John Leslie. Few too many maybes.

I draw your attention in particular to his remark:

I am saying only that it would be wrong to reject all explanations in this area, deciding that there was nothing to be explained

So Leslie is saying that it would be wrong to conclude “well there is nothing to be explained.” We don’t automatically jump from this to “therefore God is the explanation,” that requires further reason. But what Leslie show, is that we cannot just claim as Serious and many pop. level skeptics want to, "well any hand is equally improbable, therefore there is nothing to be explained.

Surely, you would agree that if we were playing 5 card draw and I won with 4 Aces 12 hands in a row that would cry out for explanation?
Or that if we came across an arrow stuck to a barn in the middle of a bullseye that it did not come to be there by chance?
Or that if for his birthday on August 9, 1955, Bob was given a car with the liscense plate BOB 891954, there would be something to be explained?

The issue is not if the event is human or not, but on coming to a specific event, what is the best explanation of it. Now, Leslie says, that we can’t just assume that a tidy explanation is correct (rightly so), because there might be a better one. But this does show why simply claiming a certain event is just the result of chance is insufficient.

As for applying this to the universe and God, there are fewer maybe’s than you think. You say “maybe” the universe is fine-tuned, but this is widely accepted, so let’s take that maybe away.

Since, this is the result of chance, necessity or design, then we would have to consider the alternatives to design. Chance and necessity strike me as weak, this leaves design.

If a designer, the designer would presumably have to be very powerful, so it is not much of a jump to get to a powerful personal agent.

Since, the fine-tuning brought a series of values into the right range to allow for life, then it seems also probable that the fine-tuner desired to produce intelligent life. So, this doesn’t seem to require too many maybe’s at all.

It only gives you a probable argument, I think, not mathematical proof, but I see no problem with that.

 

[Serious]

I just looked back and saw Serious’ solution. I’m with you on this one: as you can see from my example, I was picking two points and forming a line; in other words, I was suggesting that a solution from a series of points (n, F) should be of the form:

c[sub]1[/sub]x[sup]n-1[/sup] + … + c[sub]n-1[/sub]x + c[sub]n[/sub] = F

In other words: n equations in n unknowns (i.e., an (n-1)[sup]th[/sup] degree polynomial).

And this is correct. The simplest possible polynomial is indeed unique. Of course using a higher polynomial would yield infinitely many solutions, but there is no need to complicate the matter beyond necessity.

If there are 2 point, a linear equation is sufficient, if there are 3 points, then a quadratic equation is enough. But of course we can always find a higher degree polynimial, which will yield the same results.

 

[Serious]

would appreciate a “simple” answer.

And a simple answer is coming. As Gorgias pointed out, the simplest polynomial is always unique. A few words about linear equations in general.

First, if you have more unknowns than equations, you will have infinitely many solutions. If you have more equations than unknowns, it may very well happen than there is no solution. Three simple examples:

1. One equation, 2 variables: x + y = 10 … x = 5 and y = 5, or x = 3 and y = 7, or x = -4 and y = 14… and so on - infinitely many solutions.
2. Two equations, two variables: x + y = 10 and x - y = 2… x = 6, y = 2 and no more solutions.
3. Three equations, two variables: x + y = 10 and x - y = 2 and 2 * x + y = 100 … no solution.

Now it could be that you have 2 unknowns and two variables, and still have infinitely many solutions, for example x + y = 10 and 2x + 2y = 20. Or you have 2 unknowns and 2 two equations and there is no solution, for example x + y = 10 and 2x + 2y = 30.

Well… now I guess we can go on. For simplicity’s sake let’s consider a simple problem, when 2 number are drawn in a simplified lottery. Using your 2 numbers of 7 and 23 were drawn. Therefore

F(x) = a*x + b

F(1) = a + b = 7
F(2) = 2*a + b = 23

Eliminating B we get a = 16, and thus b = 9.

If we draw 3 numbers
F(x) = ax[sup]2[/sup] + bx + c

F(1) = a + b + c = 7
F(2) = 4a + 2b + c = 23
F(3) = 9a + 3b + c = 11

Elimintaing “c” we get

3a + b = 16
8a + 2b = 4

Eliminating “b” we get

a = -5.6

and thus:

b = 32.8
c = -25.8

The same method applies to 5 numbers, or 10 or 100…

If you need more explanation, just say it.

 

[Serious]

I do not quite believe it; having an infinite number of solutions is not a solution.

Why not? If there are two different ways for you to get to work, then you have 2 solutions to the question: “how do I get to work?”.

I hate to inform you, but RNG’s are not actually random. There is a prescribed formula to the values pulled out to make it appear random, but it is not really random; hence they are often called pseudo-random number generators.

I doubt that you can tell me anything new. I am very much aware of the method of creating a pseudo-number generators and its limitations. Of course these numbers are sufficiently random for all practical purposes. Moreover, the “seed” of these generators can be randomized based upon the computer clock… and so on.

But the number drawing in the lottery happens with a different method. Those 90 numbers are inside small balls, which are rolled and rotated around in big ball, and someone actually reaches in and pulls out one at random. It is as random as it gets. The same is true for the roulette wheel or the shuffling of the cards.

 

[Alberti_Devoveo]

Why not? If there are two different ways for you to get to work, then you have 2 solutions to the question: “how do I get to work?”.

To me, as a physicist, there is only one right answer. Having multiple solutions is not an answer, it is not even an option.

I doubt that you can tell me anything new. I am very much aware of the method of creating a pseudo-number generators and its limitations. Of course these numbers are sufficiently random for all practical purposes. Moreover, the “seed” of these generators can be randomized based upon the computer clock… and so on.

True these seeds can be further randomized by using seeds based on millisecond clock-time, the prescription for getting those numbers is still not random which is what I wanted to point out. There is a formula, so obtaining a formula post facto should not conflict with the design of the RNG.

But the number drawing in the lottery happens with a different method. Those 90 numbers are inside small balls, which are rolled and rotated around in big ball, and someone actually reaches in and pulls out one at random. It is as random as it gets. The same is true for the roulette wheel or the shuffling of the cards.

I am sure that some numerical modelers would disagree with you on it being truly random. All of these lottery ball’s motions work on Newtonian mechanics, so if one were sufficiently inclined and saw how the balls were placed initially, it is possible to predict which balls would be selected. In this scenario, assuming the prediction (which comes first) from the numerical model is correct (matches the subsequent lottery drawing), is this then a design and not randomness?

 

[Gorgias]

I am sure that some numerical modelers would disagree with you on it being truly random. All of these lottery ball’s motions work on Newtonian mechanics, so if one were sufficiently inclined and saw how the balls were placed initially, it is possible to predict which balls would be selected.

This.

Lotteries aren’t random; they are just sufficiently complex to prevent prediction. That is, they have the appearance of random behavior to the observer. That tends to be sufficient for (most? all?) observers.