Probability of life

[James]

Hi,

I thought I'd better post this proposed correction to "The Rebuttal to 'The Probability of Life'" (http://www.godandscience.org/apologetics/problife.html) as I have had no response from the guys at godandscience.org.

The probability in the example of picking balls out of a bag is not, as stated in the article:

Probability of drawing a red ball = n x p = 5 x 1/10 = 0.5

(Where n is the number of draws and p is the probability of drawing the red ball on a given draw)

It is this:

Probability of drawing (at least) one red ball = 1 - (1-p)^n = 1 - (9/10)^5 =0.41

This has serious implications on the calculation that follows it which calculates the probability of life occurring in the universe: Because n is now an exponent it has a far greater influence on the probability.
(Although I suspect n does not equate to the number of planets in any case.)

I wouldn't post a complaint like this normally, but it seems to me that such a fundamental flaw deserves pointing out.

Does anyone agree/disagree/care?!

James Irving

[Kurieuo]

Welcome James,

I'm wondering... isn't Rich simply making use of Mr. Friedman's proposed formula? Someone who originally challenged Rich's article at http://www.godandscience.org/apologetic ... slife.html, which is a summary to The Incredible Design of the Earth and Our Solar System.

But applying your formula with n = 10²³ and p = 10^-99 it still works out to practically zero. Try work it out on a calculator:

<blockquote>1 - (1-p)^n
= 1 - (1 - 10^-99)^10²³
= practically 0</blockquote>
If your calculator is anything like mine it will simply round it off and the end result would be 0.

Kurieuo.

[James]

Hi Kurieuo,

The problem with using a regular calculator is that it will round the numbers off to its maximum degree of accuracy in each part of the calculation. You need a calculator which is capable of calculating values to decimal places of greater than the order of 10⁹⁹. Most calculators have decimal places up to 10¹.

What happens when you use your calculator is as follows:
Doing the following calculation,
probability= 1 - (1 - 10^-99)^10²³

Step 1. The calculator calculates everything in brackets and rounds to its maximum degree of accuracy:
1 - 10^-99 = 1 (rounded to 10 decimal places)
The value SHOULD BE 0.9999....9 for 99 decimal places

Step 2. The calculator then raises its answer (1) to the power of 10²³:
1^10²³ = 1
The calculation should be 0.9999....9^10²³

Step 3. 1 - 1 = 0

So, as you can see, the calculator lacks the initial accuracy in step 1 to calculate the number to this large number of decimal places.

I haven't actually been able to view Mr Friedman's article as there are no references (ie URLs or copies) on the website. However I get the impression from the Rebuttal that the probability calculations are Mr Deem's:

Unfortunately, Mr. Friedman does not continue the example to include the example at hand. Let's help him out with the "trivial" math. In Mr. Friedman's example, the math works out as follows:

Mr Deem then goes on to continue the mathematics for Mr Friedman using his own method.

Best regards,

James

[Kurieuo]

The problem with using a regular calculator is that it will round the numbers off to its maximum degree of accuracy in each part of the calculation. You need a calculator which is capable of calculating values to decimal places of greater than the order of 10⁹⁹. Most calculators have decimal places up to 10¹.

Yes, I realised this... Yet, the end result is still such an extraordinary low probability as to almost be negligable.

I haven't actually been able to view Mr Friedman's article as there are no references (ie URLs or copies) on the website. However I get the impression from the Rebuttal that the probability calculations are Mr Deem's:

Unfortunately, Mr. Friedman does not continue the example to include the example at hand. Let's help him out with the "trivial" math. In Mr. Friedman's example, the math works out as follows:

Mr Deem then goes on to continue the mathematics for Mr Friedman using his own method.

This I believe is a really old article, and I thought there was a reference but couldn't find one... but I definately think there should be. Don't get me wrong, although I believe Rich may have simply decided to use Friedman's incorrect mathematics, I'd at least expect it to be pointed out in the rebuttal to Friedman's shame if he realised it was incorrect.

So thanks for pointing it out, and I'll pass it onto Rich.

Kurieuo.

[James]

The problem with using a regular calculator is that it will round the numbers off to its maximum degree of accuracy in each part of the calculation. You need a calculator which is capable of calculating values to decimal places of greater than the order of 10⁹⁹. Most calculators have decimal places up to 10¹.

Yes, I realised this... Yet, the end result is still such an extraordinary low probability as to almost be negligable.

But how do we know that the probability is negligible if the calculation has not been done accurately? We are talking about multiplying 0.999...9 (to 99 decimal places) by itself 10²³ times. Instead the calculator, due to its lack of accuracy, multiplies 1 by itself 10²³ times which is obviously 1. This effectively ignores the exponent, 10²³ which would otherwise have a significant influence.

This I believe is a really old article, and I thought there was a reference but couldn't find one... but I definately think there should be. Don't get me wrong, although I believe Rich may have simply decided to use Friedman's incorrect mathematics, I'd at least expect it to be pointed out in the rebuttal to Friedman's shame if he realised it was incorrect.

I agree, I think it would clearer (and less biased!) if Mr Friedman's article was posted on the site and referenced.

James

[Kurieuo]

The problem with using a regular calculator is that it will round the numbers off to its maximum degree of accuracy in each part of the calculation. You need a calculator which is capable of calculating values to decimal places of greater than the order of 10⁹⁹. Most calculators have decimal places up to 10¹.

Yes, I realised this... Yet, the end result is still such an extraordinary low probability as to almost be negligable.

But how do we know that the probability is negligible if the calculation has not been done accurately? We are talking about multiplying 0.999...9 (to 99 decimal places) by itself 10²³ times. Instead the calculator, due to its lack of accuracy, multiplies 1 by itself 10²³ times which is obviously 1. This effectively ignores the exponent, 10²³ which would otherwise have a significant influence.

Once you get to such an incredibly low probability of an event's occurance such as 10^-73, whether the probability is even less really doesn't matter in my opinion (especially to Rich's case), as the probability is just so low anyway. Yet, working out the probability the correct way would only strengthen Rich's case since the probability of life would become even lower. For example, consider the marble example where Friedman works out a probability of 0.5, compared to the correct formula where the probability becomes less at .41.

Kurieuo.

[James]

Sorry, I see what you mean. I was assuming that you had calculated an actual value for the probability. I agree, using these numbers would give a lower probability.

James

[Kurieuo]

Just letting you know I contacted Rich, and he just hadn't gotten to it yet (i.e., I believe your message). But you will notice the page is no longer up as Friedman's site has disappeared, so there was kind of no point for it.

Thanks again for having pointed this out.

Kurieuo.