Statistics, God, and Estimating

[ChemEngrMBA]

A great many people get wrapped up in definitions that are erroneous.
Mathematicians have been known to say, "Nothing is impossible unless its probability is zero."

While that sounds plausible, let's look at reality.
Distinguished mathematician, Emile Borel, defined "impossible" as one chance in 10 to the 50th or less.

Ten to the 50 is 1 followed by fifty zeroes.

Before reading any further, what volume do you estimate 10 to the 50 small marbles would occupy?

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Ten to the 50 marbles 1 cm in diameter would fill 288,000 billion billion spheres the size of earth.

So who thinks it is possible to select one out of 288,000 billion billion spheres, and from that enormous sphere full of 1 cm marbles, blindfolded, on your first and only try, get the unique marble?

I did the calculation as a comparison to the probability of titin's original synthesis from any natural mechanism you can imagine, being 1/20 amino acids selected one at a time to the 38,138th power times two other factors which produce a probability for titin's original synthesis of 1 in about 10 to the 72,000th power.   This is insanely beyond impossible and titin is only one of over 20,000 different proteins in the human body.

[Kamaji]

[ChemEngrMBA]

The emoji of an atheist?  Who cannot find anything to dispute?

[The_Reader_David]

This confounds possible as used in engineering and possible as used in philosophy, mathematics, and indeed pure science.

What is possible to do intentionally (as engineers must) is different from what is possible in the sense that it could happen.

And a correction:  Émile Borel was a pure mathematician whose work on measure theory underpins modern statistics, but was not, himself, as statistician.

[DefiantMassRINO]

zero is inert equilibrium, not impossibility.

[The_Reader_David]

zero is inert equilibrium, not impossibility.

No, zero is a number that has many meanings, depending on the context.  In continuous probability (the stuff that needs Borel and Lebesgue's measure theory to formulate), probability zero does not denote impossibility -- every outcome has probability zero, only measurable sets of outcomes, like intervals if the outcomes are real numbers, are ever assigned non-zero probability -- in discrete probability it does: an outcome of a discrete random variable with probability zero never occurs (e.g. rolling 7 on a standard die).  In computer science zero is one of two values of a bit.  In combinatorics is denotes the cardinality of an empty set. In the theory of rings and abelian groups, it denotes the additive identity element. Zero is only inert equilibrium in the context of numbers being used to measure free energy in a physical system. 

Without a context, zero has no particular meaning, though we try to use it in contexts where the thing we're describing is the identity element for some meaningful notion of addition in that context.  (The case of the bit in computer science being that of a "Boolean ring" where adding is "or" and multiplication is "and".)

[ChemEngrMBA]

This confounds possible as used in engineering and possible as used in philosophy, mathematics, and indeed pure science.

What is possible to do intentionally (as engineers must) is different from what is possible in the sense that it could happen.

And a correction:  Émile Borel was a pure mathematician whose work on measure theory underpins modern statistics, but was not, himself, as statistician.

There is nothing confounding about the utter absurdity of thinking that you could select THE ONE AND UNIQUE marble, on your first and only hypothetical selection from 288,000 billion billion earth-sized spheres filled with identically sized marbles 1 cm in diameter.  Nothing remotely confounding. 

[The_Reader_David]

Did you actually read the sentence, "What is possible to do intentionally (as engineers must) is different from what is possible in the sense that it could happen."

You keep using possible in the first sense, and ignoring the second.

[Hoodat]

Before reading any further, what volume do you estimate 10 to the 50 small marbles would occupy?

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Ten to the 50 marbles 1 cm in diameter would fill 923,400 billion billion spheres the size of earth.

I calculate 6.53 E22 earth spheres.  Or 65,300 billion billion, assuming earth's radius is 6,371 km.  You're off by a factor of around 14.

[ChemEngrMBA]

Did you actually read the sentence, "What is possible to do intentionally (as engineers must) is different from what is possible in the sense that it could happen."

You keep using possible in the first sense, and ignoring the second.

You are attempting to apply different definitions to "impossible".  As if engineers can do what could not "happen."  Semantics is not engineering, and you are playing semantic games that make no sense.  Tell me your engineering idea to  select THE correct sphere and then THE unique marble inside that particular sphere out of 288,000 billion billion of them.  Do it "intentionally."[/size]

[ChemEngrMBA]

I calculate 6.53 E22 earth spheres.  Or 65,300 billion billion, assuming earth's radius is 6,371 km.  You're off by a factor of around 14.

Are you trying to imply that selecting THE sphere out of 288,000 billion billion, and THEN selecting THE unique marble if you were blindfolded would therefore be possible?  Tell the audience how, please.  I'm sure they will be amused.

[ChemEngrMBA]

Patterns occur naturally – no help required from a ‘designer’. Many patterns occur in nature without the help of a designer – snowflakes, tornados, hurricanes, sand dunes, stalactites, rivers and ocean waves.  These patterns are the natural result of what scientists categorize as chaos and fractals.   These things are well-understood and we experience them every day.
Codes, however, do not occur without a designer.
Examples of symbolic codes include music, blueprints, languages like English and Chinese, computer programs, and yes, DNA.  The essential distinction is the difference between a pattern and a code.   Chaos can produce patterns, but it has never been shown to produce codes or symbols.  Codes and symbols store information, which is not a property of matter and energy alone.  Information itself is a separate entity on par with matter and energy.
 
Proof that DNA was designed by a mind:   (1) DNA is not merely a molecule with a pattern; it is a code, a language, and an information storage mechanism.   (2) All codes we know the origin of are created by a conscious mind.  (3) Therefore DNA was designed by a mind, and language and information are proof of the action of a Superintelligence.

We can explore five possible conclusions:
1) Humans designed DNA
2)  Aliens designed DNA
3) DNA occurred randomly and spontaneously
4) There must be some undiscovered law of physics that creates information
5) DNA was Designed by a Superintelligence, i.e. God.

(1) requires time travel or infinite generations of humans.  (2) could well be true but only pushes the question back in time.  (3) may be a remote possibility, but it’s not a scientific explanation in that it doesn’t refer to a systematic, repeatable process. It’s nothing more than an appeal to luck .  (4) could be true but no one can form a testable hypothesis until someone observes a naturally occurring code.  So the only systematic explanation that remains is (5) a theological one.
To the extent that scientific reasoning can prove anything, DNA is proof of a designer.

[The_Reader_David]

]As if engineers can do what could not "happen."  ][/size]

You have it backwards.  Things can happen that cannot be engineered to happen.  Indeed they do all the time at a quantum mechanical level.

[Hoodat]

Are you trying to imply that selecting THE sphere out of 65,300 billion billion, and THEN selecting THE unique marble if you were blindfolded would therefore be possible?  Tell the audience how, please.  I'm sure they will be amused.

Here again are the instructions you posted:

Before reading any further, what volume do you estimate 10 to the 50 small marbles would occupy?

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Ten to the 50 marbles 1 cm in diameter would fill 923,400 billion billion spheres the size of earth.

"Before reading any further", I estimated the volume of 1E50 1-cm diameter marbles would occupy 7.07566 E34 cubic kilometers.

4/3 * π ≈ 4.18879

Marble radius = 5 E-6 km

Marble volume ≈ 5.236 E-16 km³

Marble packing volume (tightly packed) ≈ Vol / 0.74 = 7.07566 E-16 km³

Total marble volume = 1 E50 * 7.07566 E-16 = 7.07566 E34 km³

Earth radius ≈ 6371 km

Earth Volume ≈ 4.18879 * 6371³ = 1.0832 E12 km³

Number of earth-spheres needed to hold the marbles ≈ 7.07566 E34 / 1.0832 E12 = 6.532 E22 earths.

That is 65,320 billion billion spheres the size of the earth, which is approximately 14 times less than your number.

Now you ask if it is possible?  Yes.  The odds being 1 in 1 E50, which was already given (without having to do all the mundane spherical math).  Almost impossible, yes.  But certainly not "beyond impossible".

[ChemEngrMBA]

http://MathProvesGod.blogspot.com

[Hoodat]

"Let’s look at the volume of 1050 marbles, one centimeter in diameter.

There are 100 such marbles per meter, and 100 times 1,000 per kilometer = 105 marbles per km .

However, when spheres are stacked, they drop into the valley of four other spheres, which reduces their effective diameter by a factor of roughly .166.

Therefore 105 marbles cubed equals .834 x 10 5  centimeters cubed = 5.801 x"

This is not tightly packed.  Spheres arranged in this method leave far more empty space than tightly packed spheres.

Close-packing of equal spheres

In geometry, close-packing of equal spheres is a dense arrangement of congruent spheres in an infinite, regular arrangement (or lattice). Carl Friedrich Gauss proved that the highest average density – that is, the greatest fraction of space occupied by spheres – that can be achieved by a lattice packing is

π / (3 √2) ≈ 0.74048

[ChemEngrMBA]

This is not tightly packed.  Spheres arranged in this method leave far more empty space than tightly packed spheres.

Close-packing of equal spheres

In geometry, close-packing of equal spheres is a dense arrangement of congruent spheres in an infinite, regular arrangement (or lattice). Carl Friedrich Gauss proved that the highest average density – that is, the greatest fraction of space occupied by spheres – that can be achieved by a lattice packing is

π / (3 √2) ≈ 0.74048

Again and again you try to invalidate the point I made, and you fail every time for several reasons.
First, the magnitude of the definition so far exceeds your trivial commentaries as to invalidate them.
Second, the point of my thread is to demonstrate how far in excess of truly impossible is the original synthesis of ONE protein, much less over 20,000 of them. 

Please try to assimilate these points and cease your jejune commentaries, if you can.....

[Hoodat]

So this isn't about marbles?  Then why did you ask about how much volume they would occupy? 

[corbe]

   Being somewhat of an Agnostic I stay away from Threads with G_d in the Title, especially if our local Chemical Engineer started it.   

[Hoodat]

   Being somewhat of an Agnostic I stay away from Threads with G_d in the Title, especially if our local Chemical Engineer started it.   

Apparently, I was supposed to skip over the part where he asked, "Before reading any further, what volume do you estimate 10 to the 50 small marbles would occupy?"  I see now that this thread has nothing at all to do with marbles and everything to do with titin, a protein found in muscles.  Unfortunately, there wasn't any question asked about titin, so I don't get to do any math on that.  So sad, because G-d has given me a deep love for anything 'math'.

Anyways, if this thread was supposed to be about the Creator and His creation, then it certainly took a wrong turn with that marble question.

[ChemEngrMBA]

   Being somewhat of an Agnostic I stay away from Threads with G_d in the Title, especially if our local Chemical Engineer started it.   

So I noticed @corbe

http://ProofThereIsNoGod.wordpress.com


http://Irrational-Atheism.blogspot.com

[ChemEngrMBA]

Here again are the instructions you posted:
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Now you ask if it is possible?  Yes.  The odds being 1 in 1 E50, which was already given (without having to do all the mundane spherical math).  Almost impossible, yes.  But certainly not "beyond impossible".

You never give up, especially when you are wrong.

I never applied "beyond impossible" to Borel's definition, as you so clearly imply above.
What I SAID was "beyond impossible" was my statistical estimate of the natural synthesis of titin absent The Designer.
You don't do reading comprehension very well despite your needlessly lofty estimate of yourself.
I will also ask the Administrator to add your name to my Ignore List.  I can't seem to locate the link for that modification.

ciao brutto

[corbe]

   I throw out a wide net when I search for souls who share my particular affinity.  I've noticed you slip through always. 

[Hoodat]

You never give up, especially when you are wrong.

I never applied "beyond impossible" to Borel's definition, as you so clearly imply above.
What I SAID was "beyond impossible" was my statistical estimate of the natural synthesis of titin absent The Designer.

With G-d, nothing is impossible.  (I think Gabriel said that)

[bigheadfred]

It looks to me that this thread is about marbles. Some people have all of theirs. Other(s) have lost a few.