Finely Tuned Questions – Part III

RulersIn an initial post an argument for the existence of God flowed naturally from the extraordinary degree of fine-tuning of the universe.  The argument is offered again:

Premise 1.  The fine-tuning of the universe is due to either physical necessity, chance, or design.

Premise 2.  The fine-tuning of the universe is NOT due to physical necessity.

Premise 3.  The fine-tuning of the universe is NOT due to chance.

Therefore it due to design.

Premise 2 was argued favorably in a prior post.  The argument stems that is not guaranteed that any universe that exists is fine-tuned for life.  Hence, the negation of the second premise is fallacious.  The third premise is more intricate and is argued here.

roulette

Enter Las Vegas! Intricate dining, exquisite entertainment, with casinos lining the strip beckoning you to come in.  Once in a casino, you will find a place void of clocks with fabricated and bright lighting to make it hard to decipher night from day.  They want you to stay.  Sit down at a table and you’ll be enticed to play with free alcohol and frequent dining service.  You’ll be enticed to play games of probability, for which the house employees have been trained to take advantage of in the long run.  You hear the sound of Roulette and the ball smacking against the intricate groves between the range of possibilities.  It lands on black 15.  An exchange of chips begins as bets are placed for the next spin.  It lands on black 15 again.  Another exchange of chips.  Another spin and black 15 again.  People exchange awkward glances and the bets are now beginning to stack up on that black 15.  Will it come again?  Another spin and another black 15!  Is this chance or design?  You can imagine that if this happened at a roulette table that game would be stopped.  Maintenance workers would come quickly to investigate and service the table.  Something must be wrong with it in order to hit black 15 so many times!

This, my friend, is the incredulous, incomprehensible feature of our universe.  Black 15 has been hit again, again, and again.  Consecutively.  Now, of course if you spin the table 20 times there is a chance that Black 15 will come up 20 times.  So should you be surprised if that occurs?  Or would you be inclined to investigate why that did occur?   Of course, it we have enough spins or iterations then wouldn’t this situation be likely to occur?   Yes, but only if you have enough spins.  In fact, the very reason to push for a multiverse hypothesis is to increase the odds of obtaining our universe!  Hence, its mere suggestion in academic circles is complimenting the fact that our universe is fine-tuned!

Are we part of an infinite ensemble of universes?  Not quite.  First, if there exists an actually infinite number of universes a slew of logical fallacies are had.  Just consider Hilbert’s Hotel. Nor is this what is being proposed by the dominant multiverse hypothesis, M-theory.  This theory proposes a finite number of possibilities on the order of 10^500.  Then, how many of these universes are life-permitting?  The subset of life-permitting universes is abysmally small.  However, it gets worse.  The probability of our universe’s extremely low entropy condition is estimated at 10^(-10^123)  while the chances of our solar system coming into existence by random collisions is estimated to be 10^(-10^60) (see Penrose, pgs. 762-765)!  This means that our universe is extremely rare even among the small subset of possible universes!

Hence, we are back at the casino at the roulette table.  No one has come to stop the game and investigate if the game is rigged.  What is your next bet?  I’ll tell you mine:

“Señor, I’ll take Black 15.”

Let it roll.

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Finely Tuned Questions – Part II

In a prior post an argument for the existence of God flowed naturally from the extraordinary degree of fine-tuning in order for universe to be life-permitting.  The argument is offered again:

Premise 1.  The fine-tuning of the universe is due to either physical necessity, chance, or design.

Premise 2.  The fine-tuning of the universe is NOT due to physical necessity.

Premise 3.  The fine-tuning of the universe is NOT due to chance.

Therefore it due to design.

Here we will argue in favor of the second premise.

Of course that very fact that I am writing this is evidence that a life-permitting universe exists.  Of course you may adhere to a worldview that states everything is illusory, but then who may I ask is reading this?  Not to mention that this worldview is also an illusion, hence a built-in defeater!  Nevertheless, a life-permitting universe exists as a result of fundamental constants being tuned just so.  But why were chosen this way?  In other words, why are they not other values?  The values are not determined by the discovered laws of nature.  Rather, they are substituted into such equations such that we may study aspects of our observable universe.   Hence, if the fine-tuning of the universe is of physical necessity then any values that are chosen must be life-permitting!?  But clearly this is not the case.

Oh, but what of the potential great unifier of physics, M-theory?  Not so fast!  M-theory does not eradicate the degree of fine-tuning, in fact it complicates the situation further!  In fact, it predicts that there is a wide range of around 10^500 possible universes all consistent with the same laws that we have, but varying in their respective constants.  Hence M-theory points to a multitude of universes that are not life-permitting.  In fact, it presents an even greater challenge in unlikelihood of the existence of any life-permitting universe!  Not to mention, M-theory needs 11 dimensions to work.  Why 11?  Why not 10 or 12?  Why perfectly 11?  Hence, there is no evidence supporting that a life-permitting universe is a physical necessity.  It is far more reasonable to expect a universe to not be life-permitting.

In the following post the third premise will be discussed.

“Where were you when I laid the earth’s foundation? Tell me, if you understand.”  – Job 38:4

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Finely Tuned Questions – Part I

Matrix“Given these three linear equations with three unknowns you have 30 seconds to guess the answer,” I stated.  The students befuddled and stymied by the request took a few seconds and then formed a guess. The time quickly exhausted itself.

“Please check to see if your guess is the solution and then, through email, indicate to me if you were correct or not,” I said.

Determining solutions of systems of linear equations is at the heart of many applications of mathematics.  In nonlinear problems, a linear system may rear its head as the result of trying to obtain a solution through an iterative method.  Nevertheless, solving a system of N equations for a collection of N unknowns is not a complicated task, rather it is tedious!

A linear system is best viewed as a matrix, hence a linear system of N equations is best viewed as a N x N matrix (A) of coefficients of the unknowns (x) from each of the N equations.  The terms that do not involve any of the unknowns can also be collected (b).  Hence the linear system is written as A x = b.

For a general matrix it takes roughly N cubed operations to directly obtain a solution, provided that it exists. Not a problem you say?  Standard linear algebra textbooks will suggest to a learner that these methods will always work, regardless of the tedium.  However, it if it takes that many operations then what happens if the linear system is extremely large?  In my work I commonly deal with matrices on the order of 10^5 x 10^5.  That is a small matrix relative to the large matrices employed in data analysis of experiments on the large Hadron collider, typically on the order of 10^12 x 10^12.  To appreciate the time and effort for a computer to work through the tedium of determining the solution let’s consider an example.  Say your computer’s time to perform a flop, that is a multiplication or addition, is 10^-10 seconds.  Fast. Now to determine the solution of 10^5 x 10^5 system requires 10^15 flops, that is, 10^5 seconds.  That’s over a day just to solve ONE matrix problem!  In my work I have to solve a comparable system a few million times!  So it would take a few million days to complete!  Yikes!

So what can a person do?  They iterate, that is, they attempt to find a sequence of solutions that converge to the true solution.  The hope is that each iterate is relatively fast and that it converges quickly, lowering the required amount of iterates.  Sounds good and promising!  But where does the information for the first iterate come from?  Hence, you need an initial guess.

Now would you be surprised if your initial guess was the exact solution?  Suppose that I have a system of 3 equations with 3 unknowns.  Only I know the equations, you don’t know them at all.  I want you to guess a solution.  You can email or comment to this post with your solution and I’ll tell you if it is correct.  Would you be surprised to find out that your guess was correct?  In fact, if I gave you 100,000 guesses without telling you the form of the equations, I would be shocked if you could guess it exactly with anyone one of those!  Shocked!

Hence, when I look at the degree of fine-tuning of the cosmos, I am shocked!  What do I mean by fine-tuning?  Think of sequence of knobs that are dialed in to allow a specific outcome.  If these knobs are not within an extraordinarily small range of values then the specified outcome would not occur.  For the cosmos, the outcome is allowing life to be permitted, and the knobs are fundamental constants of nature (weak force, cosmological constant, electric charge size, strong nuclear force, density of the universe, entropy, etc.).  How narrow?  Take the weak force, if this value was off by one part in 10^100 our universe would not be life-permitting.  Period.

This begs an obvious argument for the existence of God as the fine-tuning can only be possible from either physical necessity, chance, or design.  Thus the argument follows:

Premise 1.  The fine-tuning of the universe is due to either physical necessity, chance, or design.

Premise 2.  The fine-tuning of the universe is NOT due to physical necessity.

Premise 3.  The fine-tuning of the universe is NOT due to chance.

Therefore it due to design.

Premise 1 is obvious as this just lists the available options, hence one only needs to provide a plausible argument for premises 2 and 3.  The conclusion then follows naturally.

In my follow-up posts I want to address each individually.

“For since the creation of the world God’s invisible qualities—his eternal power and divine nature—have been clearly seen, being understood from what has been made, so that people are without excuse.” – Romans 1:20

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