Common Problems With Probabilities And Size

Assuming that there were 10^160 marbles in a bag, the typical picture one would draw is choosing a marble, seeing it wasn't the selected marble, and drawing another out of the bag. Eventually you get to the one you want (labeled evolution), and there you have it. And the point people then argue is that it is just as likely that that marble will appear early on, and not necessarily at the very end. ...sound reasonable, at first, until you grasp a pure, true picture of what the math really means.

The deal is that each time the you choose a marble from the bag, you have to replace it for the next choice. The bag never empties.

The whole point of the probability is saying that if you take 10^160 random marbles out of an infinite sized pile, chances are that you'll only end up with one select marble labeled evolution. Not that there IS one marble in a pile of 10^160 marbles labeled evolution.

How Big Is The Bag We Are Using For Probability

But what if instead of using a bucket, I used a sand box? Or a whole playground. Yes, find the single colored grain in a playground filled with sand? Or, a beach filled with white sand? ...now the task is getting to where you'd call it next to absolutely impossible. But wait, let's throw things really into perspecitive.

If you took 10^63 (not 10^100, not 10^160... but only 10^63 -- a 1 with only sixty-three zeros after it) grains of sand, you would find that a sphere made of this much sand would have a radius equal to the distance of the sun to the earth. [ Archimedes, "The Sand Reckoner" -- Infinity and The Mind, by Rudy Rucker ] You are now talking about a sphere larger than the Earth... larger than the Sun... larger than the orbits of the first three planets of our solar system! Technically, a sphere this size would require under 10^63 grains of sand, but to be cautiously conservative in the favor of evolution, we've overstated the number and understated the size for the illustration.

Now try pulling a select grain of sand randomly from that pile. That pile which is approxiamtely 10^94 times smaller than the probability of such a spontaneous generation of the most simple form of "life" happening by chance.

Suppose we wanted to stack 10^160 marbles into a cube, how big would that be? First each side would be (rounding down) 10^53 marbles in length. [Computed by taking the cube root, due to 3 dimensional volume.]

Before you say 'ha!' and point out this is less than 10^63, remember the sphere made moments ago was grains of sand (not marbles) and were all packed together in a 3-D volume, these marbles are end-to-end in a 1-D line.

So take that sphere apart and form a line out of its contents. Assuming a marble is half an inch in length (the average marble is a little larger than that - again we're being conserative), that means there are 24 marbles to the foot. ..or 126,720 marbles to the mile ..or (rounding down) APPROXIMATELY: 744,923,496,448,000,000 marbles to the light year. That's 744+ Quadrillion marbles per light year.

That would mean (rounding down) one side of our cube of marbles would measure 1,000,000,000,000,000,000,000,000,000,000,000,000 (10^36) light years in length. Remember a light year is the distance it takes a beam of light traveling at 670616629.384 miles per hour to go in one year. Incidently, the nearest star is 23-million-million (23,000,000,000,000) miles away; it takes light from the star (Proxima Centauri) about 4 years to reach us. Now compound the fact our cube is much longer than that distance, and that it is also high and deep, as well as long; that is a lot of marbles, more than would fit in our galaxy.