| Iterations | Min | Current | Max |
| 0 | 0 | 0 | 0 |
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| Iterations | Min | Current | Max |
| 0 | 0 | 0 | 0 |
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The purpose of this app is to demonstrate that some events, even seemingly simple events, can be so improbable that they are, for all intents and purposes, impossible!
To use this app, first select an array of "pixels", using the drop-down selector. Next, click on "Go Random". The app will then generate random patterns; when a complete checkerboard pattern is randomly created, the app will stop and tell you how many "iterations", or "tries", it took this time to find the pattern. You will find that small arrays (having less than about 12-16 pixels) quickly find the pattern. A 30-pixel array takes, on average, about a billion (109) iterations; a 60-pixel array takes a quintillion (1018) iterations! Our minds can't grasp how long a 500-pixel array takes.
The concept of a "Universal Probability Bound" (UPB) has intrigued scientists and mathematicians ever since probability theory was formulated. This is a probability so small that it could never occur in the natural world, and it would be perverse to consider its occurrence. It is so small (10-150 or 2-500) that even if every elementary particle in the known universe (1086) were to experience a new event every Planck Time (10-43 second) for a trillion years (1012), it would be unlikely that any particular event would occur.
And yet, as miniscule as the UPB is, the likelihood of life arising spontaneously is far, far smaller. Life utterly depends on at least 400 proteins to perform its basic functions, and there can be no "Natural Selection" until all are present and functioning. Yet these 400 proteins require literally tens of thousands of bits of information (compare that to the UPB's 500)! And this assumes that endless chains of DNA or RNA already exist, ready to spontaneously rearrange to seek the golden permutation of life. Furthermore, it is not sufficient that this information merely exist; it must be in order like a 3000-ring circus (consider that a newly-killed cell has all the necessary DNA and proteins, but cannot resurrect).
Ever since Pasteur, we have known that the Law of Biogenesis holds: life cannot arise spontaneously from non-life!
...the results are shown here. The 25x20 array you chose contains 500 pixels. On average, it would take about 10150 attempts to hit the desired checkered pattern.