I used a dice function on my calculator and I found some interesting results.
I found that many unusual combinations of numbers when I rolled this dice and I
doubt that it rolls randomly.
Here are some combinations.
3366, 121363, 22444, 33544533, 441116633, 11166332622336222, 4524245, 236444632, 225522, 522544544, 6226, 5555, 6116, 66566, 5151
The 5555 combination has .01286% chance of happening or 1 in 7776. The 236444632 and the 33544533 individually have a .0000099229% chance of happening or 1 in 10,077,696. It is almost impossible that these events cannot be random right? Wrong.
Here is the collection of rolls I got these improbable event from.
4644253342
336623524523361462235
12136355313
224445252
33544533444
5456135554516253132135625362356136
4411166332622336222543624244
542145246514
5242451361553566
2364446322552254454424
62261
5555352
563132225
61161463355411531415523
66566464351631341253623114
5151
The reason these events happened is that there are so many ways for a 'miraculous' collection of rolls to take place and when these are enough rolls made it is almost 100% likely some strange number combination.
When it comes to butterflies I noticed that many of those letters were shaped very funny so there were many possible ways to display something that looked like each letter. Since there are so many butterflies and each butterfly has so many combinations on its wings, it is almost 100% likely that there would be some form of some letter on some butterfly's wing by chance.
It is not a miracle that we find the english alphabet on butterfly wings. It would be a miracle if we never found anything like an english letter on a butterfly's wing.
I will be seeking a graduate degree in statistics and already know much about it. At the very beginning you are taught about how pattern appear in random series. If there were no patterns in a series that is claimed to be random, then you know that it is a forgery. Here is a paper that talkes about random patterns.
http://www.stanford.edu/group/neuroeconomics/pdfs/sh02nn.pdf