Bentley’s Snowflakes

Let us return to Bentley’s strange results: 5,381 original snowflakes without a single duplicate. One may wonder why there weren’t about 2,700 duplicates if duplicates are as likely to occur as originals. Isn’t such an investigation like recording the results of tossing a coin? Isn’t a snowflake as likely to be a duplicate as an original like a coin toss is as likely to come up heads as it is likely to come up tails? If the coin toss is a valid analogy, then the probability of such a result may be calculated with the equation Y = 2^N, where Y is the number of likely tosses to obtain such a result, 2 is the possible number of results for each toss, and N is the number of consecutive heads without the appearance of a tail, or vice versa. For example, suppose we wish to calculate the probability of tossing the coin 10 times and finding 10 heads and no tails. A result like that is possible, but unlikely. We must be prepared to do much tossing of the coin to obtain such a result. According to the equation, Y = 2^N, upon substitution it becomes Y = 2^10 or Y = 1,024. We may look forward to as many as 1,024 trials before getting such a result. How may this be changed to a probability, then compared to the standards for statistical inference? This may be done by modifying the equation to P = 1/Y or P = 1/2^N. Then P = 1/2^10 = 1/1,024 = 0.001. The probability, P, of getting 10 consecutive heads would be 0.001. The probability of getting 10 consecutive original snowflakes, or the probability of getting 10 consecutive duplicate snowflakes, would be 0.001 for each snowflake examined. Bentley found 5,381 consecutive original snowflakes without finding a duplicate. The probability of such a result is P = 1/2^N or P = 1/2^5,381. Such a probability would be about one chance in a number with 99 zeros after it. If we were tossing a coin, then getting 5,381 heads with no tails might be expected by chance once in 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000 tosses. That is vastly beyond our most stringent science standard of less than 1 chance in 10,000 chances. So we have virtually no chance of being wrong if we believe that Bentley’s results are extraordinary. Further, such a result infers that all snowflakes are originals. And if we believe that, then our chances of being wrong are about one in the number above with the 99 zeros after it. Now we know why scientists believe that all snowflakes are originals. Bentley’s research inferred it beyond any shadow of a doubt. See Figure 1 below.

snowflakes.2

And the other objects on planet, Earth? Are they unanimously original like snowflakes?
And the other objects in the rest of the universe? Are they unanimously original like snowflakes?
For answers, see Latest Book.