> The cicada simulation on that page is very misleading.

Not at all.

> You're only seeing prime numbers because you arbitrarily synchronized the cycles of the cicada and the predators at t=0.

Not true. Because of how the math works out, the starting time is irrelevant. Any arbitrary starting times for both the cicadas and predators yields the same outcome over time, because the filtering effect of prime reproductive cycles depends on synchronizing (or not synchronizing) random reproductive periods, not starting points.

Just so you won't think this is all rhetoric, and to do your homework for you, here's a short Python program that accepts any starting value and produces the same result regardless of the chosen starting point:

https://www.dropbox.com/s/7m8hq9yzcu5nztx/prime_reproduction...

Here is a typical output (the output changes in small ways with the chosen starting number, but always favors primes over composites):

2 = 6901 *********************
3 = 6395 *******************
4 = 9036 ****************************
5 = 5836 ******************
6 = 11030 **********************************
7 = 5468 *****************
8 = 10410 ********************************
9 = 7643 ***********************
10 = 9923 *******************************
11 = 4987 ***************
12 = 14110 ********************************************
13 = 4810 ***************
14 = 9199 ****************************
15 = 8988 ****************************
16 = 11051 **********************************
17 = 4528 **************
18 = 12797 ***************************************
19 = 4414 *************
20 = 12469 **************************************
21 = 8273 *************************
22 = 8251 *************************
23 = 4219 *************

> If you had chosen another starting point at t=0 ...

See above. You're mistaken. If you had tested your idea using actual mathematics, you would have realized your mistake before posting. But this would require a respect for validating one's ideas before posting them.

The effect being described counts only synchronization events between two reproductive cycles A and B over a long period of time. In this case, a given prime number A is compared to any number of values for B, and the number of synchronizations is totaled. As it happens, and regardless of the starting times, when a prime number in A is compared to a large range of values in B, and not surprisingly, the number of synchronizations is smallest if A is prime.

Another way of saying this is that a prime number has fewer factors than a composite number, hardly a controversial claim, and one that doesn't depend on the starting values for the counters.

> From somebody who criticizes psychology for wrong methodology ...

Ah, yes, the real reason for your post. I have never criticized psychology for "wrong methodology" anywhere. I criticize the field for not being scientific, as does the sitting director of the NIMH and many, many others. Today's example:

Title: "Final Report: Stapel Affair Points to Bigger Problems in Social Psychology"

Source: http://news.sciencemag.org/scienceinsider/2012/11/final-repo...

Quote: "In their exhaustive final report about the fraud affair that rocked social psychology last year, three investigative panels today collectively find fault with the field itself. They paint an image of a "sloppy" research culture in which some scientists don't understand the essentials of statistics, journal-selected article reviewers encourage researchers to leave unwelcome data out of their papers, and even the most prestigious journals print results that are obviously too good to be true.

The commissions—one for each of the universities where Stapel has worked—concluded that "from the bottom to the top there was a general neglect of fundamental scientific standards and methodological requirements." That climate made it possible for Stapel's fraud to go undetected for many years, the report says."

Somehow people like you think psychology's problems would go away if its critics would simply shut up. But this confuses the messenger with the message.