Pi digits are generally considered to be random (as judged by statistical testing). Are they??
First ten Pi digits are: p=3.141592654… (Last digit rounded).
In the last few weeks, my good friend, Oren Evron, producer of most videos about my research on the Bible and on biblical Hebrew, has been engaged finding links between Pi and the first verse of the Hebrew Bible (Genesis 1:1):
בְּרֵאשִׁית בָּרָא אֱלֹהִים אֵת הַשָּׁמַיִם וְאֵת הָאָרֶץ.
Likelihood values for his results (their probability to occur randomly) have been generated via extensive computer-simulation studies (conducted by him). His findings are astounding. A video detailing these has now been published by Oren Evron (Hebrew, English):
Code of Creation (Part 1; Hebrew) Oren Evron Nov 29 2019
Code of Creation (Part 1; English) Oren Evron April 13 2020
Code of Creation (Part 2; Hebrew) Oren Evron Jan 2022.
You may read about Pi in Wikipedia, entry: Pi. See also an earlier post on this blog:
Fibonacci series, Pi, Golden Ratio — Simple Relationships
To-date, the digits of Pi (a transcendental number) have been considered random. Are they?
In this post, I display my own, and only, contribution to Oren Evron’s research (not included in his video). Consider the first ten digits of Pi (last digit not rounded):
{3, 1, 4, 1, 5, 9, 2, 6, 5, 3}.
Next, observe word lengths (number of letters in a word) for the seven Hebrew-words comprising the first verse of the Bible (Genesis 1:1):
{6, 3, 5, 2, 5, 3, 4}.
We realize that the second sequence is contained in the first, namely, the second series is a subset of the first series (taken from Pi), comprising 70% thereof. Only three digits in the first series (marked black) are not in the second. Conversely, all digits in the second series (with their exact frequencies) appear in the first.
(Comment: Reading the second series as Hebrew, from right to left, we obtain (read from left to right):
{4, 3, 5, 2, 5, 3, 6};
This is incredibly close to the order that these digits appear in the first ten digits of Pi; In fact, one needs only two changes, swapping first 3 with 4 and moving 6 before 5, to preserve the original order of these digits, as they appear in the first ten digits of Pi!!!).
How probable is this result (second series contained in the first)?? What is the likelihood for this finding to occur by random?
We have conducted a computer simulation, in which the computer randomly generated a million sets of ten digits (each digit with probability 0.1 (10%) to be selected). We then counted the number of sets that contained exactly the second set (by exactly we mean including frequency, for example, if “5” appears twice in the second set so it is in the simulated set).
Based on this simulation experiment, we have obtained for the probability of the second set to be exactly contained in the first to be 0.0019 (0.2%), namely, for a significance level of half a percent (0.5%), a statistically meaningful result (“significant result”). By conventional norm in scientific research studies, this is a highly significant result, indicating that the finding is probably not coincidental.
This result, on its own, might be considered by some as “cherry picking”. Combined with Oren Evron’s new findings, as displayed in his latest movie (English version expected soon), any claim of “cherry picking” becomes baseless — the link between the first verse of Genesis and physical reality (as represented by Pi) is now an established scientifically-observable fact.
- Another of Oren Evron’s videos — Findings of Rabbi Yitzchak Ginsburgh about a relationship between Fibonacci and biblical Hebrew (Hebrew; For English, activate captions!):
Fibonacci in the Torah – Genesis Golden Ratio
- Links between Pi and Fibonacci numbers (post on this blog):
Haim Shore Blog 