# Are the mathematical constants e and π encoded in the Bible?

Some numerologists claim that the mathematical constants e and π are encoded in the Bible via gematria.

For example, blogger Joe Vasta argues that Genesis 1:1 encodes 3.141554508×1017.

The value of π is approximately 3.14159.

He argues that John 1:1 encodes 2.718312812×1040.

The value of e is approximately 2.71828.

He suggests:

perhaps the Bible is the inspired word of God, and this is just a “fingerprint” found in the verses.

There are similar claims about the Quran encoding the Golden Ratio.

I have seen this come up in forums before, commenting on it being ridiculous and it's just within our nature to pattern match whenever we can which is plausible, but I don't really get why it is so, which is where I need help understanding.

Are the constants encoded in the Bible? Is this more than just a coincidence?

• When you say "I don't really get why it is so", do you mean "I don't really get why it is human nature to find patterns", or "I don't really get why this pattern is not significant", or something else? In general, numerology isn't easy to "disprove", because it's not really making a claim, just an observation. Put the numbers into a different arbitrary equation, and you'll get a different, less interesting number; pick a different sentence, and a different equation, and you might get even closer to Pi, or Tau, or something else. Commented Aug 9, 2022 at 16:54
• Reminder to commenters and answerers: It is not enough for you to say "Oh, I bet there are other numbers you can find." "Oh, I bet this is a coincidence." "Oh, I don't find this surprising." because you need references to empirical evidence or why would we trust you? Commented Aug 10, 2022 at 4:18
• Does this answer your question? Are these occurences of the mathematical constants e and pi in The Bible at all exceptional? Commented Aug 10, 2022 at 12:30
• I find it funny to think that Hebrew or Greek letters being assigned numerical values, after put through some mathematical operations, are supposed to give out a couple of digits of pi and e in decimals, when neither ancient Hebrews nor ancient Greeks used a decimal system. In other words, the Lord encoded this in a way that could never have been noticed by anyone in his target audience before ca. 1600 AD. Commented Aug 11, 2022 at 3:54
• Dear new visitors from the Hot Network Questions List, Welcome! This answer is attracting a lot of poor-quality answers and comments. Please read that link. Your answer should show, with references, whether the formula works as stated, and then (perhaps) argue whether it is a coincidence. Commented Aug 11, 2022 at 10:12

Are the mathematical constants e and pi encoded into the Bible?

Based on the provided evidence,

NO.

Disclaimer of bias: I consider myself a Christian who believes that the Bible is divinely inspired. I admit that if these numerical values were encoded into the Bible before they were known to the mathematical community, this would be an impressive piece of evidence for divine inspiration. So I might hope that a claim like this is correct. But it isn't.

The issue here is that the method of encoding presented is entirely and completely arbitrary. At no point does the author justify how he selected various methods of calculation. Consequently, as Dan Romik points out in his answer elsewhere on this page, this method suffers from the research degree of freedom problem.

Consider his method of equating numbers with letters. This method, as pointed out by David K and LangLangC (thanks y'all) is native to the Greek alphabet; however, it was not adopted into the Hebrew alphabet until long after the book of Genesis was written, and would not make sense to apply to the Hebrew text of Genesis 1:1. One could argue that God would know the future, and consequently place the verse in such a way as to be decoded in the future. However, Joe Vasta goes on to make clearly arbitrary decisions in his line of reasoning.

Consider the expression that he uses to create the values similar to pi and e: (number of letters)(product of letters)/(number of words)(product of words) Why did he select this combination of multiplication, division, and summing? No explanation is provided.

Now consider that the resulting numbers only match pi and e if you divide by 10^17 and 10^40, respectively. Why are these values different? On what basis are they the "right" numbers to divide by to get the "right" mathematical constants? No explanation is provided.

Now consider that in the original Greek and Hebrew Bibles, there were no chapters and verses! No Christian that I know of claims that the modern divisions of chapters and verses is divinely inspired. They are simply arbitrary markers for ease of navigation. See Kurt and Barbara Aland, The Text of the New Testament and Ernst Würthwein, The Text of the Old Testament.

With so many arbitrary choices, it is possible to claim to find encoded messages anywhere. For proof of this, take a look at my tongue-in-cheek response to a puzzle on Puzzling.SE. I managed to find a "secret message" within the first few digits of pi itself, with the exact same arbitrary way of thinking.

To conclude, due to the apparently arbitrary operations performed, there is no evidence that finding pi and e in this manner is a remarkable or miraculous occurrence. I suspect (but cannot prove) that this is simply a man with too much time to devote to trial and error mathematical calculations.

• It's well documented that the Greek and Hebrew letters have been assigned numeric values 1 through 10, then 20, 30, etc. There are standard equivalences (I didn't check to see if the ones in the claim were standard). I point this out in particular because I have no disagreement with anything else in the answer. Commented Aug 10, 2022 at 5:07
• Commented Aug 10, 2022 at 5:11
• But those values aren't accurate to 3 or 4 decimal places. They're accurate to one decimal place. Commented Aug 10, 2022 at 23:50
• Re: "Now consider that in the original Greek and Hebrew Bibles, there were no chapters and verses!": This is true to a point, but it doesn't mean what you're suggesting. The first verse of the book of Genesis and the first verse of the book of John are both well-defined (and of particular significance) whether or not they're known as "Genesis 1:1" and "John 1:1", and even though there are other places in the Bible where the division into verses is not so unanimously agreed upon. Commented Aug 11, 2022 at 0:51
• @ruakh I would disagree, and argue the following. John's "In the beginning was the Word" mirrors Genesis's "In the beginning God created the heavens and the earth" and then "And the word was with God, and the Word was God" mirrors "and the earth was without form and void." Precise correlation could be argued, but I don't believe that they are so well defined as to indicate that the verses are completely parallel. Commented Aug 11, 2022 at 1:41

I've not seen anything directly addressing Vasta's claim. But this feels rather like a case of the well known phenomenon Apophenia - which is the human tendency to attribute significance to otherwise random data.

The text of the bible verses used here aren't exactly random data - but applying a fairly arbitrary numerical value to them, then applying an even more arbitrary mathematical operation to them which then gives two numbers (and by their nature will generate fairly large numbers), and then seeing similarities between the digit sequences of those numbers and the digit sequences of two numbers whose very nature as irrational numbers basically ensures you'll be able to find a similar digit sequence. e and π aren't random data either but for Apophenia purposes they might as well be.

The reason I focus on digit sequences there rather than actual numeric values is because despite Vasta's claim when comparing π to Genesis that:

The absolute error is less than 0.00004

it is nothing of the sort - the number he calculated for Genesis 1:1 was 17 orders of magnitude larger than π and for e it was 40 orders of magnitude larger!

So all they really found encoded were 4 to 5 digit long sequences that matched. It sounds cool - but I'd be very surprised if you couldn't find a similar level of "encoding" of these irrational numbers in many works of text of sufficient size.

• This may be pedantry, but I am having trouble ascribing this to apophenia which is defined as "the unmotivated seeing of connections [...]". These numerologists have had to go to some effort to cherry-pick these answers, selecting from dozens or hundreds of potential Bible Code formula, and discarding tens of thousands of other verses in the Bible that gave random results, and picking from dozens of potential constants, to get two examples. Ascribing motivation is hard, but this doesn't seem unconscious. Commented Aug 10, 2022 at 0:09
• @DenisS John 1:1 is definitely the New Testament corollary to Genesis 1:1 though, due to its content. Commented Aug 10, 2022 at 6:25
• @Fattie But the number is not 3.141554508, it is 314,155,450,800,000,000 - which as moto points out is a LONG way from pi. Commented Aug 10, 2022 at 14:07
• @Fattie It's not a sheer guess, it's basic probability. Pick any 50 random letters for this. Then the number of sequential combinations of letters is 50 factorial, which is 3.04*10^64. If we assume the formula is reasonably random (which it is), then the odds of not finding any given 6-digit number are 3 in 10^59! That's close enough to certainty. :) Commented Aug 10, 2022 at 15:47
• @thedefault. You've missed the point. Any 50 characters, used with any encoding scheme that (like this one) gives a large random output, is basically guaranteed to have this within it through simple probability. Commented Aug 13, 2022 at 10:26

Let's judge this discovery by the standards of scientific research, and note two major flaws with Vasta's thesis:

1. He has not provided statistical analysis that supports the hypothesis that this numerological observation is anything more than pure coincidence.

2. He offers no explanation for why any of the many choices he made on the path to the discovery (e.g., which bible verses to look at, how to encode them into numbers, what mathematical formula to plug those numbers into to produce an approximation of a mathematical constant, which mathematical constant to look for, why look for a mathematical constant in the first place, etc) are logical ones rather than being completely arbitrary.

Each of these flaws is, independently of the other, a complete deal-breaker as far as what it means for getting serious people to accept the "bible encodes e and pi" hypothesis as even remotely credible. For the first one: without a statistical analysis, what makes this observation any more unusual than, say, "I saw a rainbow while driving to work today, and it was shining directly on the church on the top of the hill"? (To which a skeptic might counter, "Well, I saw a cloud today and it was casting a shadow directly on the same church. And from where I was looking, the cloud looked live the devil with two horns!")

The second flaw is arguably worse than the first one, and its presence would make even a sophisticated statistical analysis highly suspect and possibly invalid. The issue here is that Vasta has taken advantage of what is known as researcher degrees of freedom. As Wikipedia explains:

The term reflects the fact that researchers can choose between multiple ways of collecting and analyzing data, and these decisions can be made either arbitrarily or because they, unlike other possible choices, produce a positive and statistically significant result. As such, researcher degrees of freedom are often related to data dredging and other questionable research practices. Their widespread use represents an inherent methodological limitation in scientific research, and contributes to an inflated rate of false-positive findings.

[...]

Steegen et al. (2016) showed how, starting from a single raw data set, applying different reasonable data processing decisions can give rise to a multitude of processed data sets (called the data multiverse), often leading to different statistical results.

Based on these issues, it's clear that Vasta's observation could not be published in any serious scientific peer-reviewed journal. Now, you might say that this criticism is unfair because the standards for scientific publication are too high. But is science really the only area in which we hold people's claims to high standards of evidence? Consider:

1. Would you let your child take a medication whose efficacy was supported by an "analysis" like Joe Vasta's? Would the FDA ever consider approving such a medication for public use?

2. If you were serving on a jury, would you vote to convict a person accused of a crime when the evidence of guilt was of a similar vein to what Vasta is presenting? E.g.: "I urge you to find Mr. Jones guilty today, based on the fact that the product of the digits of his phone number and the digits of the murder victim's phone number, plus the sum of their social security numbers, is a decent approximation of the square root of 2. Can this be a coincidence? Surely not!"

3. Would you believe a car salesman, or anyone else for that matter, who tried to convince you to buy a product or give money for something based on claims supported by evidence like Vasta's? Etc.

Bottom line: the burden of proof lies on the person making an extraordinary claim to provide convincing evidence for the claim. Vasta has not done so.

• "Reaearcher degrees of freedom" Thank you!! I knew there was a term for this and I could not recall it. Commented Aug 10, 2022 at 21:10
• @Brandon_J a related term is data dredging, which is roughly speaking the practice of using the researcher degrees of freedom intentionally to come up with hypotheses that seem statistically significant when researcher degrees of freedom are ignored. Commented Aug 10, 2022 at 23:54
• Thanks, Dan. I have decided not to include data dredging in my answer because it is already fairly lengthy. You seem absolutely correct, though. Commented Aug 10, 2022 at 23:56
• @RayButterworth Except they do not. Genesis is in Hebrew. John is in Koine Greek. The word order in each of those respective languages is not the same as the word order in proper English syntax. Commented Aug 18, 2022 at 9:53
• @RayButterworth רֵאשִׁית can be just as accurately translated "first" and בְּ is a preposition that could just as easily mean "at". The shade of meaning of ἀρχῇ is more along the lines of "chief" or "preeminent", and seems to be addressing the eternal preexistence of the logos, not the start of the temporal creation. Neither includes an article ("the"). Insisting both have the same meaning is a real stretch unless one assumes all other languages are just different words for thinking in English, which of course is ridiculous. Commented Aug 18, 2022 at 17:21

You might be interested in this website, which in particular shows that the kind of 'bible code' rules that people like to use can be applied to any sufficiently long text such as to Moby Dick to find related words for essentially anything you want.

Also, simple mathematical analysis invariably dispels this mystery. Just for example, if your desired word is k letters, and your text has n letters from an alphabet of size c, the number of ways to pick an arithmetic progression of k indices (such as those bible codes in the linked website) is at least (n/2)·(n/2k) (i.e. pick the first index from the first half and then pick the distance between the first two indices), so you have n^2/4k possible choices and ought to expect to see your desired word roughly (n^2/4k)/c^k times, as a first-order estimation (ignoring the letter frequency distribution). For (k,n,c) = (7,10^6,26), we have (n^2/4k)/c^k ≈ 4.

For vague or unspecified rules, such as in your case, the correct way to analyze the phenomenon is to understand Kolmogorov complexity, which is an essentially objective way to measure how much information is encoded into a proposed explanation of some pattern. Informally, if the specification of the rule itself takes m characters, then it should be completely unsurprising if the rule generates a pattern of only m characters.

K-complexity is a mathematically precise form of Occam's razor, where we can define comparison between two hypotheses for some data that are each given by a program, simply by favouring the shorter program. This notion is truly objective in the sense that, if the correct explanation can be captured by a program, then once you have sufficiently large amount of data, you will eventually stabilize on favouring the correct explanation. To get the most out of this even for not that much data, use a general-purpose programming language such as Python.

Many people underestimate how long a pattern must be in order for a proposed explanation to be favoured by this K-complexity-based analysis. For example, see this post showing that the pattern of primes is probably favoured only given a rather long initial segment, in particular long enough for the desired program to check primality to win other programs.

We cannot directly apply this to your question, because there is simply too little data generated by the proposed rule. In particular, the claim is that some text encodes some data, and the rule to retrieve it must be simple enough that it actually shows that the output was really encoded in the text and not in the rule! With this in mind, the cited achievement of these numerologists is utterly disappointing. They only managed to recover 6 decimal digits despite injecting a huge amount of gematria!

We can still apply K-complexity in the following way. Since the claim is that some text T is special, and there is a rule to retrieve some data from T, then there must be a program P and parameters given by S such that:

1. P(S,T) is the desired data (e.g. first m digits of π).
2. S is very short. (It had better be shorter than m!)
3. P(S',T') is not the desired data for any other text T' and short S'.

Clearly, you can achieve such a thing if your P is complicated enough (e.g. using gematria in an over-fitting sense). So the true challenge is to find such (P,S) with P having minimum length. To invalidate the numerology, it suffices to find some (P',S') with length(P') ≤ length(P) that produces the desired data from a different text, as it would demonstrate that the numerology captured by P fails to support the claim that T is special. jpa's answer can be viewed as an instance of this kind of invalidation!

• You asked about my answer being deleted. It was deleted by @Oddthinking due to the long-standing Skeptics policy of math being unverifiable. To be honest I expected that to happen, it was just too fun to pass by. Here is the text: paste.dy.fi/RnA/plain
– jpa
Commented Aug 11, 2022 at 16:33

Analyzing this is like unraveling a stage magic trick. If you want to know how, or at least when, the trick actually happens, work through it backward.

There are two ways these amazing results can be found:

• Notice something unusual, analyze it, discover that the result is very close to π (or "e" or whatever), and be amazed.
• Know what the value of π is, look for things that can be converted to numbers, look for ways of combining those numbers to produce an approximation of π, and amaze gullible people.

Here's an example of the second case, presented as if it were the first case:

• The Genesis 1:1 calculation results in 3.1415545…, which is 99.998786…% of the true value of π, almost 5 nines of precision.
• Can we do better than that?
• The word "creator" occurs only 5 times in the King James Bible.
• It also contains 71 "womb"s and 113 "firstborn"s.
• Calculating: "creator × womb ÷ firstborn" = 3.1415929…, which is 99.999991…% of the true value of π.
• That's 7 nines, one hundred times closer than the Genesis 1:1 nonsense.
• In addition, 5, 71, and 113 are all prime numbers, a strong confirmation these words are special.
• It also demonstrates that the KJV is the only real version of the Bible.

What's not shown above is the initial step:

• A well known, very close approximation of π is 355/113, which prime factors into 5 × 71 ÷ 113.
• Find three lists of words that occur 5, 71 and 113 times in the KJV.
• Find three words, one from each list, that look like they belong together.

Coincidence?

• "It is up to the answerer to provide valid, verifiable and potentially replicable evidence." — What here isn't valid, verifiable, or replicable? Calculating `5×71÷113` doesn't require highly specialized data analysis skills. Commented Aug 30 at 13:47