The Code and the Law of Truly Large Numbers

A principle sometimes called 'the law of truly large numbers' or 'the improbability principle' is often employed in attempts to debunk unusual phenomena such as synchronicities, miracles and bible codes. Here is Wikipedia's opening statement on the subject:

"The law of truly large numbers, attributed to Persi Diaconis and Frederick Mosteller, states that with a sample size large enough, any outrageous thing is likely to happen. Because we never find it notable when likely events occur, we highlight unlikely events and notice them more. The law seeks to debunk one element of supposed supernatural phenomenology."

A good example of a situation in which this law can debunk an apparently miraculous coincidence is the phenomenon of lottery machines quickly repeating winning draw numbers against apparently astronomical odds. This has happened several times and on one occasion a machine produced the same six winning numbers (between 1 and 49) on consecutive runs, at odds of 14 million-to-1 against. The lottery was run twice weekly and it should have been many thousands of years before there was a reasonable chance of those six numbers repeating.

However, every few days that machine produces another set of six numbers and because the number of possible combinations of those sets [1] increases exponentially over time, the length of time before any two sets of six numbers from that machine are more likely to repeat than not is 43 years, much less than we might expect. That is still a long time, but there are a large number of national lotteries. If there were 100 national lotteries running in the world (which I imagine to be a conservative guess) then the length of time we should wait before a lottery somewhere in the world repeats a set of numbers now reduces to a matter of months. This itself will vary randomly, so occasionally a lottery machine somewhere will repeat numbers it produced only a few weeks before, or even sooner. So there is no miracle to explain, because although the odds against a repetition of the numbers is always astronomical, there are astronomical numbers of possible matching pairs and a lot of lottery machines spewing out numbers.

The Bible is a huge data set of numbers which can easily be misused in the service of someone's favourite theology or end-time speculations. Without some understanding of probabilities one can very easily go astray and imagine they have revealed some hidden code for the world to marvel at, when all they have is meaningless numbers.

Someone like me?


Cutting the TLOTLN Down to Size

Most of the encoded numbers in the NIV Bible are found in strings of two or more consecutive words, or occasionally in single words. I will refer to these as word strings. There are a large number of possible word strings in only a small piece of biblical text and they increase exponentially as the text gets longer. Genesis 1.1, for example, has ten words and 55 word strings within the verse, more than one might imagine. But the first five verses, which contain 83 words, harbour 3486 possible word strings! If we start numerating every word string within those first five verses of Genesis we can find the standard values of many English words and short phrases there - and virtually the entire lexicon of the English language within the first chapter of Genesis. The Law of Truly Large Numbers makes its first, threatening appearance.

But what if we place restrictions upon our search for encoded numbers? We have already placed one restriction on ourselves by numerating only complete words, rather than strings of letters. But we can do more. For example, we can numerate only the word strings that proceed from the Bible's first word. So we have word 1 as the first string, words 1 and 2 as the second string, words 1, 2 and 3, as the third, etc. This reduces the number of word strings in Genesis 1.1 from 55 to 10 and the number of word strings in the first five verses of Genesis from 3486 to a mere 83, which is only 2.4% of 3486! Individual ordinal values vary widely, but the average word ordinal value in the first few verses of Genesis is 45. So as we calculate from first word we will have about the same 1-in-45 chance of hitting any particular number, no matter how far into the text we go.

To summarise, if we are free to choose any string of words within the first few verses of Genesis, we are almost certain to hit any given word standard value within the first ten or twelve verses. But if we pin ourselves down to the string beginning at word 1, then we only have about a 1-in-45 chance of hitting any particular number, no matter how long the string. This is the basis of my argument, but there are details I'll add as I go along.

I will use one set of encodings I found several years ago to show that the law of truly large numbers almost certainly does not apply to the New Bible Code. I picked this example because the probabilities are easier to calculate and the reality of the code is more obvious than other examples. Remember that in the New Bible Code's two-part decoding procedure, numbers are encoded as the ordinal values of word strings and that number is then the standard value of an encoded word or phrase.


String of Pearls

The following table shows a number I found encoded along the first word string in Genesis.

Ark of the Testimony

'Ark of the Testimony' is the first formal title used for the ark, found in Exodus 25.22. [2] The 1-in-45 chance of hitting its standard value is about the same as choosing a named card from a deck on the first pick. Impressive? No! This on its own does not make a code, because although the ark is a central theme throughout the Bible, a skeptic could point out that there are other important themes. What about the Lord God himself? Jesus Christ? The Holy Spirit? Moses? Israel? The Most Holy Place? The New Jerusalem? Then there is the fact that the ark has about twenty other formal titles, such as 'ark of the covenant', 'ark of God' and 'ark of the covenant of the Lord'. The definite article 'the' could have been added, doubling the possibilities. That increases the odds from 1 in 45 to virtual certainty - again, as the law of truly large numbers would predict.

The winds of chance should deposit only meaningless numbers, but the wind of Spirit could arrange the text so that meaningful patterns appear. So one sign that we might be dealing with intelligent design rather than chance is finding clusters of thematically related numbers. For instance, the ark had two important components: the atonement cover, on which the high priest sprinkled sacrificial blood on the Day of Atonement, and the cherubim of the glory, sitting at either end of the atonement cover and between which manifested the Glory of the Lord. The standard values of both items are also found in strings beginning on the first word.

Atonement Cover 

Notice that again there is no definite article used in either case. Another indicator of design is the use of titles found within the NIV Bible. In particular, of the forty-eight versions of the Bible I checked, only five use 'atonement cover', rather than 'mercy seat' or 'lid'. Only two, the NIV and Youngs Literal Translation, use 'cherubim of the glory', and Youngs Literal Translation uses 'mercy seat' instead of 'atonement cover'. So these three numbers are found within the only version in which they happen to be the correct standard values. It begins to look like we have a code that is self referential, which could only be the product of intelligent design.

Another objection can be raised here. Could not other words or phrases be found with standard values of 1754, 1623 and 1169? Definitely, although less than 1 in 1000 words will have a standard value around this range. The number of possible phrases will be larger, though, because you are combining words. Again we are in danger of being lost in the forest of TLOTLN. But the three phrases I have used have very special properties. Firstly, they are very strongly thematically related, in that they refer to the ark, its atonement cover and the two cherubim on top. Secondly, no material object has greater biblical significance than the ark. Thirdly, these particular phrases are only found together in this Bible version. Random words and phrases could be found. But it would be very difficult to find three phrases that also satisfy these requirements. Each one cuts down the forest of possible phrases until it is little more than a copse, perhaps a single tree.

The simple odds against those three phrases appearing here are 1 in (45 x 45 x 45) or 1 in 90,000. However, I already stated that it was virtually certain that the standard value of some important biblical word or phrase would be found there, so if we make 'ark of the testimony' a given, the odds against its two principle features also being found there are 1 in (45 x 45), which is 1 in 2025 - still fairly impressive.

One further objection might be raised. There are about twenty formal titles for the ark in the NIV Bible, therefore many different numbers that could have been found on that first word string, all representing the ark. But the ark encoding was not part of the calculation of the odds, because the calculation was essentially asking what were the chances of finding 'atonement cover' and 'cherubim of the Glory', given that the ark encoding was already there. So the odds are still 1 in 2025. But of the many titles for the ark, it's significant that this one was found there. Most, such as 'ark of your might', are used only a few times. 'Ark of the testimony' is found eighteen times, more than any other title except 'ark of the covenant of the Lord', and is the first title used in the Bible [4] and throughout the book of Exodus, where the Lord gives Moses instructions for building it.


Another Pearl

Each of my arguments is strengthened by another number found here. According to Hebrews 9.4 the only other piece of furniture in the Most Holy Place was the altar of incense. [3] This too is found in that initial word string as its standard value, again without the definite article.

Altar of Incense

Notice also the little pattern of 14, 24 and 34 for the ends of the first three word strings. The connection between the ark and the altar seems less solid than between the ark and its own component parts, so another objection might be raised here, especially since Exodus 40, which tells us that the altar was located in the Holy Place, just behind the curtain, seems to contractict Hebrews 9. However, although the physical location of the altar of incense was the Holy Place, in a religious sense it belonged with the ark. On the Day of Atonement the curtain was opened and the censer filled with coals and taken into the Most Holy Place: this could be considered to be an extension of the altar. In a religious sense the altar "stood before the Lord" (Lev. 16). Both the ark and the altar were sprinkled with blood by the high priest (Ex. 30). The altar was said to "belong to the oracle" (I Kings 6.22). So you can see that in terms of its religious significance, the altar belonged with the ark and that this is more important than its precise physical location.

Taking the latest find into account increases the odds against a chance occurence to 1 in 90000.


Patterns of Meaning

It is a standard assertion of Christian theology that Jesus Christ atoned for our sins on the Cross and was therefore our 'atonement cover'. Jesus was also 'the word made flesh', according to the opening verses of John. Both of these assertions are illustrated in two further encoded numbers. One of them again proceeds from the first word. The other follows it and both are found by bisecting the 'atonement cover' word string into two twelve-word strings.

Atonement Cover Jesus Word

Here we see 'Jesus' and 'word' coincident with 'atonement cover', in a perfectly symmetrical pair of word strings. The whole stands as a visual symbol of this essential Christian teaching. Again, we see that the basis of the code is meaning, something only an intelligent agent could weave into numerical patterns. The word string representing 'Jesus' proceeds from the first word, like the strings representing the ark and its features, another coincidence the law of truly large numbers cannot explain.

Jesus is also our altar of incense (Heb. 13.10) and we again see two numbers, this time proceeding from either end of the 'altar of incense' word string. 391 is the Hebrew gematria of Yehoshua (Jesus). Mashiach (358) is there too, in a word string beginning at word 8 and again ending at word 14.

Altar of Incense Jesus Yehoshua

Observing the integration of these word strings with others in regular patterns (and there is much more than I've shown), it is now easier to see that these are the product of intelligent design. The law of truly large numbers can explain the existence of the numbers, but it cannot explain the patterns they form and the meaning thereby conveyed, other than to say that somewhere within the NIV Bible they will have randomly configured. That is probably true, but finding these configurations proceeding from the NIV Bible's very first word, lying within the Bible's most important verses, which describe God's creation of the heavens, the earth and everything therein, is a neon sign indicating that these patterns are also the creation of God.

Anyway, the code itself, in a miracle of self reference, tells us that - and even marks the ark encodings with an 'X'. [5]


ELS Code in Genesis 1.1-2
Skip interval: 29

This piece of code ends on the last letter of word 24, exactly where 'atonement cover' ends!

ELS Code in Genesis 1.1-3
Skip interval: 37



This piece of code ends on the final letter of word 27, the reduced value of 'the ark'!


Bill Downie 29/3/17

Revised 7/4/17



1. For example, if there are two data sets (A, B) there is one combination: AB. Three data sets (A, B, C) gives three possibilities: AB, AC, BC. Ten data sets gives us 55 combinations, 100 gives 5050, etc. The number of possibilities soon becomes enormous.

2. The 2011 version of the NIV now calls the ark the 'ark of the covenant law'.  However, I am claiming that the code is contained in full only within the 1984 version.

3. This is contentious, because it appears to contradict passages in Exodus, but some have argued that when the curtain between the Holy Place and the Most Holy Place is open the altar can be considered to be part of the Most Holy Place.

4. An important principle in the New Bible Code is primacy. The first name or title found in the Bible is usually the one encoded. See here, for example.

5. These are two equidistant letter sequence codes I've found within Genesis 1.