The Mathematics of DNA

Imagine that someone gives you a mystery novel with an entire page ripped out.page_ripped_out2

And let’s suppose someone else comes up with a computer program that reconstructs the missing page, by assembling sentences and paragraphs lifted from other places in the book.

Imagine that this computer program does such a beautiful job that most people can’t tell the page was ever missing.

DNA does that.

In the 1940’s, the eminent scientist Barbara McClintock damaged parts of the DNA in corn maize. To her amazement,

the plants could reconstruct the damaged section. They did so by copying other parts of the DNA strand, then pasting them into the damaged area.

This discovery was so radical at the time, hardly anyone believed her reports. (40 years later she won the Nobel Prize for this work.)

And we still wonder: How does a tiny cell possibly know how to do…. that???

A French HIV researcher and computer scientist has now found part of the answer. Hint: The instructions in DNA are not only linguistic, they’re beautifully mathematical. There is an Evolutionary Matrix that governs the structure of DNA.

Computers use something called a “checksum” to detect data errors. It turns out DNA uses checksums too. But DNA’s checksum is not only able to detect missing data; sometimes it can even calculate what’s missing. Here’s how it works.

In English, the letter E appears 12.7% of the time. The letter Z appears 0.7% of the time. The other letters fall somewhere in between. So it’s possible to detect data errors in English just by counting letters.

In DNA, some letters also appear a lot more often (like E in English) and some much less often. But… unlike English, how often each letters appears in DNA is controlled by an exact mathematical formula that is hidden within the genetic code table.

When cells replicate, they count the total number of letters in the DNA strand of the daughter cell. If the letter counts don’t match certain exact ratios, the cell knows that an error has been made. So it abandons the operation and kills the new cell.

Failure of this checksum mechanism causes birth defects and cancer.

Dr. Jean-Claude Perez started counting letters in DNA. He discovered that these ratios are highly mathematical and based on “Phi”, the Golden Ratio 1.618. This is a very special number, sort of like Pi. Perez’ discovery was published in the scientific journal Interdisciplinary Sciences / Computational Life Sciences in September 2010.

Jean-Claude Perez discovered an evolutionary mathematical matrix in DNA, based on the Golden Ratio 1.618

Jean-Claude Perez discovered an evolutionary mathematical matrix in DNA, based on the Golden Ratio 1.618

Before I tell you about it, allow me to explain just a little bit about the genetic code.

DNA has four symbols, T, C, A and G. These symbols are grouped into letters made from combinations of 3 symbols, called triplets.  There are 4x4x4=64 possible combinations.

So the genetic alphabet has 64 letters. The 64 letters are used to write the instructions that make amino acids and proteins.

Perez somehow figured out that if he arranged the letters in DNA according to a T-C-A-G table, an interesting pattern appeared when he counted the letters.

He divided the table in half as you see below. He took single stranded DNA of the human genome, which has 1 billion triplets. He counted the population of each triplet in the DNA and put the total in each slot:

When he added up the letters, the ratio of total white letters to black letters was 1:1. And this turned out to not just be roughly true. It was exactly true, to better than one part in one thousand, i.e. 1.000:1.000.

Then Perez divided the table this way:

Perez discovered that the ratio of white letters to black letters is exactly 0.690983, which is (3-Phi)/2. Phi is the number 1.618, the “Golden Ratio.”

He also discovered the exact same ratio, 0.690983, when he divided the table the following two alternative ways:

Again, the total number of white letters divided by the total number of black letters is 0.6909, to a precision of better than one part in 1,000.

Perez discovered two more symmetries:

tcag_symmetry5Above: Total ratio of white:black letters = 1:1
tcag_symmetry6Again, total ratio of white:black letters = 1:1

So for three ways of dividing the table, the ratio of white to black is 1.000:1.000.

And for the other three ways of dividing it, the ratio is 0.690983 or (3-Phi)/2.

When you overlay these 6 symmetries on top of each other, you get a set of mathematical stairs with 32 golden steps. Then an absolutely fascinating geometrical pattern emerges: The “Dragon Curve” which is well known in fractal geometry. Here it is, labeled with DNA letters in descending frequency:



Animated Dragon Curve

You can see other non-DNA, computer generated versions of this same curve here.

Other interesting facts:

  • Similar patterns with variations on these same rules are seen across a range of 20 different species. From the AIDS virus to bacteria, primates and humans
  • Each character in DNA occurs a precise number of times, and each has a twin. TTT and AAA are twins and appear the most often; they’re the DNA equivalent of the letter E.
  • This pattern creates a stair step of 32 frequencies, a specific frequency for each pair.
  • The number of triplets that begin with a T is precisely the same as the number of triplets that begin with A (to within 0.1%).
  • The number of triplets that begin with a C is precisely the same as the number of triplets that begin with G.
  • The genetic code table is fractal – the same pattern repeats itself at every level. The micro scale controls conversion of triplets to amino acids, and it’s in every biology book. The macro scale, newly discovered by Dr. Perez, checks the integrity of the entire organism.
  • Perez is also discovering additional patterns within the pattern.

I am only giving you the tip of the iceberg. There are other rules and layers of detail that I’m omitting for simplicity. Perez presses forward with his research; more papers are in the works, and if you’re able to read French, I recommend his book “Codex Biogenesis” and his French website. Here is an English translation.

(By the way, he found some of his most interesting data in what used to be called “Junk DNA.” It turns out to not be junk at all.)

OK, so what does all this mean?

  • Copying errors cannot be the source of evolutionary progress, because if that were true, eventually all the letters would be equally probable.
  • This proves that useful evolutionary mutations are not random. Instead, they are controlled by a precise Evolutionary Matrix to within 0.1%
  • When organisms exchange DNA with each other through Horizontal Gene Transfer, the end result still obeys specific mathematical patterns
  • DNA is able to re-create destroyed data by computing checksums in reverse – like calculating the missing contents of a page ripped out of a novel.

No man-made language has this kind of precise mathematical structure. DNA is a tightly woven, highly efficient language that follows extremely specific rules. Its alphabet, grammar and overall structure are ordered by a beautiful set of mathematical functions.

More interesting factoids:

The most common pair of letters (TTT and AAA) appears exactly 1/13X as often as all the letters combined – consistently, the genomes of humans and chimpanzees.

If you put the 32 most common triplets in Group 1 and the 32 least common triplets in Group 2, the ratio of letters in Group1:Group2 is exactly 2:1. And since triplet counts occur in symmetrical pairs (TTT-AAA, TAT-ATA, etc), you can group them into four groups of 16.

When you put those four triplet populations on a graph, you get the peace symbol:


Does this precise set of rules and symmetries appear random or accidental to you?

My friend, this is how it is possible for DNA to be a code that is self-repairing, self-correcting, self-re-writing and self-evolving. It reveals a level of engineering and sophistication that human engineers could only dream of. Most of all, it’s elegant.

Cancer has sometimes been described as “evolution run amok.” Dr. Perez has noted interesting distortions of this matrix in cancer cells. I strongly suspect that new breakthroughs in cancer research are hidden in this matrix.

I submit to you that the most productive research that can possibly be conducted in medicine and computer science is intensive study of the DNA Evolution Matrix. Like I said, this is just the tip of the iceberg.

There is so much more here to discover!

When we develop computer languages based on DNA language, they will be capable of extreme data compression, error correction, and yes, self-evolution. Imagine: Computer programs that add features and improve with time. All by themselves.

What would that be like?

Perry Marshall

P.S.: Dr. Perez and I are friends. Perez worked on HIV research with the man who originally discovered HIV, Luc Montagnier. Perez also worked in biomathematics and Artificial Intelligence at IBM. I’m familiar with this work because last spring I had the privilege of helping him translate his groundbreaking research paper about this into English.

You can read it here: “Codon Populations in Single-stranded Whole Human Genome DNA Are Fractal and Fine-tuned by the Golden Ratio 1.618”

Click here for a more in-depth PDF version of this report.

38 Responses

  1. kalimsaki says:

    From Risalei Nur collection by Said Nursi

    Through the light of belief, man rises to the highest of the high and acquires a value worthy of Paradise. And through the darkness of unbelief, he descends to the lowest of the low and falls to a position fit for Hell. For belief connects man to the All-Glorious Maker; it is a relation. Thus, man acquires value by virtue of the Divine art and inscriptions of the dominical Names which become apparent in him through belief. Unbelief severs the relation, and due to that severance the dominical art is concealed. His value then is only in respect to the matter of his physical being. And since this matter has only a transitory, passing, temporary animal life, its value is virtually nothing.

    Man is such an antique work of art of Almighty God. He is a most subtle and graceful miracle of His power whom He created to manifest all his Names and their inscriptions, in the form of a miniature specimen of the universe. If the light of belief enters his being, all the meaningful inscriptions on him may be read. As one who believes, he reads them consciously, and through that relation, causes others to read them. That is to say, the dominical art in man becomes apparent through meanings like, “I am the creature and artefact of the All-Glorious Maker. I manifest His mercy and munificence.” That is, belief, which consists of being connected to the Maker, makes apparent all the works of art in man. Man’s value is in accordance with that dominical art and by virtue of being a mirror to the Eternally Besought One. In this respect insignificant man becomes God’s addressee and a guest of the Sustainer worthy of Paradise superior to all other creatures.
    However, should unbelief, which consists of the severance of the relation, enter man’s being, then all those meaningful inscriptions of the Divine Names are plunged into darkness and become illegible. For if the Maker is forgotten, the spiritual aspects which look to Him will not be comprehended, they will be as though reversed. The majority of those meaningful sublime arts and elevated inscriptions will be hidden. The remainder, those that may be seen with the eye, will be attributed to lowly causes, nature, and chance, and will become utterly devoid of value. While they are all brilliant diamonds, they become dull pieces of glass. His importance looks only to his animal, physical being. And as we said, the aim and fruit of his physical being is only to pass a brief and partial life as the most impotent, needy, and grieving of animals. Then it decays and departs. See how unbelief destroys human nature, and transforms it from diamonds into coal.

  2. Dennis says:

    Dear Perry

    I accept your algorithmic evolution theory but not the millions of years. Any reading of the Bible rules out millions and billions. You need to go back to Genesis. My investigations of the proofs for long ages lead me to believe that when all the evidence is considered including the fossil records that long ages are not at all certain. Why do you have so much invested in the long age ideas?

  3. Les says:

    Perry, I did read your book. What is God’s role in the model of evolution that you propose? Is he just the designer of the laws of nature according to which life originates by chance and then evolves in an unguided manner? Do you believe that God interferes into his creation by e.g. originating the first life form?

    • Les,

      I hesitate to say. On the face of it, based on what we know RIGHT NOW, the genetic code has every appearance of being designed. Especially to a communications engineer who used to work at a networking company, where people developed their own networking languages on an almost daily basis.

      However I am wary of “God of Gaps” arguments. I talk about this in chapter 24. There is ALWAYS a gap, and if you understand Godel’s incompleteness theorem, there ALWAYS will be. It is fundamentally impossible for science to ever answer all the questions it raises. (Which is why scientism is a fool’s errand.) But increasingly I’m disinclined to point to any ONE single fact, or measurement, or phenomenon, and say “Here it is right here, THIS is the finger of God.” I’m more inclined to say it’s found in the totality and grandeur of nature as a whole.

      A LOT of Christians are, whether they realize it or not, looking for that specific finger-of-God piece of data. It’s very comforting to find it… but then disquieting if someone then comes up with a natural explanation and pulls the rug out from under you. Newton thought that the proof of God was that the universe didn’t collapse from gravitational attraction. Well, now we know that laws account for that. I find that philosophically informed Christians are nervous about God of Gaps arguments.

      What we don’t know is where the laws come from. That question always seems to point us back towards God.

      What I’m comfortable with is that at the highest level, belief in God gives us grounds for believing that the universe is intelligible, discoverable, rational and mathematical. And that there’s always another layer of discovery. You also consistently find that, at the edges of science, atheists often revert to random chance, “the universe is senseless and incomprehensible,” “we may never solve this,” “there’s an infinite number of universes and this is just one of the lucky ones” and other anti-scientific, non-testable forms of abdication. Belief in God propels you through that muck. It worked 500 years ago and it still works today.

      As for my own “Where is God in all this question” – I find the answer more readily in my personal experiences with God and in miracles. I’ve seen quite a few first hand, see

      I think it’s curious that many conservative evangelical Christians who embrace beliefs like Young Earth Creationism (a 6-day series of VERY LARGE miracles) tend to overwhelmingly as a group NOT believe in the gifts of the Holy Spirit.

      It strikes me that their rejection of the latter (in my view their arguments for rejecting miracles are weak and unbiblical) is why they cling so tightly to YEC. Everyone, after all, gropes to find the presence of God in their life somewhere. I even find most atheists wanted that at one time – and then gave up.

  4. arash says:

    ancient aliens

  5. Peter Grafström says:

    I’m afraid my conclusion after reading the article is that it strengthens the case for ‘old-school darwinism’. But I agree about the nonmathematical biologists’ lack of understanding of the subject. They are merely believers. But since evolution works they are not really to blame for adhering to an idea they dont fully grasp. I consider the problem of evolution by random mutation to be still unproven but since the disproof is absent time is on the side of the usual view. The problem with proving it is about outruling significant probability for divergent processes, which despite selection would lead to the end of life or to some other unfavorable overall condition.
    The article simply shows that DNA regulates the extent of available mutation which eliminates the problem of strongly varying environmental conditions. DNA seems to be well-engineered whether or not it happened on purpose or by chance.
    An entirely different aspect is that there is no profound theory of matter available. Quantum mechanics is an extremely economical recepy for extracting quantitative information about something, the nature of which isnt even believed to exist independently. So there is room for a great mystery beyond the chemical model of DNA, even though I dont think this article makes that apparent at all. Sorry 🙂

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