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.

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57 Responses

  1. Old Git Tom says:

    Mr Marshall,
    many thanks for that – it’s absolutely astonishing. OGT

  2. DDD says:

    I enjoy your site. I do however have a problem with some of the math–
    “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:”
    Right below this is a table 1st letter T –White, next first letter C is black, next first letter A is white, next first G is Black
    White / Black = Sum T+ Sum A / Sum C + Sum G =0.690983
    Later in another matrix it is stated “There are two more symmetries that Perez discovered: and that matrix has the White/Black reversed
    Sum C + Sum G /Sum T+ Sum A = 1 to 1
    Simplifying T+A / C +G = 0.690983 and C+G / T+A =1 I don’t believe math works that way unless you are changing the inputs and not calling them out.
    or am I missing something here?

    • The 2nd matrix does not reverse the black/white, there are a total of 6 distinct matrices, 3 are 1:1 and 3 are 0.69. Perez’s paper makes this clear. If I’ve made an error in representing Perez’s paper I’m open to having that pointed out.

      • EHMAI justin says:

        I ask you this Mr insult…but I see you as an intellectual being would you open your ear to me knowing how to construct God’s dna…I will show you but it is complicated and your mind has to be open on different ssubjects

      • Jean-Robert Colimon says:

        I will show/demonstrate/prove the Origin of the golden ratio 1.618 of the X chromosome, and all subsequent golden numbers/ratio. On top, I will show How to find the DNA/ Chromosomes of any living thing, Introduce you to the orchestra Chief. You will find out, Why mammals (us) have 5 fingers~( fractal base 5) birds (4) for ex, we will have to literally swim in Fibonacci/ Golden numbers.

        • brian pope says:

          Hi–I was so fascinated by your remark about the underlying mathematics principles governing mammalian 5-fingered ante, and (fractal base 5) and base 4 for birds, you say. I’d be so grateful if you’d be willing to tell me anything about where this principle is discussed as a deterministic influence, or even what the area of inquiry is called–i’m interested in the logic that arrived at the realization that the numbers (or rather the symmetries that the numbers describe) influenced, or even determined such things and whether it has ever been suggested and has been subsequently disproven ( as i now hope) the opposite dynamic–the idea, for example, that just because a given numerical ratio can be applied to describe a complex system’s behavior so elegantly and aptly doesn’t necessarily mean that thing was shaped or governed by it, right? Why could this not have been a coincidence or an accident? I can direct my own researches of course, but I just wondered if you’d be willing to direct me toward the specific areas of knowledge you’re drawing on –and more specifically even– if you remember it ever being discussed as a possibility that cause should not be presumed where only an effect has been witnessed. (I always find I like the magic better if I’ve tried and failed to find the trick!)… hope to hear back from you!

          • Jean-Robert Colimonn says:

            Time is not on my side anymore, turning 70 years old in 2 days. I am not going to beat around the bushes, by telling, now my aim is to sale to a responsible party, my discovery/work of the last 10 years. It was so absorbing/hypnotizing; that I am still perplexed, about that 10 years period. I want to retire for real now. I did believe that the $10000000 was real, still hope, but I have received NO sign that, they want to follow through , while I am still available/ alive. Proof that nothing is 100% sure secure, now the Corona virus. I would not mind a serious collaborator; Solved the scientific Origin of life/DNA, actually working on a practical pathway for organ production. If you can see yourself as an investor on 2 levels, monetary and scientific, let’s connect. Think at the market for such a thing.

          • jean-robert colimon says:

            I tried earlier to reply, but it seems it didn’t go trough. At 5000% for sure , I solved the scientific Origin of Life/DNA programming, some 10 years ago; Actually I am trying to establish a pathway as to produce replacement Organs on demand at the theoretical level. The $10000000 prize seemed to be fresh/fair start, BUT no valid proposal from Mr Marshall, so I am forging ahead as to have a patent application. No man is an island, If you can see yourself as an investor on 2 levels monetary and scientific, we can come to an agreement. I am turning 70 years old, in 2 days; so the need to sale and share before it’s too late. Proof that nothing is sure; now we have the Corona virus. Waiting for a feedback.

  3. NoMoreGames says:

    Very interesting article, but being biologically educated, I have a few comments.

    Junk DNA has long been believed to have some sort of function, we are just unsure of what that function is (most likely regulatory). The term “junk” has just stuck around from an older time.

    “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%”

    Considering there are about 3 billion base pairs in the human genome, that would still allow for some 3 million bases to not be controlled by this matrix, essentially offering counter evidence for your first example. That’s a lost of potential random mutations. Please correct me if I interpreted this data incorrectly.

    I haven’t had a chance to read it yet, but I’m wondering if his paper mentioned if he factored the highly variable and repeating telomeres into his matrices?

    Thank you for your input!

    • If the Evolution Matrix controls codon populations to 0.1% then that means that copying errors cannot account for more than 0.1% of the difference between, say, bacteria and humans. It means that 99.9% comes from processes that obey the rules of the matrix.

      I’m sure there is some teeny tiny percentage of random mutations that have turned out to be beneficial. But then saying that random mutations are therefore the source of evolutionary progress is a complete non-sequitur. It’s sort of like a story I remember hearing somewhere, where a guy had some kind of physical problem and he was struck by lightning and it went away. It could be true, and freak accidents do happen, but nobody I know is volunteering to get struck by lightning. Science is not about freak accidents, it’s about systematic explanations.

      Evolution is driven by transposition, horizontal gene transfer, epigenetics, symbiogenesis and genome doubling. All of those things are very well documented, all are systematic processes, and they obey the rules of the matrix. Random Mutation doesn’t obey the matrix and is dead last in the lineup of beneficial evolutionary mechanisms.

      I’m not sure about your last question. I’ll forward it to Dr. Perez.

      BTW The term “junk DNA” needs to be discarded. As does other derisive terms like “degenerate code” which is a misnomer for a brilliant error minimization scheme.

      (Or maybe we need to keep the term ‘junk DNA’ around as a reminder of how much damage atheism has done to the study of biology and the practice of science.)

      • brian pope says:

        Hi Perry, I very much enjoyed your article about the Mathematics of DNA… your style, at least in this article, was really well-balanced, very clearly voiced, confident and assertive almost to the point of coming off as aggressive or arrogant –but JUST shy of it, which makes you a powerful writer–and your explanations were very clear without being condescending. (Even though this is all very far from the scientific fields I tend to read about–so thanks!) So with that in mind, your last sentence in response to a reader’s question completely blew me away and I’m dying to know more! You wrote: “…a reminder of how much damage atheism has done to the study of biology and the practice of science.” I was barely able to find why you felt that was in context at all, but nore importantly, you clearly feel strongly about it and I’m interested in your view on this. Any chance you can elaborate on what/why your response included these extremely polarized statements about atheism and why you feel atheism has caused so much ruination? I’d agree that almost any paradigm or belief can become dogmatic and dangerous if over-applied, but generally, I myself have tended to lay credit at the feet of those who tend to claim they’ve heard God very clearly–and are empowered to speak on his behalf– for having held back science and culture back for 500 years, repeatedly, scattered here and there over the millennia… the villains for me have always been the likes of those who burned Galileo, destroyed the Alexandrian Library or, more recently, turn science fact into “fake news.” (And who tortured me throughout my adolescence in the South with their pained expressions of regret that I, for being an atheist AND a homosexual, would burn in eternal hellfire–but if I’m not gay (i was and am) I could still date their daughters but, hey, can you just try believing since, as they said, “if you’re right–you’ll never know as you’ll just simply be dead–and if I’m right, well, then going to Hell would sure be terrible–you seem like a nice boy if it weren’t for all these confused views–surely you can see that my position is a better bet, young man.” Usually, I just quietly sighed to myself that such should be their motivation, almost in its entirety, becuase, hey–the alternative is so much worse. Through their crocodyle tears over my imminent condemnation, their belief system, their culture, and their social status as god-fearing Chritians blinded them–utterly– from being able to see their own intellectual and moral cowardice, probably across many facets of their lives…. and the corruption of their critical thinking faculties seems to be DIRTY TRICK #1 in the religious playbook–but now I’m curious about my own position (i try to re-examine my more extreme or inflexible beliefs every 6 months to a few years as both an intellectual, endeavoring to keep my thinking from being too rigid as I’m getting older but also to be morally clear, to be certain, that I’m behaving correctly (correct as I can) for reasons I personally believe in and for which I am accountable for with no excuses and no one else to blame, as an agnostic who finally felt it was important to take a stand for a reasonable position based on available facts and held only so dear as to, should God make him or herself known to me, (and after answering for quite a few bits of either mischief or inexcusable neglect, thank you very much!) I would then, being a reasonable person confronted with overwhelming evidence, cheerfully say, well, damn, I kind of liked it better paradigmatically when i thought i was charged, myself, with the responsibility for figuring out good or bad, being curious or not, being moral or being Donald Trump… without you being brought into the equation. But okay–well, fine. Since you’re here and you appear to be legit, can we talk about all this crap they say about you? Cuz you’ve always seemed like you’d be a real dick–so insecure, demanding and rage-based… but, looking forward to hearing the whole story–told credibly–without threats of damnation. Please. But you would say the atheists have been as bad or worse for science than that crowd? “Believer” was turned into such a bitter word almost every time it entered my ears, seeing the people owning it. No matter your response, I doubt my position will change radically–because, after all, I’ve been listening for arguments that speak well of this God guy, that direct my thinking down a path of reason but at least get me to the first layover before embarking on the soft and seemingly delusional wings of faith to get me safely there–and that side tends to be soft when it comes to the rigorous challenges of defending their beliefs (and their actions, all too frequently) without in fact finally falling on faith as their only defensible argument. But hearing your argument might turn out to be sufficient to reduce whatever destruction is being wreaked by my own “toxic atheism.” I think Dawkins was right about so many things–but I can also certainly see that his shrillness and condemning treatment of all things religious has left him, his beliefs and his arguments for them as almost equally unattractive and indefensible as the believers he detests. (His own version of crocodile tears is hinted at when he laments how lost those poor stunted God-deluded fools are.) But I’m guessing that just his shrill and caustic tone is NOT why you say these things, yes/ no? So: Hit me! I can take it! (And I’m genuinely, respectfully interested.)

        • Brian,

          Thanks for your great question.

          A way-too-short answer is that atheism turned neo-Darwinism into a pop religion, literally for the last 80 years, and has severely misrepresented the science; has actively opposed the real science, a truth to which many scientists I know can attest. (Non-Christian scientists for the most part.) If you read Evolution 2.0 you will begin to see exactly what I mean.

          Another example is the Junk DNA hypothesis. Junk DNA has been almost entirely a pet argument used by atheists, and while the Junk DNA hypothesis is for all practical purposes dead, the last holdouts right now are all staunch atheists. (Larry Moran and his fans for example.) Did you know that the bacterial coding sequences that led to the discovery of CRISPR gene editing technology were proclaimed for years to be “junk DNA”?

          The Junk DNA hypothesis alone likely represents a 30 year setback in scientific advancement, and there are multiple versions of this that I don’t have time to get into here. The misunderstanding of evolution itself is partly the reason for the fact that cancer research has made shockingly little progress in 40 years.

          All this is just the tip of the tip of the iceberg.

          Think of it like this: If you take the ultra-conservative creationists on one side, and the claims of a 6000 year old earth and all that on the right (and how many plainly obvious facts you have to ignore in order to believe that), just understand that the left has misrepresented the science just as badly – and most people actually think it’s true. The article about mathematics of DNA here above attests to just how wrong their notion of “random unintelligent evolution” is.

          Evolutionary biology is one of the most politicized and nasty professions you have ever seen. If you think the Galileo story is nasty, you should talk to all the scientists whose quality work has been vigorously opposed and vandalized by the champions of Neo-Darwinism over the last 50 years. Only in the last few years has that begun to change. (More of the story here

          Richard Dawkins has been vigorously opposing real science for his entire career, while appearing to be a champion of it. The science in his books is a blend of quality true facts with rubbish, all mixed together.

          Denis Noble, my prize judge at Oxford University, was on Dawkins’ PHD review committee and will attest to everything I have just said.

          I’m not joking. This is one of the biggest untold stories in science. (Yet you can find evidence for it all over the place if you know where to look.) See this for example


          This is such a good question I am going to devote an entire podcast episode to it. There is SO much more to say.

          I’m sorry for how you have been treated by Christians – which is a whole ‘nother topic, so there are really two topics here. More to come.

  4. tetrahedral says:

    Languages may be as precisely tuned re the Golden Ratio as DNA. There is a doctoral student at UArizona doing his thesis on Phi in phrase and clause structure. Others have shown strong typological relations between prosody type and syllable type, between numbers of features in phonemes and total average sentence length, etc. And language types tend to be highly coherent, re word order and other factors between heads and dependents. It just hasn’t been looked at through the window of fractals, the Golden Ratio, etc. Since languages change these things cyclically, and pack/unpack the individual feature bundles into new configurations, linguists specializing in one aspect or another can’t help but fail to see the larger picture.

    There are also many strong parallel analogical relations between linguistic and genomic structure. Languages can separate basic meaning bearing units, adjoin them, or overlap them. Same thing happens with genomes, in terms of protein coding sequences. Meaning bearing units can bootstrap their forms from their underlying sequence (sound symbolism) or get them imposed from above. Generally the relative importance of these two extrema depends on how elaborated morphosyntax is, or how often used. There is evidence of the same thing in the genome.

    Finally, re ‘junk’, it has been shown that in eukaryotic organisms the more junk, generally, the more environmental context sensitivity is present for determining the right time to become sexually mature- they wait for optimal conditions. They also tend to have larger, less complex cells, less internally ramified or externally connected. or overlapping organs. Those with reduced junk tend to have smaller more specialized cells, often mixed in organs (sometimes from separate origins). They ignore the resource environment and are instead ‘on the clock’ for maturation, so that the process is more or less in synch with the seasons, the day/night cycle, etc.- automated. Also earlier life stages tend to be de-emphasized or reduced. Thus metamorphoses- in plants and animals.

    Junk cumulates either by wholesale duplications or from inputs from outside the organism (viruses). And it can be lost as well. Constant updating. Old viruses get defanged by breaking up genes into fragments, etc. And there is exchange between the junk and the split gene system.

    Same thing happens in languages. But I’ll leave off here unless there is more interest.

    As for Phi in nature, in the past year I discovered a link between the Periodic Table and Pascal’s Triangle, and Fibonacci and related sequences. Just for one example if one divides Fib numbers into triplets (two odds, one even- that is, an even number of odds vs. an odd number of evens), and maps them AS atomic numbers in the periodic system, then within known elements ALL the odd Fib numbers map to leftmost positions in the table where there is one electron in one new orbital lobe: s1,p1,d1,f1. But orbitals are split in two, the left/first half with singlet electrons in lobes, and the second/right half with two per lobe. Within the known elements ALL the EVEN Fib numbers map to the leftmost positions in the second half of the orbital, where the first doublet electron is in one lobe.

    The related Lucas number map instead to RIGHTMOST positions within the orbitals, with half or completely filled status- where there are exceptions, the electron configurations or the behaviors of the elements themselves are altered to better fit the Lucas trend (ex. 29Cu and 47Ag steal an electron from a filled s to donate it internally to make a full d. Half s is just as ‘Lucas’ as full).

    This thing goes on and on with other related sequences. And the exceptions themselves seem to be patterned between the sequences. One finds such things in languages as well.

  5. 3rdMLNM says:

    Good-News to All,

    Here is the wonderful “Symmetry & Mathematics”
    –perhaps the equivalent of DNA codes in some respects–
    within the WORD of one and only true GOD,
    that Jesus unmistakably promised for this Third and Last Day (=Millennium),
    thus also as an “Eternal Food” for all truth-seeking brains, souls and minds (John 6/27-40)
    herein now:

    • Paradise Holding says:

      Recently it seems the gospel of St. John wasn’t written by John at all but Mary Magdalene. God isn’t in the material word but Spirit world. These thoughts go back to Aristotle 329BCE and the Gospel according to Thomas. They weren’t included in the cannon of scripture never the less were written.

  6. helixbender says:

    Perry do you even have an idea of what Barbara McClintock discovered? Look up class II Transposons read about them what the do and how they work. See Genes IX page 538.

  7. helixbender says:

    I not sure I get what you mean when you try to explain McClintock’s experiments. It doesn’t match what I’ve seen in the literature about class II transposons. I’ve never seen a paper talking about fixing the ‘damaged’ gene using ‘other parts of the DNA strand’. Could you give me the reference for this?

    • From

      In addition to proofreading systems, cells have a wide variety of repair systems to prevent or correct DNA damage from agents that include superoxides, alkylating chemicals and irradiation (33). Some of these repair systems encode mutator DNA polymerases which are clearly the source of DNA damage-induced mutations and also appear to be the source of so-called “spontaneous” mutations that appear in the absence of an obvious source of DNA damage (34). Results illustrating the effectiveness of cellular systems for genome repair and the essential role of enzymes in mutagenesis emphasize the importance of McClintock’s revolutionary discovery of internal systems generating genome, particularly when an organism has been challenged by a stress affecting genome function (Fig. 4; 5).

      In repair responses, we know that DNA damage triggers the activation of mutator polymerases and non-homologous end joining activities

      Sometimes, much larger multiprotein assemblages are involved, like the apparatus for carrying out homologous genetic recombination or for repairing severed DNA molecules by non-homologous joining of broken ends (36). Among the most important systems are those called “mobile genetic elements” (MGEs; 7, 8), which make up about 43% of the human genome (21). These MGEs include the transposable “controlling elements” discovered by McClintock, and they comprise integrated systems of proteins and nucleic acids that interact to mobilize DNA to new locations in the genome.

      See the illustration next to this text of segments of DNA being re-arranged via transposition.

      • helixbender says:

        Thanks I see where the misunderstanding comes from. Again it is thought provoking. I’ll find some papers that will help you understand my understanding of how this kind of thing works.

  8. livemike says:

    Ok, so basically the author claims that there is a pattern in something that is supposed to evolved, therefore it cannot have evolved. The problem is that evolution produces patterns, indeed if it didn’t it wouldn’t be evolution. The fact that certain mathematical ratios are produced in nature, particularly the “Golden Ratio” is not news. Nor is the presence of fractal patterns (indeed if you’re describing fractals it sometimes helps to say “they’re like tree branches” everybody gets that). There have been many examples of scientists finding such ratios and then explaining them in terms of reproductive advantage. This is almost certainly another of those. Biologists have long know (as this article points out) that DNA has error correction, indeed this is easily predicted by evolutionary theory because a creature that didn’t have error-correcting DNA would be more likely to produce mutated nonviable children. It doesn’t prove that the mutations aren’t random, it just proves that the sum of the mutations over billions of years has a strong tendency to produce patterns. Which is pretty much exactly what Darwin said.

    Of course it could be argued that if DNA acts as described above that heavily limits the way in which random mutations could occur. But that’s exactly what an error-correction capacity is SUPPOSED to do. Nobody with any scientific credibility claims that an error correction mechanism in DNA prevents evolution.

    • Nobody here is denying that evolution happened. What I am saying is that none of these checksum rules can be derived by the laws of physics; and most importantly they have to be in place before evolution itself can be possible. Perez is saying that these patterns could not have emerged from randomness.

      What this does mean is that the Neo-Darwinian theory that random mutation and natural selection explains everything is wrong. The mutations are not random. They’re non-random, modular and systematic. (Transposition, Horizontal Gene Transfer, Epigenetics, Genome Doubling – ALL governed by this matrix.)

  9. MikeFromOhio says:

    I believe Perry is correct when he says that mutations are not strictly random and can involve Transposition, Epigenetics etc.

    However evolution happens at many levels. It’s possible that the genome matrix has evolved in a coupled manner to the cells that it represents. This is typically referred to as “the evolution of evolvability”.

    As I said elsewhere, we need to work out a prototype with Genetic Programming and *try* to evolve a simple design/code and see what happens. Doing such an experiment might add weight to Perry’s argument, or it might prove otherwise. Either way we would learn more.

    In other words, saying that evolution is mutation/random based and that its not very powerful, is like saying that a car with 1.5 wheels won’t get you very far so why believe in cars.

    Evolution = Variation In Population + Phenotype Selection + Time
    Evolution Random Mutation

    Perry, your TextMutator is very much the car with 1.5 wheels. It does not use a population and only looks at the genotype (there is no phenotype and no environment for selection).

    With that said, I still think you make brilliant points about Design and Language. The question of where did the DNA mechanism come from is spot on. I want to help get deeper into that question. Why not open that box and see what is inside?

    • Roger Sawtelle says:

      Evolution = Variation In Population + Phenotype Selection + Time
      Evolution Random Mutation

      Evolution is not random because while Variation is random, Selection (by ecology) is not.

      Nature through God’s plan creates a broad range of differences in offspring. Most of these differences based on genes are not significant, but some are. Most of these are negative and the offspring do not survive or flourish.

      However those offspring who do survive and flourish do so because the change help the allele adapt to its environment. This is very important because the environment organisms live in is constantly changing. Again most of these changes are not significant, but sometimes they are and the organism must adapt, move on, or die out.

      Most of the dinosaurs died out a long time ago, not because of competition for food and water, but because they lost their habitat when the climate grew colder. The dinosaurs which did not become extinct became birds.

      The avian dinosaurs were able to adapt to a colder climate because 1) They grew feathers for insulation, 2) They became smaller, while other dinosaurs grew larger, and 3) They found food in the air that was not as vulnerable to climate change. They slowly adapted to the change in climate, whereas the other dinosaurs did not and could not.

      Natural Selection is not based on conflict with others for resources and survival. Natural Selection is interacting with other organisms, the climate, and the habitat to maximize resources for all. It is adapting to the ecological niche or making the ecological niche meet its needs.

  10. Old Git Tom says:

    This site may be of interest. It mainly concerns the radical findings of Russian scientist Garjajev, or Garaiaiev (?). Ie., DNA is stored information, a language, & a communications medium. DNA (allegedly) also formed the template of the original grammar of all languages – much sought after by linguists of the Chomsky school.

    I’m scientifically ignorant, so can’t comment, beyond saying that it supports Perry Marshall (et al) in rejecting the idea of ‘junk’ DNA, & the materialist dogma that DNA is ‘dumb’ chemical matter. OGT

  11. […] the process – that all this, could just happen, from the beauty of the oceans and mountains, to the perfection of dna. To decide this happened by accident and not plan, is in itself pretty unrealistic to me. To […]

  12. Xiao-Jun Yang says:

    Local fractional functional analysis, gradually conquering one stronghold after another, may become a nearly new universal mathematical doctrine, not merely a new area of mathematics, but a new mathematical world view. Its appearance was the inevitable consequence of the evolution of all of twenty-once-century mathematics, in particular analysis and mathematical physics in fractional-dimension spaces. Its original basis is formed by theory of sets from Cantor sets to fractional sets. Its existence will answer the question of how to state general principles of a broadly interpreting fractal mathematics and fractal engineering.

  13. Xiao-Jun Yang says:

    Local fractional Fourier analysis, Advances in Mechanical Engineering and its Applications, 1(1) (2012)12-16

    Local fractional calculus (LFC) deals with everywhere continuous but nowhere differentiable functions in fractal space. In this letter we point out local fractional Fourier analysis in generalized Hilbert space. We first investigate the local fractional calculus and complex number of fractional-order based on the complex Mittag-Leffler function in fractal space. Then we study the local fractional Fourier analysis from the theory of local fractional functional analysis point of view. We finally propose the fractional-order trigonometric and complex Mittag-Leffler functions expressions of local fractional Fourier series.

  14. Old Git Tom says:

    Xiao-Jun Yang,
    mathematics; yes, super stuff, but what exactly are you stating? In ordinary language, if possible, please? Thanks, OGT

  15. Xiao-Jun Yang says:

    In this paper we point out the interpretations of local fractional derivative and local fractional integration from the fractal geometry point of view. From Cantor set to fractional set, local fractional derivative and local fractional integration are investigated in detail, and some applications are given to elaborate the local fractional Fourier series, the Yang-Fourier transform, the Yang-Laplace transform, the local fractional short time transform, the local fractional wavelet transform in fractal space.
    Cited from: Local fractional calculus and its applications, FDA 2012,

  16. Xiao-Jun Yang says:

    You need to obtain the orginal paper, and find these results. I look forword to hearing from you, and thank you very much.

  17. Old Git Tom says:

    Xiao-Jun Yang,

    your post writes about some kinds of higher mathematics – a closed book to me, so I fear the original paper would be even less comprehensible! But thanks anyhow. OGT

  18. […] write up on the golden ratio. I understand that he helped translated the work into English. Same? The Mathematics of DNA. […]

  19. God Chaser says:

    “Premise #2 – All codes we know the origin of, that are capable of storing and retrieving pictures of aunt Harriet, a couple of your favorite novels, and back up your computer data, come from a mind!”

    That brings the concept home!

    Hey Perry, are you going to do a write-up on being able to code and store a biology book in DNA?

  20. Old Git Tom says:

    God Chaser,
    no problem: there are many forms of ‘code’, not just mathematical. Broadly, which one is used depends on the kind of info to be best transmitted. Eg., a movie reel contains graphics as code. In principle, the moving images might be translated into scrolling formulae, but it would not be a rewarding viewing experience! And not all codes are interchangeable. Musical notation cannot become language text, & only skilled musicians can ‘decode’ a composition to unlock the audio ‘message’. AFAIK, we are not sure how many code-modes there are, so we cannot talk about transformations ‘in principle’. Some codes might not translate into others at all. But any biology book might be encoded as DNA. I’ve read that computer scientists are researching this very area, since DNA encodes far more densely than any known alternative – so, libraries on a pinhead, etc. OGT

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