When people discuss the mathematician Alan Turing, the word that is most commonly used is "brilliant." Turing did act very brilliantly during the 1940's when he led a secret British effort during World War Two to figure out how to decipher messages from a machine the Nazis were using to transmit secret messages. The Nazis were using a complicated machine called Enigma to transmit their secret messages. Devising novel technology that rather resembled a digital computer, before any digital computer had been invented, Turing devised machinery that eventually was capable of deciphering the secret Nazi messages, so that the British could read and understand them. The efforts of Turing and his colleagues played a large role in helping the Allies win World War Two.
But in the 1950's Turing did not act brilliantly when he addressed the problem of morphogenesis, the problem of how a speck-sized human zygote (a fertilized ovum) is able to progress to become a full-sized human body. In 1952 Turing wrote a paper with the misleading title "The Chemical Basis of Morphogenesis." The first sentence of the abstract was this: "It is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis." But the theory he suggested in the paper did nothing to explain any of the harder-to-explain wonders of morphogenesis.
The theory Turing suggested explained so little that it is misleading to even call it a theory of morphogenesis. It would be more accurate to call it a theory relating to morphogenesis. Turing's theory was scarcely more than a mere claimed explanation of the arising of a few simple ring-like structures. Of course, within biological organisms we see a vast diversity of functional structures, almost all of which are not ring-like.
The beginning of the paper should have alerted the careful reader that something very suspicious and shady was going on. The first lines of the abstract are below:
"In this section a mathematical model of the growing embryo will be described. This model will be a simplification and an idealization, and consequently a falsification. It is to be hoped that the features retained for discussion are those of greatest importance in the present state of knowledge. The model takes two slightly different forms. In one of them the cell theory is recognized but the cells are idealized into geometrical points. In the other the matter of the organism is imagined as continuously distributed."
We see some gigantic "red flags" here. By telling us that in one form of the theory cells would be "idealized into geometrical points," Turing was revealing that what would be going is kind of "biological baby talk" rather than a realistic treatment of the problem of morphogenesis. The origin of fantastically organized and intricate cell structures is one of the chief aspects of the problem of morphogenesis. Cells are units so complex they have been compared to factories and jet planes. When someone tells us that he is going to be treating cells as mere "geometrical points," that is an indication that the person will not be realistically assessing the complexities of biological organization. Also, when someone says that he is going to imagine matter in an organism as being "continuously distributed" (which means having the same concentrations everywhere), it is also an indication that he is not dealing with organisms realistically. By calling his model a "simplification," "idealization," and "falsification," Turing was also hinting that he was in some kind of theoretical fantasy world.
On the second page of his paper, Turing introduces the term "morphogens," a term meaning chemicals that produce a form. He introduced the term in a way that suggested the term had no precise meaning. He stated this:
"These substances will be called morphogens, the word being intended to convey the idea of a form producer. It is not intended to have any very exact meaning, but is simply the kind of substance concerned in this theory. The evocators of Waddington provide a good example of morphogens (Waddington 1940). These evocators diffusing into a tissue somehow persuade it to develop along different lines from those which would have been followed in its absence. The genes themselves may also be considered to be morphogens. But they certainly form rather a special class. They are quite indiffusible. Moreover, it is only by courtesy that genes can be regarded as separate molecules. It would be more accurate (at any rate at mitosis) to regard them as radicals of the giant molecules known as chromosomes. But presumably these radicals act almost independently, so that it is unlikely that serious errors will arise through regarding the genes as molecules. Hormones may also be regarded as quite typical morphogens. Skin pigments may be regarded as morphogens if desired."
Introducing this concept of morphogens, Turing was all fuzzy and imprecise. After defining a morphogen as a "form producer," he told us skin pigments may be regarded as morphogens. But skin pigments do nothing to produce biological forms.
On page 41 Turing very strangely says, "According to the cell model then, the number and positions of the cells are given in advance, and so are the rates at which the various morphogens diffuse between the cells." There did not exist during his life and still does not exist any "cell model" in which "the number and positions of the cells are given in advance." Neither the number nor the positions of any cells are specified in DNA, which also does not specify the structure of any cell. Turing seems to have been just confabulating here. He excused himself from explaining the great mystery of how cells arise in particular numbers and particular positions by claiming that some "cell model" specified such things "in advance," when no such thing was true.
On page 42 of the paper, Turing shows that he is in a kind of puerile fantasy land by stating this: "The contents of either cell will be supposed describable by giving the concentrations X and Y of two morphogens." Cells are units of enormously high complexity, and often described as being complex as factories. Claiming their contents are "describable by giving the concentrations X and Y of two morphogens" is a statement indicating a complete lack of insight into the complexity of cells.
In the paper's last paragraph, Turing basically admits that his theory only applies to a very small number of biological structures. He states this:
"It must be admitted that the biological examples which it has been possible to give in the present paper are very limited. This can be ascribed quite simply to the fact that biological phenomena are usually very complicated. Taking this in combination with the relatively elementary mathematics used in this paper one could hardly expect to find that many observed biological phenomena would be covered. It is thought, however, that the imaginary biological systems which have been treated, and the principles which have been discussed, should be of some help in interpreting real biological forms."
So in the last paragraph of the paper, Turing gets all modest and humbly speaks as if his theory is only applicable to a few cases, saying "one could hardly expect to find that many observed biological phenomena would be covered," which conflicts with the delusional claim he made at the beginning of the paper, the groundless boast that his theory "is adequate to account for the main phenomena of morphogenesis."
Similarly, in a letter to a colleague quoted here, Turing made only very modest claims about his morphogenesis theory, merely claiming that it would explain a few things here and there. He stated this:
"At present I am not working on the problem at all, but on my mathematical theory of embryology, which I think I described to you at one time. This is yielding to treatment, and it will so far as I can see, give satisfactory explanations of --
(i) Gastrulation
(ii) Polygonally symmetric structures, e.g. starfish, flowers.
(iii) Leaf arrangement, in particular the way the Fibonacci series
(0,1,1,2,3,5,8,13...) comes to be involved.
(iv) Colour patterns on animals, e.g. stripes spots and dappling.
(v) Pattern on nearly spherical structures such as some
Radiolaria, but this is more difficult and doubtful."
If you explained such things, you would have solved less than a thousandth of the problem of morphogenesis; for you would not have explained how protein molecules achieve folded three-dimensional shapes, how immensely organized cells arise, how tissues arise, how organs arise, or how something like the human body arises. Gastrulation takes only about 1 week, less than 3% of the 273 days needed for a human baby to form in a womb. So why did Turing write a paper with the title "The Chemical Basis of Morphogenesis" when his theory explained so little? And why did he make the hugely inaccurate claim that his theory "is adequate to account for the main phenomena of morphogenesis," so contrary to what he said in the letter to his colleague?
Nowhere in Turing's paper did he show that he had insight or understanding of the complexity and organization of living things. The paper failed to even use the words "organization" or "organized." Turing acted like a mathematician who could not be bothered to study the complexity of cells and protein molecules and anatomy, which had been well-discovered by the time his paper was written.
Turing certainly did not do a hundredth of what would be needed to explain the appearance of even simpler animals such as a starfish. Explaining how a starfish arises would involve explaining how the thousands of types of protein molecules used by starfish manage to get their three-dimensional shapes needed for their functionality, shapes vastly more complicated than the simple shape of a starfish. Explaining how a starfish arises would also involve explaining how a starfish gets all of the different cell types it has, each an organization of matter vastly more intricate than the simple shape of a starfish. Turing did nothing to explain either of these things.
Eager to claim some progress on a problem that is a thousand miles over their heads (the problem of how a speck-sized human egg manages to progress to become a full-grown human body), biologists have tried to look for places where theories such as Turing's could help explain morphogenesis. But such places have been few and far-between. A leading expert in developmental biology (L. Wolpert) stated in 2017, "It is still not clear whether diffusible morphogens provide cells with positional information and so pattern a tissue during development." Another paper ("Biological notion of positional information/value in morphogenesis theory") states this: "The fundamental role of morphogens as a basis for positional information in a complicated living body is still questionable." Claims that morphogen gradients encode positional information are not well founded, and are examples of the extremely common phenomena of biologists making unwarranted claims, such as when they claim that memories form by synapse strengthening.
The often advanced idea that a "morphogen gradient" (the mere intensity of some chemical) could tell cells where to go in three-dimensional space has always been a ludicrous one. Such a gradient would at best supply a single number, but you need three different numbers to specify a position in three-dimensional space. And if a cell were to receive three different numbers telling it where to go in three-dimensional space, it would have no way of acting on such information. Not knowing its own position in three-dimensional space, the cell would have no way of knowing how to modify that position to go to some other position.
We can compare the theory of morphogen gradients to the theory of panspermia, the theory that life on Earth came from outer space. Panspermia does not solve the problem of how life arose, because it leaves you with this unanswered problem: how could life have originated in outer space? That's just as hard as the problem of how life could have originated on Earth, so there's no real explanatory progress made if you imagine life came from outer space. Similarly, the theory of morphogen gradients attempts to solve the problem of how cells find their correct position in a forming human body by imagining that their correct position is told them by signals from some external chemicals (morphogen gradients). But that leaves unanswered the equally big question: how could such chemicals know what the correct positions of the cells should be? They could not have got the information from DNA or genes, which specify neither how to make cells nor how cells should be arranged. So imagining signaling chemicals that tell cells where to go accomplishes nothing, because no explanation is given as to how such chemicals knew where the cells should go. We've simply gone from "inexplicably high-knowledge cells" to "inexplicably high-knowledge signaling chemicals," which accomplishes nothing in reducing the mystery of how a fertilized ovum progresses to become an adult organism.
Worthless for reducing the mystery of how a fertilized ovum progresses to become an adult organism, the concept of morphogen gradients serves mainly as "busy work" for developmental biologists. Endless chemicals can be tested by them to see whether they act like morphogen gradients, by scientists failing to realize that very rare successes in such searches can be best explained as mere coincidences they should expect to get given all that searching, even if morphogen gradients is a mythical concept. When we read developmental biologists make statements such as "secreted signals, known as morphogens, provide the positional information that organizes gene expression and cellular differentiation in many developing tissues," or "morphogen gradients play a crucial role in development," we are reading folklore with no robust evidence to support it, and we seeing an example of an unwarranted speech custom of a small ivory tower tribe that is very susceptible to groupthink effects and ideological contagion phenomena.
Around the 25:00 mark in the video here, a scientist tells us this about a morphogen gradient, which supposedly works through diffusion:
"The diffusion constants are.. ten-fold, twenty-fold less than what you'd actually need to visually establish the gradient... So we simply don't have enough time in development for a gradient to be established with diffusion constants that we see."
On the page here, a PhD in chemical physics lists many problems with claims about morphogen gradients, and repeatedly compares those who advance such claims to the advocates of the Ptolemaic theory of the solar system, who would keep complexifying their theory by postulating speculative details (epicycles) when their theory failed tests. We read, "Many doubts about the functioning or existence of these so-called 'morphogen' gradients have been raised." Turing appealed to morphogen diffusion, but another paper states that "arguments against morphogen movement by diffusion have been raised by many."
The scanty observational evidence commonly cited for morphogen gradients (involving appeals to Drosphilia, decapentaplegic/transforming growth factor beta, Hedgehog/Sonic hedgehog, Wingless/Wnt, epidermal growth factor, and fibroblast growth factor) will not seem convincing after you consider that there are countless millions of protein molecules and biological chemicals scientists can study, and that given a large body of developmental biologists eagerly seeking for evidence for "morphogen gradients," we would expect that a few chemicals or proteins could be found that sometimes seem to act rather like morphogen gradients purely by chance, even if the concept of morphogen gradients is a myth that has no foundation in reality. Similarly, given some large community believing that animal ghosts live in the clouds, and searching eagerly for evidence of such ghosts by taking many photos of clouds, we would expect such a community to occasionally produce some cloud photos that look like animals, even if there are no ghosts of animals in the clouds. Pareidolia (the tendency of humans to find patterns they are eagerly seeking) can plausibly explain all of the few examples given of evidence for morphogen gradients.
The purveyors of morphogen gradients folklore have papers with line graphs supposedly showing some relation between a concentration of a morphogen gradient and the position of something in a developing embryo. The lines in these graphs are very rarely diagonal lines showing a straight-line relationship, but other types of lines which may look a little diagonal. In general, the papers providing such graphs fail to qualify as good evidence, because (1) there so often is no indication of the number of observations that were used to make the graph; (2) we have no way of knowing whether the graphed data points were cherry-picked to produce such a graph, with data points that did not fit the hoped-for story line being discarded. It is extremely common for scientists to discard data points that do not fit their story line, justifying such conclusion as "outlier elimination." In general, line graphs made from only a few data points are not convincing evidence of a causal relation.
Some of the graphs you see in the morphogen gradient literature involve a "lying with lines" type of procedure in which only a few data points are graphed, but some kind of curve-fitting software is used to project a line using the small number of points (using linear interpolation). If there is no listing of the exact number of observations, such graphs are deceptive, because they make it look like there were many observations, when there were actually few. In general, in papers of the morphogen gradient literature you will find no mention that a blinding protocol was followed. But the crucial measurements that are made are very much the type of measurements in which subjective observational bias might come into play, particularly seeing that the measurements are usually of very small distances such as nanometers (billionths of a meter), and particularly since the measurements often involve subjective judgments about very tiny distances between two microscopic things without precise edges (rather like judging the distance between two clouds or two waves or two cold fronts, but far more subjective). So we must always suspect that the researchers were gathering and analyzing information in a biased way, trying to fit observations to some hoped-for curve so that some nice line graph could be produced suggesting a relationship between the intensity of the gradient and a position of some cells during development. Any such paper that fails to mention the following of a detailed blinding protocol has little value as evidence. Given so many observers acting so oblivious to good scientific protocols (by failing to follow a blinding protocol), we may wonder: has anyone ever really reliably observed any chemical behaving like a morphogen gradient?
Although his original paper merely referred to a "French Flag" problem rather than a model, we are repeatedly told that the biologist Lewis Wolpert tried to advance some "French Flag" model that molecules might encode positional information telling cells where to go to. But in later years he was candid about admitting the lack of evidence for such an idea. In 2015 he was asked this: "Where do you think the French Flag model fits with our current understanding of positional information, and what do you think are the exciting questions at the moment?" He answered this:
"There are problems we haven’t solved. It is terrible, but we still don’t have a molecular basis for it. If I still had an active lab, finding the molecular basis for positional information would be my objective, but would be quite tricky, since I’m not a biochemist or molecular biologist. There is one case of a molecule that might encode positional information, Prod 1, which is graded along the amphibian limb and was discovered by Jeremy Brockes. But it would be nice to find similar molecules in other systems."
Figure 3 of the paper here helps to make clear that sociological effects caused a myth to arise on this matter. Wolpert's original 1969 paper merely referred to a "French flag problem," and never mentioned a "French flag model." The term "French flag model" was almost never used in the scientific literature until about 1998. Then between 1998 and the year 2010 more and more scientific papers started to refer to a "French flag model," with about 60 papers a year referring to such a thing by the year 2010. A myth had been socially constructed, that a scientist (Wolpert) had advanced some "French flag model" when his paper never even used such a term. This is the same Wolpert who confessed in 2015 (in the quote above) that "we still don't have a molecular basis for it."
In the wikipedia.org article on the "French flag model," we read the following reasons for doubting it:
"The difficulties with all gradient based models of morphogenesis were extensively reviewed by Natalie and Richard Gordon and include seven[5] specific points:
- In order to maintain a gradient at steady state there has to be a sink i.e. a way in which diffusing molecules are destroyed or removed along the way and/or at some boundaries. Sinks are rarely, if ever, even considered when the gradient model is invoked.
- Diffusion must occur in a confined space if a gradient is to be established. However, many organisms such as the axolotl develop normally even if the vitelline membrane and jelly layers are removed and development occurs in flowing water.
- Diffusion is temperature dependent yet development can proceed normally over a wide variety of temperatures in animals whose eggs develop external to the mother.
- Diffusion gradients do not scale well yet embryos come in variety of sizes.
- Diffusion gradients follow the superposition principle. This means that a gradient of one substance in one direction, and a gradient of the same substance in a perpendicular direction, result in a single one-dimensional gradient in the diagonal direction, not a two dimensional gradient. Developmental biologists frequently invoke a two dimensional gradient even though a two dimensional gradient system requires two morphogen gradients with two different sources and sinks placed approximately perpendicular to one another.
- Fluctuations in gradients always occur, especially at the low concentrations commonly found during embryogenesis, making a specific response by an individual cell to particular concentration thresholds problematic.
- Each cell has to be able to 'read' the morphogen concentration accurately, otherwise boundaries between tissues become ragged. Yet such ragged boundaries are rare in development."
A French flag is a two-dimensional arrangement of matter, and it was always absurd to be suggesting that a three-dimensional positioning of cells could be explained by referring to the positioning of squares on a two-dimensional flag. The work that has been done on "morphogen gradients" is a "grasping at straws" wild goose chase affair, something that often goes on in the world of science. The claim that scientists have helped explain morphogenesis by postulating "morphogen gradients" by which cells reach the correct positions is a socially constructed triumphal legend that is not well-grounded by observations, one of very many such legends in the world of modern science.
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