If only it were so simple (100 years, part IV)

Ever since I have been enquiring into the works of Nature I have always loved and admired the Simplicity of her Ways. (1)

In his book (yes, it’s about that again), D’Arcy supports his ideas through examples, through observations on biological systems that he can either explain through mathematical equations or directly compare to purely physical phenomena such as bubble formation. You might think that these are grave simplifications.

However, even in biology, which some people might call a “complex science”, simplifications are often used. Using cell culture rather than tissue. Isolating a single player in a pathway to see what its effect is. And quite often, a simplification holds true within the limits that have been set up to define it.

As was pointed out to me recently, the definition of “complex” is that something is “composed of many interconnected parts”. Meaning that this is not necessarily the antonym to “simple”. But “complex” is often seen to mean the same thing as “difficult”, even if that’s not necessarily the definition. In any case, it is definitely not so that physics is a “simple science”:

But even the ordinary laws of the physical forces are by no means simple and plain. (2)

It makes sense to break down a complex system into its individual components and analyse these, perhaps more simple concepts, separately. There is great value in simplifying things. First of all, there is a certain beauty in simplicity:

Very great and wonderful things are done by means of a mechanism (whether natural or artificial) of extreme simplicity. A pool of water, by virtue of its surface, is an admirable mechanism for the making of waves; with a lump of ice in it, it becomes an efficient and self-contained mechanism for the making of currents. Music itself is made of simple things – a reed, a pipe, a string. The great cosmic mechanisms are stupendous in their simplicity; and, in point of fact, every great or little aggregate of heterogeneous matter involves, ipso facto, the essentials of a mechanism. (3)

When reading this paragraph, two things jumped out at me. Two weeks ago, I was at the annual meeting of the British Society for Cell Biology (joint with other associations) and heard an interesting talk by Manuel Théry. Part of his story relied on putting boundaries on a system. Without boundaries, whatever we would like to study just gets too complicated, and we are unable to understand what is happening. For example, when explaining how waves originate, it is much easier to use a system where water is confined in a box. We can then directly observe the wave patterns that start to occur and understand their interactions.

And then this: “Music itself is made of simple things – a reed, a pipe, a string. The great cosmic mechanisms are stupendous in their simplicity.” D’Arcy sure knew his way around words.

Simplifying also heavily increases our understanding of the principles of life, the universe and everything. When you think about it, it is used so often, you hardly even notice that certain simplifications have been made. D’Arcy points this out as well:

The stock-in-trade of mathematical physics, in all the subjects with which that science deals, is for the most part made up of simple, or simplified, cases of phenomena which in their actual and concrete manifestations are usual too complex for mathematical analysis; hence, even in physics, the full mechanical explanation is seldom if ever more than the “cadre idéal” towards which our never-finished picture extends. (4)

When considering biological systems, he states the following:

The fact that the germ-cell develops into a very complex structure is no absolute proof that the cell itself is structurally a very complicated mechanism: nor yet does it prove, though this is somewhat less obvious, that the forces at work or latent within it are especially numerous and complex. If we blow into a bowl of soapsuds and raised a great mass of many-hued and variously shaped bubbles, if we explode a rocket and watch the regular and beautiful configurations of its falling streamers, if we consider the wonders of a limestone cavern which a filtering stream has filled with stalactites, we soon perceive that in all these cases we have begun with an initial system of very slight complexity, whose structure in no way foreshadowed the result, and whose comparatively simple intrinsic forces only play their part by complex interaction with the equally simple forces of the surrounding medium. (5)

For many biological and non-biological systems, the initial conditions might not seem complex. It is by interactions between other – perhaps on their own relatively simple – environmental conditions, other simple systems, that it grows out to be complex. Obviously, as in the definition. But a complex system is more difficult to understand conceptually, more difficult to model. And that brings us the value of simplification, looking at smaller, simpler systems that more closely resemble the “cadre idéal”, allow us to pick apart the different players in a larger system. If we understand their individual behaviour, perhaps this can shed light on the collective behaviour.

As we analyse a thing into its parts or into its properties, we tend to magnify these, to exaggerate their apparent independence, and to hide from ourselves (at least for a time) the essential integrity and individuality of the composite whole. We divide the body into its organs, the skeleton into its bones, as in very much the same fashion we make a subjective analysis of the mind, according to the teachings of psychology, into component factors: but we know very well that the judgment and knowledge, courage or gentleness, love or fear, have no separate existence, but are somehow mere manifestations, or imaginary coefficients, of a most complex integral. (6)

As far as D’Arcy goes in his book, his simplifications hold true:

And so far as we have gone, and so far as we can discern, we see no sign of the guiding principles failing us, or of the simple laws ceasing to hold good. (7)

Of course, this does not automatically lead to complete understanding. We only get that tiny bit closer to seeing the bigger – and smaller – picture:

We learn and learn, but will never know all, about the smallest, humblest, thing. (8)

Because we must never forget that adding together those simplifications does not automatically lead to the answer to the complete problem (and I find this oddly poetic):

The biologist, as well as the philosopher, learns to recognise that the whole is not merely the sum of its parts. It is this, and much more than this. (9)

To end, D’Arcy also makes note of things beyond his comprehension:

It may be that all the laws of energy, and all the properties of matter, and all the chemistry of all the colloids are as powerless to explain the body as they are impotent to comprehend the soul. For my part, I think it is not so. (10)

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Contact surfaces between four cells, or bubbles. This has nothing to do with the soul. It does have to do with how we can often simplify cells to their “shells”, and for certain principles this approximation holds true.


Sources:

(1) Dr. George Martine, Medical essays and Observations, Edinburgh, 1747.

(2) On Growth and Form, p. 19
(3) On Growth and Form, p. 292
(4) On Growth and Form, p.  643-644
(5) On Growth and Form, p. 289
(6) On Growth and Form, p1018
(7) On Growth and Form, p. 644
(8) On Growth and Form, p. 19
(9) On Growth and Form, p1019
(10) On Growth and Form, p. 13
(2-10) from D’Arcy Thompson, On Growth and Form,  Cambridge university press, 1992 (unaltered from 1942 edition)

Physics, but not vs evolution (100 years, part III)

As you may well know, because you have read it here or heard it elsewhere, this year is the 100 year anniversary of D’Arcy Thompson’s On Growth and Form. The book is over 1000 pages long, and while extremely interesting, it can be quite a task to get through. Therefore, I figured I’d share some of the thoughts I had while reading – and to be honest, this was sometimes diagonally – through this masterwork.

To place this and future posts within context, I will first focus on how its main premise (physical forces as the driver of morphology) fits into the context of the time where the general sentiment was:

No other explanation of living forms is allowed than heredity, and any which is founded on another basis much be rejected… (1)

But that is not to say that no one in the scientific community was open to the idea that physics had some part to play:

To think that heredity will build organic beings without mechanical means is a piece of unscientific mysticism. (1)

It seems D’Arcy Thompson’s book was the first major publication on this idea, and his book is an inspiration for biomathematicians and biophysicists today. Or at least it is thought-provoking: throughout the book he underlines through several – 1000 pages worth of –  analogous observations from the material (non-living) and biological (living) world his theory, that the way biological systems grow, and the shape and size they eventually take, is driven by physical principles:

Cell and tissue, shell and bone, leaf and flower, are so many portions of matter, and it is in obedience to the laws of physics that their particles have been moved, moulded and conformed. … Their problems of form are in the first instance mathematical problems, their problems of growth are essentially physical problems. (2)

It is important to point out that he never claimed that physics is the only driving force of the shape and size of living things, just that it is one of the drivers, and that heredity is extremely important in understanding the processes of biology in its own right. But if outlining the physics of growth and form takes over a thousand pages, we should almost be thankful that heredity was taken out of the picture:

We rule “heredity” or any such concept out of our present account, however true, however important, however indispensable in another setting of the story, such a concept may be. (3)

Ruling it out of the picture doesn’t stop D’Arcy from occasionally musing on the limitations of heredity:

That things not only alter but improve is an article of faith, and the boldest of evolutionary conceptions. How far it be true were very hard to say; but I for one imagine that a pterodactyl flew no less well than does an albatross, and that Old Red Sandstone fishes swam as well and easily as the fishes of our own seas. (4)

This goes to show that while D’Arcy did not consider evolutionary theory in his story, it was not something he hadn’t thought about. He regularly quotes Darwin (I’m working through The Origin of Species myself at the moment… at least D’Arcy’s book had some pictures!) and as a professor in zoology, it stands to reason that he was knowledgeable on the subject.  Throughout his career, he published around 300 articles and books, and some day I’ll go through all of them to show he has written more on heredity.

To conclude, while On Growth and Form outlines an alternative theory to explain the morphology of biological systems, it is in no way trying to replace or contradict the theory of evolution or any idea of genetics-driven development. I’ll wrap up with one of D’Arcy’s final thoughts:

And though I have tried throughout this book to lay the emphasis on the direct action of causes other than heredity, in short to circumscribe the employment of the latter as a working hypothesis in morphology, there can still be no question whatsoever that heredity is a vastly important as well as a mysterious thing; it is one of the great factors in biology, however we may attempt to figure to ourselves, or howsoever we may fail even to imagine, its underlying physical explanation.  (5)

Well, that’s all folks. More on growing and forming next time! Have I mentioned that this book is over a thousand pages long?

p2000f69bg8001

D’Arcy in his twenties (University of Dundee Archive Services)


Sources:

(1) Haller, 1888

(2) On Growth and Form, p. 10

(3) On Growth and Form, p. 284

(4) On Growth and Form, p. 873

(5) On Growth and Form, p. 1023

(2-5) from D’Arcy Thompson, On Growth and Form,  Cambridge university press, 1992 (unaltered from 1942 edition)

Mathematical beauty (100 years part I)

Exactly a century ago, D’Arcy Thompson published his book On Growth and Form.

I’ve spoken about Mr. D’Arcy before, but as it is the 100-year anniversary of his masterwork, I feel it fitting to revisit the topic. Since mentioning him last, I have finished reading his book, and have also started to write up my thesis. I bring up my thesis because my work is related to D’Arcy’s work in the sense that I have been trying to bridge the gap between biology and physics, and I predict that some of my reading will inspire me to write more (hopefully more of my thesis but presumably also more on the general topic of bio-meets-phys).

Mr. D’Arcy wrote On Growth and Form to collect his observations on the mathematical principles of nature. He explains how biological phenomena of form and growth closely resemble physical and mathematical principles. Especially for some of the more simple examples (e.g. the shape and size of single or doublets of cells) the similarities between biology and physics (e.g. single and doublets of bubbles) are almost uncanny. These simple systems can easily be described using simple formulas, and he suggests that even more complex systems can be explained in a similar way (though he remarks that it will take a lot of formulas and paper space, luckily we have computers now). In 1917, this idea was pioneering, to say the least. Bio-mathematics and biophysics were nowhere near being the hot topics they are today.

One of the events organised for the anniversary of On Growth and Form, was the exhibition A Sketch of the Universe at the  City Art Gallery in Edinburgh, showcasing works of art that were inspired by the book, or by the idea that mathematics and biology are closely intertwined. The exhibition is closed now, but this weekend I did get the chance to go visit it.
So, I present to you, some of the highlights that I found interesting or cool-looking:

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Trifolium repens L – top view – No 10 by Macoto Murayama (2016) – 2D rendering of a 3D model depicting the structure of a white clover flower.

“I know that in the study of material things number, order and position are threefold clue to the exact knowledge; and that these three, in the mathematician’s hands, furnish the first outlines for a sketch of the Universe.” (D’Arcy Thompson, On Growth and Form)

20170218_154126.jpg

Aggregation 24/27 by Andy Lomas (2005) – These prints were “grown” using computer algorithms that simulated the paths of millions of particles flowing in a field of forces.

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Untitled by Gavin Rutherford (2010) – Prints citing D’Arcy Thompson.

“For the harmony of the world is made manifest in Form and Number, and the heart and the soul and all the poetry of Natural Philosophy are ebmodied in the concept of mathematical beauty.” (D’Arcy Thompson, On Growth and Form)

20170218_161903.jpg

Radiolarians by Amy Barber (2010) – The single-celled Radiolardia aggregate into complex and very diverse shapes. Their skeletons are incredibly delicate and look pretty neat.

“The waves of the sea, the little ripples of the shore, the sweeping curve of the sandy bay between the headlands, the outline of the hills, the shape of the clouds, all these are so many riddles of form, so many problems of morphology.” (D’Arcy Thompson, On Growth and Form)

20170218_161730.jpg

Scarus, Pomacanthus by Darran McFarlane (2012) – This painting was created by subjecting an existing portrait of D’Arcy to mathematical transformations.

You can read more about D’Arcy Thompson, On Growth and Form and some of the events being organised this year in honour of the 100 year anniversary, here. And presumably in the near future on this very blog.

[Note: Again, I realise that D’Arcy Thompson’s last name is “Thompson” so “Mr. Thompson” would be a more appropriate title (or Prof. Thompson) but I just cannot resist his practically Austenesque first name.]

# Trust Me I’m An Engineer

Some time ago, on my usually waste-of-time website, I found a post about the first female engineer. As a female engineer – let’s not go into whether that’s self-proclaimed or not – , I naturally wanted to find out more.
First, it seemed necessary to find a definition for “engineering”.
As so many other words, engineering is derived from Latin. It can have originated from either – or perhaps both – ingenium or – and – ingeniare. As the word ingenious might hint, the first means something in the lines of cleverness, though I’ve also seen it translated as talent; the latter means to devise (according to wikipedia, I had more trouble finding the word through other sources). The stem of the word seems to resemble ingenerare (to implant) and ingenere (to instill by birth). Therefore it seems that the word initially meant something along the lines of having a natural talent for something but slowly evolved to coming up with clever tricks or solutions to solve a certain problem.
Nowadays, the current official definition of “engineering” is (according to Engineers’ Council for Professional Development):

The creative application of scientific principles to design or develop structures, machines, apparatus, or manufacturing processes, or works utilising them singly or in combination; or to construct or operate the same with full cognisance of their design; or to forecast their behaviour under specific operating conditions; all as respects an intended function, economics of operation or safety to life and property.

Hmmm, that’s one of those sentences that I still haven’t completely grasped after reading it three times and then I usually just give up. Let’s give that definition another try then. According to my understanding (and self-proclaimed experience), engineers aim to design (or invent, or optimize, or improve) something by the application of scientific and mathematical principles. This something can range from materials, instruments, software, living systems, you name it; basically anything that you can imagine inventing or improving on.
It differs from science mostly due to the fact that sciences aim to build on knowledge starting from predictions and hypotheses about the universe (or, anything).
If this not making much sense… Well, probably this comic by Saturday Morning Breakfast Cereal does a better job on describing the essence of engineering:

So, I guess you can say that engineers are more interested in applying scientific knowledge to whatever they are working, while scientists are more aimed at acquiring said knowledge. In my opinion (and again, “experience”) the distinction between the two is not always very straight cut, and a lot of people are more somewhere in between, say applied scientist, or scientific engineers, or engineering scientist (though that last one sounds more like someone trying to create a race of super-scientists through genetic engineering). I also think it’s quite obvious that both (or all people on that spectrum) need each other to achieve progress.
Nevertheless, my post was going to be about the first female engineer. Because whichever way you look at it, women are still underrepresented in these fields, even if the situation is already much more balanced than it used to be. It also strongly depends on the type of engineering. For example, while there are about 50% of women studying bio-engineering or architectural engineering at my formal school, only 15% of engineering (that later splits into mechanical, civil, chemical, biomedical, computer, and mathematical engineering) consists of female students. Perhaps “us girls” just need some role models?
The first candidate-rolemodel, and the “first female engineer” according to that post I mentioned, is Elisa Leonida Zamfirescu.

Elisa Leonida Zamfirescu

Elisa was born in 1887 in Romania, in a quite engineery – yes that is a word, stop it red squiggly line – family.  Her grandfather, on her mother’s side, was an engineer and so was her older brother Dimitrie. I imagine her as a child inventor, a bit like Violet Baudelaire, who did not give up after being rejected from engineering school (School of Bridges and Roads in Bucharest). No, she just applied to other schools, and in 1909, she was accepted at the Royal Academy of Technology Berlin. Three years later, she graduated, and started her career in geology laboratories back in Romania. She passed the war years (World War I) in the Red Cross, around which time she met her husband, Constantin Zamfirescu, a chemist.  She spent her engineering career leading several geology labs in the Geological Institute in Romania and teaching physics and chemistry. Her contributions include her role in identifying new resources of coal, natural gas and copper. She worked until she was 75, and died in 1973.
Despite her contributions to the world of engineering, Elisa was not technically the first engineer. Alice Jacqueline Perry, an Irish cailín born in 1885, graduated a few years before. Her family sounds very well educated; her father was co-founder of the Galway Electric Light Company as well as county surveyor for the County Council and her uncle invented the navigational gyroscope (two of her sisters also continued into higher education, by the way), Alice was quite a mathlete, or would have been if they had those in the 1900s.

Alice Jacqueline Perry

She received a scholarship to study at the Queen’s College in Galway in 1902, where she pursued a degree in engineering. She graduated in 1906, with first class honours. Alice was the first female engineering graduate in Ireland, the UK, and in my understanding, the world. A month after her graduation, her father’s death caused her to take up his position temporarily for County Council, making her the only woman to have been a County Surveyor – basically a Council Engineer – in Ireland. She moved to London in 1908, starting a job as a Lady Factory Inspector. She moved to Glasgow in 1915 (and seemed to have continued an inspector job there as well). In 1921 she grew bored of engineering, and started writing poetry (eventually publishing seven books of poetry). She was heavily involved in the Christian Science movement, and moved to Boston headquarters in 1923, where she worked until her death in 1969, about a month after the moon landing.
These may seem like quite ordinary lives, but I can only imagine the challenges Elisa and Alice might have faced as female engineers in those days, just as female scientists or female doctors had a whole stream of male criticism and prejudice to swim up against.
I assume that there were some female engineers before 1900, though perhaps not with an official engineering degree; after all, inventors have been around forever and it is no great leap of imagination that some of those inventors were women. And you might argue that we don’t really know any famous female engineers because they haven’t contributed anything major, but I will argue back that a lot of progress happens in little bits and every little contribution has been necessary to get to those major leaps. (Come to think of it, I don’t think I can name any great engineers off the top of my head.)
As there are quite some great female scientists, there are some great female engineers, and naming the first ones is only the start of a long list, that I am positive will grow longer in the future. Perhaps one day, I’ll find my name on that list. (I doubt it, but it can’t hurt to be ambitious, eh.)

On Growth and Form

Before I start, a short comment on personal growth:
After a quite frustrating day yesterday, I decided to get up bright and early, go for a run and then head to work today. It’s actually a national holiday here (Ascension), but as I have to take my holidays explicitly, and “I’m here for work and not for fun (except for weekends)”, that was my plan. So I was up and ready to leave for my jog, when my flatmate just entered the front door, after a night out. Made me think.
I guess I’m a “real grown-up” now…
But now, On Growth and Form.
I have discovered that Dundee has had quite an interesting inhabitant. His name is D’Arcy Wentworth Thompson. I had never heard of him until sometime last year when we went out to dinner in a restaurant called The D’Arcy Thompson. A plaque on the wall informed us he was a biology professor in Dundee (at the time the university was still part of the University of St. Andrews) around 1900.
Sometime later, I went to a talk about penguins, more specifically about the two penguins that Dundonian Arctic explorers had brought back from their trip south. The penguins had gone through quite a bit, one even was the official mascot of a student faculty club, but they are now on display in the D’Arcy Thompson Zoology Museum on the campus of the University of Dundee. We went to go see the museum after the talk, it’s a room stuffed with, well, stuffed animals. Quite an impressive collection, including a giant crab. (Giant means more than a meter across. Imagine running into a wild one!)

A stuffed penguin in a vitrine of a zoology museum

The penguin before it went missing. (ca. 1900)

But it wasn’t until last week that I realised how interesting Mister D’Arcy really was – and I just realised that sounds like a sentence from Pride and Prejudice. A research letter in Nature Physics on the combined mechanics of cells in tissues mentions the following:

In 1917, D’Arcy Thomson published a treatise On Growth and Form in which he suggested that morphogenesis could be explained by forces and motion – in other words by mechanics.

You might recall that my PhD is about the mechanics of gut cancer. And I didn’t know about D’Arcy, shame on me! In the meantime I’ve tried to get my hands on the book, not too difficult because there are some on line pdfs circulating with the whole thing. Unfortunately, I’m the worst at reading from a computer screen, so I haven’t gotten very far*, but it seems that Mister D’Arcy was quite interesting indeed. His 1136-paged book reads a bit a philosophy book (or it does in the first 304 pages). He tells the story – for it’s written like a story – of how the mechanics in biology is quite similar to the mechanics of inanimate bodies, and that growth and morphology can essentially be explained by physics. He gives a whole list of examples, where he makes analogies between biological systems and physical systems. He admits that this will not explain every detail of biology, but that it is possible to explain certain simpler phenomena of organic growth and form using mathematical and physical descriptions. His studies on fractal patterns and linear transformations (rotation, translation, shearing) have been important for image analysis, architecture, mathematics and probably many other fields.

Left: sketch of a fish in a grid. Right: transformation of the fish showing the deformed grid

Mathematical transformations of homologous features in fish.

Then how had I never heard of Mister D’Arcy (I realise it should be Mister Thompson but that just doesn’t have that ring to it)? Luckily I’ve figured my lack of knowledge on time and can rectify that mistake. D’Arcy had innovative ideas, that have been pushed to the sidelines by molecular and genetic research in morphogenesis. Nevertheless, is book is merely descriptive, so there is still much to be learned. Which is where projects like mine come in.
Hurray, I have a purpose!

D'Arcy Thompson holding a skeleton of a parrot

Thank you Mister D’Arcy!

*If anyone knows where I can get my hands on a good hard copy, please let me know! Amazon only cells “bad quality and incomplete” versions, so it’s proving quite difficult.