A matter of kilos

It’s been the topic of a weighted discussion for quite some time, but today it has been decided: “Le Grand K” will no longer be used to define a kilogram.

“Le Grand K” is not a big box of Special K, but a platinum-iridium cylinder stored by the International Bureau of Weights and Measures in an underground vault in Paris that has defined a kilogram of mass since 1889. There are a few official copies, and many more copies, so each country has their own kilogram to calibrate to.

Last Friday (November 16th) the kilogram has been redefined so it no longer depends on a material object. Because a material object can be scratched, chipped or destroyed. Or stolen. Or accidentally thrown into the bin. And it can degrade – in fact, “Le Grand K” weighs about  50 µg lighter than its six official copies. You don’t really want to gold – ahem, I mean platinum-iridium – standard for weight to change in weight, right?

So now the kilogram will be defined based on a universal, unchangeable constant. Much better, I think you would agree. The constant of choice here is the Plank’s constant, a number that converts the macroscopic wavelength of light to the energy of individual constants of light. Representatives from 58 countries universally agreed on this new definition, so from next year, the kilogram will be constant forever.

The ampere (electrical current), the kelvin (temperature) and the mole (amount of chemical substance) have also been redefined. That means that all seven units in the International System of Units (S.I.) will be defined by universal constants:

meter unit of length
  • Originally defined as a 10-millionth of the distance between the North Pole and the Equator along the meridian through Paris, later as the distance between two scratches on a bar of platinum-iridium metal
  • Since 1983 defined as the distance traveled by a light beam in vacuum in 1/299,792,458th of a second, with 299,792,458 m/s being the universally constant speed of light.
kilogram unit of mass
  • Initially defined in terms of one liter of water, but since as a small ~47 cm3 cylinder stored in a basement in Paris.
  • Now redefined in terms of the Plank constant h = 6.62607015×10−34 J*s (J = kg*m2*s−2)
second unit of time
  • Originally defined as 1/86,400th of a day
  • Since 1967 it has been defined as the time it takes an atom of cesium-133 to vibrate 9,192,631,770 times
ampere unit of electrical current
  • Originally defined as a tenth of the electromagnetic current flowing through a 1 cm arc of a circle with a 1 cm radius creating a field of one oersted in the center
  • Now redefined in terms of the fixed numerical value of the elementary charge e (1.6602176634×10−19 C with C = A*s and second defined as above)
kelvin unit of temperature
  • The centigrade scale was originally defined by assigning the freezing and boiling point of water as 0 °C and 100 °C respectively. Note: absolute zero is the lowest temperature (0K =  -273.16 °C)
  • Now redefined in terms of the Boltzmann constant k = 1.380649×10−23 J⋅K−1
mole unit to describe the amount of substance
  • Since 1967 defined as the amount of substance which has as many elementary particles as there are atoms in 0.012 kg of carbon-12.
  • Now one mole substance contains exactly 6.02214076 × 10^23 particles. This constant is known as Avogadro’s number*
candela unit to describe the intensity of light
  • Originally taken as the luminous intensity of a whale blubber candle in the late 19th century.
  • Since 1979 the light intensity of a monochromatic source that emits radiation with a frequency 5.4 x 1014 hertz and has a radiant intensity of 1/683 watt per steradian in a given direction **
So that was “this week in science.” I’ll leave y’all with a related joke:

kilogram

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Sources/Further reading:

The international system of units: en.wikipedia.org/wiki/International_System_of_Units

The new kilogram was in the news: www.nytimes.com/2018/11/16/science/kilogram-physics-measurement.html and www.theregister.co.uk/2018/11/17/amp_kelvin_kilogram/

Comic from xkcd.com

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* Avocado’s number, however, states that 6.02214076 × 10^23 guacas make up one guacamole. (I knooooow, I already made this joke).

** I have to be honest and say that I have no idea what this all means

A Nobel Cause

So, the news is out. At least in terms of the sciency Nobel Prizes (sorry Economic Sciences, you don’t really count here), the 2018 Laureates have all been announced, so here’s a short overview of what was Nobel-Prize-Worthy this year:

1. Nobel Prize in Chemistry (press release)

And… *drumroll* the Nobel prize in Chemistry goes to Prof. Frances H. Arnold, Prof. George Smith and Sir Gregory Winter for their contributions to protein biology, where they all worked on directed evolution of proteins.

Directing protein evolution is used to create proteins with a specific function that can be used in biofuel, pharmaceutical, and medicine manufacturing. Half of the Nobel Prize was awarded to Prof. Arnold, who works on directed evolution of enzymes (proteins that are used to accelerate or direct chemical reactions). The other half, that of Prof. Smith and Sir Winter, celebrated a method called phage display. This process uses viruses to develop specific proteins that can be used for medical purposes.

My personal excitement for this prize:
Well, Prof. Arnold is a professor in bioengineering, which is, in my opinion, an underacknowledged field, so that’s pretty cool. And this has nothing to do with the fact that I’ve studied bioengineering. Nothing at all.

 

2. The Nobel Prize in Physiology or Medicine (press release)

The Nobel prize in Physiology or Medicine was awarded to Jim Allison and Tasuku Honjo for their work in cancer therapy. By now, the concept of “immune therapy” may not sound extremely new anymore. However, just think about how amazing it is: someone’s immune system (in other words, an attack system that is already present in your body) can be used to fight cancer cells (which isn’t really straightforward – cancer cells originate from normal cells so are not detected as “foreign” by the immune system).
My personal interest in this prize: 
First of all, yay for biology completely highjacking the Nobel Prizes. But on the topic: radiotherapy and chemotherapy are both notorious to have a huge amount of side effect. By effectively using the natural defense system of the body, immune therapy usually is a lot less taxing on a patient, which I think is a laudable goal.

3. The Nobel Prize in Physics (press release)

*Final Drum Roll, please*

The Nobel Prize in Physics is all about lasers (Did you know that LASER is an acronym for “Light Amplification by Stimulated Emission of Radiation? Well, you do know). Arthur Ashkin was honors for his development of optical tweezers (which I will simply explain by referring you to my fabulous friend who has worked with optical tweezers herself) and the other half was awarded to Donna Strickland and Gerard Mourou for their work on laser pulses. The most known application of laser pulses is in laser eye surgery.

My personal input to this prize:
I have two thoughts, first, how has this not won a Nobel Prize yet? Actually, to be honest, I think that quite often when the Nobel Prizes, which is probably why they get a Nobel Prize in the first place. The other thought has to do with the same reason why this prize has been in the press a lot: it has been 55 years since a woman won a physics Nobel prize. Only two other women have a Nobel Prize in Physics to their name: Marie Skłodowska-Curie (obviously!) and Maria Goeppert-Mayer (go google her, now).

Some thoughts on women and Nobel Prizes

Historically, science has always been pretty male-dominated. And even now, women are underrepresented in research: worldwide the female share of persons employed in R&D is approximately 30% and I will not even get into high-level academics here.

In terms of Nobel Prizes, as of this year, there have been 49 women who have won Nobel Prizes (that’s all of them), compared to 844 men. In the sciency fields, five women have won the Nobel Prize in Chemistry (2.8%), twelve have won the Nobel Prize in Physiology or Medicine (5.6%), and – as stated – three have won the Nobel Prize in Physics (1.4%). Actually, only one woman has won the Nobel Memorial Prize in Economic Sciences (also 1.4%), but that doesn’t really count as a science anyway!

In any case, none of the Nobel Prizes have a good track record, and it makes me a bit sad that “First woman Physics Nobel winner in 55 years” is a news headline, but ah well, we may have come some part of the way but we are not there yet.

And until we are, having positive role models of all shapes and sizes and sexes for STEM fields is crucial. As a wannabe science-communicator, or science-populizer if you will, one of my aims is exactly that. So that every child can look up to a scientist and think “that could be me!”

And – even if I say so myself – I think that’s a pretty noble cause.

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Bubbles!

Let’s talk bubbles…

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Calm down there, buddy.

Over the summer, I have tapped quite a few beers. Some of those beers were Guinness. The first few times I went through the Guinness-tapping-process (who am I kidding, all the times), I would marvel at the fact that the bubbles were going down.

So, Guinness is an easy but slightly time-consuming beer to tap. First, you need to fill the glass about 4/5ths and let the bubbles settle. When you get that nice black/white beer/foam divide, you top it off by pushing on the tap (which is a slower flow). So that all takes a while. But that means you can stare at these sinking bubbles for quite some time.

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Guinness bubbles going down down down.

But wait. Bubbles aren’t supposed to sink? Aren’t bubbles gaseous and therefore lighter than liquid? Hence, shouldn’t they rise as bubbles do in normal bubbly beverages? What’s going on?

From a uni class some time ago, I remembered that Guinness bubbles sink, so at least I wasn’t hallucinating. But why I forgot why exactly. (Com’on, the class was years ago and who remembers anything anyway. There’s the internet for that.)

Of course, there is science about this. I mean. Scientists are basically fueled by coffee and beer. And Guinness is sort of both.

It seems that there are a few factors that contribute to the sinking bubbles: the type of bubbles, the size of the bubbles, and the shape of a Guinness glass.

First of all, not all bubbles in Guinness sink, just the ones you can see. When the beer starts to settle, larger bubbles start to rise (as bubbles do). Because of the shape of the glass, you can’t really see this happening: the bubbles originate in the bottom of the glass, which is narrower than the top, and they form a central column of rising bubbles. This causes an upward liquid movement. As a result (because the liquid doesn’t magiacally fountain out of the glass), a downwards liquid flow occurs along the walls of the glass. If all the Guinness bubbles were large (> 50 µm), as it is with lighter beers, the buyancy would counteract the liquid flow (they’d be superlight and not care about what the liquid is doing) and rise. However, Guinness has teeny tiny bubbles (< 50 µm) that just get dragged along with the flow. And therefore, along the walls of the glass, they appear to be sinking.

Flow pathlines in a glass of Guinness. Image c/o Fluent Inc.
Psychadellic flow lines in a Guinness glass. (Image © Fluent Inc.)

So the second factor is the small bubbles. Guinness taps have fine holes that cause these small bubbles to form*. Moreover, Guinness bubbles are nitrogen and not carbon dioxide, which is more easily dissolvable in liquid. Most bubbly beverages, including lager beers and soft drinks, contain carbon dioxide to create the fizz. In these cases, gas bubbles appear from tiny defects in the glass surface and continue to grow as more carbon dioxide undissolves**. But nitrogen gas doesn’t dissolve in liquid as well as carbon dioxide, so the bubbles that do appear don’t grow in size. In other words, bubbles stay small enough to be dragged along with the downward liquid flow.

Finally, add the fact that Guinness is very dark, causing a high contrast with the light coloured bubbles, and you see these nice sinking bubbles.

Now, if you are in a place where the drinking time is acceptable (pm), go get yourself a Guinness. Otherwise, just stick to coffee.

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Reverse yellow bubble fish looks even more insane.

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* In a can of Guinness can there is a small ball that, as far as I can tell, serves the same purpose. Edit: it’s confirmed that this small ball – also called a “widget” (thanks to my uncle Tim for this factoid) – indeed causes the slow release of nitrogen after the can is open.

** What, that’s not a word? What’s the opposite of dissolving then? *googles* Condensing? That doesn’t sound right?

Sources: Bubbles the fish is from Pixar and most of the info is from: https://plus.maths.org/content/probing-pint

And of course, there is more beer physics if that’s your thing (read it while drinking some beer responsibly): https://www.npr.org/sections/thesalt/2013/11/20/246390302/beer-tapping-physics-why-a-hit-to-a-bottle-makes-a-foam-volcano?t=1537774279547

An ignobel cause

Disclaimer: if you’re a bit hungry and/or know that reading about spaghetti will make you hungry, I suggest you go eat some spaghetti before you continue reading… But if you do, keep at least a few strands uncooked, you might need it later on.

An odd article popped up on my go-to news site the other day. And then the day after that, an article on the same topic popped up in the newspaper I was reading. It was an article reporting on the science of breaking an uncooked spaghetti.

No, I’m not joking.

And apparently, the research solves a decade-old problem. I never knew spaghetti could pose a decade-old problem, except for maybe the secret spaghetti-sauce recipe of an Italian-American family but that’s a century-old problem, I would say.

So if you’d go into your kitchen now, take a strand of uncooked spaghetti, hold it at the ends, and start bending it until it snaps, you will see what this mystery is all about. Most probably, you have now ended up with three or more bits of spaghetti. If you are super bored or think snapping spaghetti is super-fun (this is what Richard Feynman apparently thought), you can try it again. And you will notice the spaghetti almost never snaps into two pieces. Or you can just take my word for it…

In 2005, some French physicists came up with a theoretical solution to why spaghetti never breaks into two, because this unsolved mystery Richard Feynman broke his head about merited some further research…

When a very thin bar (or strand of spaghetti) is being bent, this will cause the strand to break somewhere near the middle. This first break will cause a “snap-back” effect which essentially causes a vibration to travel through the rest of the strand, causing even more points of fracture, which results in three or more pieces. In other words, is very rare to end up with exactly two pieces of spaghetti.

These French researchers were rewarded with an Ig Nobel prize for their finding. An Ig Nobel prize is a prize that is rewarded “for achievements that first make people LAUGH then make them THINK” and also the reason for my best quiz achievement ever.*

crack-control-1
Experiments (above) and simulations (below) show how dry spaghetti can be broken into two or more fragments, by twisting and bending. (Image: MIT)

And now, years later, mathematicians from MIT have added to that research by coming up with a way to ensure a dry spaghetti strand does break exactly in two: by first twisting the spaghetti before bending it. The twisting part causes stresses in the spaghetti strand that counteract the snapback effect when it eventually breaks. When the spaghetti does break in to, the energy release from a “twist wave” (where the spaghetti pieces untwist themselves) ensures there is no extra stress that would cause more fracture points. So there we go: the spaghetti breaks in exactly two pieces as long as you twist it enough.

crack-control-2
Experiments (above) and simulations (below) show how dry spaghetti can be broken into two or more fragments, by twisting and bending. (Image: MIT)

Now, this theory isn’t only limited to breaking spaghetti. Understanding stress distributions and breaking cascade also have some practical applications, according to the authors: the same principles can be applied to other thin bar-like structures, such as multifibers, nanotubes, and microtubules.

Now, if you haven’t already, go get yourself some spaghetti.

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* The question: who has one both an Ig Nobel and a Nobel prize and for what?
The whole table looked very confused and I just said very confidently “André Geim, levitating a frog and graphene” so it turns out a degree in nanotech is super useful for winning quizzes. (Actually, I’m not even sure we won and I doubt it was thanks to me answering that one question correctly, but I’m pretty sure I will never live up to that moment ever again.)

Not just your usual conference (100 years, Part VIII)

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Spotted in the Bell Pettigrew Museum of Natural History (St. Andrews)

Last weekend, I attended the Centenary conference commemorating the 100-year anniversary of the publication of On Growth And Form by D’Arcy Wentworth Thompson. You might have heard me mention this book and its centenary at some point?

It was not just your usual conference. While most conferences centre around a certain field or topic, this one explored the influence of D’Arcy and his book on many different fields It was the most interesting mix of people and topics at any meeting I’ve been at, it succeeded in bringing scientists, mathematicians, computer scientists, historians, artists, architects, musicians and knitters in the same room.

Also, the sessions were not organised topically, but pretty much random, which meant that even if you were just interested in a few talks (on paper), you ended up hearing the wide variety of topics that have something to do with D’Arcy. Personally, I thought this was a very clever choice of the organisers (kudos to them), and I enjoyed hearing about art, architecture, history, and yes, knitting, instead of boring ol’ science for a change.

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I also feel like I made some type of personal achievement. I was accepted to give a talk on the Physics of Cancer, which you might remember as the topic of my two FameLab contributions. For each of these, I had written a little song. So, in a crazy phase of over-confidence, I decided to incorporate these songs into my talk. And, why not, I also incorporated Star Wars references, weird cartoon cell drawings and pretty dodgy doodles I had drawn myself.

The response was amazing. I’ve given talks at conferences before but never have I received such positive feedback. Not only because they found the songs entertaining (I can assure you no-one fell asleep during my presentation) but I was also complimented on the clarity and accessibility of my talk (the very mixed audience, remember) and my optimistic approach to a “heavy” topic. If possible, I will from now on take this approach for every talk.

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Finally, I have a new favourite D’Arcy quote (it’s quite convenient to have three days full of inspirational quotes to muse about):

“(…) things are interesting only in so far as they relate to themselves to other things; only then you can put two and two together and tell stories about them.”

Closely followed by this one, actually:

“Facts are pointless unless they illustrate greater principles.”


(The comics snippets and the second quote are from the graphic novel “Transformations“.)

Final thoughts (100 years, part VII)

To end my series of posts on the man and the book (D’Arcy Thomspon and On Growth and Form respectively, the latter a book with over 1000 pages), I wanted to share a few more quotes from and about him that I found interesting enough to type out:

“In his figure and bearded face there was majestic presence; in is hospitality there were openness, kindness and joviality; in his ever quick wit were the homely, the sophisticated and, at times, the salty… in status he became a very doyen among professors the world over; in his enquiring mind he was like those of whose toungue and temper he was a master, the Athenians of old, eager ‘to tell or hear some new thing'” – Professor Peacock (1)

  1. With the name Professor Peacock, I can’t help but imagine a flamboyant, multicolour-labcoat-wearing, frizzle-haired man…
  2. I hope the meaning of the word salty has changed over time…

There is a certain fascination in such ignorance; and we learn without discouragement that Science is “plutot destine a etudier qu’a connaitre, a chercher qu’a trouve la verite.” (2)
(Rather than destined to study for knowledge, (we are) searching to find the truth.)

#IgnoranceIsBliss?

In my opinion the teaching of mechanics will still have to begin with Newtonian force, just as optics begins in the sensation of colour and thermodynamics with the sensation of warmth, despite the fact that a more precise basis is substituted later on. (3)

As a self-proclaimed science communicator, it is often difficult to judge how much to simplify things. On the other hand, making things relatable to everyday experiences does not necessarily mean telling untruths. Classical physics may not be valid for every single situation, but it is often enough to describe what is happening without needing to resort to more complicated relative physics. And you don’t have to start quoting wavelengths when a colour description would do just as well. Fill in the details later, if necessary.


Some quotes on evolution and natural selection:

And we then, I think, draw near to the conclusion that what is true of these is universally true, and that the great function of natural selection is not to originate, but to remove. (4)

Unless indeed we use the term Natural Selection in a sense so wide as to deprive it of any purely biological significance; and so recognise as a sort of natural selection whatsoever nexus of causes suffices to differentiate between the likely and the unlikely, the scarce and the frequent, the easy and the hard: and leads accordingly, under the peculiar conditions, limitations and restraints which we call “ordinary circumstances,” one type of crystal, one form of cloud, one chemical compound, to be of frequent occurrence and another to be rare. (5)


We can move matter, that is all we can do to it. (6)

On a fundamental level, are we really able to build things? Aren’t we just rearranging the building blocks?

I know that in the study of material things, number, order and position are the threefold clue to exact knowledge; that these three, in mathematician’s hands, furnish the “first outlines for a sketch of the universe“, that by square and circle we are helped, like Emile Verhaeren’s carpenter, to conceive “Les lois indubitable et fecondes qui sont la regle et la clarte du monde.” (7)

(The unquestionable and fruitful laws that rule and clarify the world.)

For the harmony of the world is made manifest in Form and Number, and the heart and soul and all the poetry of Natural Philosophy are embodied in the concept of mathematical beauty. (8)

Delight in beauty is one of the pleasures of the imagination … (9)

#MathIsLife. Thank you, D’Arcy, for the 1000+ pages of mind-expanding, educational and philosophical topics.

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Sources:

(1) D’Arcy Thompson and his zoology museum in Dundee – booklet by Matthew Jarron and Cathy Caudwell, 2015 reprint

(2) On Growth and Form – p. 19

(3) Max Planck

(4) On Growth and Form – p. 269-270

(5) On Growth and Form – p. 849

(6) Oliver Lodge

(7) On Growth and Form – p. 1096

(8) On Growth and Form – p. 1096-1097

(9) On Growth and Form – p. 959

(2, 4-6, 8-9) from D’Arcy Thompson, On Growth and Form,  Cambridge university press, 1992 (unaltered from 1942 edition)

When size matters (100 years, Part VI)

Neat process diagrams of metabolism always gave the impression of some orderly molecular conveyer belt, but the truth was, life was powered by nothing at the deepest level but a sequence of chance collisions. (1)

Zoom down far enough (but not too far – or the Aladdin merchant might complain) and all matter is just a soup of interacting molecules. Chance encounters and interactions, but with a high enough probability to happen. In essence, life is a series of molecular interactions (that, in turn, are atomic interactions and so on and so on…)

The form of the cellular framework of plants and also of animals depends, in its essential features, upon the forces of molecular physics. (2)

Quite often, we can ignore those small-scale phenomena, but only as long as the system we are describing is large enough. As in physics, in biological systems size does matter (*insert ambiguous joke here*). We have to adapt the governing physical rules depending on the scale that we are observing. Do we consider every quantum-biological detail, can we use a cell as the smallest entity or even use whole organisms as the smallest functional entity?

Life has a range of magnitude narrow indeed compared to with which physical science deals; but it is wide enough to include three such discrepant conditions as those in which a man, an insect and a bacillus have their being and play their several roles. Man is ruled by gravitation, and rests on mother earth. A water-beetle finds the surface of a pool a matter of life and death, a perilous entanglement or an indispensable support. In a third world, where the bacillus lives, gravitation is forgotten, and the viscosity of the liquid, the resistance defined by Stoke’s law, the molecular shocks of the Brownian movement, doubtless also the electric charges of the ionised medium, make up the physical environment and have their potent and immediate influence on the organism. (3)

Observing life at the smallest scales (by which I mean cells and unicellular organisms) at least has the advantage the rules driving form and structure can, at least in many cases, be considered relatively simple: surface-tension.

In either case, we shall find a great tendency in small organisms to assume either the spherical form or other simple forms related to ordinary inanimate surface-tension phenomena, which forms do not recur in the external morphology of large animals. (4)

While on the topic of size, as many things in the universe: size is relative. I have noticed in conversations with colleagues and supervisors that what is considered small or large, definitely depends on the point of perspective (and often: whatever the size is that that person typically studies). I could assume that for a zoologist, a mouse is a small animal, but tell a microscopist they have to image an area of 1 mm² and the task seems monstrous. For a particle physicist, a micrometre is immense, but for an astrophysicist, the sun is actually quite close.

We are accustomed to think of magnitude as a purely relative matter. We call a thing big or little with reference with what it is wont to be, as when we speak of a small elephant of a large rat; and we are apt accordingly to suppose that size makes no other or more essential difference. (5)

Undoubtedly philosophers are in the right when they tell us that nothing is great and little otherwise than by comparison. (6)

There is no absolute scale of size in the Universe, for it is boundless towards the great and also boundless towards the small. (5)

That’s the amazing thing about science: we strive to understand the universe on all scales. The universe is mindblowing in its size, in both directions on the length scale.

We distinguish, and can never help distinguishing, between the things which are at our own scale and order, to which our minds are accustomed and our senses attuned, and those remote phenomena which ordinary standards fail to measure, in regions where there is no habitable city for the mind of man. (7)

Good thing we have scientists, amazing minds, capable of studying, visualising and even starting to understand the universe on all its scales…

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My mind might be boggled, but here’s a man that looks like his mind contains the universe. (D’Arcy in his 80s)

(1) Permutation city – Greg Egan, p. 67

(2) Wildeman

(3) On Growth and Form – p. 77

(4) On Growth and Form – p. 57

(5) Gulliver

(6) On Growth and Form – p. 24

(7) On Growth and Form – p. 21

(3-4, 6-7) from D’Arcy Thompson, On Growth and Form,  Cambridge university press, 1992 (unaltered from 1942 edition)

Let’s get physical (100 years, Part V)

[…] of the construction and growth and working of the body, as of all else that is of the earth earthy, physical science is, in my humble opinion, our only teacher and guide. (1)

You might have seen the xkdc comic ranking different scientific disciplines by their purity (and if you haven’t, it’s just a bit of scrolling away). The idea it portrays is that all sciences are basically applied physics (which is in turn applied mathematics). In other words: if you go deep enough to a subject, you eventually end up explaining in with principles from physics. And this is the same principle D’Arcy explores in his book. That has over 1000 pages, did you know that?

purity

A famous D’Arcy quote states that the study of numerical and structural parameters are the key to understanding the Universe:

I know that the study of material things number, order and position are the threefold clue to exact knowledge, and that these three, in the mathematician’s hands, furnish the ‘first outlines for a sketch of the Universe.’ (2)

You can ask the average high school student about mathematics, and the usual response would probably be something in the lines of: “Ugh, I’ll never use this for anything.” Sometimes, it might be difficult to see the every-day use of mathematics, or even the not-so-everyday use. But in reality, the possibilities are endless (given that we are open to having long lists of endless equations that need a supercomputer to solve – probably).

We are apt to think of mathematical definitions as too strict and rigid for common use, but their rigour is combined with all but endless freedom. The precise definition of an ellipse introduces us to all the ellipses in the world; the definition of a ‘conic section’ enlarges our concept, and a ‘curve of higher order’ all the more extends our range of freedom.

It might not be straightforward to see how mathematics (or physics for that matter) would help a biologist in the understanding of natural processes. However, there are a few examples of how physical properties, forces or phenomena are used in biology, such as helping bone repair:

The soles of our boots wear thin, but the soles of our feet grow thick the more we walk upon them: for it would seem that the living cells are “stimulated” by pressure, or by what we call “exercise,” to increase and multiply. The surgeon knows, when he bandages a broken limb, that his bandage is doing something more than merely keeping the part together: and that the even, constant pressure which he skilfully applies is a direct encouragement of the growth and an active agent in the process of repair. (4)

Nowadays the link between physics and biology is more accepted that a century ago, leading to new research fields such as biomechanics, mechanobiology and “physics of cancer”. I have eluded to some of the links between cancer and physics in previous posts (Physics of Cancer, Part I and II). Mathematical models are commonly used to better understand biological processes, including signalling pathways, tissue formation and growth and changes occurring in cancer.

This goes to show (again) that “interdisciplinary” is not just a fancy buzzword, it is a core principle of scientific research. While I must admit from own experience that carrying out interdisciplinary research might not be the easiest path, the potential discoveries and applications are even more endless. And while it might seem mind-boggling, I would argue that mind-bogglement is a good thing, stretching the potential of our minds and our understanding of the universe. And as far as I can read, D’Arcy agrees:

… if you dream, as some of you, I doubt not, have a right to dream, of future discoveries and inventions, let me tell you that the fertile field of discovery lies for the most part on those borderlands where one science meets another. There is a cry in the land for specialisation … but depend on it, that the specialist who is not reinforced by a breadth of knowledge beyond his own speciality is apt very soon to find himself only the highly trained assistant to some other man … Try also to understand that though the sciences are defined from one another in books, there runs through them all what philosophers used to call the commune vinculum, a golden interweaving link, to their mutual support and interpretation. (5)

So I guess my point is (if there even was a point in this post, apart from that the book has like over 1000 pages, in case you didn’t know): if you are a biologist, don’t be afraid to break some sweat and get physical. And the opposite goes for physicists. You might want to get a bit chemical as well, while you’re at it.

The Homo Universalis is back!

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Featured image: math and shells.

(1) On Growth and Form, p 13.

(2) On Growth and Form, p. 1096

(3) On Growth and Form, p. 1027

(4) On Growth and Form, p. 985

(5) D’Arcy Thompson and his zoology museum in Dundee – booklet by Matthew Jarron and Cathy Caudwell, 2015 reprint

(1-4) from D’Arcy Thompson, On Growth and Form,  Cambridge university press, 1992 (unaltered from 1942 edition)

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?

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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)