Science, maths and computers.
The 21st century’s version of creationism, intelligent design, can be summed up by the Blind Watchmaker argument - that like a watch, whose intricacy implies a watchmaker, life displays such vast complexity that it must be the result of a creator or designer. Intelligent design proponents will say that if you take the parts of a clock, put them in a box, and jumble it around randomly, you will never construct a working clock. Similarly, they say, random mutations in DNA cannot therefore be responsible for the evolution of complex life.
However, this is both a straw man and a false analogy. It’s a straw man because it grossly misinterprets the theory of evolution. By drawing a false analogy between DNA replication and jumbling up cogs and springs inside a box, it presents evolution as some kind of ‘Randomise’ button on an Elder Scrolls character creation menu.
This is not the case.
So anyway this video is pretty cool. It deconstructs the straw man, and instead creates a true (or almost true) analogy between evolution and clock making. It presents a simulation of a large population of clocks, each with its own (initially random) genome, containing all the information about which components connect to which. At random, three clocks are selected and pitted against each other and measured for their ability to tell time. The loser is banished from the population and the winning two mate and create offspring. This process is repeated thousands of thousands of times, and guess what the result is?
3 or 4 handed clocks which tick and tock with the utmost precision.
There are a couple of really interesting things I noted about this video:
It’s quite difficult to see whether or not 1 and 2 are fully an artefact of the program - simplifying the full complexity of life down to a few-component system - or whether or not they are an intrinsic (but more subtle) part of real evolution. I think it would be interesting to see if real populations underwent these kinds of phenotypic phase transitions over short periods of time (hundreds of generations).
Stare at this painting for a while. Regardless of what you perceive its artistic merit to be (“my little sister could do that…” some of you will no doubt be saying), you have to admit there is some strange aesthetic quality to it. It guides your eye from one focal point to another, giving your brain a plane of seemingly infinite detail to explore and it seems to - in some sense - resonate with your gaze. Artsy bullshit? Or science?
Jackson Pollock was a controversial figure. His work has been described as “mere unorganized explosions of random energy” and even “a joke in bad taste”. However it just so happened that his unconventional painting technique generated what a mathematician would instantly recognise as a fractals. We see fractals a lot in nature and mathematics and their most distinct feature is their display of self-similarity on many scales. Bronchi of a lung, branches of a tree and the Sierpinski triangle are examples of fractals (have a look and you’ll get a good idea).
If we zoom/enhance a portion (say, around a quarter) of the painting above, we get something that looks a lot like the original painting itself!
This is what is meant by self similarity - zoom in and you see the same thing again. We can quantify the ‘fractalness’ of an image by calculating its fractal dimension. Though I won’t go in to the maths here, it will suffice to say that while a 1D line has a dimension of D=1 and a 2D square has one of D=2, fractals can have non integer dimensions such as D=1.71, or anything!
Now, why does the Pollock look pretty? There have been interesting studies on how the human eye assess an image. In one, subjects were asked to look at pictures while their eye motion was tracked. It was found that the eye trajectories themselves were fractals! This makes sense. A 1-dimensional eye motion (below, left) does not give us enough information about a scene, however a fully 2-dimensional gaze (below, right: where the eye attempts to perform a full scan of every point in front of it) is way too much for the visual cortex to process at any instance. Instead, the eye has come up with a much more efficient method of looking - doing an intensive 2D scan of a small area before making a 1D leap to another area. The overall result (below, middle) is a kind of 1.5-dimensional fractal scan; it allows isolated ‘islands’ of detail to be put together by the brain to make a complete image!
It turns out that there is also a ‘resonance’ effect that occurs when viewing an image with a fractal dimension similar to that of the eye. Subjects were asked to view a series of computer generated fractal images and rate their aesthetic quality. It was found that images with a dimension of around 1.5 (same as the eye) had by far the most positive response. Furthermore, fMRI scans indicated that viewing such images activated regions of the brain associated with emotions such as happiness.
It is quite easy to analyse a Pollock painting and calculate its fractal dimension. You can kinda tell where I’m going with this… It turns out that his artwork does indeed possess a fractal dimension of around 1.5! Haters can hate, but science proves that Pollock is good. Who ever said that art was subjective?
Though it may be stretching it a little bit too far to attribute all of Pollock’s success to a mathematical quirk, there’s one thing for sure: Your little sister can’t do it.
How do we define life? If you asked this question to a biologist, he or she would point you towards the seven commandments of life science (‘thou shalt metabolise’; ‘thou shalt adapt’; ‘thou shalt reproduce’ etc.) Life, they would say, is a label we give to anything displaying these seven features. This stone tablet has been able to bestow the status of ‘living’ unto all the fish and trees and mushrooms and amoebae that biologists have so far wanted to study. However is this statutory definition enough?
I don’t think it is. It seeks to sort any given collection of molecules into one of two camps: ‘living’ or ‘not living’. It’s a tautological distinction that takes no prisoners. Importantly, rather than attempting to form a truly encompassing definition, all it does is list seven characteristics that are common to everything that had already been colloquially defined as life! It is no more of a definition than an affirmation. It in no way reflects the complex nature of, well… Nature.
An individual mammal and the cells inside it are both considered to be living in their own right. Contrast this with a swarm of bees which isn’t generally thought of as an organism in of itself, but rather a collection of organisms. Our intuition seems to only accept something as living if it’s encapsulated in its entirety by skin, scales or a membrane. Yet in many ways a swarm or hive will act as a single coherent organism when reacting to a stimulus. A hive is even organised into subsystems (workers, soldiers, a queen etc.) which all interact with each other in a way that’s fundamentally similar to the way cells interact in a mammal.
We live in hives too, but we call them cities.
Cities are often described through metaphors such as ‘thriving’ or ‘alive’, but are these more than metaphors? A city metabolises coal to power and heat itself, it has a body clock and transport network, it’s organised into cells (us) which function to keep it homeostatic, it can grow and die, it adapts to environmental changes over time…
Despite all this it we as humans remain very objectionable to the idea that a city might be an actual living organism. But then again, if a red blood cell could philosophise would it too reject the notion that its host was in some sense just as much an individual as it was? Would it not ascribe the seemingly intelligent behaviour of the human it lives in to the computational work performed by individual neurons that it supplies oxygen to rather than the human itself? The human would certainly ascribe intelligence to itself! Or its brain, where it considers the ‘seat of its consciousness’ to be.
In what ways, then, is a computer different to a brain? While I’m not going to get into a discussion of consciousness, I will raise the question: do computers think? Well, they don’t think like a human, but that’s not to say they don’t in some sense think. In any case, the answer certainly isn’t either a yes or a no, but complex and multi-faceted one.
And I think this is true not just of thought but of life itself. The questions raised here are ones that cannot be addressed (or even asked!) by the limiting definiton that biology has given us. In this sense it is blind to many possibilities of life that we could learn from. Life cannot be defined in such a way that makes it a binary digit (either living or not living). Nor should it be a scale of 1-10. If anything, it’s a many-dimensional vector. The seven pillars should not serve as committee in charge of (lifelong?) membership to the Living Club. Rather, they should be thought of as a set of features that emerge out of the complex behaviours characteristic to life and governed by evolution. Life, if anything is a single individual composed of sub-individuals, sub-systems, subsub-individuals, self-similar on many scales, all interacting, all ecompassing. It is a networked fractal array of cogs and axels but most of all: hugely, vastly, complex.
Above is a resin cast of a lung. Notice its fractal nature - how it displays self similarity at smaller and smaller scales. You might also notice how this structure is quite ‘tree-like’. Why are they so similar?
Well actually, both lungs and trees want to maximise the surface area of their functional components while constrained to some maximum volume. For lungs this strict constraint is the size of the thorax, but for trees is more relaxed and is to do with the mass they can achieve through photosynthesis and mineral uptake and density of trees around them.
Interestingly, nature has solved both these mathematical problems of optimisation using the mathematical solution of fractals. This is a great example of complexity and universality. Complex structures such as trees and lungs emerge from very simple mathematical rules, laws and constraints. The result is some kind of universality to the structures that we humans see and assume to be very different, though they are fundamentally the same.
Check out this animation I made of a simple fractal construct being transformed into a ‘tree-like’ (or ‘lung-like’!) structure.
Mathematical Mountains is a collection of generative art pieces by Steve Brunton. These are bifurcation diagrams, which map the stable and chaotic dynamics of a system. Bifurcation essentially means changing a parameter of a system until one stable point forks (or bifurcates) into two. These forks get smaller and smaller and denser and denser until the system has no stable points at all an exhibits chaotic dynamics.
tree by pretendy
This animation aims to demonstrate how a simple fractal can be transformed into a structure reminiscent of a tree, highlighting one of the many facets of fractal geometry in nature.