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August 6 - September 15, 2022
That desire to know is programmed into the human psyche. Those early humans with a thirst for knowledge are those who have survived, adapted, transformed their environment. Those not driven by that craving were left behind.
Desire to know
In 2011 the complete neuronal network of the C. elegans worm was published, providing a complete picture of how the 302 neurons in the worm are connected.
Book
Although we teach students to question any information that pops up from a Google search, research has revealed that Wikipedia’s accounts of topics at the less controversial end of the scientific spectrum, like the theory of general relativity, are regarded as on a par with accounts in the scientific literature.
Wiki
Just because the scientific community accepts a story as the current best fit, this doesn’t mean it is true. Time and again, history reveals the opposite to be the case, and this must always act as a warning that current scientific knowledge is provisional.
Provisional
theory of everything. They even give it a name: ToE.
Five years later Einstein announced his extraordinary new conception of time and space, followed shortly after by the revelations of quantum physics.
Lord Kelvin comment. 1900. "There is nothing new to be discovered in physics"
The US politician Donald Rumsfeld strayed into the philosophy of knowledge with the famous declaration: There are known knowns; there are things that we know that we know. We also know there are known unknowns; that is to say, we know there are some things we do not know. But there are also unknown unknowns, the ones we don’t know we don’t know.
Types
Rumsfeld very concisely summed up different types of knowledge. He perhaps missed one interesting category: The unknown knowns.
There is another reason why I have been driven to investigate the unknowable, which is also related to my new job. The previous incumbent of the chair for the Public Understanding of Science was a certain Richard Dawkins. When I took over the position from Dawkins I braced myself for the onslaught of questions that I would get, not about science, but about religion. The publication of The God Delusion and his feisty debates with creationists resulted in Dawkins spending a lot of the later years of his tenure debating questions of religion and God.
Richard Dawkins
I am more interested not in the existence of a God to fill the gap, but in equating God with the abstract idea of the things we cannot know. Not in the things we currently don’t know, but the things that by their nature we can never know. The things that will always remain transcendent.
Main
Religion is more complex than the simple stereotype often offered up by modern society. For many ancient cultures in India, China and the Middle East, religion was not about worshipping a Supernatural Intelligence but precisely the attempt to appreciate the limits of our understanding and language. As the theologian Herbert McCabe declared: ‘To assert the existence of God is to claim that there is an unanswered question about the universe.’ Science has pushed hard at those limits. So is there anything left? Will there be anything that will always be beyond the limit. Does McCabe’s God exist?
Mccabe.
god doesnt do dice.
probability invented to replace god.
The unpredictable and the predetermined unfold together to make everything the way it is. It’s how nature creates itself, on every scale, the snowflake and the snowstorm. It makes me so happy. To be at the beginning again, knowing almost nothing. Tom Stoppard, Arcadia
Archaeological digs of settlements dating back to Neolithic times have revealed a disproportionately high density of heel bones of sheep or other animals among the shattered pottery and flints that are usually found in sites that humans once inhabited. These bones are in fact ancestors of my casino dice. When thrown, the bones naturally land on one of four sides. Often there are letters or numbers carved into the bones. Rather than gambling, these early dice are thought to have been used for divination.
Divination. Bones with number.
King Louis XI of France even went as far as prohibiting the manufacture of dice, believing that games of chance were ungodly.
Dice
It was in Italy at the beginning of the sixteenth century that an inveterate gambler by the name of Girolamo Cardano first realized that there are patterns that can be exploited in the throw of a dice. They weren’t patterns that could be used on an individual throw. Rather, they emerged over the long run, patterns that a gambler like Cardano, who spent many hours throwing dice, could use to his advantage.
Cardano. Pattern of dice.
As much as I’ve studied the mathematics of probability, it has always left me with a feeling of dissatisfaction. The one thing any course on probability drums into you is that it doesn’t matter how many times in a row you get a 6: this has no influence on what the dice is going to do on the next throw.
Exactly!
Idleness is not necessarily such a bad trait in a mathematician. It can be a powerful incentive to look for some clever shortcut to solve a problem rather than relying on hard graft. But it’s not generally a quality that teachers appreciate. Indeed, Newton was doing so badly at school that his mother decided the whole thing was a waste of time and that he’d be better off learning how to manage the family farm in Woolsthorpe. Unfortunately, Newton was equally hopeless at managing the family estate, so he was sent back to school. Although probably apocryphal, it is said that Newton’s sudden
...more
Newton lol
When bubonic plague swept through England in 1665, Cambridge University was closed as a precaution. Newton retreated to the house in Woolsthorpe. Isolation is often an important ingredient in coming up with new ideas. Newton hid himself away in his room and thought. Truth is the offspring of silence and meditation. I keep the subject constantly before me and wait ’til the first dawnings open slowly, by little and little, into a full and clear light.
But Newton was stumped when he introduced a third planet. Trying to calculate the behaviour of a solar system consisting, say, of the Sun, the Earth and the Moon seemed simple enough, but already you are facing an equation in 18 variables: 9 for position and 9 for the speed of each planet. Newton conceded that ‘to consider simultaneously all these causes of motion and to define these motions by exact laws admitting of easy calculation exceeds, if I am not mistaken, the force of any human mind’.
Three body problem
If nature were not beautiful it would not be worth knowing, and if nature were not worth knowing, life would not be worth living. Henri Poincaré
Poincare
Beyond r = 3.56995 (or more precisely the limit point of the solutions of a system of equations of increasing degree), the behaviour becomes very sensitive to what the initial population looks like.
r=3.56995
Two populations with r = 4 that start off with a difference of just one animal in a thousand. Although they start behaving similarly, by year 15 they are demonstrating very different behaviours.
R
What about May personally? What impact did the discoveries he’d made have on his view of science’s role in society? ‘It was weird. It was the end of the Newtonian dream. When I was a graduate student it was thought that with better and better computer power we would get better and better weather predictions because we knew the equations and we could make more realistic models of the Earth.’ But May is cautious not to let the climate change deniers use chaos theory as a way to undermine the debate.
Hmm
climate change
One of the protagonists, Valentine, declares: We’re better at predicting events at the edge of the galaxy or inside the nucleus of an atom than whether it’ll rain on auntie’s garden party three Sundays from now.
Working with Andrew Haldane at the Bank of England, he has been considering the financial network as if it were an ecosystem. Their research has revealed how financial instruments intended to optimize returns to individual institutions with seemingly minimal risk can nonetheless cause instability in the system as a whole.
Banking
May believes that the problem isn’t necessarily the mechanics of the market itself. It’s the way small things in the market are amplified and perverted by the way humans interact with them. For him the most worrying thing about the banking mess is getting a better handle on this contagious spreading of worry. ‘The challenge is: how do you put human behaviour into the model? I don’t think human psychology is mathematizable. Here we are throwing dice with our future. But if you’re trying to predict the throw of the dice then you want to know the circumstance of who owns the dice.’
Psychology
‘I think many of the major problems facing society are outside the realm of science and mathematics. It’s the behavioural sciences that are the ones we are going to have to depend on to save us.’
Bob may
‘I’ll tell you one of the questions that I think is a particularly interesting one: trying to understand our evolutionary trajectory as humans on our planet. Is the trajectory we seem to be on what happens on all or most planets, or is it the result of earlier fluctuations in the chaos which took us on this trajectory rather than another. Will we ever know enough to be able to ask whether the disaster we seem to be heading for is inevitable or whether there are lots of other planets where people are more like Mr Spock, less emotional, less colourful, but much more detached and analytical.’
Until we discover other inhabited planets and can study their trajectories, it’s difficult to assess whether evolution inevitably leads to mismanaged ecosystems based on just one dataset called Earth.
Hmm
dataset
The past even more than the future is probably something we can never truly know.
In retrospect it looks like amazing chance that you see so many 6s in a row. But the point is that you don’t see any of the other rolls of the dice because they don’t survive. What looks like a rigged game is just the result of the combination of chance and natural selection.
But that’s the point, because given the billion billion or so possible planets available in the universe on which to try out this experiment, together with the billion or so years to let the experiment run, it would be more striking if that outside chance of creating something like DNA didn’t happen. Keep rolling 36 dice on a billion billion different planets for a billion years and you’d probably get one roll with all 36 dice showing 6. Once you have a self-replicating molecule it has the means to propagate itself, so you only need to get lucky once to kick off evolution.
This is the characteristic feature of a shape mathematicians call a fractal. If you zoom in on a small part of the tree it looks remarkably like the large-scale structure of the tree. This self-similarity means that it is very difficult to tell at what scale we are looking at the tree. This is the classic characteristic of a fractal.
Fractal
The evolutionary biologist Stephen Jay Gould has contended that if you were to rerun the tape of life that you would get very different results. This is what you would expect from a chaotic system. Just as with the weather, very small changes in the initial conditions can result in a dramatically different outcome.
Different result
If the Lyapunov exponent of a system is positive, it means that if I make a small change in the initial conditions then the distance between the paths diverges exponentially. This can be used as a definition of chaos. With this measure several groups of scientists have confirmed that our solar system is indeed chaotic. They have calculated that the distance between two initially close orbital solutions increases by a factor of ten every 10 million years.
Chaos - exponential
When the dice hits the table a certain proportion of the dice’s energy is dissipated, so that after sufficiently many bounces the dice has lost all kinetic energy and comes to rest.
Energy
kenetic energy
Tendency
Even if Laplace is correct in his statement that complete knowledge of the current state of the universe together with the equations of mathematics should lead to complete knowledge of the future, I will never have access to that complete knowledge. The shocking revelation of twentieth-century chaos theory is that even an approximation to that knowledge won’t help. The divergent paths of the chaotic billiard table mean that since we can never know which path we are on, our future is not predictable.
Laplace
When scientists started to look inside the dice to understand what it is made of, they discovered that knowing the position and the movement of the particles that make up the dice may not even be theoretically possible.
Hmm
Everyone takes the limits of his own vision for the limits of the world. Arthur Schopenhauer
with an optical microscope I can magnify the dice by a factor of 1500, which would scale my dice up to the size of a large building. Peering inside this huge dice still won’t reveal much about the secrets of how it is built. Everything still looks pretty smooth and continuous.
What happens, for example, if I take my dice and keep dividing it in half? Just how far can I go? The mathematical side of me says: no problem. If I have a number I can keep dividing it by two: There is no point mathematically where I have to stop. Yet if I start trying to do the same thing with the physical dice sitting on my desk and cut it in half, then in half again, just how far can I keep going?
Everything we call real is made of things that cannot be regarded as real. Niels Bohr
The electron has withstood any attempts to divide it further. But revelations over the next decades would lead scientists to believe that there was another layer of reality hiding below the other two building blocks.
The hope was that the periodic table would be simplified once scientists had discovered how it was put together using electrons, protons and neutrons. But these three particles turned out to be just the tip of the iceberg. Now there were over a hundred particles that seemed to make up the building blocks of matter. As Enrico Fermi admitted to a student at the time: ‘Young man, if I could remember the name of these particles, I would have been a botanist.’
Since mass is equivalent to energy via Einstein’s equation E=mc2, and nature favours low-energy states, particles with larger mass often try to find ways to decay into particles with smaller mass.
Main
THERE IS NO EXQUISITE BEAUTY WITHOUT STRANGENESS
In total there are 24 different moves I can make (including a strange one where I just leave the cube where it is and do nothing). This collection of symmetrical moves is given the name S4, or the symmetric group of degree 4. If I include mirror symmetry, which means I also view the dice in a mirror, there are in total 48 different symmetries of my cube.
Symmetric groupof degree 4
The different geometric representations of the symmetries of SU(3) seemed to be responsible for the different physical particles that make up matter in the universe.
Heisenberg was right when he wrote: ‘Modern physics has definitely decided in favour of Plato. In fact, the smallest units of matter are not physical objects in the ordinary sense; they are forms, ideas which can be expressed unambiguously only in mathematical language.’ Plato’s watery icosahedron and fiery tetrahedron have been replaced by this strange new symmetrical shape SU(3).
Hmm
The weird thing is that this pyramid of triangles and hexagons giving rise to different representations of SU(3) goes on to infinity, implying that you could keep on gluing together more and more of these quarks to make more and more exotic particles.
Hmm
