Joseph Fourier, French mathematician (1768-1830) is one of my heroes. Join me back in 1994 during a lonely nightshift in the control room of the LEAR antiproton decelerator at CERN.
The walls are made from stacked computer racks and other equipment. Indicator lights flash quietly; cooling fans whir and oscilloscopes scan traces across the screens, showing the heartbeat of the particle accelerator. “AIW” I write in the paper log book, All Is Well.
On the eternally long and lonely nights, we – a small team of operators – kept CERN’s accelerators running. Most of the operations are automated and except for the occasional intervention or dealing with equipment breakdown, the nights leave a lot of spare time. We can’t sleep and have to stay alert and so, most of us turn to programming: developing software to automate our jobs even further.
At that time I was developing software that controlled the Ultra Slow Extraction of antiprotons (most expensive material known to man: 100 MUSD for 1 microgram!) from the accelerator. LEAR was designed as a “storage ring” that kept the antiprotons in orbit and an electrostatic knife would peal the beam of antiprotons slowly and send them to the detectors of groups of sleepy physicists, dreaming of Nobel prizes.
This process is governed by the Diffusion Equation. This equation was formulated by Joseph Fourier is also referred to as the Heat Equation, as he was trying to understand how heat diffuses through steel. To put it simply: if you put a metal rod in the fire, how long will it take before it gets to hot to hold on to?
Although the equation is short (I won’t show it to avoid math alerts going off and scare you away), it is very hard to solve. Joseph Fourier did something amazing to solve it: he invented a new type of analysis. The amazing part is its beauty and universal importance: without it we would not have had radio, TV, mobile phones etc. It is the first thing every engineer learns when starting a degree course. But Fourier never knew that as it happened long after he died. He invented it to analyze heat.
Under the fluorescent lighting of the LEAR control room, this Diffusion Equation occupied me. This equation governs more than heat or antiproton beam extraction: it is a formula for natural decay of things. For example when you build a sand castle on the beach, after a short while it will start collapsing. Perhaps it dried out or perhaps a wave came over it but within hours, you will have a blobby mound of sand left over. That is diffusion too. As is the decay and collapse of any man made structure over time in absence of maintenance.
So, I thought, if the diffusion equation tells us how things collapse, what would happen if we turn it around? What if we start with a blobby mound of sand and we let the inverted equation lose at that, would we get a sandcastle? During those night shifts I wrote software to simulate this and using a numerical approach, I managed to conjure sand castles out of blobby mounds.
So what? Geeky stuff for tired operators, or what!?
Not so fast… By creating sand castles out of blobby mounds using an inverted diffusion equation, I had created a new mathematical beast: the Creation Equation.
Imagine that: an equation that creates things out of formless blobs; a world out of nothing: the holy grail of science!!!
However … I had a problem. Although my night shift experimentation worked well enough using computer simulations, I never managed to actually invert the diffusion equation using mathematics. I used numerical approximation on a computer instead. As beautiful as Fourier’s solution was, it wasn’t suitable for inverting the diffusion equation.
That was 1994 and to this day, 20 years later, I occasionally wake up wondering when I’m going to solve the riddle of the inverting the Diffusion Equation.
It’s strange how such personal challenges can drive us. It can push us into a life time of searching. So it is with the Creation Equation. There is a sequel. On the surface it is quite unrelated and it has nothing to do with Fourier’s equations.
As some of you know, a few years ago I “discovered” genetic fractals. You can see them in the pretty pictures I plaster all over this blog. But there is also a mathematical theory behind that.
A short while ago, after trying for 3 years, I finally found a proper formulation for these genetic fractals. An equation, if you like. This equation describes how things grow and evolve in nature. It is driven by a mathematical formulation of DNA and depending on that DNA the formula will generate trees, flowers, kidneys or any other natural form, or unnatural form for that matter.
Now, you may not be into maths or perhaps even dislike it. The amazing thing about maths is how much news and information can be packed into a few symbols. Mathematicians read these equations like books and draw out the most surprising rabbits.
For example, using this genetic fractal equation with the approximate DNA for a tree, you can study what happens when the tree matures. The animation below shows that. You can also see what happens if the branches were to grow further. It can grow fruit etc.
This too is a Creation Equation: it creates life forms from DNA. But here is the cracker: I can invert this equation. I can reverse time and see the opposite of growth: see the tree shrink back to its origins. Where was the tree before it grew its first branch, i.e. a small green trunk?
From experience we know the answer: an oak tree comes from an acorn. So will this Creation Equation show that?
Sadly, my Creation Equation didn’t give that answer. It gave a very strange answer that bothered me for a while. A tree, it said, doesn’t come from a seed; instead it comes from another tree. The Creation Equation tells me that a tree is in fact a branch of a much bigger tree.
Upon reflection, this is the perfect answer! A tree is itself a branch of its parent which is itself a branch of its parent etc. However, because trees couldn’t grow infinitely large, occasionally the ends of branches, packed with nutrients in the shape of an acorn, drop onto the ground and continue growing there.
That’s an amazing perspective. Every tree of a species is truly and out growth of its earliest predecessor. There is only one tree that happens to have fallen apart into billions separate branches across the world.
That’s what this Creation Equation tells us.
By extension it also tells me that every living species not only has a single common ancestor, in fact, every living being is part of that same organism whose root is that common ancestor. “We are one” is not just New Age speak: we really are one.
But we knew this already, right?
That often happens in science, we discover equations that match what we know already. It tells us scientists that we are on the right path. The next step is to look back further. What preceded the first common ancestor? The science of evolution tells us that it all started with a hot cocktail of monomers of life: Amino acids, Phospholipids and Nucleotides. How exactly this soup merged into life, has not been fully understood. And that is an understatement.
I wonder what my Creation Equation has to say about that? One thing I can already see and that it wasn’t a random event. It is pointing at a single point of origin, a true singularity.
When I figure that one out, I promise to update you.
PS: in case you wonder – the Creation Equation is not a metaphor, here it is (in its 2-dimensional form).
It includes Euler’s “God Equation”, as it should 😉 The key lies in the DNA formulation, D which is a multi-valued function. I know this doesn’t tell you much but I’m sure to publish this properly somewhere, some time.