**Science can often seem far-fetched and out of touch with the world, studying minute details of ever-more intangible and abstract phenomena. The truth, however, is that in science and mathematics, seemingly unrelated phenomena can explain wide ranges of behaviour and crop up in the most unexpected places. What may have seemed a mere mathematical curiosity may end up describing the rhythms and palpitations of the heart in stunning detail, and what was thought to describe only the most extreme conditions in the universe may end up having a crucial influence in the way our modern technology operates. Here are some fascinating examples…**

##### Quantum Tunnelling in The Body

One of the weirdest phenomena of the quantum world is tunnelling: the possibility of any particle to *instantly teleport* to a different location, usually a position of lower energy, like a ball teleporting through a hill to reach a lower valley. It turns out that respiration, which powers the energy production of all living things and without which we would die in minutes, relies on the flow of electrons (the tiny charged particles that whizz around the outside of atoms and also flow as electricity) down a chain of proteins that are separated by gaps of less than ten ångströms – about ten times the size of a single hydrogen atom, the smallest atom in the periodic table.

The electrons teleport across these gaps in a rate determined by, amongst other things, the size of the gap. Amazingly, if the gap is made one ångström wider, the rate of electron flow is decreased by ten times! This turns out to be one of the main causes of mitochondrial diseases – if the DNA encoding this structure results in the shape being even the tiniest bit different, it can be catastrophic to how much energy is produced by that organism, indeed, that person.

What’s more is that the DNA which describes this structure is split between the cell nucleus and the mitochondria itself – a bizarre and wholly impractical outcome of the blind process of evolution. This is the reason that scientists are now able to replace the mitochondrial DNA of a woman’s egg cell, allowing mothers who carry mutations which alter that gap width to give birth to children free from life-threatening mitochondrial diseases, but who are still genetically descended from them. Research of this controversial “three-parent” mitochondrial gene transfer procedure was legalised in the UK before anywhere else in the world in 2015.

##### Relativity and GPS

GPS is based on a constellation of 32 satellites orbiting the Earth, each carrying a precise atomic clock. A GPS receiver on Earth detects the radio signals from overhead satellites to determine its position to the nearest five metres. These satellites are orbiting the Earth at 14,000 km/hr, circling the globe twice per day. Despite the fact that this speed is just 0.001% of the speed of light, it is enough for relativity to become important.

Einstein’s theory of special relativity tells us that for an object travelling at high speed, time runs more slowly. The GPS satellites are also orbiting 20,000 km above the Earth, where they experience gravity four times weaker. General relativity states that gravity curves space *and* time, causing the satellites’ clocks to run slightly faster. Overall, a GPS satellite clock runs fast by about 38 millionths of a second per day.

This may not sound like much, but for a system which depends on timing the time for radio waves (travelling at the speed of light) to reach a receiver to the nearest 15 nanoseconds – 15 *billionths* of a second, and the time taken for light to move five metres – it is. Ignoring those 38 microseconds per day would result in navigational errors accumulating faster than 10 km every day. GPS would fail to measure your position to five metres of accuracy after just over a minute. Fortunately, the same theories which can be used to predict the existence of black holes can be used to keep GPS in check with our clocks on Earth – pretty cool.

##### Chaos Theory and The Weather

In the 1600s, scientists such as Johannes Kepler, a German astronomer who described the orbits of the planets, began to build up revolutionary deterministic models of how the world works. Newton’s laws of motion and gravitation are still the foundation of most modern science, and they can be used to make accurate predictions about objects far in the future. For instance, you could calculate the position of the planets in one hundred years’ time as long as you know their initial conditions – the parameters of the system right now. Scientists like Laplace began to postulate that if one could measure the present state of the entire universe, the future would be entirely predictable.

All of this assumes that if you can exactly replicate the initial conditions of a system – say, a snooker shot – then the outcome will be exactly the same. In a situation like this, if the shot is taken at 1/100^{th} of a degree to the side you can still expect it to end up in more or less the same place.

This is not so with chaotic or *non-linear* systems. In 1961, a meteorologist working at MIT named Edward Lorenz was working with a state-of-the-art supercomputer to predict the weather. One day, wanting to recalculate a peculiar result, he restarted a simulation but accidentally entered a variable as 0.506 instead of 0.506127. In a chaotic system such as weather, this tiny discrepancy is enough to throw the result off completely. Indeed, he found that his answers would vary wildly with even the slightest change to the initial conditions. This lead to the coining of the Butterfly Effect, from his conference presentation title *Predictability: Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?.*

Distilling this idea, Lorenz tried to simulate a small section of weather defined by three simple-to-solve equations, with only three variables. When he ran the calculations, however, they never settled into an equilibrium and, in fact, kept looping around forever, as seen in the picture. It never retraces or intersects a single line, yet shows a strange kind of order and structure emerging out of the chaos.

Astonishingly, it turns out that many everyday systems end up being almost totally unpredictable in their behaviour yet display these emergent properties. For instance, fractals (described by chaotic equations) can be found everywhere in nature. Another example is the heartbeat, which turns out to be extremely sensitive to initial conditions. It can slip into an arrhythmic pattern in a way that can be predicted by a chaos equation, and can be “kicked” back into regular rhythm by a strong pulse like a defibrillator. Even things as simple as the irregular drips from a tap and the rise and fall of populations are now known to be described more easily with non-linear maths than standard Newtonian maths – a breakthrough in our understanding of the world.

*If these didn’t whet your appetite, have a read about quantum theory in semiconductors and electronics, nuclear magnetic resonance and MRI scanners or particle accelerators in cancer treatments and drugs testing.*