Is Life a Mathematical Equation?

Solving a Rubik’s Cube tests key mind skills – memory and visual thinking and sometimes challenges in life can be overcome.

It took Ernõ Rubik more than a month to solve his namesake puzzle the first time. Today, competitive cuber’s can best the classic brain teaser in less than five seconds, and casual players can do it in minutes. Their not-so-secret weapon is math. More specifically: algorithms. Devising or memorizing sequences of moves that accomplish a particular goal—for instance, swapping two corners—is key to cracking your Rubik’s Cube. When game designers start stacking more layers onto a standard 3-by-3-by-3-square cuboid, it doesn’t change those algorithms much; it just makes the solve mega-tedious. But changing other variables like rotation angles and block depths creates puzzles for many skill levels and breaking points.

There are 43,252,003,274,489,856,000 ways to solve a Rubik’s Cube. That’s just over 43 quintillion for the less numerically minded. But don’t try to figure them all out – at a rate of one turn per second, it would take you 1.4 trillion years to make your way through all the configurations!

‘When you are studying from a book, lots of people go straight to the end to look for the answers. But that’s not my style. For me, the most enjoyable part is the puzzle, the process of solving, not the solution itself. Erno Ribik.’

What’s the answer to the ultimate question of life, the universe and everything? In Douglas Adams’ science fiction spoof ‘The Hitchhiker’s Guide to the Galaxy’, the answer was 42; the hardest part turned out to be finding the real question. I find it very appropriate that Adams joked about 42 because mathematics has played a striking role in our growing understanding of the universe.

The idea that everything is, in some sense, mathematical goes back at least to the Pythagoreans of ancient Greece and has spawned centuries of discussion among physicists and philosophers. In the 17th century, Galileo famously stated that our universe is a “grand book” written in the language of mathematics. More recently, the Nobel laureate Eugene Wigner argued in the 1960s that “the unreasonable effectiveness of mathematics in the natural sciences” demanded an explanation.

Soon, we’ll explore a really extreme explanation. However, first we need to clear up exactly what we’re trying to explain. Isn’t math all about numbers? You can probably spot a few numbers here and there but these are just symbols invented and printed by people, so they can hardly be said to reflect our universe being mathematical in any deep way.

When you look around you, do you see any geometric patterns or shapes? Here again, human-made designs like the rectangular shape of a book or a magazine don’t count. But try throwing a pebble, and watch the beautiful shape that nature makes for its trajectory.

The trajectories of anything you throw have the same shape, called an upside-down parabola. When we observe how things move around in orbits in space, we discover another recurring shape: the ellipse. Moreover, these two shapes are related: The tip of a very elongated ellipse is shaped almost exactly like a parabola. So, in fact, all of these trajectories are simply parts of ellipses.

We humans have gradually discovered many additional recurring shapes and patterns in nature, involving not only motion and gravity, but also electricity, magnetism, light, heat, chemistry, radioactivity and subatomic particles. These patterns are summarized by what we call our laws of physics. Just like the shape of an ellipse, all these laws can be described using mathematical equations.

Equations aren’t the only hints of mathematics that are built into nature: There are also numbers. As opposed to human creations like the page numbers in this magazine, I’m now talking about numbers that are basic properties of our physical reality.

For example, how many pencils can you arrange so that they’re all perpendicular (at 90 degrees) to each other? The answer is 3, by placing them along the three edges emanating from a corner of your room. Where did that number 3 come sailing in from? We call this number the dimensionality of our space, but why are there three dimensions rather than four or two or 42?

There’s something very mathematical about our universe, and the more carefully we look, the more math we seem to find. So, what do we make of all these hints of mathematics in our physical world?

Let’s look at mathematics in a wider context:

1. Science mostly frames data in mathematical relationships. But physicists like Joscha Bach are updating that nature “written in mathematics” picture, repainting the universe as “not mathematical, but computational.”

2. “Computation is different from mathematics.” Math mostly isn’t computable ( = unsolvable). But matter computes (it always knows what to do).

3. For Bach, physics is about “finding an algorithm that can reproduce” the data. He calls this computationalism, but “algomorphism” better emphasizes algorithmic structure.

4. Algorithms are detailed instructions, recipes that specify every ingredient and processing step. Beyond Bach’s desire for computability, algorithms can better express critical properties of sequence and conditionality.

5. The algebraic equation language (AEL) that physicists are trained to love has key limitations (classic case “the 3 body problem”).

6. Deeper consequences lurk in AEL’s grammar. X + Y = Y + X, but cart before horse ≠ horse before cart. Sequences often matter (in life, even if not in AEL syntax).

7. Some seek only AEL. Sabine Hossenfelder challenges anyone “to write down any equation … that allows … free will.” Perhaps AEL can’t paint the needed picture?

8. Freeman Dyson says “the reduction of other sciences to physics does not work.” Living cells aren’t best viewed just “as a collection of atoms.”

9. Your bag of atoms, to be you, takes mind-bogglingly complex processes, orchestrating trillions of ingredient atoms (= massively sequential, utterly algorithmic, not algebraic).

10. Biology also needs algorithmic logic because life unavoidably involves choosing (like choosing what to avoid to avoid being eaten). Algorithms provide a language naturally fit to describe choosing. AEL can’t easily express rules like, “If predator, then run; otherwise graze.”

11. Natural selection is itself a meta-algorithm. Likewise economics (~productivity selection) is deeply algorithmic (sadly its modelers mainly write AEL).

12. The universe abounds with algorithms in action. Physics has mostly painted AEL-suited pictures. But life expresses richer logic in its empirical patterns.

13. Choosing is key (as is choosing the right language). Even non-living systems — e.g., computers — embody choosing logic.

14. Babies, of necessity great causality detectors, distinguish two pattern types — physicsy things (=unchoosing) from what’s living (=exhibits “contingency patterns”).

15. What if systems could be described by a “choosing quotient,” CQ, that works sorta like electric charge. Things with electric charge (net charge > 0) do things that things without it don’t. Perhaps CQ > 0 systems can use energy to respond differently than physics’ CQ=0 systems?

16. Causation itself could be pictured as that which enables transitions between algorithmically computable states.

17. AEL can’t usefully paint all empirical patterns. Algorithms provide a richer palette.

The Mathematical Universe Hypothesis, which states that our external physical reality is a mathematical structure, to answer this question….we need to take a closer look at mathematics. To a modern logician, a mathematical structure is precisely this: a set of abstract entities with relations between them. This is in stark contrast to the way most of us first perceive mathematics — either as a sadistic form of punishment or as a bag of tricks for manipulating numbers.

Modern mathematics is the formal study of structures that can be defined in a purely abstract way, without any human baggage. Think of mathematical symbols as mere labels without intrinsic meaning. It doesn’t matter whether you write “two plus two equals four,” “2 + 2 = 4”.

The notation used to denote the entities and the relations is irrelevant; the only properties of integers are those embodied by the relations between them.

In summary, there are two key points to take away: The External Reality Hypothesis implies that a “theory of everything” (a complete description of our external physical reality) has no baggage, and something that has a complete baggage-free description is precisely a mathematical structure.

The bottom line is that if you believe in an external reality independent of humans, then you must also believe that our physical reality is a mathematical structure. Everything in our world is purely mathematical — including you.

As Erno Rubik once said:

“If you find a solution with the Cube, it doesn’t mean you find everything. It’s only a starting point. You can work on and find something else: you can improve your solution, you can make it shorter, you can go deeper and deeper and collect knowledge and many other things.”

Biochemistry is pure purpose, passion and dedication to innovation

Every now and again, we hear the clichéd question, ‘What is the meaning of life?’ or ‘What is the purpose of life?’ or ‘Why are we born?’. In most cases, we have our own agenda on what our purpose in life is.

To become a scientist today, you need experience in experimentation – but getting lab experience if you’re an undergraduate can be incredibly difficult.
Biochemistry itself determines, to a large extent, the sort of passion you have in you towards Biochemistry and as you know with success, you require a passion, a vision, a plan an objective.

Why I love Biochemistry

From biotechnology and digital media to sustainable energy and cloud computing, almost everything today is somehow affected—and sometimes entirely reshaped—by scientific and technological advances.

As a society, we have come to take the fruits of science for granted, such as our use of computers, our access to running water and electricity, and our dependence on various forms of transportation and communication. But all such benefits follow from the discoveries and inventions of scientists as they pursue deep insights into the workings of nature and its materials.

Some scientists are enormously influential as culture critics or public intellectuals. In this respect, figures like Richard Dawkins and Lawrence Krauss, or Carl Sagan and Stephen Jay Gould a generation back, come to mind.

Biochemists study the structure, composition, chemical processes and chemical reactions in living organisms. They analyse the chemical reactions in the cells and tissues of living things, study the expression of genes, and research on the effects of food, medicine and other substances on living tissues. Biochemistry is an interdisciplinary field and encompasses elements of molecular biology, molecular genetics, microbiology, and organic and inorganic chemistry. Pure research in biochemistry is conducted to further human knowledge of the subject while applied research is conducted to solve practical problems.

The work of biochemists is applicable to a variety of fields like medicine, food science, agriculture and industry. In human and veterinary medicine, biochemists analyze drug function and mechanism, and help in the development of new drugs. Biochemists engaged in agriculture and food science determine the chemical composition of foods to explore different sources of nutritious food, and study the effects of herbicides and other chemicals on crop plants. They use advanced tools and techniques like radioactive isotopes, spectrophotometers, centrifuges, electron microscopes and specialized software to perform experiments.

When I was younger, I remember studying the work of Louis Pasteur, a French chemist and microbiologist who developed the first vaccines for rabies and anthrax. He is also credited with the invention of the technique of treating milk and wine to stop bacterial contamination, a process named “pasteurisation” after him.

One of the pioneers in the field of microbiology, Pasteur, along with Ferdinand Cohn and Robert Koch, is regarded as one of the three main founders of bacteriology. Born as the son of a tanner who had served in the Napoleonic Wars, Louis grew up listening to his father’s patriotic tales which instilled in him a deep love for his country. As a young boy he loved to draw and paint, but his parents wanted him to focus on his studies. He was an average student who even failed in his first attempt to clear the entrance test for École Normale Supérieur though he eventually went on complete his doctorate.

In his career as a chemist he disproved many of the long-held erroneous “scientific” beliefs such as the concept of spontaneous generation. He received international acclaim for developing the first vaccination against rabies and for his seminal work in the field of germ theory. Although much renowned for his ground-breaking scientific works, Pasteur’s life has also been the subject of several controversies.

You have to feel nostalgic when you start to think of some of the greatest discoveries ever created, and just maybe without these genius biochemists we may not even have the revolutionary world that exists today, here are some of those great discoveries:

1. Galileo Galilei (1564 to 1642)
Legend has it that in order to test how gravity worked, Galileo dropped two balls, a heavy one and a light one, from the Leaning Tower of Pisa, showing that they landed at the same time. Historians doubt this – because his actual experiment was much better.

The Italian carved a groove down the centre of a board about 20 feet long and 10 inches wide. Then he propped it at an angle and timed how quickly the balls rolled down the track. What he discovered was that the distance the ball travels is proportional to the square of the time that has elapsed. But how, in an age before clocks, could Galileo measure this so precisely? He probably used music. Along the ball’s path, he placed cat-gut frets, like those on a lute. As the rolling ball clicked against the frets, Galileo sang a tune, using the upbeats to time the motion and discover a new law.

2. William Harvey (1578 to 1657)
Galen had taught that the body contains two separate vascular systems: a blue “vegetative” fluid, the elixir of nourishment and growth, coursed through the veins, while a bright red “vital” fluid travelled through the arteries, activating the muscles and stimulating motion. Invisible spirits, or “pneuma”, caused the fluids to slosh back and forth like the tides. The heart just went along for the ride, expanding and contracting like a bellows.

Harvey was dubious. Cutting open a snake, he used a forceps to pinch the main vein, or vena cava, just before it entered the heart. The space downstream from the obstruction emptied of blood, while the heart grew paler and smaller, as though it were about to die. When Harvey released the grip, the heart refilled and sprung back to life. Pinching the heart’s main artery had the opposite effect: the space between heart and forceps became gorged with blood, inflating like a balloon. It was the heart, not invisible spirits, that was the driving motor, pushing red blood to the extremities of the body, where it passed into the bluish veins and returned to the heart for rejuvenation. There was one kind of blood and it moved in a circle: it circulated.

3. Isaac Newton (1642 to 1727)
In Newton’s day, Europe’s great scientists believed that white light was pure and fundamental. When it bounced off a coloured object or passed through a tinted liquid or glass, it became stained somehow with colour – whatever “colour” was. Newton, holed up in a dark room at his family farm in Woolsthorpe, turned the idea on its head. He cut a hole in his window shutter and held a prism in the path of the sun, spreading the light into an oblong spectrum.

Then he funnelled the spectrum through a second prism. White again. Finally, he allowed the colours to pass, one by one, through the second prism. Starting at the red end and progressing toward the blue, each colour was bent a little more by the glass. Light, Newton had discovered, “consists of rayes differently refrangible”. It was white that was the mongrel – not just another colour, but a combination of them all, a “heterogeneous mixture of differently refrangible rayes”.

4. Antoine-Laurent Lavoisier (1743 to 1794)
In the 18th century, the conventional wisdom was that things burned because they contained something called phlogiston. Set a piece of wood on fire and it exuded this mysterious essence, leaving behind a pile of ash. Wood, it logically followed, was composed of phlogiston and ash.

Likewise, heating a metal under an intense flame left a whitish brittle substance, or calx. Metal was thus composed of phlogiston and calx. But Lavoisier was troubled by one thing: with the phlogiston expelled, the calx was heavier than the original metal. How could phlogiston weigh less than zero? By cooking mercury in a flask, he showed that, as the calx formed, something was sucked from the surrounding air. He isolated the gas and lit a taper, noting that it burned “with a dazzling splendour”. Calx was not metal without phlogiston, but metal combined with what Lavoisier would name oxygen. Left behind in the flask was a gas that extinguished flames – what we now call nitrogen. Fire and rust produced similar reactions. Lavoisier had discovered the nature of oxidation – and the chemical composition of the air.

5. Luigi Galvani (1737 to 1798)
One day in Bologna, Galvani was startled to see a dismembered frog’s leg twitch when an assistant cranked a static electricity generator on the far side of the laboratory. The same effect occurred during lightning storms. Even more remarkably, Galvani found, the frog’s leg would move, seemingly of its own accord, as it hung from a hook, even in the clearest weather. He concluded that some kind of animal electricity was involved. His compatriot Alessandro Volta was just as sure that the electricity was non-biological, produced by the touching of two different metals: the frog’s leg had hung on a brass hook from an iron rail.

Though neither man could quite see it, they were dancing around a single truth. Volta confirmed that electricity can indeed come from two metals – he had invented the battery. But Galvani went on to show that there is also electricity in the body.
Taking a dissected frog, he nudged a severed nerve against another using a probe made of glass. No metal was involved, but when nerve touched nerve, the muscle contracted, as surely as if someone had closed a switch.

6. Michael Faraday (1791 to 1867)
In his youth, Faraday had performed a suite of experiments showing the linkage between electricity and magnetism, inventing, along the way, the electric motor and the dynamo. But by the time he was 53, he had fallen into a deep depression.
Maybe it was a barrage of flirtatious correspondence from Lady Ada Lovelace, the daughter of Byron, that snapped him out of his funk: whatever the cause, he decided to push the unification a step further, and show that electricity and magnetism are related to light.

Using an Argand oil lamp, Faraday projected polarised light through a block of glass, alongside of which sat a powerful electromagnet. Holding a polarising filter, called a Nicol prism, to his eye, he rotated it until the light was extinguished. Then he switched on the current. The image of the flame suddenly reappeared. He turned the magnet off and the flame disappeared. The magnetic field, he realised, was twisting the light beam – and if the polarity of the field was reversed, the light beam rotated the other way. Faraday had unified two more forces, demonstrating that light was actually a form of electromagnetism.

7. James Joule (1818 to 1889)
Lavoisier had done away with phlogiston, but before his death he had introduced the idea of caloric, his name for an invisible substance – a “subtle fluid” – said to be the carrier of heat.
Put a metal poker in a fire, he argued, and the caloric will rise up the shaft until you can feel the warmth in the handle. According to this theory, the reason something gets hot when you rub it is because you abrade the surface and let some caloric out.

But why, no matter how long you rubbed, did the heat keep coming? Either there was an infinite supply of caloric in every object or, as Joule suspected, heat was something else altogether. With a rigging of pulleys and weights, he spun a paddle wheel inside a vessel of water and carefully measured the change in temperature. The motion of the paddle made the water warmer, and the relationship was precise: raising one pound of the liquid by one degree took 772 foot-pounds of work. Joule had discovered that heat was not a thing. It was a form of motion.

8. A A Michelson (1852 to 1931)
For a Navy man such as Michelson, it was unthinkable that the Earth could be adrift in the infinitude with no landmarks to measure by. So he set out to prove the existence of the aether, the fixed backdrop of the universe and the substance in which our planet swam as it moved through space. In his apparatus, two beams of light travelled in perpendicular directions. The beam moving upstream – with the earth’s orbit – should, he predicted, be slowed by the wind of the aether, while the other beam should be less effected. By comparing their velocities with an interferometer, Michelson would calculate the motion of the Earth against the heavens. But something was wrong: the speed of the two beams was the same. With help from Edward Morley, Michelson made the measurements much more precisely. Still there was not a hint of aether. In fact, the experiment was a beautiful failure.

As Einstein went on to show, there can be no fixed space or even fixed time. As we move through the universe, our measuring sticks shrink and stretch, our clocks run slower and faster – all to preserve the one true standard, which is not the aether, but the speed of light.

9. Ivan Pavlov (1849 to 1936)
Contrary to legend, Pavlov hardly ever used bells in his experiments with salivating dogs. His animals were more discriminating. In his “Tower of Silence”, sealed from distractions, he and his assistants conditioned the animals to distinguish between objects rotating clockwise or counter-clockwise, between a circle and an ellipse, even between subtle shades of gray.

But for his most remarkable experiment, he used music. First, a dog was trained to salivate when it heard an ascending scale, but not a descending one. But what, Pavlov wondered, would happen if the animal listened to the other combinations of the same notes? The melodies were played and the spittle collected. Through simple conditioning, the dog had categorised the music it heard into two groups, depending on whether the pitches were predominantly rising or falling. The mind had lost a bit of its mystery, Pavlov had shown how learning was a matter of creatures forming new connections in a living machine.

10. Robert Millikan (1868 to 1953)
By bending a cathode ray with an electrical field, Cambridge scholar J?J Thomson had shown electricity to be a form of matter, and measured the ratio of its charge to its mass. It followed that electricity was made of particles, but to clinch the case someone needed to isolate and measure one.

In Millikan’s laboratory in Chicago, two round brass plates, the top one with a hole drilled through the centre, were mounted on a stand and illuminated from the side by a bright light. Then the plates were connected to a 1,000-volt battery. With a perfume atomiser, Millikan sprayed a mist of oil above the apparatus and watched through a telescope as some of the droplets – they looked like little stars – fell into the area between the plates. As he tweaked the voltage, he watched as some drops were pushed slowly upward while others were pulled down. Their passage through the atomiser had ionised them, giving the drops negative or positive charges. By timing their movement with a stopwatch, Millikan showed that charge, like pocket change, came in discrete quantities. He had found the electron.

Biochemistry is fast developing into an extremely important subject. Forming the basis of a great deal of research, its study can make for a successful career offering more alternatives than many other streams of science.

Its applications are of vital significance to the fields of medicine, diagnostics, pharmaceuticals, biotechnology, microbiology, veterinary, agricultural and dairy sciences.

Biochemists study the structure and function of enzymes, proteins, carbohydrates, fats, and their metabolic processes, molecular basis of the action of genes, etc. Biochemical engineering harnesses the knowledge of living organisms and systems to create safe and efficient processes. Mainly concerned with biological changes, it is an essential input in the production of pharmaceuticals, foodstuff and waste treatment.

There is an increasing demand for biochemists involved in biochemical genetic research all over the world, especially for those with a specialisation in cell biology, genetics, proteomics, developmental chemistry, organic and medical chemistry, biochemical methods and research. Openings for biochemists exist in R & D in scientific departments in industry, public sector laboratories, universities and hospitals.

It is clear the world needs more biochemists for evolution and revolutionary creations of innovation across its applications.

As Donald J. Cram, American chemist who shared the 1987 Nobel Prize in Chemistry, once said:

“Few scientists acquainted with the chemistry of biological systems at the molecular level can avoid being inspired. Evolution has produced chemical compounds exquisitely organized to accomplish the most complicated and delicate of tasks. Many organic chemists viewing crystal structures of enzyme systems or nucleic acids and knowing the marvels of specificity of the immune systems must dream of designing and synthesizing simpler organic compounds that imitate working features of these naturally occurring compounds.”