Why Does Science Love Simplicity?

Given the intricate nature of our complex universe, it is quite natural to ask the question: why does science love simplicity? English mathematician and philosopher Alfred North Whitehead once wrote the “aim of science is to seek the simplest of explanations of complex facts.”

That quote is so fitting that it could possibly explain the very goal of my writing venture. But alas! That is where simplicity stops being so simple. What is this “simplicity” that I seek? Is it the same as the one that you seek?

What’s more, it’s not just us. Every scientist and mathematician is driven by the pursuit of this “simplicity” in laws and theorems. If scientists and mathematicians were asked to come up with an objective definition of simplicity, would they be able to?

Even if they did, would it be something measurable? Suppose that all of this indeed happened, how can we benefit from measuring simplicity in our scientific approaches? If any of these questions intrigues you, join me in this discussion that seeks to explore the notion of simplicity in science.

This essay is supported by Generatebg

Why Does Science Love Simplicity? — A Vague History

17th century German polymath Johannes Kepler fiercely defended his initial conception of the circular orbits of planets. He believed that it simply had to be circular because the circle is the simplest closed curve.

Eventually, he figured out that the planetary orbits were, in fact, elliptical and not circular. He was not pleased about it though. He wrote of the elliptical orbital system as “dung” that he had to introduce in order to get rid of bigger piles of dung in astronomy.

In essence, he wished for the simplest scientific model that did the job. Years passed; people of science discovered more complex models. But the allure of simplicity remained strong. Isaac Newton famously said the following about simplicity:

“Nature is pleased with simplicity, and affects not the pomp of superfluous causes.”

— Isaac Newton.

While being more complex than Galileo’s original equations for falling bodies, Newton’s laws were arguably still simple. Yet, they were replaced more complex equations from Albert Einstein. And what did Einstein have to say about this?

“Our experience justifies us in believing that nature is the realisation of the simplest conceivable mathematical ideas.”

— Albert Einstein

For his famous theory of gravitation, he chose the simplest tensor-equation set that explained the phenomenon. In a discussion with mathematician John G. Kemeny, Einstein said:

“God would not have passed up an opportunity to make nature that simple.”

So, it appears that science has historically loved simplicity despite the fact that none of these people of science ever defined the term objectively. How does simplicity fare in science these days? Let us find out.

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Why Does Science Love Simplicity? — A Meaningful Present

Suppose that a data scientist is trying to establish a functional relationship between two variables. She plots her empirical observation as points on a graph as follows:

What’s interesting is that our data scientist will most certainly try to connect these points using the simplest curve possible. Since these points fall near a straight line, she would typically assume that her recordings are slightly off and draw a straight line that misses every point.

If this line fails to predict further observations, she would consider the next higher-order curve. Why is this? Well, it turns out that with all else being equal, the simplest possible curve has the higher probability of explaining the observed phenomenon.

Many of the laws of nature that people of science have discovered are surprisingly simple. Take nature’s drive for extrema for instance. Such processes seek the value of a function when the function’s derivative results in zero. This brings us to a natural question.

Is Nature Really so Simple?

When it comes to nature, one has to be careful about simplicity. It is not necessarily the case that nature loves simplicity. We do! And it is our interpretation that is trying to pursue simplicity.

Whitehead warned in one of his writings that we are susceptible to making the error of assuming that nature is fundamentally simple “because simplicity is the goal of our quest.”

Take the equation E=mc² for instance. It appears to explain a natural phenomenon using just three variables. But if you go into the meanings of each one of these variables, you land on more complex derivations.

Laws typically have limitations as to which extent they can explain a phenomenon. As we discover newer, more complex laws, we push the boundaries of these limitations. So, while we locally strive for simplicity, we are globally increasing complexity with our scientific ventures.

Could this notion of simplicity, then, just be an irrational human compass? Or is there hope for employing an objective measure of simplicity in science?

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The Scientific Search for Simplicity

Suppose that you are a scientist. Let us say that you have been working on two different theories concerning the same phenomenon. If these two different theories have the same likelihood to be true but lead to different predictions, which one would you choose to test first?

The answer is most likely that you will choose the simpler one among the two. But what does this ‘simplicity’ actually mean. Just like E=mc², ‘simplicity’ in this context is an umbrella term for a whole host of factors.

You would consider the testing apparatus you have at your disposal, the financial funding required for carrying out the test, your knowledge of the topic, etc. Let us say that you somehow quantify all of these factors and set out to objectively and quantitatively define scientific ‘simplicity’.

Your motivation for this is that such a definition would enable you to choose for the fastest testing approaches in the future. However, there are at least a few practical issues that hold you back with this venture.

For instance, one testing method could be simpler for you based on your background knowledge, but it could be complicated for another scientist based on his background knowledge. So, even quantitative “simplicity” struggles to gain escape velocity from the gravitational pull of subjectivity.

Before we call it quits on simplicity, let us give it one last chance.

The Mathematical Search for Simplicity

I know that by now you must be tired of playing scientist. So, why don’t you switch roles to that of a mathematician? Let us say that you are trying to figure out which of these geometrical figures is the simplest one:

If you consider the number of sides, the triangle is arguably the simplest one, since the circle can be seen as a polygon with infinite sides.

If you consider the formula for calculating the area, the triangle stops being the simplest one; the award goes to the square since its area is a function of one variable only (its side).

The area of the circle, on the other hand, involves the symbol π. While π is a beautiful mathematical symbol in its own right, if you were to represent its value using integers only, you will need an infinite series. So, in essence, it compresses complex information into a simple-looking symbol.

So, all in all, even mathematics seems to be a dead end. So, what option do we have left to make sense of our quest for simplicity?

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Why Does Science Love Simplicity? — A Complex Future

As far as I was able to make out, our scientific discoveries are getting anything but simpler over the course of time. Mathematicians are struggling to check the latest state-of-the-art proofs.

These proofs are so complex that not many mathematicians have the expertise and knowledge to check them within a reasonable time frame.

One aspect of science that could explain this trend could be entropy. Our ‘human’ (read: not scientific) drive for simplicity strives to minimise entropy locally in the moment. But over a long period of time (globally), entropy maximisation seems to be unavoidable.

If you wish for a non-technical introduction to entropy, check out my essay on the origins of entropy.

Coming back to simplicity, as much as scientists and mathematicians love it, it seems to be more of a human thing than a scientific thing. That said, it does serve a purpose. Focus on simplicity makes our lives easier; it employs the most efficient local methods available.

All this leads me to believe that no objective notion of simplicity actually exists. Yet, the subjective notion of simplicity may very well be a welcome necessity in our scientific ventures!

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Reference and credit: Martin Gardner.

Further reading that might interest you:

• Is ‘0.99999…’ Really Equal To ‘1’?
• The Thrilling Story Of Calculus
• What Really Happens When You Invent Infinite Infinities?

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