The Occam–Einstein Incongruence

Razor

No, this is not an episode of The Big Bang Theory you missed, but instead the seeming tension between two of science’s best-loved heroes: William of Occam (who, incidentally, was a Franciscan friar and is revered in the Anglican Church as a saint) and Albert Einstein.

Let’s set the ground first by seeing what these two guys say about simplicity versus complexity, that is often applied also to scientific theories. Occam is almost exclusively known for his razor, which goes as follows:

“Plurality must never be posited without necessity” (which he also expressed by saying that “[i]t is futile to do with more things that which can be done with fewer.”)

while Einstein has, among many other things, warned that:

“Everything should be kept as simple as possible, but no simpler.”
and that
“For every problem there is a solution which is simple, obvious, and wrong.”

At first sight it may seem like Occam is arguing for simplicity, while Eistein is warning against its excessive application, but a closer reading suggests to me that Einstein is simply being cautious of simplicity in the absolute. Just looking at some theory and judging it to be complex does not automatically make it a candidate for being cut to size with Occam’s razor. Instead, it is its simplicity relative to the simplicity of the entities and events that it refers to that needs to be considered. Neither is it the case that two theories can be compared solely on the grounds of simplicity, with the conclusion that Occam would side with the simpler one. It is only when the competing theories have the same level of descriptive/predictive performance that the razor comes into play.

Bringing Occam and Einstein together, we can say that problems of varying degrees of simplicity require solutions of commensurate complexity – if a solution’s simplicity exceeds that of the problem’s, it is likely not to be a solution, while if it falls short of it, there is room for simplification and the added baggage is unnecessary.

Instead of being a battle axe, Occam’s razor looks more like a surgical implement, requiring careful deliberation both before and during application. As for our protagonists, they are more likely to star in an episode entitled ‘The Occam-Einstein Equivalency’ :).

Does science require beliefs?

Rembrandt anatomy

I am not talking about a belief in God, or anything whatsoever to do with religion. All I am asking is whether the practice of science requires the holding of beliefs or not. If you ask most scientists, engineers or even random members of the public, you are likely to get a negative answer (for a vigorously atheist answer see here). Science, after all, is about knowledge and repeatable process. The scientific method delivers predictive, explanatory models of the universe, that are derived from, and agree with, hard facts – measured data. We know there is gravity from repeatable experiments and we have models that let us make predictions about how it acts. Therefore, we have no need for beliefs to explain that an object lifted off the ground drops when let go.

That does sounds pretty convincing. Given a law of nature we can explain how the entities and events it refers to interact and we can make predictions about how they will behave under some new, future conditions. This requires no beliefs.

Or does it? If you were to ask Max Planck (yes, the Nobel prize winning author of quantum theory and the guy after whom the Planck constant is named), he’d promptly admonish you as follows:

“We have no right to assume that any physical laws exist, or if they have existed up until now, that they will continue to exist in a similar manner in the future.”

No amount of past data is grounds for expecting the same, previously observed relationships to hold into the future (whether under past or new conditions), for which – by definition – we have no data. Making predictions fundamentally relies on the belief that the laws of Nature are constant and will persist as observed and deduced previously. Now, you might argue that this is a reasonable belief to hold, and I’d agree with you, but you’d be hard pressed not to concede that it is a belief rather than a (scientific) fact. Almost as an aside, there is some evidence though that puts a question mark over the belief that the laws of nature are constant (e.g., see this article in the journal Nature or reports like the one in ABC Science).

The above is just a specific application of the more general problem of induction, whereby we “[p]resuppos[e] that a sequence of events in the future will occur as it always has in the past.” A great, more recent thought experiment to illustrate the problem has been proposed by Goodman in the form of the purpose-built predicate “grue.” “Something is grue if and only if it has been observed to be green before a certain time or blue after that time.” Therefore all emeralds that have ever been observed are not only green, but also grue and we have no basis for assuming that after some future time T we will find green but not grue emeralds. Coming back with saying that emeralds have always been green is beside the point …

As you may have noticed, the above reasoning deliberately took shortcuts and did not explore other instances of belief in science, which may well be rectified in future blog posts (we just can’t tell yet).

Finally, it is worth noting that the ideas presented above are in no way an attack on science! Science, on the basis of its underlying beliefs and assumptions, sheds light on how the world around us may work, allows us to make predictions (which for some phenomena have so far always come true), lets us harness the potential of materials around us for the benefit of humanity and dramatically demonstrates the advances that human intelligence is capable of. This makes science greatly valuable and something to be proud of, but let us not delude ourselves into thinking that it is devoid of belief.

The God of Explanations

God of explanations

Not to be confused either with the God of Small Things or the God of Rain, the God of Explanations1 is fast running out of business. At the dawn of civilization he was busy with lifting the sun across the sky, with making fire, with curing the possessed; by the middle of the 20th century he only had to flip the switch of creation and now we can even notionalize a self–creating Universe and affirm that the God of Explanations is “not necessary,” “surplus to requirement.” And I totally agree! [but apologize for the sarcasm :)]

Leaving to one side the awkward question of where the laws that govern such a self-creating existence come from and that a “[complete unified] theory [that explains our universe] itself would determine the outcome of our search for it!” (Stephen Hawking, A Brief History Of Time“), I would like to argue that applying criteria of “necessity” and “explanatory goodness” to God is a category mistake. It is akin to a child saying that their mother is not necessary for explaining breast milk – true, but not very much to the point …

An atheist has no need for God in their world view – a huge amount of what is going on can be explained by science and some cannot, but is firmly believed to be scientifically explainable. This is a self-consistent view, which rightly looks at God as an unnecessary bolt-on. Someone like me, who believes in the existence of a loving, personal God, can take the same science though and can also split phenomena into explainable and as yet unexplained and, just like my atheist friends, hope for a future increase of the former and decrease of the latter. Neither do I have to equate the unexplained with God’s actions and view the former as having been wrestled off God by science (à la the “God of gaps” argument). On the contrary! I see science as telling me how it is that God’s creation works and I marvel at the beauty of the Standard Model, evolution, neuroscience and cognitive psychology, to mention a few. I also derive pleasure from looking at the history of science, with its drive towards greater understanding peppered with herculean paradigm shifts and all the good that its advances have have done and “to [which] humanity owes so much of its current development” (Fides et Ratio, 106).

Instead of coming to a conclusion that science and belief in God end up being irreconcilable (like Christof Koch does in his interesting “confessions”), I would like to say that a greater understanding of science and a science that has greater and greater predictive and explanatory powers leads to a fuller and greatly enriched understanding of God.

Finally, it is worth realizing that this view is nothing new, as already St. Paul says that “[e]ver since the creation of the world, [God’s] invisible attributes of eternal power and divinity have been able to be understood and perceived in what he has made.” (Romans 1:20) and in the 1960s the Second Vatican Council affirmed that “if methodical investigation within every branch of learning is carried out in a genuinely scientific manner and in accord with moral norms, it never truly conflicts with faith, for earthly matters and the concerns of faith derive from the same God” (Gaudium et Spes, 36).


1 I would like to thank my bestie, Margaret, for coining this phrase and for reminding me that “all holy people reject that kind of a God.” 🙂