There are surely as many ways to slice an onion as there are to skin a cat.
Humans are pattern-detecting machines that excel at detecting symmetry, and the vast majority of us slice an onion by taking account of its vertical axis of symmetry. In fact, we find symmetry so incredibly meaningful that we have invented a special word for it: beauty. So, when we look at an onion with intent, we see its vertical axis of symmetry and act accordingly, either slicing it up along lines that are parallel to this axis, or perpendicular to it.
This is all very well and proves to be quite efficient, but slice one onion and you have sliced them all. Onions are, ultimately, simple things and the novelty of slicing them soon wears thin. Having just cooked a pheasant and chorizo casserole for 32 people, I know what I am talking about. For people who prefer thinking to doing, cooking involves a multitude of incredibly tedious processes, not just slicing lots of onions. If the onions don’t make you cry, the tedium will.
What you see is how you slice. Your initial belief of how an onion is structured will determine how you slice it. If you believe that symmetry must reveal structure, then you will likely do as most sous chefs, and slice it perpendicularly to its access, revealing a neat, Russian doll concatenation of layers.
Meanwhile, whether you are studying an onion or cooking it, the end result will not be an onion any more. By slicing it you destroy it. Such is the nature of observing things that are smaller than us. We are more like baboons than gorillas. Give a gorilla a little bird, and it will help it to fly away. Give it to a baboon, however, and it will tear it to pieces to see how it is put together and what it tastes like.
The result of this destruction can be rewarding. For example, the chicken and chorizo casserole, or the realization that symmetry is, all too often, a sure indicator of the easiest route to new understanding, especially about things like onions. Slice an onion randomly, with disregard for its axis of symmetry, and your choice reveals layers of obfuscation rather than clarity.
The key, guiding assumption for learning about onions is symmetry. It turns out that this applies to other lines of inquiry too.
Take the observable Universe. Then try fitting what you observe with the arrogant belief that we stand at the God-given centre of this Universe, around which everything else in the heavens revolves as they evolve. The Sun, the Moon and the “fixed” stars will, at a first approximation, behave as expected, but you will soon notice that, if Earth is at the centre of the Universe, then the planets move along very weird paths indeed. Or rather, that is what Medieval astronomers observed when they took a closer look.
Space, it seems, doesn’t make sense if the Earth is the Cosmic linchpin.
These inquiries into the nature of space have gone haywire not so much by the mixing beliefs with observations but by giving more weight to the beliefs than they merit. The beliefs are a guide, not a preordained result.
The simplest observations and assumptions you can make about the night sky are two: one, that all celestial bodies appear to be roughly spherical and two, that all are in rotation about something, either themselves when they are spinning, or around some other celestial body. More generally, both rotations can happen at the same time. This has to be saying something, but what precisely?
Well, for example, the Cosmos behaves like one humongous ballet with everything spinning around something and Saturn wearing a tutu. All we observers need to do is sit back, listen to the music and try to make sense of the choreography.
For this purpose, we have two options:
One is to refer to preconceived religious beliefs such as that we are at the centre of this balletic Cosmos and that everything else is rotating around us. As stated above, this requires the planets to move along really weird paths, that violate, amongst other things, our simple principle that all things in the Heavens above follow simple paths around themselves or each other. Add in the belief that the Earth is flat, in other words, different to all the other celestial bodies, and things get even worse. The whole thing becomes an unintelligible mess. Therefore, the belief that God put us at the centre of the Universe contradicts the belief that God created the World according to a plan, intelligible by us.
The other option is to believe that the Earth is just another celestial body: it is spherical, it rotates and is not necessarily at the centre of anything. This leaves us with the option of choosing a different centre around which everything rotates. If you choose the sun as the centre around which the planets rotate, and also assume that the Earth is just another spherical planet that spins around itself, then things come into sharp focus. Problems dissolve, complexity plummets and we have a neat little theory that matches most of our observations without contradicting our assumptions. The World has become simpler and God had a plan after all. Phew!
So, we cannot just believe what we want, if we do not want our beliefs to contradict each other.
What still stands, however, is that we need beliefs to guide our curiosity. To build a theory from our observations, we first need to believe something, that acts as our guiding assumption. Conflict between observation and belief will only arise if the guiding belief is unquestionable. In other words, when the data MUST comply with belief rather than the other way round. Empirical evidence is anathema to the mental state of belief. If Reality must conform to a belief, then all science is heretic. Fortunately, we are no longer in the Middle Ages for which we owe a debt of gratitude to Galileo. Our culture is not stuck with rigid beliefs and so we can make better use of our beliefs. For example, a belief that symmetry is meaningful guides you to the most efficient way to slice an onion.
The question that remains is this: how to tell in advance which belief will lead to clarity and advancement, and which to confusion and dead ends? Is there a formula, a way to rule out one belief in favour of another?
Surprisingly enough, to some degree there is. To believe the Earth is the centre of the Universe is nothing if not self-important, presumptuous and arrogant. Apply these terms to any being, let alone to an entire species, and they are usually deemed to be negative. By contrast, beauty, simplicity and elegance have an undeniably positive ring to them. So when in doubt, the positive vibes are more likely to lead you in the right direction. I note that this is NOT the same thing as believing what you want.
But even this has a fallacy at its heart. Not everything is an onion. Some things just ARE complex rather than simple, drab rather than elegant, ugly rather than beautiful. That we live in a simple solar system, where the movements of planets are regular and predictable ellipses, does not mean that the rest of Reality is like that. Mathematics is the language that best describes physics, so it follows that symmetry, and therefore simple, elegant beauty is at the core of Physics because it is, in turn, at the core of Mathematics.
Not every system is like that, however, with stable laws, based on Mathematics, that rule the roost – even the ones that are, like Physics, defy computation of their laws in all but the simplest scenarios.
The reality of complex systems such as economies, societies and ecologies is intrinsically unpredictable and anyone who says otherwise is barking up a tree.
That goes for Marx, Hitler, Lenin, Freud, Donald Trump, Nigel Farage and Theresa May and everyone else who succumbs to the temptation of putting their Beliefs at the core of Reality itself.
Not everything is like slicing an onion because not everything is like an onion. Or even a Solar System.