Wednesday, 15 March 2017

How to slice an onion without dying of boredom

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.

Thursday, 2 March 2017

Belief and Certainty

“Belief is the state of mind in which a person thinks something to be the case, with or without there being empirical evidence to prove that something is the case with factual certainty.”

Or so says

As definitions go, it is a deft one. If a belief is a state of mind, it is therefore entirely subjective, and any consideration of objective reality or absolute truth are coolly avoided. Truth and Reality are replaced with the oblique “factual certainty”.

Deft it may be, but it gives no sense of how and why humans have evolved to create such a “state of mind”. Nor does it even hint at why, in some cases and circumstances, people will lay down their lives for a belief. Or why they get so emotional when their beliefs are challenged.

Worse still, however, is that’s definition gives no sense that beliefs cannot exist in isolation, in the mind of an individual. To have any meaning, a belief must be contained within a system of beliefs as part of a culture (otherwise it is called delusion by everyone else). Just as no culture exists without a community that lives by its rules.

Belief is therefore a social construct. What validates your beliefs is that other people believe them too. Belief is, in other words, more a state of belonging than a state of mind. Believing makes you part of a community of believers, whilst disbelieving will identify you in the community’s eyes as the mad and bad ‘other’, a valid target to be overwhelmed, repressed or even destroyed.

What is common to most definitions of belief, including’s, is that empirical evidence is surplus to requirement. Beliefs are just stories that we tell ourselves, myths and narratives that become the building blocks, the basic assumptions of our thoughts and identity. Taken literally, this means that if you change your beliefs, you would not survive the experience: you would become a different person. This explains, to some degree, why literal people get so aggressive when their beliefs are challenged. It might also explain the death of saints, as well as some aspects of their lives.

Of course, the validity of such definitions depends on people being willing to see their beliefs as a psychological device, a mere function, be that a state of mind or a state of loyalty and belonging to a community. Which is precisely the opposite to how most people view their beliefs. Instead, they “believe” their beliefs to be incontestable, absolute Truths.

Put another way, “true” believers believe they are Right. This contains the rather unliberal implication that unbelievers must therefore be Wrong. In the absence of arbitration by empirical evidence, this definition of the believer is the same as the definition of a bigot. What is more, the “true” believer believes in a stunted, excluding reality, one in which there is only one possible Truth, instead of a richer version where truth is not so much absolute as dependent on the believer and the available evidence that each one chooses to ignore.

So, by scratching a bit deeper than’s disappointing definition of belief, we find that the concepts of Truth and Reality goose-step back into the discussion. It also reveals that beliefs are social constructs, enforced by the community via bonds of loyalty and belonging that accredit the believer with a membership card that be verified or rejected, based on an individual’s overt behaviour.

Beliefs, from this viewpoint, are therefore the social glue, pointless in isolation, that bind people into communities.

The benefit this provides is simple: trust. Shared beliefs create in humans a state of social trust (ask any conman), and mutual aspirations, that are highly valuable for the overall community’s survival in the face of a harsh, uncompromising and unpredictable Reality. In turn, belief gives an emotional, if false, substance to safety in numbers. Ask any economist and they will say that a lack of trust in a society is expensive and inefficient. This explains why treason is such a heinous crime: it violates trust and reduces the chance of success of the community. So, more than just a binding agent, this sharing of beliefs is nothing short of the foundation stone of society.

What can be learnt from taboos, that sort of institutionalized belief, such as incest or eating rats.

Taboos encapsulate tried and tested wisdom that is hard to dispute: they spare a community the Russian Roulette of trial and error.

What taboos do is “compile” acquired knowledge into the socially enforced ban of a certain practice. In other words, they conveniently reduce the amount of thinking that an individual must perform to survive. Apply the taboo, and you can delegate the act of thinking onto the community, the only cost to the individual being to help enforce the taboo. The downside to taboos is that they cannot be questioned and so, if circumstances change, they can prove to be an inflexible burden. I’m not advocating that brothers should marry their sisters – the realities of genetics are unbending - but if properly cooked, there is nothing wrong with eating rats and it may well become one way of feeding a growing population, as rats breed and grow faster than rabbits. Indeed, it is alleged that a lot of Chinese restaurants in Buenos Aires fed rats instead of chicken to their unsuspecting patrons. They gobbled them down with no discernible ill effect.

The taboo is ultimately a blunt instrument of social organization, that doubles as a primitive form of health care. By violating a taboo, you cease to belong to your group. You are a disgusting person who eats rats, for example. By breaking the ban, you become an “other”, just as if you did not share the beliefs of your community. In that role, at least, taboos are indistinguishable from beliefs.

It would be nice if we could generalize what we have learnt about taboos to other categories of belief. Specifically, that they contain compiled wisdom, involve a delegation of the act of thinking, and are social norms that accredit your belonging in the social life of the group. 

It is easy to discard the first, i.e., that all beliefs contain compiled wisdom: clearly, not every belief is wise. For example, God does not always provide so get off your arse and get going. However, the other two notions, that beliefs allow individuals to delegate the act of thinking onto the institutions of the community and that they provide a form of accreditation do seem, to me at least, reasonable propositions.

A belief in climate change, for example, delegates thinking on scientists and experts, and results in useful social behaviour such as recycling your rubbish and trying to produce less pollution in your daily life. A disbelief in climate change, on the other hand, delegates thought on the likes of Donald Trump, encourages people to thunder around town in a gas guzzling Humvee, and ends up as a vote for changing the rules of social organization, such as liberal values or all the “Mad Nanny” impositions of political correctness.

So much for all that. But what is behind beliefs, what gives them their potency, their energy, their relevance in our mental life.

To a believer, a truth that is not absolute cannot be a truth at all, which is what makes them bigots. However, if you are an even minded sort of person and accept that there are no absolute Truths, then our world becomes tainted with uncertainty. This is quite terrifying to most people, so what to do?

We all crave Certainty. We want to be told that we are loved, we want to be told that we are right. We don’t need these things validated by facts, we just want them validated by fellow believers. Why? Because we want to be part of the herd, the pack.

But above all else, we want to be Certain.

President Donald understands this well: what, if not Certainty, does the snake oil salesman supreme offer to his believers?

Sadly for us all, Certainty is precisely what NO ONE can deliver because, like True Happiness and Enduring Love, there exists no such objective state of grace (other than as a highly subjective state of mind, the very definition of belief that is so disappointing).

What exists, at best, is a fragile form of Stability. Belief systems only survive if they provide some Stability to the believers. Safety in numbers, for example. Only when there is Stability can you safely delegate thought on someone else. In other words, society will only function properly when there is Stability. When that happens, we get Nirvana on Earth, allowing everyone to get on with procreation, attending truck rallies, paying the mortgage and all the other things that give meaning to life.

And now, at long last, we come to the punchline. If there is any substance to this discussion, then beliefs, other than taboos are, more often than not just a means of denying the fact that we live in an uncertain world. A world that one day will roll on without us, quite unperturbed by our discontinued existence.

The awful, unspeakable truth is that we are just an insignificant part of Reality. Add us all up, add all the groups that subscribe to all systems of belief and we are still insignificant.

And so, this way of looking at belief yields a final, speculative, insight:

Most beliefs have at their core a denial of our Insignificance. The Certainty that our Egos crave is the certainty of our Significance.

So, my best guess is that this intense horror of Insignificance, the primary emotional energy behind our beliefs, is none other than our instinct of self-preservation.

Put another way, if we are insignificant, then what is the bloody point?

Wednesday, 1 March 2017


Vera Rubin died on the night of Christmas Day, 2016. Her lights went out at the ripe old age of 88 and she never won a Nobel Prize.

Hardly surprising, you might think, given that not many people win the Nobel Prize. So she was a woman? Well, a lot of men died in 2016 and they didn’t get a Nobel Prize either. Leonard Cohen, for example.

However, Vera Rubin was no ordinary person.  A dedicated wife and mother, she found the time and the energy to become one of the greatest astronomers of her time and probably any other time. In terms of the importance of what she observed, she is up there with Nicolaus Copernicus, Johannes Kepler and, closer to our time, Edwin Hubble, the astronomer who confirmed that the Universe is expanding. Hubble, better known for the space-based telescope named after him, didn’t win a Nobel Prize either, as he died before the Nobel Committee conceded that Astronomy was actually a branch of Physics and so he hadn’t qualified for the prize.

So at least Mrs Rubin is in good company. 

And anyway, she won just about every other accolade going in physics and astronomy, including the 1995 Royal Astronomical Society’s Gold Medal, the first woman to do so since Caroline Lucretia Herschel in 1828. However, back in the 1970s, Vera Rubin had to look for a subject where she wouldn’t be elbowed out of the limelight by her predominantly male colleagues. At the time, the astronomy herd was obsessed with black holes, so Vera decided to steer clear of the subject. She settled on an intelligent choice, the biggest known objects of all, galaxies, and used modern technology to take a closer look at some of their features. Specifically, she studied galaxy rotation curves, or rather the distribution of rotation speeds of their outer reaches. Pretty soon she came up with her Cosmic rattling result: the stars and the gas in the outer reaches of any galaxies she observed were rotating much faster than expected on the basis of the observable mass of these galaxies, and so should have been flying off into the surrounding void. But they weren’t, so either Einstein and Newton were wrong about a universal law of gravitation, or else what you see is NOT all there is. I.e., dark matter doesn’t just exist, everywhere, but a lot of it exists.

Dark Matter (I prefer the term in German, dunkle materie, which strikes me as more colourful) is an idea that dates back to the likes of Lord Kelvin and Henri Poincaré at the beginning of the 20th Century. Evidence of dark matter had already been observed in 1932 by the astronomer Jan Oort within the Milky Way, i.e., our very own home galaxy. What Vera Rubin did was confirm this result in galaxies beyond our own, as distant and far away as you cared to look. As a result, she showed that Dark Matter cannot be explained away by some statistical glitch in the movement of stars in our galaxy. It is a momentous achievement, but it was not enough to win her the Nobel.

Why not? You might ask. I certainly do and it is pretty hard to come up with a plausible explanation.

The Nobel Committee is a conservative institution, but it is not above the odd publicity stunt. The reputation of the prizes they dish out on a yearly basis are waning, so they need to stir things up. In this respect, Vera Rubin offered them a golden opportunity in our allegedly inclusive times. Her life story is not just one of scientific achievement, it is also one of a triumph against the sexism and prejudice of her time.

She was the first woman to work at Caltech’s Palomar observatory, back in the days when there wasn’t a separate ladies’ toilet. When she attempted to enrol in Princeton’s graduate course, she was told women weren’t accepted. George Gamow, a renowned cosmologist, became her doctoral adviser, but she was not allowed to attend one of his lectures because “wives were not allowed”. When Gamow spoke to her, they had to talk in the lobby because women weren’t allowed in the offices upstairs. The anecdotes of discrimination against her go on and on. Later in her life, Vera Rubin championed women’s place in science and helped many young women to establish their careers in a man’s world. However, not even gender issues and publicity stunts were enough for the Nobel committee either.

So again, why did she not win the Nobel Prize? What, for example, are the criteria for the selection of nominees?

Nobel Prizes in Physics are only awarded if a discovery has “passed the test of time”. Which in the case of the Swedish Academy of Sciences amounts to around twenty years. Live fast and die young, by all means, but don’t expect to win the Nobel, and many big names in Physics who died young did not.

Vera Rubin presented her results on galaxy rotation curves in 1980, ie, 36 years before her death, so well within the Nobel Goldilocks zone. You therefore have to look elsewhere to explain her absence from the Nobel hall of fame.

Dark matter refers to a hypothetical type of matter that is non-luminous, ie, that does not absorb or emit light, radio waves, x-rays or infra red radiation. Observing this “luminous” radiation is what astronomers, most of them male, do for a living. So to be told by a woman that most of what is out there can’t be “seen” in this way knocked them down a peg or two. Rubin’s observations were not exactly welcome ones. Interesting,  but not welcome. Astronomers are human and, if you believe the winner of the 2002 Nobel for Economics, behavioural psychologist Daniel Kahneman, we humans, astronomers included, have a distinct bias towards believing that What You See Is All There Is (WYSIATI). Not so, said Vera Rubin’s observations.


Nominations for a Nobel Prize in Physics are currently obtained by the Nobel Committee by sending out confidential forms to be filled in by previous Nobel laureates. The list of nominations are kept secret for 50 years, so it will be a long time before it will be known who, if anyone, ever nominated Vera Rubin. As a result, one is left with the evil of idle speculation. It goes, roughly, like this:

Since the Nobel Prize for Physics was first awarded in 1901, only two women have won it, Marie Curie (who also won the Nobel Prize for Chemistry) in 1903 and Maria Goeppert-Mayer in 1963.  Both are now dead. By comparison, over 350 men have won the prize (up to 3 people can win it every year). In other words, the annointed group that nominates physicists and astronomers for the Nobel Prize in Physics is a bit like a lot of golf clubs: men only.

Is that the answer to my question? Who knows? The fact remains that Vera Rubin did not win the Nobel Prize for Physics.

But prizes aren’t everything, are they? In a life as rich and productive as Vera Rubin’s, they ultimately mean very little. The call from Stockholm never came, but in the astronomical scheme of things, so what? It’s what you do that matters. And who you are. In both regards, Vera Rubin blew our minds.

Well, some of us anyway, albeit at the outer reaches of the anorak scale.

At the other end of the scale, people have spent the last months bemoaning the passing in 2016 of the author of the following lyrics:

There's a starman waiting in the sky
He'd like to come and meet us
But he thinks he'd blow our minds

Me? I wish I had met the starwoman.