## Will affluence replace Christianity?

The current edition of the New Scientist contains a fascinating, if I think ultimately flawed, article on the rise – and putative fall – of moralising religions such as Christianity.

Nicolas Baumard, an evolutionary psychologist at the École Normale Supérieure begins by asking how did Jesus go from dying on the cross with a few dozen followers to, inside four centuries, being celebrated as the central figure in the official religion of the Roman Empire – and reasons that this is because the moralising religion of Christianity suited the evolutionary/ideological needs of the Empire’s elite at a moment of profound societal transition.

Christianity, reasons Baumard, was very different from the religions it replaced because it emphasised rewards in the afterlife for morally correct behaviour, as opposed to the material focus on the here and now of the sacrificial approach of ancients. This, he argues, reflects a process seen in evolutionary psychology: when resources are scarce organisms pursue a “fast” psychology, seeking immediate rewards, both sexual and material and eschewing longer-term approaches even if they might bring bigger rewards: if you risk dying young, you sow your wild oats quickly.

In environments where resources are more plentiful then a “slow” psychology dominates – Baumard gives the example of falling birth rates and older parents in affluent societies: babies get more care and attention in wealthier homes.

The key here, he argues, is that around 2500 years ago humans in the Eastern Mediterranean began to enjoy better, more affluent, lifestyles – as measures by the proxy of energy use the per capita usage rose from around 15,000 kcal per day to something over 20,000.

Such affluence was not evenly spread, of course, and those who could afford to practise a “slow” lifestyle were threatened materially and sexually by the continuing “fast” livers – so it suited rulers to promote an ideology and religion that encouraged “slow” living.

Christianity, argues Baumard, was not the only sign of this – the Augustan turn towards morality was another symptom.

So what do I think are the flaws of this? Well, firstly, it does not really explain the first 350 years of Christian growth. Christianity is estimated to have grown by 40% a decade in its first two centuries. There seems to be good evidence that the new religion had a wide appeal across all social strata, not simply for the well off. (I am discounting the idea that the religion grew because of divine providence – after all Islam could make exactly the same, inherently unfalsifiable, claim.)

As Baumard makes clear, exhortations of morality were nothing new – and Augustus’s claim to found a new golden age of morality and honour, strongly supported by his propagandist poets, are the most obvious example. But this ideology seems to be about suppression of revolutionary agitation after a long period of civil war and upheaval – Rome’s need for stability around the turn of the millennium was much more immediate than because of a change in long-term economics.

Then we have the present day – Baumard suggests that as affluence spreads then the need to condemn the remaining “fast” livers will decline and moralising religion will fade too. Yet the world’s most prosperous country, the United States, is significantly more religious than almost anywhere in Europe.

To borrow a term from the Marxists, the argument seems to ignore the relative autonomy of ideology: in other words this religion spread because people liked what it said as much as because it reflected a material change in circumstances.

## Let us now praise insufficiently famous men: Claude Shannon

Claude Shannon, who was born exactly a century ago, is the reason you are reading this – his work on signal processing lies behind all the communication on the internet.

Shannon’s master work was his MSc thesis – the unreachable target which is dangled in front of every computer science masters student.

## I refute it thus?

A while ago I read Max Tegmark‘s “Our Mathematical Universe” (Amazon link) – which introduced me to the concept of “Quantum Suicide” and the idea that if the “many worlds” interpretation of quantum physics is correct then, if death is a result of quantum processes (e.g., does this particular atomic nucleus decay, releasing radiation, causing a mutation, leading to cancer and so on), then, actually, we can expect to live forever – in the sense that our consciousness would continue on in that universe where all the quantum randomness was for the best.

It’s a powerful, if quite mind-bending idea, and it had quite a profound effect on me.

Until, that is, at the end of January, when I slipped on a London street, smashed my face on the pavement and swallowed the broken piece of tooth. Three months later the pain in my upper left arm – with which I tried to break my fall, is a constant reminder that maybe Niels Bohr and the Copenhagen Interpretation was right after all.

## Love and Math: a review

When I started reading this book by Edward Frenkel (Amazon link here) I became so engrossed in it on my morning commute that I missed my Tube stop – and the next one. I got an insight into life in the Soviet Union on the cusp of perestroika from a contemporary (if somewhat higher achieving student), including into how academic (and anti-scientific in the sense that some were desperate to discredit Einstein) anti-Semitism was on the increase from the 1970s onwards, as well as a new take on group theory in geometry and an introduction to braids.

It really was great – the main text skated over the maths while the footnotes explained it in some detail. Not all of it was perfect – the attempt to explain symmetry at the start left me confused about something I thought I understood – but it seemed to all hit the right note.

But it seems my Leicester Square moment was the pinnacle. Even by the time I had retreated back to Holborn I was starting to struggle as the maths just went off the deep end and the explanations offered no quarter.

It’s a pity, because I do think that just some small additional efforts to explain what some of the concepts meant could have gone a long way – for instance we just get Riemann surfaces dumped on us as though they were something different from manifolds (I am sure they are, but a little more effort at explaining why would have helped). While at the end we get a long, and dry, description of branes and A-models and B-models which we are told are potentially important in quantum physics, but we never quite are told why they are important.

My overall impression was the maths has run away with the science a bit – but I am not really in any position to judge.

This could have been a great book, but unless you really are well read on your complex topologies then I’d have to warn you to stay clear.

## The maths and physics of walking in the sand

I love this – which I picked up from Ian Stewart’s now slightly out-of-date (e.g., pre-proof of Fermat’s Last Theorem) and out-of-print The Problems of Mathematics (but a good read and on sale very cheaply at Amazon) – because it demonstrates the harmony of physics with maths, is based on a common experience and is also quite counter-

intuitive.

Most of us are familiar with the experience – if you walk on damp sand two things happen: firstly the area around our foot becomes suddenly dry and secondly, as we lift our foot off, the footprint fills with water. What is happening here?

Well, it turns out that the sand, before we stand on it, is in a locally optimised packing state – in other words, although the grains of sand are essentially randomly distributed they are packed together in a way that minimises (locally) the space between the grains. If they weren’t then even the smallest disturbance would force them into a better packed state and release the potential energy they store in their less efficiently packed state.

This doesn’t mean, of course, that they are packed in the most efficient way possible – just as they are randomly thrown together they fall into the locally available lowest energy state (this is the physics) which is the locally available best packing (this is the maths).

But this also means that when we stand on the sand we cannot actually be compressing it – because that would actually imply a form of perpetual motion as we created an ever lower energy state/even more efficient packing out of nothing. In fact we make the sand less efficiently compressed – the energy of our foot strike allowing the grains to reach a less compressed  packing – and, as a result, create more space for the water in the surrounding sand to rush into: hence the sand surrounding our foot becomes drier as the water drains out of it and into where we are standing.

Then, as we lift our foot, we take away the energy that was sustaining the less efficient packing and the grains of sand rearrange themselves into a more efficient packing (or – to look at it in the physical sense – release the energy stored when we stand on the sand). This more efficient packing mean less room for the water in the sand and so the space left by our foot fills with water expelled from the sand.

## Struggling with coin tossing paradox

I was led to this by the discussion on the non-random nature of prime numbers – as apparently it inspired one of the authors of the paper that noted this. I am struggling a bit with the maths of this, so hopefully writing it out might either help me grasp what is wrong with my exposition or else somebody will explain to me what I am doing wrong.

The paradox, taking H for heads and T for tails, is this – if you have a coin and toss it twice there is an equal probability (0.25) that you will see the sequence HH or HT.

But if you have two coins and toss them then, on average, it will take six tosses before you see HH but ocannly four to see HT.

I have no problem with the HT sequence – inside four tosses you can reach this via:

HT
HHT
HHHT
THT
THHT
TTHT

which a simple sum of probabilities shows comes to: $\frac{4}{16} + \frac{2}{16} + \frac{1}{16} + \frac{2}{16} + \frac{1}{16} + \frac{1}{16} = \frac{11}{16}$, greater than half, while just three tosses would give a probability of 0.5.

So, the issue is with the HH combination. With just five tosses we can get:

HH
HTHH
HTTHH
THH
TTHH
TTTHH
THTHH

Which sums to: $\frac{8}{32} + \frac{2}{32} + \frac{1}{32} + \frac{4}{32} + \frac{2}{32} + \frac{1}{32} + \frac{1}{32} = \frac{19}{32}$ – i.e., more than half (four tosses give us odds of 0.5).

So where is the flaw in my reasoning?

## Is dark matter locked up in primordial black holes?

To be honest, I have an issue with both “dark matter” and “dark energy” – they both look like close-to-metaphysical constructs to me: we have a hole where theory and observation do not match so we’ll invent this latter-day phlogiston and call it “dark”.

Then again, I’m not really qualified to comment and it is pretty clear that observations point to missing mass and energy.

I have another issue – if most of the mass of the universe is in the “dark matter” why is there no obvious evidence of it nearby? I don’t mean why can’t we see it – as obviously that is the point – but even though we sit in an area (Earth) of local gravitational field maximum we are struggling to see any local mass effects. (For instance this paper talks about how “local” conditions should impact any dark matter wind but, as far as I can see at least, it’s all entirely theoretical: we haven’t seen any dark matter wind at all.)

So the suggestion – reported in the New Scientist – and outlined in this paper – that actually dark matter is locked up in black holes caused by sound wave compression in the earliest moments of the universe has an appeal. It also potentially fits with the observational evidence that dark matter appears to be knocking around in the halos of galaxies.

These primordial black holes are not a new concept – Bernard Carr and Stephen Hawking wrote about them in 1974 (in this paper). The new evidence for their potential as stores of dark matter comes from the already famous Laser Interferometer Gravitational-Wave Observatory (LIGO) experiment – as that leaves open the prospect that the two black holes that generated the detected gravitational waves could both be in a galactic halo and of the right mass spectrum to suggest they and similar bodies accounted for the gravitational pull we see from dark matter.

All this is quite speculative – the paper points the way to a new generation of experiments rather than proclaims an epoch making discovery, but it’s obviously very interesting and also suggests that the long search for WIMPS – the hypothesised weakly interacting particles that have previously been the favourites as an explanation for dark matter – has essentially been in vain.