Meet the micromort
Don’t drink red wine! You’ll increase your risk of colon cancer!
But wait, it also lowers the risk of lung cancer. Cheers! Mine’s a large.
The nutritional science media splits things up into those that will kill you and those that will save you. Sometimes they are the same thing. How are we to figure out what we should actually eat?
The first thing is that you need to know the absolute magnitude of the affects. It doesn’t matter if the chance of death is increased by 500% if there was only a one in a million chance of getting it anyway. Conversely, a modest increase of 20% could be important if your basic risk is high.
David Spiegelhalter of Cambridge University is advocating a new unit of measurement for risk – the micromort. This is a one-in-a-million chance of dying in a day. We are all exposed in everyday life to a background 50 micromorts of danger – i.e. 50 out of every million people die of normal (but non-natural) causes per day. Additional activities we do can increase our risk relative to this average. You need to clock up a further 50 in order to double your chances of dying.
So how can we “spend” our micromorts? Well, we can travel – 200 miles by car costs 1 micromort, as does 20 miles by bike or a paltry 6 by motorcycle. However, to measure the real value in doing something you need to allow for all the benefits and dangers. Its well known that cycling brings health benefits that outweigh the risks when compared to driving, so we must “gain” some morts in fitness benefits. But at least we can compare the risks.
For example, Equasy (addiction to horse riding) is as dangerous as Ecstasy. The risk of dying (in micromorts) for taking a pill of ecstasy is roughly the same (or less) than taking a ride on a horse – both around 1. Now of course there are other factors – long-term problems associated with addiction to an illegal drug – but the point remains that drug laws cannot be justified on the basis of absolute risks alone. Some things we think of as dangerous, well, aren’t. And other things really are.
Returning to the wine, often you don’t get the information needed to calculate risk in a media article. I couldn’t obviously see the relative risks associated with the wine in the top two articles, for example. But these numbers are definitely out there, and they can be measured in a simple and clear way. Why not tell us that, so that we can make an informed decision?
You Are What Those Around You Eat
When I step on my Wii Fit and it tells me I’ve gained 2lb, how worried should I be? Well, that depends on how variable my weight is, day to day. Anna and I have done a simple study, and found that each others weight accounts for 50% of the variation in our own weight. And large variation occurs over the scale of days – meaning that it is all water. Our weights are (on a day to day basis) determined by the things we share in common – food and drink intake.
Dan's (black line) and Anna's (red line) weights over time, plotted in normalised units (*see below) making both weights 1 on average. These were recorded over a period of 56 days from July to September 2007.
There are some surprising results here. The range of values is 5% of the average – meaning that if I weighed 10 stone, I could measure myself twice in a month and differ by half a stone! the standard deviation is 1%, meaning that though I weigh on average 10 stone I would on an average day be 1.4lbs away from it. And daily we vary by 0.8%, so I’d differ by just over a pound on average. So for every day with no change, there is a day with 2lbs difference.
The numbers become more meaningful when our weights are compared. My weight and Anna’s correlate at 49%, meaning that half of our variation is explained by a common factor. During the months of note taking, I was cycling to work and Anna was exercising at home. We were getting exercise together only really at weekends. But we ate dinner together every evening, and we drank beer and wine at the same times. That is what is controlling that 50%. And because it comes off so quickly, its can only be weight stored as water – we vary this much simply by varying how much water we are retaining in our bodies.
Dan and Anna's weight plotted against each other. The correlation line is a least-squares fit with correlation 0.5 and p-value 0.003, meaning that there is only a 0.3% chance that such srtrong correlation could be spurious.
Most trends in weight are gone in 4 days, but there is strong evidence (p<0.001) for a (weak) trend over the study period. Yet our weights now match the mean of the data, so this trend is also variation – its just happening over very long times. In other words, we vary day-to-day, and we vary month-to-month, yet we don’t vary year-to-year.
Problems with the study
To start with, the data isn’t taken over a very long time (or for enough people). It would be interesting to see if there were weekend effects or monthly effects. Secondly, we didn’t record any useful information about food intake, exercise levels, etc, so we can’t examine where the correlation really does come from and what other factors help to explain it. Additionally, like all long-term measurements, the conditions aren’t always identical. The readings are all in the mornings but sometimes before, sometimes after breakfast.
However, the weights recorded here are statistically identical to our recent weights so they were taken from our average variation – there were no long term trends that could have effected them.
Conclusions
Don’t fret small changes in weight! It takes a long time to lose fat, and small changes in water retention can mask it all. What we eat clearly does matter a lot, but over the long term it comes down to the simple equation:
Weight gained (energy units) = energy consumed – energy used
Over the short term, all diets will simply change water retention, so keep an eye on your weight over months to be sure that the trend is real! Even if weight is gained or lost for a month it would return to where it was if there are no lifestyle changes. Simply put: lifestyle determines weight, and that is a very difficult thing to modify.
And don’t let Wii Fit tell you off for a couple of extra lbs 
* Units of measurement
In order to protect Anna’s and my own privacy on the web, the results have been presented in convenient units. Anna’s weight is measured in “Metric Anna’s”, so the average weight is one. Dan’s weight is measured in “Imperial Stormtroopers”, since he is one (in his head at least) and therefore his weight also averages to 1.
Interestingly, the “Imperial Stormtrooper” is also the traditional unit of measurement for ineffectiveness – 1 Stormtrooper achieves exactly nothing, although it can shoot wildly and miss. However, this causes problems in this study when Dan measures more than 1 Stormtrooper, as he becomes negatively effective. This is sometimes apparent when he washes up, as plates can mysteriously get dirtier with washing. The measurement for Annas used to be Imperial as well, but they declared themselves Queen and insisted the servants had to do the washing up (clearly a bad idea with only Stormtroopers around). Hence the need for a more modern measurement that neatly averaged to 1 as well as tidying up after themselves in the kitchen.
We are the many
This news is related to the research I did when working at BioSS in Aberdeen:
There are two important facts in here:
- that only 10% of cells in our body are human: the rest are bacteria and other microorganisms, and these vary a lot between people.
- What we eat affects which bacteria thrive inside our digestive system, and which bacteria are inside us affects us dramatically. For example, our bacteria can change whether we get fat when eating food. It can also affect our chances of getting cancer.
The findings of this research are a little depressing for anyone wanting to lose weight: if you are fat, your gut bacteria will give your more calories back from food than if you are thin. But if you diet properly you can get a thin person’s gut bacteria whatever your weight – so all is not lost!
The bugs may have power over you, but you can still control the bugs.
Thinking through games.
Most games are idle distraction from reality. However, sometimes we can learn things from them. I think I’ve uncovered something very important playing Civilisation 4.
How, you might well ask? In the game, you control a civilisation from its origin through to the colonisation of another planet. Your civilisation grows from a small band of farmers to a world spanning empire. And here is the thing: it only ever gets bigger and better.
Can you think of another empire throughout history for which this is true? There isn’t one. The ancient Mesopotamian empires were very short lived. The Greeks were culturally powerful but soon lost their influence. The Romans controlled the basin of the modern world and an unmatched army yet fell within a few hundred years of their empire being established. China failed to capitalise on its huge cultural, scientific and organisational lead in the European dark ages, was repeatedly overtaken by barbarians, and later dominated by European merchants. Simply put: in history the powerful have always failed to keep their power.
Why is this – what is missing from the game? Civilisation is designed to be fun, not realistic – perhaps it misses out some key scientific knowledge. After a years worth of scientific reading, I can conclusively say – nobody knows! I find this shocking, and exciting. There is huge potential here for research – about a fundamental process that has shaped our world as much as religion, and will determine our future.
I don’t mean to say there is nothing known. There are several good books on the subject – “Historical Dynamics: Why States Rise and Fall” by Peter Turchin is a good place to start, as is “Guns, Germs and Steel” by Jared Diamond. There are three basic explanations offered:
- Internal economics. As a state gets powerful, it develops various methods for doing things. These might be successful initially but eventually they cause problems, and the society can’t change as fast as some other, weaker societies. Essentially: a strong society causes problems that bring about its decline.
- External events, such as barbarians and other empires.
- Environmental change. This can be either caused by the society (so is really internally caused) or natural changes such as mini ice-ages (and thus an external event).
Clearly, external events aren’t enough on their own to explain why a big empire falls, because bigger societies have more resources available to cope with the event than smaller ones. So there must be some internal explanation, and there is little agreement about how different societies cope with things so differently.
I’ll make another blog post another time to describe some things that cause societies to become weaker, and whether they mean dramatic changes for the future of our society. But in the current knowledge there is:
- No causal understanding of what leads to societies weakening, nor when. (1)
- No accepted way to interpret the evidence to support or reject explanations.
What does this mean, in terms of computer games? It means there are good set of ideas of how societies might get weaker, but no knowledge of how “game rules” can be made from these. And nobody really knows which rules influenced the decline of specific empires in history.
Both of the issues could be addressed through a mathematical framework for societal change (which the game of Civilisation actually is!). So, to get a more realistic game of civilisation, we need to do some fundamental research – maybe Firaxis Games will pay my wages?
Note (1): Turchin’s book is actually the first to try to address this by using mathematical models, but he focusses more on larger scale issues such as european versus eastern influence (which he calls “World Systems”). This sort of modelling is the only way to establish that a given mechanism is really causal of society weakening, and under which conditions.
Why do atheletes cheat?
This very interesting article by a scientist who was a former world class cyclist discusses why taking drugs is likely to be the norm for many high end athletes. Why? Because the system favours it. This can, surprisingly, be demonstrated very easily with mathematics known as “Game Theory” (don’t worry, the article is free of maths).
Roughly speaking, taking beneficial drugs (“doping”) is worth it because it both increases your chances of winning, and decreases your chances of being cut from the team. Playing by the rules is the “suckers” option, since your chances of getting cought are so low.
Of course, the analysis is somewhat simplistic. In reality, whether someone should (rationally) cheat depends on their skill level, whether their teammates are cheating, whether their team supports the cheating, and more. The suggestions for fixing the cheating problem do address these issues, however. They include: punishing the whole team if one is found cheating, lifetime bans for the cheater, and allowing cheaters to speak out after the event without punishment. This will increase the chances of being caught, and decrease the likelihood of teams having “organised” cheating. It will also help to identify teams that persistently cheat so that they can be more extensively tested.
The theory is based on the “prisoners dilemma”. In sports terms, the problem can be written in terms of a “payoff” (i.e. money) that the athlete may expect depending on whether they cheat, and whether their opponent does. If both players don’t cheat, they both have even chance to win. If they both cheat, then they both have an even chance to win but might get caught. But if one cheats and the other doesn’t, the cheater will most likely win and most likely not get caught.
| Your action | Opponent action | |
|---|---|---|
| Don’t Cheat | Cheat | |
| Don’t Cheat | $2M | $0.5 |
| Cheat | $3M | $1 |
From this, it is clear that whatever the opponent does, it is best to cheat. The dilemma is that if neither player cheats, then they are both better off than if they both cheat! Of course, the simplest solution is to reduce the payoff for cheaters, so that whatever the opponent does, your payoff is higher for not cheating.
The history of mathematics…
“The history of mathematics is a Markov Chain”. This is a joke (probably not apparent to non-mathematicians!), but like the best jokes, is based in truth.
Because not everyone here knows what a Markov Chain is, I should explain. A Markov Chain describes things that change in a way that has no memory. What happens in the future doesn’t depend on what happened in the past. Picture a drunk, staggering home after a night out. Each step he takes is in a random direction. He might recognise the local shop, and walk towards it – but if he gets lost, and finds the shop again, there is nothing to stop him making the same mistake twice and walking in circles – because he can’t remember where he’s been, but only where he is.
The joke says that mathematics reinvents the same concepts over and over – which is true of this concept. It was independently invented in physics by Einstein for his description of Brownian Motion, and in mathematics by Andrey Markov in work on probability theory.
A post at Scienceblogs reminded me of this, and it is interesting because (as they argue well) all of Science is like this. Scientists are not Historians, so we only remember what is important enough to get into textbooks. If it doesn’t make it it – the next generation don’t know about it, and it becomes forgotten, doomed to be repeated again and again.
I wonder if the Internet will help us overcome this? When (say) PhD students of 2050 do a literature search for some obscure gene, will they find information from now about it in databases and papers, and will that be of any use to them? Can we use this to allow science to progress in useful directions, by remembering those that were failures? Or will failures of the past be viewed as caused by ignorance or lack of equipment, that enlightened folk of “today” can deal with without problem?
Without it, Science will be doomed to proceed as a Drunkard’s Walk, lurching between discoveries on the same old path of failures. We can easily explore the area around the pub like this, but it takes an awfully long time to stumble back home.
