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Blog: What's in a number?
How our lives are dominated by numbers yet we somehow get it wrong

2. In this season of good cheer, what is a unit of alcohol?

The tumbler in the photograph is 7.8 cm in diameter and the depth of whisky is 2.1 cm, giving a volume of 100 ml = 4 units of alcohol. The wine glass contains just over 1/3 bottle of 15% alcohol wine and is also 4 units of alcohol.

Doctors are generally very good at using the metric system, certainly in Britain. They are not always so good in communicating things: I only relatively recently found out what a unit of alcohol was. But before I get on to that, a good example of the medical profession's use of consistent units is the use of the Body Mass Index (BMI) which is a rough indication of obesity.

BMI is simply a person's mass divided by their height squared with the units in SI. So, for example, I'm 65 kg and 1.72 m, so my BMI is 65/1.722 = 22.0, which is close to the supposed healthy value. That didn't stop one doctor suggesting that I was a bit too skinny (until I pointed out what my BMI was). I suppose most doctors are more used to seeing overweight adults these days. Even American doctors use the same BMI so that means they have to introduce awkward conversion factors to transfer from their medieval units of pounds and inches.

The one area where British doctors do not do quite so well is in the measurement of blood pressure which is in mm of Hg. The irony is that mercury is a bio-hazard! It would be far better if they used proper pressure units, pascals (Pa), with the approximate conversion 1 mmHg = 133 Pa.

Regarding alcohol, 1 unit is simply 10 ml of alcohol. It would have been better if the medical profession had used 1 unit = 1 ml, as we'll see below but no matter. Unfortunately, there seems to be little information conveying the facts directly. Instead, we get given a diet of rough equivalences that I have a terrible job trying to remember.

Is a pint of beer 2 or 3 units? Is a glass of wine 2 units or more? Everything in pubs nowadays seems to be labelled with the alcohol content so with some simple numbers at your disposal, you can do the calculations yourself. Likewise, most bottles come with information on the alcohol content so the calculations can be done in your head. It was while looking at a wine bottle label that I worked out what the medical profession were going on about.

I typically drink red wine, and as my wife seems not to care for alcohol of any kind, I know exactly how much I'm consuming. I tend to drink a bottle over 3 days, and on a 4th day in the week, I'll often have a half glass of whisky (neat). The rest of the week I don't feel like drinking.

I have two wine bottles in front of me one is rated 13% and the other 15%. 14% is typical of red, while white usually has a little less, say 12 or 13%. The bottle is 750 ml so the total alcohol in the 15% bottle is 0.15x750 = 112.5 ml. Indeed it is marked on the back of the label as "11.3 UK units". The other bottle has 0.13x750 = 97.5 ml, and it is marked "9.8 UK units". In both cases, the numbers have been rounded up and in any case are probably only accurate to within a few percent.

Suppose that I drink the stronger wine in 3 days then my consumption on each occasion would be 3.75 units. On other occasions I'll drink a whisky as mentioned, and for curiosity I have been measuring my consumption.

It seems I drink a 700 ml bottle of whisky over 6 occasions (for some weird reason spirit bottles are slightly smaller than wine bottles). This works out as 700/6 = 117 ml on average and this time the bottle is labelled as "40% alcohol, 28 UK units", which is consistent with 1 unit = 10 ml alcohol. So on this occasion my alcohol consumption was 117x0.40 = 47 ml or 4.7 units. It is slightly higher than the wine, but to all intents and purposes it is near enough the same. If 1 unit were instead defined as 1 ml of alcohol, the figures would have been near enough 37 and 47, and we could usefully have dispensed with the decimal point. Also because the numbers are larger many people might think of them as more threatening and therefore limit their consumption more.

It answers the question for me, of whether from a financial point of view I would be better off drinking whisky or wine. Well, I don't buy cheap wine, so it comes in at 2.50 per occasion whereas the whisky was on special offer giving 1.67 per occasion. I knew that when I lived in the USA, because of the tax situation, drinking spirits was the best strategy to obtain that warm contented feeling! Here, it is less clear cut but whisky still has the edge! However, I love my red wine, so no change there.

A few weeks ago there was an article in a newspaper (I can't remember which one now) comparing wine and spirit consumption and their effects on alcohol intake. It showed a really misleading picture of a wine glass with wine, next to three glasses each with one measure of spirit. As we saw from the above, spirit has three times the alcohol content as wine, but the picture was not to scale so it looked as if the volume of spirit was comparable to that of the wine. For a proper scaling see the photograph above, in which the whisky and wine glass are the same distance from the camera.

This was a typical scaremongering newspaper article foisted on the public, with the idea of scaring you that drinking wine can be just as intoxicating as several shorts. Scary! As we saw from my own consumption there is not necessarily any particular increase in alcohol just because you are drinking a lower percentage alcohol fluid. It doesn't take a genius to work out that wine (or beer) can be as intoxicating as spirits.

These sorts of articles really annoy me. The journalists who write them are either cynically exploiting the confusion that exists about alcohol or are quantitavely ignorant themselves. There is no excuse for either position.

Incidentally, for the beer drinker, calculations are slightly more difficult, as for some bizarre reason, in pubs we serve beer in pints. You just have to know how big a pint is that's all. So, if your beer is 4%, a UK pint is 568 ml, so the consumption is 568x0.04 = 22.7 ml or 2.3 units of alcohol (approx.). The American pint is 473 ml.

I hadn't thought of these ideas when I wrote my book, Measuring the World: Making complicated problems simpler by really going metric, but I expect they'll appear in a 2nd edition.

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