Carnival of Mathematics 98

Hello!

First of all, regular readers confused by suddenly arriving at #98 in a series you’ve never seen before should read this page to find out what’s going on. In short, it’s a monthly collection of user-submitted maths blogging, hosted by a different blog each month.

Everyone else, welcome to the 98th Carnival of Mathematics! As per tradition, here are some facts about the number 98:

98 is 77 in base 13, and also 7²+7². (This sounds impressive but all numbers of the form 2n² do that in base 2n−1.)
98 is a Wedderburn-Etherington number, which is to say the number of weakly binary trees you can draw with a given number of nodes. The first three such numbers are 1. Then it grows. Fast.
98 is a nontotient. (Don’t Google that. Trust me.)

Maths and things

Patrick Honner has been given a speeding ticket and has used maths to prove that he definitely did the crime for at least a moment. It seems unlikely that either the cops or a judge has thought it through this far, though, so it might be worth arguing the toss. It’s worked before.

Tallys Yunes has devised an alternative set of times for microwaving food such that the ten digits are used roughly equally. I suppose in theory it could help protect your microwave from wear and tear, but really it’s delightfully pointless. My old microwave would accept times like 2:90, so maybe we could take this work even further…

Niles Johnson has blogged a gallant attempt to draw some shapes that presumably live in 8-dimensional space. Since my grounding in such things extends basically to having nearly completed Antichamber, I’m afraid I don’t fully understand it.

Oluwasanya Awe has submitted a nice proof for a puzzle in the Maths Olympiad.

Stijn Oomes submitted a post on ‘rational trigonometry’ which is rather nice maths. I can’t see the use for it, but then, when has that ever made maths worse?

Richard Elwes has blogged about totients, handily explaining what “nontotients” are for anyone who obediently didn’t Google them earlier. The formula for finding them quickly is neat — and sort of obvious in retrospect so maybe try to find it before he tells you.

Wolfram’s blog has a good writeup of the Ramanujan Gap recently filled using their software. The Gap is a handful of missing solutions from Ramanujan’s old notebook. It has some nice 2D colour graphs in it too.

Lastly, here is a post by Mohammed Ladak about how intuitive and obvious the rules of Set are, which makes our attempts to explain it at MathsJam all the more pitiful.

Resources, books and so on

Colleen Young has found a nice set of stats resources, and Justin Lanier has found some more general-interest ones including a website for playing the Four Fours game (and variants thereupon). Frederick Koh has sent a quiz about vectors and has some others on the site so they might be useful for anyone learning such things.

John Hunter has written an obituary of George Box, and Shecky Riemann has reviewed a book about P and NP. We also have a list of maths ladies you should follow on Twitter.

Colin Beveridge tells us about the Mathematical Ninja’s ten favourite numbers, and Christian Perfect sent in a blog by Adriana Salerno who has found x in a museum.

Lastly, Katie sent me a post by Mr Reddy with photos of all the things in his Maths Cupboard. It’s best played as a sort of maths-nerd version of the Conveyor Belt round from the Generation Game.

I’m glad I’m not the only one with too much maths to take this seriously.

I saw this on xkcd the other day:

What’s always bothered me about this claim is that everyone knows bacteria grow exponentially. If you kill 99.99% of them, they need only double about 13.3 times before the population returs to its original size. Under optimal conditions, that’s roughly 133 minutes. That’s only as long as it takes to watch Donnie Darko or have a perfect Christmas. If you wash your hands, kitchen or whatever less often than that, the bacteria will win.

And I’m pretty sure Dettol only claims to kill 99.9% of germs. That might not sound like much, a difference of 0.09%, but it only takes bacteria 98 minutes to claw back that difference. That’s a quarter of an hour you’ve lost.

But I can see how their marketing people thought “kills 99.99% of all germs” sounded better than “buys you an hour and a half in your doomed battle against the unstoppable onslaught of disease”.

How to beat “Blue Monday”

So, another Blue Monday is upon us. It’s not clear exactly when Blue Monday is, but we do know it’s upon us. The Daily Mail has gone with last Monday; The Training Room, one of the four billion companies who have used it for marketing, have gone with next Monday. But we can work it out, because we have the equation:

$Misery = \frac{(W + (D-d)) \times TQ}{M \times NA}$

…unless it’s this one

$D = N + M (T+1) C R \frac{B-S}{J}$

but nobody uses that one. Anyway, it’s definitely a Monday, and it’s definitely in January because $T$ is time, which increases with time and so is highest in December, and $Q$ is how many new year’s resolutions you’ve given up on which is also highest in December look don’t think about it shut up.

Anyway, we know these formulæ are real because they make predictions. One intrepid PR man compiled a formula for the perfect marriage which results in thirty-some pre-specified romantic gestures you have to make every month. Since months are of different lengths, that means you need be less romantic in the longer ones.

This formula about a marriage clearly makes the unrelated prediction that February should be the most romantic month; that there should be some kind of festival of romance smack in the middle of it. Since every restaurant I’ve been in lately has taken great pains to confirm that this is indeed the case, the only rational, skeptical or scientific conclusion is that these formulæ represent the very real cutting edge of science.

While it is obviously bad news that we are all scientifically depressed either last or next Monday, it does offer a ray of hope. Here, you see, is the formula for the perfect Christmas:

I’m assuming that the second “divided by 3D” on the bottom is a typo. Firstly because this formula otherwise defines some kind of festive acceleration, which even a cursory analysis of the Twelve Days Of Christmas song teaches us is dangerous, but mostly because if it’s a real fraction then the numerator has an equals in it.

The point of this equation is—

Actually, first I should point out that $W$ appears twice: once to represent a walk, and once to represent a glass of wine. This might be an error, but I prefer to assume it is a deliberate simplification introduced because walking and wine are somehow equal. I say this because this is the Times’ “Offset Your Carbs” wallchart:

It quite clearly shows that going for a walk is equal to garlic bread:

It also shows (although I haven’t got a close-up photo of this) that a glass of wine is equal to some sex. Taking the new result that wine equals walking,

$Garlic Bread = Walking = Wine = Sex$

The strangest thing here is that mathematically, Peter Kay is now the filthiest comedian in Britain.

Anyway, the point is that the $D$ in the formula for misery is Christmas debt. If we can reduce that value we can all-but eliminate Blue Monday. So how do we do that? Well, the formula for the perfect Christmas is:

$ P_\chi = \frac{8F \times (4P + £23)}{3D} + \frac{3G}{3D} + \left(1+\frac{1}{4C}\right)\frac{2W}{3D} + \frac{5T}{3D \times 1NR}$

Christmas debt is $8F \times 4P \times £23 = £736$. Quite a whack. But we can reduce it without affecting $P_\chi$ — I’m generously assuming what is probably an $X$ is a $\chi$ — because it’s in a fraction. Dividing top and bottom by 4, we get

$ P_\chi = \frac{8F \times (1P + £5.75)}{18 hours} + \frac{3G}{3D} + \left(1+\frac{1}{4C}\right)\frac{2W}{3D} + \frac{5T}{3D \times 1NR}$

That gets us below £50, but that’s still a lot. Let’s dispense with seven family members and divide through by eight.

$ P_\chi = \frac{1F \times (1P + £5.75)}{135 minutes} + \frac{3G}{3D} + \left(1+\frac{1}{4C}\right)\frac{2W}{3D} + \frac{5T}{3D \times 1NR}$

Now our only problem is that the times are inconsistent: 135 minutes in the first term, and three days thereafter. Never mind, just divide all the fractions by 32, top and bottom:

$P_\chi = \frac{1F \times (1P + £5.75) + \frac{3}{32}G}{135 minutes} + \left(1+\frac{1}{4C}\right)\frac{\frac{1}{16}W \times 32NR + 5T}{135 minutes \times 32NR}$

This new, abbreviated Christmas is interesting. $G$, for example, represents a nice family game, of which we must play three thirty-second fractions, and while the formula for the perfect family game (obviously there is one) doesn’t readily divide by 32, there is a game that does.

Three Chess Over Thirty Two features six squares with three pieces on them, and luckily for anyone wanting to knock out Christmas in a little over two hours, requires only one move for checkmate.

But however dull a game Three Chess Over Thirty Two can be, however unsatisfactory one sixteenth of a glass of wine (or walk), and however overfilling you find the 32 portions of nut roast you are forced to consume because it was inexplicably on the denominator, the cold, mathematical reality is that $P_\chi$ has not changed and therefore Christmas has been totally and objectively perfect, while costing less than six pounds. This, in turn, means that our formula for misery loses much of its sting, and that is how you beat Blue Monday.

This is adapted from part of my Stupid Formulæ Talk which can come to your local Skeptics in the Pub or similar event if you think your audience would enjoy hearing me be approximately this silly for the better (or at least longer) part of an hour.

On reflection, perhaps they shouldn’t go this far. It’s a bit sad, isn’t it?

I saw this post about the graphs of National Novel Writing Month on my brother’s blog ages ago, but an RSS malfunction showed it to me again today, and I got to thinking about his final graph: words written on any given day, plotted against how far behind he was that day (or, more precisely, words left to write / day left, normalised to the same value on day one). He correctly notices “a hint of a positive correlation”, and notes that that may not be causation, but could be an external factor, such as his determination to show his doubting wife what for.

I have my own theory, arguably more prosaic but also more interesting, so I created a simulation to test it. I assigned a random number to each of the 30 days of November, using the formula RAND()*RAND() to create a nice distribution. I assigned a number of words to each day by multiplying this random number by 50,000 and dividing by the total of all 30 random numbers. This created a month of simulated writing with random ups and downs, but a guaranteed total output of exactly 50,000. (For these purposes I allowed non-integer numbers of words.) I worked out the cumulative wordcount and behindness index for each day, and plotted them, with a trendline (in red) and R2 value, and ran simulation after simulation.

My theory was proven: every single one had a positive correlation.

Of course it did — any deviation from the 1666.7-word daily target will be reflected in your behindness score on every subsequent day, and if you write your 50,000th word on day 30, then it will be balanced by an equal and opposite deviation spread unevenly across those same days. Any novel of exactly 50,000 words will have this hint of positive correlation between behindness and words written. I suspect this would hold even if we allowed some days to have a net deletion of words. Novels of just over 50,000 (such as almost all of them) will get a slightly reduced version of the same effect. There are only two ways to avoid it. One is to write a wildly different number of words — say, 40,000 or 60,000. The other is to write exactly one thousand, six hundred and sixty six and two thirds of a word every single day, although that involves using a lot of three- and six- letter words.

I’m not sure that someone who writes 60,000 words really worked to the 50,000-word target at all, so if you want to know if ‘behindness’ affects performance, you’ll have to examine the stats from people who failed to complete the novel, between day one and whenever they eventually gave up. And to be honest, how useful a sample are they to a study of productivity?

Anyway, I suppose I hope this can be a nice example of how something plausible and supported-by-the-data-looking can turn out to just be randomness viewed from a funny angle.

I can’t believe I have to explain to the Guardian that the moon is larger than a jogger.

The tedious and ridiculous “Supermoon” is back.

The Guardian call it “one of the natural world’s most spectacular light shows”. In fact, the moon is at the closest point to the Earth in its orbit, and it also happens to be a full moon. According to both the Guardian and the BBC,

The phenomenon, known as a perigee full moon, means the Moon appears up to 14% bigger and 30% brighter than when it is furthest from the planet.

Robert Massey, of the Royal Astronomical Society, told the BBC that although the phenomenon makes the moon appear 30% brighter, it is the apparent 14% increase in size … that is most striking. “The eye is so good at compensating for changes in brightness that you simply don’t notice so much,”

No, the reason we don’t notice the moon appearing 30% brighter is that it doesn’t.

The amount of light that hits the moon depends on the distance from the sun. Light leaves the sun equally in all directions, and if you imagine a load of photons leaving it at the same moment, you get a sphere, and as they fly through space they get more and more spread out. If you move the moon further away, more of them will miss it. The difference in light hitting the moon, between its closest and furthest points, is roughly 0.03%. That only accounts for a .05% change in brightness (and in fact, it’s dwarfed by variations in the Earth’s orbit around the Sun) so where does the other 29.95% come from?

Ah, but the distance to the Earth changes by more, right? Yes — by 14% if you go by the newspapers’ figures. Wolfram|Alpha puts it at nearer 12%. It’s not important. The important point is that once again the nearer the moon is to the Earth, the more light we get — but the more of the sky it takes up. And because both the amount of light and the area of moon in the sky increase at the same rate (the square of the distance) the actual brightness of the moon remains exactly constant. The brightness of the night, on the other hand, increases by a factor of (114%)² = 129.96%. I think it’s pretty clear what’s happened here.

It’s a coincidence that those numbers work out so neatly, obviously, but it does mean we can quantify the accuracy of the “30% brighter” claim: it is 0.17% truth and 99.83% misunderstanding of basic physics. Here’s that data as a graph:

Ah, but look! They have photos! How can I pooh-pooh it when they have photos? Here’s the Guardian’s shot:

That’s a pretty big moon, but not because of the “supermoon”. That’s because of perspective. We all know the moon is larger than a jogger. It shouldn’t be impressive if it seems that way in a photo.

If you doubt me, here is that information presented as a graph:

I mean, I think this is a pretty epic moon:

That was taken on 21 October 2005, when the moon was a little further away than normal. All you have to do to get this effect is to walk backwards and zoom in. Think about it: you can walk backwards for ages and the distance between you and the moon will basically stay the same. The distance between you and the jogger or the building in front of the moon will change a lot. So you can control the relative size of moon and jogger really easily, just like you can take a photo of your giant kid holding up a tiny Tower of Pisa if you really feel you must. And if you make the jogger small, then crop the image around the moon, the moon looks massive.

Because it is. Of course it is, it’s the sodding moon.

I suppose what annoys me about this story is that the ‘supermoon’ is too pathetic to be of interest to photographers, too banal to be of interest to astronomers, and arbitrarily not of interest to astrologers. So who cares? Nobody. Nobody cares. And yet it’s been in every newspaper going, two years on the trot. And it’s one thing when a newspaper does it, because it’s cheaper than doing journalism. But the BBC should be above it.

A round-up of a mathsy week

Maths!

First of all, I’ve written an article for the Aperiodical, an irregular maths blogging collective kind of a thing. It’s about voting systems, crazy dice, paper, lizards and Spock.

“Grime Dice” are a set of five coloured dice with unusual combinations of numbers on them. The red die, for example, has five fours and a nine. The blue one has three twos and three sevens, so it loses to the red die about 58% of the time. The green die has five fives and a zero, and will lose to the blue one in 58% of rolls. What makes them interesting is that the green die will beat the red one in 69% of rolls. These three dice behave rather like rock-paper-scissors — in mathematical terms, they are ‘non-transitive’. The full set of Grime Dice also has a purple and a yellow die, so a better analogy would be rock-paper-scissors-lizard-Spock.

You might ask which is the best Grime die, and the obvious solution is just to roll all five dice at once, a hundred times, and see which one wins the most times. This is why you should never believe something simply because it is obvious.

Read the rest at Aperiodical.com

I’ve been quite reasonably asked what Ranked Pairs did to deserve omission, to which my only answer is “be a bit inelegant and have a boring name” (not that I have any particular room to criticise it for either of those). If you’re interested, in Ranked Pairs, you start with the strongest preference the voters expressed (say, Labour are better than UKIP), “lock it in”, then keep locking in preferences, in decreasing order of strength and skipping any that would create Grime-dice-style cycles, until you’ve figured out an ordering on all the candidates. The winner is the one who beats every other candidate in the final, locked-in pairings. It’s not so very different from Beatpath (which I did include) but even after Paul’s recasting of it in more elegant terms it still feels a bit clunky to me. I appreciate that “a bit clunky” is not a completely valid mathematical criticism.

Secondly, my maths-based comedy rant thing about stupid formulæ in PR newsfodder will be on at the new Kingston Skeptics in the Pub group on Thursday 2 August. It’s at the Ram Jam Club, which is here:

Come down if that sounds like somewhere near where you live. You’ll learn how to derive the existence of tiny shoe-horns using quantum physics and a cheap advert for some guy’s book. (Connection fans may note that the golf club to the east shares its name with a popular electoral system.)

Lastly, here is some maths I found scattered around the web, which I may bring out at Manchester MathsJam tonight (spoiler alert). It’s about counting, binary, puzzles and hypercubes (as is all maths).

Picture a counter, like the ones used to count people into clubs or on the obnoxious Lynx adverts a few years ago. When a digit ticks over, all the digits to the right of it also tick over to zero. If you had a really big club (or a really noxious deodorant) you might end up changing hundreds of digits at a time. Binary is no different — but sometimes having to change all those bits at precisely the same time causes problems, so you’d much rather only change one digit at a time. To this end, Frank Gray invented a revised binary counting system where that is exactly what happens. In 3-bit, you start as normal at 000, then 001, and then you go to 011 — the nearest unused number. Next, you go to 010 which you missed out, then skip to 110. Next, comes 111, then 101, and then 100 — the only number left. To get back to zero, you flip that single bit at the front back to 000. To get to eight, you need four bits, and it’s 1100 — again only one bit has changed.

So how do you know which bit to flip? Every second flip, starting with the first, is the right-most bit. Every fourth, starting with the second, is the next rightmost bit. Every eighth, starting with the fourth, is the third rightmost. And so on. I think this is interesting, because it’s also the solution to the Towers of Hanoi game: in that, you move the smallest disc first, and every second move after that. You move the second smallest second, and every fourth move after that. You move the third smallest fourth, and every eighth move after that. And so on. This is a neat way to visualise why the time needed to solve Hanoi increases as 2ⁿ. (It’s also the solution to the Chinese Ring Puzzle which, generalising from myself, I shall assume you haven’t heard of and ignore.)

Counting in Gray Code is also equivalent to visiting every corner of a hypercube without visiting any twice: if you think of a binary number like 101 as a set of co-ordinates (1, 0, 1), then the numbers 000 to 111 denote the corners of a cube. 00 to 11 give you a square, and 0000 to 1111 give you a four-dimensional hypercube. Obviously you could visit them in standard binary order (0000, 0001, 0010… 1111) but that means taking diagonal tracks through the cube. Gray Code’s system of only changing one bit at a time means you can do it just tracking along the edges — and because you can always change that last bit to get back to zero, you can do a full Hamiltonian cycle, just along the edges, by doing nothing more taxing than counting.

I honestly don’t remember what possessed me to look up Gray Code. It had been sitting in the back of my mind for about two years, and suddenly I thought maybe it was interesting enough to mention at MathsJam. It hadn’t occurred to me that it might have any relevance to traditional wooden puzzles, hyperdimensional navigation, or indeed anything else. But it did. And that is why maths is awesome.

Can a simple mouth rinse help Muslims win Olympic gold?

Lester Sawicki is a dentist from Austin, who specialises mainly in spamming Amazon affiliate links across Blogger, Digg, Twitter, and generally whatever other site he can find a ‘submit’ button on. It’s hard to tell if his blog is intended as a real blog that he simply happens to have plastered with more adverts than a multi-bus pileup in Times Square during the Superbowl, or if he just shoves content there from time to time to give Google that impression, but I strongly suspect it’s the latter. It took me so long to find the bit about Muslim athletes that I started to suspect the tweet I used as the title of this post was generated by something like the Daily Mail-o-Matic. (In fact, it’s an energy-packed mouthrinse for use during the Ramadan fast.) He also writes sells ridiculous books with names like Yin Ain’t Yang: the ancient way to better health that only a Texan could come up with.

This came to my attention, anyway, because said ridiculous book was recently highlighted in the British Dental Journal, which is part of the Nature publishing group and therefore should know better. Here is the news story in its entirety. The first paragraph is a textbook case of “technically true” and it goes downhill from there.

A book written by a dentist in Austin, Texas reveals how the teeth, tongue and jaws are powerful tools that can unlock ‘vital energy that may improve overall health, fitness and longevity’.

According to Dr Lester Sawicki, author of Yin ain’t yang, the ancient way to better health, modern science is beginning to understand ancient wisdom about the link between healthy teeth, gums and jaw function and boosting general fitness, health, and longevity. New evidence proves that teeth are joined to vital organs by way of energy channels and when the teeth, tongue and jaws are included in a regular meditative exercise routine you can access and refine the body’s ‘chakras’ to promote a long, healthy, strong existence.

Dr Sawicki believes that meditative exercise using your teeth, body, and mind can relieve stress, improve cardiovascular function and flexibility, increase bone density, balance hormones, circulate lymph, detoxify organs, increase brain function and induce happiness.

The book offers a series of energy-building visualisations and physical exercises aimed at strengthening and aligning the ‘chi centre’ of the oral cavity with the ‘power centres’ of the body.

This was in their “news” section, which accepts press releases, so I can only assume he did that. Which is a bit sad – I expect this sort of thing from tabloids, I’m a bit disappointed when the Guardian do it, and now here it is in a scientific journal, listed as “news”. And the second sentence in the second paragraph is missing the phrase “Dr Sawicki believes”.

It’s just a bit sad when you’re jumping through hoops trying to get a paper through someone’s review system, if they’re publishing just any old shit in the news and comment sections.

Valentine’s In Space

As far as romantic anniversaries go, I always liked the idea of celebrating prime-numbered months. One month is a bit soon to start celebrating, but thereafter you get quite frequent parties early in the relationship where a couple of months can make a difference to how serious it feels, then it tails off until they’re annual or less frequent, but still occasionally giving you two pretty close together. Instead, though, my girlfriend and I put the start of our relationship into nerdiversaries.com.

Nerdiversaries is a website built by Matt Parker. The idea is, you put your date and time of birth into the site, and it will spit out a calendar of alternative birthdays you may wish to celebrate: 69³ seconds, for example, or 333,333 minutes. I don’t think it was meant for romantic anniversaries, but there’s nothing much he can do to stop us using it that way.

According to the website, Monday would be our one-year anniversary if we lived on Venus. A Mercurian year is shorter still (around 88 days), and the next one is an Earth year with which I assume you’re familiar. This should not be a surprise: we can use Newtonian mechanics to derive an equation for the orbital period T of a body given the mass of, and distance from, the sun (M and r respectively). It’s called Kepler’s Third Law, and it comes out at:

T² = 4π²r³ ÷ GM
where G is the gravitational constant.

Anyway, the point is that if the length of your relationship so far is T, this equation gives you the distance at which you would have to orbit the sun for today to be your first anniversary:

r = 1.819 × ∛T²
where r is measured in millions of miles, and T in days

You can now think of your first anniversary as a spacecraft, which set out from the sun the day you got together. When you had been together for one year, it passed Earth. It passes Mars after 687 days, Jupiter after 12 years, and Uranus 72 years after that.

The furthest any man-made object has ever travelled from Earth is 119AU — this is Voyager I, but you would have to stay together for rather more than a millennium to pass that. It seems that the solar system is a practical limit on anniversaries, as well as spacecraft, but it’s not just romance we should celebrate, and the first anniversary of any event before November 713AD is further out than Voyager I.

To be honest, though, I quite like that your first anniversary will approach the edge of the solar system almost asymptotically. It’s a pretty way of visualising how well you’ve done.

Judge Bans Thinking

Hello!

I just saw this news story on singingbanana’s Tumblr:

The footwear expert made what the judge believed were poor calculations about the likelihood of the match, compounded by a bad explanation of how he reached his opinion. The conviction was quashed. But more importantly, as far as mathematicians are concerned, the judge also ruled against using [Bayes' theorem] in the courts in future.

What?

In case you don’t know, Bayes’ Theorem is a formula from the days when mathematicians could get away with just naming bits of common sense after themselves, and states:

P(A|B) = P(B|A) × P(A) ÷ P(B)

That is,

(probability A is true given evidence B) = (probability of finding B if A is true) × (probability of A being true) ÷ (probability of finding B)

Obviously that’s pretty useful in court, and it’s also pretty easy to understand: clearly, (probability of finding B) = (probability of finding B if A is true) × (probability of A being true) + (probability of finding B if A is false) × (probability of A being false). That’s all the options: A must be true or false. All Bayes’ theorem does is work out in what the proportion of the cases in which B is found, A is true. It’s almost obvious, in an informal kind of way, if you have the right kind of brain.

Point is, you’re now not allowed to use that reasoning in court, which means if your defence depends on any evidence more subtle than “fifteen people saw me across town” then you’d better find another way of phrasing it than this. It’s basically maths, so you ought to be able to work round it and find a more circuitous way of showing the same thing.

Strictly, the ruling was that you can’t use Bayes’ theroem “unless the underlying statistics are firm” but that doesn’t help a lot. In qualitative terms, all the theory says is that something is more likely if you have evidence for it — so I think we can safely assume it’s the use of maths that the judge objected to. It’s the same reasoning behind the Drake equation: people are bad at guessing big, complicated things like “how many aliens might there be” or “how likely is this guy to be guilty given we found this footprint”, but pretty good at estimating simple things like “how long might an alien race beam signals into space” or “how likely is it there’d be a footprint like this just here”. You can do the same thing if you get to the tie-break in a pub quiz: come up with a way to work out the answer from easier to estimate quantities and crunch the numbers. You’ll almost certainly do better than the team that guesses the final answer directly.

And that is why this ruling is worrying: because not only has a judge fallen foul of the natural but wrong tendency for humans to overestimate their own judgement and distrust logic and reason, but they’ve ruled that all other judges and lawyers have to make the same error. It’s a shame, because while any large group tends to be a bit rubbish at thinking, judges are usually pretty good — as, I think, is anyone impartial with the time and inclination to look into things.

I didn’t know they could do that. (I actually suspect they can’t and the story is overblown, but I wouldn’t know enough to decide.) What’s next — a judge commits the prosecutor’s fallacy and then rules that everyone else has to do it as well? Idunno, seems a bit dangerous to me.

It just seems like it’d be fairly easy to set someone up if there’s a big list of thought processes their defence lawyer isn’t allowed to invoke. Or design a crime that could be easily proven but not with the limited methods of thinking allowed in the courtroom.

There are some interesting mental exercises there — coming up with crimes or frames for differently handicapped justice systems — but not ones actual lawyers should have to bother with.

Can we not save herbal medicine?

A bit ago, Avaaz sent me a somewhat hyperbolic email asking me to help them “save herbal medicines”. I tend to distrust anybody who uses the phrases “ban” and “big Pharma” in their very first sentence:

Dear friends,

In 3 days, the EU will ban much of herbal medicine, pressing more of us to take pharmaceutical drugs that drive the profits of big Pharma.

The EU Directive erects high barriers to any herbal remedy that hasn’t been on the market for 30 years — including virtually all Chinese, Ayurvedic, and African traditional medicine. It’s a draconian move that helps drug companies and ignores thousands of years of medical knowledge.

We need a massive outcry against this. Together, our voices can press the EU Commission to fix the directive, push our national governments to refuse to implement it, and give legitimacy to a legal case before the courts. Sign below, forward this email to everyone, and let’s get to 1 million voices to save herbal medicine:

http://www.avaaz.org/en/eu_herbal_medicine_ban/?vl

It’s hard to believe, but if a child is sick, and there is a safe and natural herbal remedy for that illness, it may be impossible to find that remedy.

On May 1st the Directive will create major barriers to manufactured herbal remedies, requiring enormous costs, years of effort, and endless expert processes to get each and every product approved. Pharmaceutical companies have the resources to jump through these hoops but hundreds of small- and medium-sized herbal medicine businesses, across Europe and worldwide, will go bust.

We can stop this. The directive has been passed in the shadows of the bureaucracy, and it cannot stand under the light of democratic scrutiny. The EU Commission can withdraw or amend it, and a court case is currently challenging it to do so. If European citizens everywhere come together now, it will give legitimacy to the legal case, and add to growing pressure on the Commission. Sign below, and forward this email to everyone:

http://www.avaaz.org/en/eu_herbal_medicine_ban/?vl

There are arguments for better regulation of natural medicine, but this draconian directive harms the ability of Europeans to make safe and healthy choices. Let’s stand up for our health, and our right to choose safe herbal medicine.

With hope and determination,

Ricken, Iain, Giulia, Benjamin, Alex, Alice, Pascal, Luis and the rest of the Avaaz team.

I thought they were being a bit silly, so I sent them this email:

You do a lot of great campaigns, but this isn’t one of them. Why shouldn’t herbal medicines be subject to the same rules as, well, real medicines? Herbal medicines are not being banned. And no future regulations will ever affect any remedies that have been proven to be safe and effective. If the medicines are as safe and effective as you say, they’re quite safe forever.

What the status quo represents is a huge loophole for selling dangerous or useless medicines, endangering lives for profit, simply because the remedies are “traditional”.

What we need a huge outrcy against is that quacks are allowed to sell vulnerable people false promises.

Andrew

This is the email I got back:

Dear Andrew,

Thanks for writing in about the EU Herbals campaign.

You may not believe in herbal medicines as a remedy, but that is not what is on trial here, and Avaaz hasn’t endorsed herbals as an alternative or proven from of medication, nor have we said that these products should not be subjected to regulation. What we are calling for is for this Directive to be amended, because it’s heavy-handed regulation that undermines consumer choice and will force small producers out of business.

We have written a more detailed response here: http://www.avaaz.org/en/eu_herbal_response_to_concerns

Avaaz weighs every campaign decision closely. In this instance, we polled a random 10,000 person sample of our EU list, and found that 79% of responders supported the campaign. We also carefully monitor feedback from our members on every issue and this one in particular seems to have drawn a very heated response. Our small team cannot answer every single email we receive, which is why we’ve attempted to answer concerns publicly.

We hope these answers help clarify what we’ve said and why, and that even if you still cannot agree with this campaign, you will continue to support other Avaaz campaigns in the future.

Thanks,

Dominick

I sent this reply:

Okay, but one question:

What I believe is irrelevant. Would you start an email with “herbal remedies do not work, but…”

You say Avaaz hasn’t endorsed herbals as proven medication, but plainly it has: sending out an email to all your subscribers with hyperbolic language like “it’s hard to believe, but if a child is sick, and there is a safe and natural herbal remedy for that illness, as of this week it may be impossible to find that cure” is reckless and irresponsible.

The proposed rules include a generous grandfathering scheme for established traditions, but I just can’t accept that a quack’s right to profit from vulnerable, sick people is important, or that “consumer choice” should include the choice to be conned by them.

I think this sort of thing is always really complicated and reducing it to bans and petitions is more damaging than it is useful.

Andrew

That was a couple of months ago. They haven’t replied, but they did email me asking for my help freeing a lesbian blogger who never existed. I should have asked about that, see if I got a response saying “you may not believe in Amina Abdallah Aral al Omari, but…”

There’s a case to be made that herbal medicine is an area where it’s possible to make an effective product on a small scale even when you haven’t the resources to perform proper trials — but by the same token it’s impossible to know if your product works or not if you haven’t the resources to perform a trial, so it would be a tricky case to present coherently.

Since Avaaz did not bother to explain properly, preferring a tabloidesque “ban this draconian ban” approach, the regulation in question is the European Directive on Traditional Herbal Medicinal Products, and was passed on 30 March 2004. Avaaz (established January 2007) alerted the world to it on 29 April 2011, fully three days before the seven-year grandfathering period ended.

Generally, to be honest, I find the tone of many campaigns annoying: they start with the assumption that I agree with them and then try to spur me into action, and I think they would be more effective if they started with the assumption that I didn’t know or care about the issue in question, inform me, enrage me, and then ask me to help. If nothing else, it would force them to explain their position more fully.

In this case I think it would have undermined their argument a bit had they had to send an email saying “in three days, a ban on unproven and/or dangerous medicines passed in 2004 will come into affect and the quacks who sell it could go out of business”, which is of course exactly why I’d like them to at least draft that email before badgering me with their silly concerns.

https://secure.avaaz.org/en/eu_herbal_medicine_ban/?rc=fb