Defending tau

The Daily Mail today has a piece about the proposed alternative to the number pi, tau (τ), equal to 2 x π.*

Basically, the reason we might want to change to tau is simple:

Pi is defined as the circumference of a circle divided by its diameter. We came up with this definition thousands of years ago, before modern geometry had taken off, and it’s a perfectly good number.

However, we now know that the diameter of a circle – the distance all the way across – isn’t really the best way to measure a circle. Instead, it’s better to measure the distance the radius of the circle – the distance from the centre to the edge. For example, if you’re working out a planet’s orbit, the distance from the planet to the Sun (radius) is a nice logical thing to measure, but the distance from the planet to the other side (diameter) of its orbit doesn’t really mean anything important.

Since the radius is half the diameter, circumference divided by radius is twice as big as circumference divided by diameter, which is why tau is twice as big as pi.

The definition of 1 radian. The red line (radius) and blue line (arc length) are the same length. By Stannered, CC-SA-BY-3.0

Tau is also nice because it makes working with angles a bit easier. The most natural way of measuring angles – the way you have to do it if you’re doing maths or physics – is to measure them in radians. The radian is defined in terms of the circle’s radius – one radian is the angle you get if you walk around the circle for a distance of one radius. If you travel 2π radians, you travel a distance which is 2 times pi times the radius, or pi times the diameter; in other words, you travel the length of a full circle, 360°.

However, that 2 in there is a bit of a pain. It basically means that, in physics or maths, whenever you’re dealing with a circle or a wave you get annoying factors of 2 popping up in your equations, and unless you’re very careful, it’s easy to forget a factor here or put an extra one in there, making your sums completely wrong. For example, to switch between ordinary frequency and angular frequency (effectively, switching from revolutions per second to radians per second), you multiply the frequency by 2π. This is a change we need to make a lot when working with waves, and it’s so easy to lose a factor of 2 when you’re working with a bulky equation.

That factor of 2 is only in there in the first place because we made the mistake of basing pi on the diameter instead of the radius. If we replaced pi with tau, 1 circle would be τ radians, and that factor of two would disappear. It wouldn’t be a groundbreaking change, but it would still be quite nice, and it would make the mathematics of circles a bit easier to understand. Of course, the hassle of teaching people to use tau instead of pi is probably greater than the benefits, so its unlikely we’ll ever give up pi.

Unfortunately, the Mail is quoting from a (paywalled) interview in The Times with University of Leeds lecturer Kevin Houston, whose and they seem to cut down what he’s said to just:

‘Mathematicians don’t measure angles in degrees, we measure them in radians, and there are 2pi radians in a circle,’ Dr Houston said.

“That leads to all sorts of unnecessary confusion. If you take a quarter of a circle, it has a quarter of 2pi radians, or half pi. For the number of radians in three quarters of a circle, you have to think about it. It doesn’t come naturally.

‘How much simpler it would be if we just used tau instead of pi,’ Dr Houston added. ‘The circle would have tau radians, a semicircle would have half tau, a quarter of a circle a quarter tau, and so on. You don’t have to think.’

Trimmed like that, it sounds like Houston is only promoting tau because he’s too stupid to work out three quarters of two (his Youtube video, linked by the Mail, explaining the mathematics of tau, shows this is not the case). So perhaps naturally, Daily Mail commenters have leapt at the chance to prove that they’re smarter than a mathematician, because really, what do mathematicians know about mathematics?!

If an ‘A’ level Maths student has trouble with the difference between Tau and Pi, then they should be on another course. Any excuse to dumb down the kids and stop them thinking for themselves!

Alan, Frankfurt, Germany (ex pat)

Right on! How dare we dumb maths down by making it slightly clearer!

‘The circle would have tau radians, a semicircle would have half tau, a quarter of a circle a quarter tau, and so on. You don’t have to think.’ …..It may be appropriate for DM readers who like not to think, but I’m afraid mathematicians do think, and aren’t interested in tau, thank you very much.

rupert, Yors4hire, UK

Except for all the mathematicians and scientists who support tau I daresay because they think.

This tau thing is clearly aimed at mindless rote learners but to those of us who actually understand maths, pi expresses something meaningful which is precisely why we refer to it so much.

Vincent, Glasgow

Pi and tau express more or less the exact same thing – the shape of a circle – tau just expresses it in a slightly more logical way.

As a retired Maths teacher this idea lacks intuitive sense. The whole point of the exercise is to relate the circumference of a circle to its diameter – and the ratio is the irrational number 3.14159… The ratio is NOT 6.whatever! That’s the basic theory. Then there are various formulae needed at basic school level: for example, the area of a circle is pi time radious squared. The new formula would be tau times radius squared divided by four: an extra calculation step. Or the volume of a cone pi r squared h…. and so on. And in times of austerity how many schools could afford a new set of textbooks filled with tau? (And all authored by Leeds people, no doubt!) And then there are the millions of calculators with the pi button built in…. No! This idea is like trying to say that from 2012 we’ll all drive on the right – indeed the idea of tau is worse than that because there are regions of the world already driving on the right….. This is a big UM and No No

Andrew, Cwmbran

No, but the ratio of the circumference of a circle to its radius IS 6.whatever (6.28318… in fact). The fact that the area of the circle becomes a half times tau r squared (0.5 τr² – there’s no dividing by four involved) is one of the downsides to tau, but as Kevin explains in the video, there is a deeper mathematical reason why we would expect that half to be there, so while it’s annoying it does make sense.

This is the way you can waste a lot of time while avoiding doing anything of real interest or value to anyone. What a waste of brain cells!! Is this supported by public funds? There are real problems in the world today that are worthy of serious consideration, but when academics waste their time on things like this, they prove that they have no value to society at large and should be dismissed.

Samuel, Dubuque, Iowa

One mathematician making a 5 minute Youtube video in his spare time? How dare he! He should devote every second of his life to curing cancer!

Big Wow… Is “2pi” the only mathematical innovation Leeds University can come up with, it’s best 21st Century contribution to the advancement of mathematics? Talented Maths kids doing their 5 science A levels must be crossing Leeds off as even a 5th choice.

Russ H, Bucks

Again, this is one guy working in his spare time. This is not the only thing the University of Leeds Maths department does! (Incidentally, 55% of Leeds pure maths research is “world leading” or “internationally excellent”, and a further 40% is “internationally recognised”.)

BUT….e^([pi]i)]=-1 and this does not work for tau. There are uses for Pi beyond circles!

Miles, Australia

(This refers to Euler’s identity, e^πi = -1, which gives us a nice way of representing imaginary numbers using angles. And despite what Miles says, it’s all about circles.)

That’s true, it doesn’t. Instead, e^τi = 1. This is even better than Euler’s original version, since we no longer have that minus sign (and all that minus sign told us is that pi radians = half a circle, something we already know). Quite a few comments are like this – “OH NO EULER’S FORMULA IS BEAUTIFUL, WE CAN’T CHANGE PI COS THAT WILL BREAK IT” – and yet no-one actually bothers working out what it would look like with tau.

Professional jealousy. Eienstein acceepted Pi and I can assure you he was more intelligent than this egghead. This man just wants to make a name for himself. Change all the books indeed. He is “daft” !

Ruckus, myrtle Beach SC (ex pat)

And why do we bother speaking English? If German was good enough for Einstein, it’s good enough for us!

All those comments have been upvoted, by the way, unlike this comment, which currently has a score of -1:

I am in full favour of this proposition. Unfortunately, a large number of these comments seem be be from people with only a basic understanding of mathematics. Using Tau in place of Pi would reduce the need for a constant in a plethora of standard calculations involving circles and spheres, the like of which children will be schooled in. Furthermore, the simplicity of the equations using Tau may increase understanding and encourage children to pursue an interest into further mathematics. From my experience of mathematics lessons, the majority of students didn’t dislike mathematics, but rather found it too complicated to enjoy. Once provided with a topic they were able to grasp, students began to enjoy working the problems. Once children have achieved a satisfactory grasp of simple circle equations, the transition to understanding the calculus is a much easier one. I think that should the readers have been taught using Tau the comments here would be better informed.

Pep, Manchester

Good old Daily Mail comments, eh?

* They claim the idea was invented by Kevin Houston at the University of Leeds. In fact, it’s much older than that – Bob Palais first came up with it in 2001 – and Houston is just promoting it. Also, as a conflict of interest thing, I guess I should point out that Kevin taught me a few years ago, and is a thoroughly nice guy.

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Trivialising domestic abuse, Mail-style

Partner abuse. It’s often a difficult topic to discuss, and the countless factors involved – from victims defending their abusers, to the devastating affect it can have on the children of the families – mean you often have to handle it with utmost sensitivity. Unless you’re the Mail that is!

The Supreme Court ruled that women whose partners shout at them persistently can claim they are effectively ‘homeless’ – and will be entitled to a council house.

In a test case, the judges ruled that Mirhmet Yemshaw was the victim of ‘violence’ at the hands of her husband even though she was never physically attacked.

Her local authority had earlier ruled that she was at low risk of being physically attacked by her partner.

The decision could have wide-ranging implications for councils across the country.

If a couple split and the ‘abused’ partner is shouted at they will potentially be entitled to be handed a new home by their local authority.

First of all, the law in question is gender neutral on this issue – men who are the victims of abuse have exactly the same rights as women to receive council accommodation if they are made homeless.

But look at the Mail‘s wording, and how it uses scare quotes. Yemshaw wasn’t homeless, she was ‘homeless’. She wasn’t a victim of violence, she was a victim of ‘violence’. She wasn’t abused, she was ‘abused’. Time and time again, it’s almost as if the Mail is trying to downplay the abuse, not least by repeatedly characterising this abuse as just “being shouted at”.

Of course, the Mail‘s readers – obsessed as they are with council houses and the people who may or may not deserve them – have picked up on the dog-whistles and run with them, apparently oblivious of the difference between a loveless relationship and an abusive one.

What a joke … This can’t be right ! A horrible nagging mad cow ex-wife used to shout at me all the time. How come she ended up with the house , the contents and most of my wages then? Maybe I should have shouted at her and she could have been given a council house instead.

There’s a lot of “What about the men?” comments too – understandable given that the Mail hints (falsely) that this the law benefits women at the expense of men (and yes, for you concern trolls out there, it also applies to gay couples) – and even more comments from readers who think that the housing system is clogged with women pretending to be abused for a free council house:

Saves going to all that trouble of having a baby, just move in with some poor mug for five minutes then start crying that ‘he shouted at me’ and bingo. Next ruling will probably make the man responsible for paying the rent/bills/council tax. The government have been treating grown people like babies for the last 13 years so I’m not surprised that vast swathes of the population now act like babies. Victim culture is a pathetic selfish ideology that might seem OK to the ‘protected groups’ that can claim compensation for anything but it’s going to end in tears one day

So if you want another house just go down to the local council office and tell your husband / partner has shouted at you. Do these judges live in the real world?

Women who are shouted at by partners should be entitled to council property? Well, Mugs UK, you’d better start building a great deal more council property. I see another clever little scam looming.

SHOUT AT ME!! I WANT A COUNCIL HOUSE!! I never realised it was that easy.

Of course, none of them can say why this system would be any more open to abuse than the current system, or why the risk that some people might try to take advantage of the system automatically means no-one should receive its protection.

Those comments all had dozens of green arrows, by the way, though that’s not to say every top-rated comment is dreadful. I’ll leave you with this comment, from Nina, Suffolk, which has 94 upvotes at time of writing.

A friend of mine recently finally left her husband after suffering years of aggression from him. He never actually hit her but threw things which narrowly missed her making holes in the wall, hit walls & doors with his fists, screamed at her in the steet on a daily basis, screamed at her at home on a several times a day basis, screamed at their friends who dared to point out that his behaviour was unreasonable and never once was prepared to take responsibility for his anger and tried to blame her. When she asked for examples of what she did that upset him so much, he couldn’t give an answer. But it was still all her fault, not his. Thankfully she had her family to go back to in the end but a lot of women aren’t that lucky. What kind of a society do we live in if a woman (or a man) has to actually be physically attacked before they can get help? Surely helping them get out before that happens is better?

Edit: Natalie Dzerins points out that overnight, the Mail has managed to make that headline even worse. How?

Yes is no, hot is cold, Telegraph is a denialist cesspool

Is climate change simply caused by the Sun getting hotter? A scientific paper (paywalled) in Nature this week has looked at this question, measuring the connection between solar activity and warming. The conclusion they came to?

Over the three-year study period, the observed variations in the solar spectrum have caused roughly as much warming of Earth’s surface as have increases in carbon dioxide emissions, says [Professor Joanna] Haigh. But because solar activity is cyclic it should have no long-term impact on climate, regardless of whether similar spectral changes have occurred during previous solar cycles.

“If the climate were affected in the long term, the Sun should have produced a notable cooling in the first half of the twentieth century, which we know it didn’t,” she says.

So in other words, the Sun goes through warmer and cooler phases, but the planet keeps warming even during the cool phases. Interestingly, it turns out to be coolest when it’s most active – apparently because an active Sun uses its energy to make ultraviolet light (the type of light that causes suntans and skin cancer) instead of infrared light (the type of light that carries heat). Yet more proof that climate change is real and man-made.

How does The Telegraph spin it?

An increase in solar activity from the Sun actually cools the Earth, suggests new research that will renew the debate over the science behind climate change.

The research overturns traditional assumptions about the relationship between the sun and global warming.

Focused on a three-year snapshot of time between 2004 and 2007, the findings will be seized upon by those who believe that man’s role in rises in the earth’s temperature has been overstated.

Eventually, when you reach the sixth paragraph the article does eventually explain that “long term analysis suggests it actually provides further evidence that the heating of the planet is more than a natural, cyclical phenomenon“, but only after hinting to people that the data in fact says the very opposite – an interpretation that even the article itself eventually admits is false.

Sure enough, it looks like the vast majority of readers who’ve left comments stopped reading before that sixth paragraph. There were 207 comments on the article at the time of writing – of those whose position I could clearly discern, 101 were denialist while just 17 were from people were from people who’d read to the bottom of the article. A good chunk of the denialist comments seem to be arguing that climate scientists are so stupid that they didn’t realise the Sun existed until just now, and some of the rest are from people who’ve been confused by the article not explaining why a stronger sun is cooler, but among them are some real treats:

Climate change treaties is the start of World Government. After all, this is how the EU started .

A classic example of girly science.

You cant possibly agree with this,its against Marxist New Labour,Green,we hate mankind,and all the rest of those highly esteemed organisations who have spent our money proving we are to blame,you know,evil mankind!

And the most popular comment, with a +99 recommendation rating?

I think Global Warming shit should be really stopped right now. It’s SO annoying to see those politician telling me what to do and what not to do

Of course that doesn’t mean that everyone who read the article came out of it disbelieving in climate change – after all, denialists are more likely to have something to say on the subject than people who believe in climate change – but it’s still depressing. I’m just waiting for the inevitable Delingpole article now; I wonder whether it’ll turn out this study was carried out by the Bilderberg group or the Illuminati.

The Daily Express hates Pepé Le Pew

Three-quarters of French people report some dissatisfaction with their sex lives. How does the Daily Express report on this story? With grace? With sensitivity? With tact?

No, of course not. Instead, it runs with the headline “Frenchmen admit they’re a flop in the bedroom”

FOR A country that prides itself on being a nation of lovers, French egos took a blow ­yesterday when it was revealed that three-quarters of them have miserable sex lives.

I can’t find the survey itself online, but according to the article, the survey in fact found that around a quarter of those polled (men and women, not just men) reported turning down sex because they were stressed or unwell, and half reported they sometimes (but apparently not all the time, or even necessarily often) had “no desire”.* That’s not “Frenchmen are a bad in bed” (sour grapes much, Express?), that’s “French people sometimes experience sexual dysfunction, which is not exactly uncommon among older people in any country”. Pointing and laughing at someone else’s health problems is not funny or dignified.

The comments by the way are classy. There are two on this article:

Nice.

PS. There seems to be some churnalism going on with this story. The Daily Mail‘s article is almost exactly the same as The Telegraph‘s with the last couple of lines of The Daily Express‘s added on at the end. As far as I can tell, the story went Telegraph > Mail > Express.

* Without looking at the survey, I can’t tell whether those groups are mutually exclusive – in other words, whether people can be in both groups or not. If they’re not, then simply adding the quarter to the half to make three quarters is wrong and overstates the problem.

Immigrants and conspiracy theorists

A new antibiotic-resistant bacteria has been found. So far, it’s only infected 37 people, and while it has shown some signs of person-to-person transmission, it’s been detected early and will hopefully be controllable, unlike MRSA.

Fairly pedestrian news so far. But what’s that you say? The resistance gene is believed to have evolved in India?

GOVERNMENT LIES Government up to its old phoney controlled statements why not telli the truth nevermind the cosmetic surgery lies,ITS IMMIGRATION FROM FROM THESE THIRD WORLD COUNTRIES THAT’S THE PROBLEM.stop it now “”””””””””””

The grace of the God particle

The Higgs boson... will probably not look like this.

A BBC article today on the apparent confirmation of the top quark at the LHC, plus a discussion with a friend about about Thursday’s episode of Newsnight (specifically, the part about science funding), got me thinking. Why do we – the public and the media – care so much about the Higgs boson?

There are dozens of proposed but undiscovered particles which physicists are currently searching for, both in the LHC and elsewhere: the graviton, the WIMP, the whole host of supersymmetric partners, perhaps – although rather less likely – even tachyons and strings. In some ways, these are more important than the Higgs – the Higgs boson is a bit of a dead end, scientifically speaking. If we find it, we’ll finish the Standard Model, but it’s unlikely to shed any new light on physics – especially since we’ve spent the last 30-40 years working under the assumption that it does exist anyway.

Mail Male Fail

Since yesterday’s post ended up an epically long graph-on-graph orgy, I’ll try to keep this short and sweet.

The Daily Mail‘s improperly interpreted study today is “Why modest men get the brush-off from women“. The first paragraph sets the tone:

Modest? Shy? Reluctant to tell everyone how brilliant you are? If you’re male, you can probably add ‘single’ to that list.

Now if that isn’t a Nice Guy dogwhistle, I don’t know what is.

Rather confusingly, they give Hugh Grant as an example of the modest man no-one ever wants to date, and Simon Cowell as the super-confident Casanova, which I’m fairly sure undermines their entire argument before the science even starts.

The Sunday Times wants women to be more grateful for their unwanted pregnancies

Today the media has vomited up a delightful little piece of rhetoric, twice by The Sunday Times, once under the title “IVF babies aborted as mothers lose in love” and once as “Scandal of aborted IVF babies“,* along with the The Mail on Sunday parroting the The Times‘s findings under the headline “Dozens of IVF babies aborted ‘after women change their minds about becoming a mother’“.

All the articles are based on the news that 80 abortions per year are carried out to terminate foetuses produced by IVF treatment. That’s the entirety of the factual content of the articles. The statistics that this is based on actually seem to have been released two years ago. Oddly, The Times claims it had to use the Freedom of Information act to prise these data out of the Human Fertility and Embryology Authority (HFEA)’s hands, and the paper carries a snide dig from Dr. Mohamed Taranissi that the HFEA should be “much more open with the data they have” (the paper of course neglects to mention that Taranissi and the HFEA have a somewhat fraught relationship, and that he might not give the most unbiased opinion). In fact, you can download these statistics from the HFEA’s website and have a play with them yourself, although be advised they are in a rather human-unfriendly format.

80 post-IVF abortions, up to half of which are performed on women aged 18-34. Note the use of the word “up to half”, not just “half”. This will be relevant later.

AGW – Astroturfing global warming

Coral islands - another proof of climate change

Two stories on climate change today. Both are fairly depressing, though one at least carries a silver lining. The Times reports on Nasa findings that the year 2009-10 was the hottest on record, while The Daily Mail and The Independent both carry articles about a recent discovery that because coral growth is improved by higher sea levels, islands perched around coral reefs have grown, counteracting the effect of the sea level rise; though given the sustained bleaching and die-off of reefs around the world, it’s difficult to say how long this can go on for.

Still, one article of bad news, one of tentative good news, with one thing in common. They both put forward fairly strong proof that climate change is happening. Not that you’d know this from the comments.