Apathy Sketchpad

On my brother’s wall is a map of Earth with the South Pole at the top. It uses an equal-area projection to show the true relative sizes of, say, Africa and Greenland. It aims to make a point about the more common North-up, Mercator projection. Mercator projection maps enlarge areas near the poles so that shapes are preserved. I like the sentiment but I think switching to an equal area projection and printing it upside-down is a little unimaginative. So I created this:

This is a map of Earth created using a Mercator projection, but with the magnified poles moved to the Atlantic and Pacific oceans. I created it using the Blue Marble map from Wikipedia. The dashed lines are the conventional latitude and longitude lines. You get a much better feel for the shape of Antarctica than normal Mercator maps give you, instead exaggerating Kamchatka.

Because, the Mercator projection doesn’t need to make Africa small and Greenland big. It can do anything you want it to. So for example, here is my little rebellion against Mercator’s underplaying of Africa’s troubles: a Mercator map in which the continent is infinite in area:

I’ve cropped the image here. In principle a Mercator projection can be continued infinitely in the vertical direction, and in this case the ‘north’ pole is in Africa, so the map would be Africa all the way up. The level of detail would, source image notwithstanding, get bigger and bigger until eventually sub-atomic particles started to appear. Theoretically, you could exploit this to produce a map where Britain opened out as Africa has at the top, and extend the map up to include a road map of England, including  a large-scale street map of Manchester, eventually opening out to provide a floor-plan of one particular building, then room, and eventually the layout of one table. This, however, seems like it would be very difficult so I haven’t bothered.

Here’s another Mercator map, this time with the poles near Australia and Africa again:

And here’s one with poles in Asia and South America, creating a world with one central ocean:

Here’s the maths in case you want to make some maps yourself. Feel free to stop reading here if you wrongly find maths boring. I haven’t worried about sign conventions or being especially rigorous, though. It’s just enough to make some nice pictures. I treated the Earth as a sphere of unit radius centred at the origin.

Converting between (x, y) and (latitude, longitude) is fairly trivial if you read Wikipedia, although I did have to kludge the formula a bit for ‘negative’ (south) latitudes. To reorient the map, I converted the latitudes φ and longitudes λ to three-dimensional Cartesian coordinates using the following formulae:

x = cos φ × cos λ
y = cos φ × sin λ
z = sin φ

I’d planned to rotate these and then convert them back into spherical coordinates, but in the event I found it easier to go directly into rotated spherical coordinates. They’re defined by two points, called North Pole N and Greenwich G, each chosen at random from the surface of the sphere, and described by a set of (x, y, z) coordinates. So the new latitude and longitude are given as follows:

φ′ = ½π − cos⁻¹ P⋅N
 = ½π − cos⁻¹ (x x_N + y y_N + z z_N)
λ′ = tan⁻¹ (P⋅G′ ÷ P⋅G″)

where G′ = N × G ÷ |N × G| and G″ = N × G′. Using the cross product this way generates two points on the new equator separated by 90°. In fact the conversion to new-longitude is more complex than this, because you have to mess around with quadrants, but I used the atan2 function to do that for me so I’ve not bothered working out all the steps.

I don’t know if this is the best way of doing this but welcome to stream-of-conciousness mathematics.

NHS Scotland are advertising a job for a ’specialty doctor in homeopathy’, which pays up to £68,638. They are also letting go of hundreds of other staff who have actual jobs. Obviously this is fucking stupid, and so several bloggers have applied for it already, and obviously so have I. You can read their supporting statements at the following URLs, and you can read mine below those links.

• http://xtaldave.wordpress.com/2010/08/14/in-which-i-apply-for-a-job-as-a-homeopath/
• http://sciencedigestive.blogspot.com/2010/08/my-application-for-job-as-homeopath.html
• http://www.dcscience.net/?p=3339
• http://www.realityismyreligion.com/alternative-medicine/i-applied-to-be-a-homeopath

Update: there’s no point us both maintaining a list, so here’s Zeno’s.

Statement in Support of Application – please tell us your personal qualities, skills and attributes, experience and any major achievements and show how they match those needed for this job.

Obviously I’ve got this post pretty well sewn up, but in case I am unavailable you might want to apply here.

You may remember I was fairly unimpressed with the claim that

At exactly 06 mins and 07 seconds after 5 o’clock on Aug 9th 2010, it will be 05:06:07 08/09/10. This won’t happen again until the year 3010.

Well. I’ve just been told

AN INTERESTING FACT ABOUT AUGUST 2010. This August has 5 Sundays, 5 Mondays, 5 Tuesdays, all in one month. It happens once in 823 years.

And while the first claim was mostly unimpressive and only slightly false, this one is just false. Massive, shovel-loads of false. Honestly, this may be the falsest (earnest) statement I’ve read all year.

August contained five Sundays, five Mondays and five Tuesdays in 1999. It will happen again in 2021. Okay, so that’s still quite a while, but I can’t imagine how anyone arrived at the figure of 823 years. August is 31 days long. It necessarily has five of three days of the week in it. Why on Earth would it be these three so rarely? How can people not see how implausible that is? Quite aside from anything else, the calendar loops every 400 years. Nothing could possibly happen every 823 years any more than Wednesday could happen every nine days.

It fascinates me how these stories come around. It’s everywhere. This may be my favourite example, for this paragraph:

In 1187, or 823 years ago, the Gregorian calendar hadn’t existed yet (it was introduced in 1582) so there was no ado about this strange happenstance.

And it’s not just this year. August 2009 (which started on a Saturday) was just as special. It’s beginning to look like 816/823 years just don’t have an August. And look, here’s a version with the ridiculous 05:06:07 08/09/10 ‘fact’ glued onto the bottom. This version (quite aside from trying to credit God with the whole thing)

August 2009 is a unique month which has 5 Sundays and 5 Saturdays.  Experts says to see another month with 5 Sundays and 5 Saturdays, we need to live another 823 years. We are blessed to go through and experience this unique month.  Now we have to wait for generations to see another month with 5 Sundays and 5 Saturdays. Let us thank God for allowing us to see this unique month.

even ignores the Mondays, so this amazing, once-in-823-years freak of nature actually rolls round after only five years. In fact it doesn’t even specify that the month must be August, by which standard it happened again the following January. I especially like the use of the word “experts”, in this case to mean “people who own calendar software”, as if somehow predicting what dates will occur in the future is some kind of complex science that us mere mortals can’t be expected to follow. It’s nice to see that in many of the discussion threads someone eventually does bother to sit in front of Google Calendar and click through checking.

I keep being told people aren’t interested in maths. Clearly they are. This stuff is pure mathematics, and it’s capturing people’s imaginations.

Just a shame it’s total bullshit.

The very worst joke I have ever heard from a professional stand-up comedian is (roughly) as follows:

I don’t trust Barack Obama. Call me paranoid, but the last time a black man with an imperialist agenda had that much military power, it was Darth Vader.

It did raise a laugh from some of the audience, but I’m forced to assume they were drunk because the joke makes no sense. It makes no sense because it relies on the audience subscribing to his somewhat contentious views on Obama’s politics, but mostly because Darth Vader is white. He just dresses in black, as has every US president since forever. Basically the uncontroversial similarities he’s found between Obama and Vader are that they’re both in charge of powerful armies and while that’s a fair reason to be wary of them, it’s not funny and I’m not capable of finding something funny if it relies on me selectively ignoring facts.

In The Salmon of Doubt, Douglas Adams makes much the same argument about the joke “if the black box is so indestructible, why don’t they make the whole plane out of the same stuff”, which he described as “the teller and the audience complacently conspiring together to jeer at someone who knew more than they did”.

No, I like my comedy to be smart, and to mock people who, either through dishonesty or ignorance, promote nonsense. So this sounded fairly good to me:

You have a 0.000043% chance of dying during this show. We can’t tell you what you’ll die FROM. It could be heart attack, shark attack, or insertion of a sharp object into an orifice. But we will make sure you at least die laughing.

Stand up mathematician Matt Parker and comedian Timandra Harkness got sick of reading ill-founded stories about how eating this or doing that was going to add six months to your life span, or halve your risk of dying from something or other. So they got a grant from the UK’s biggest biomedical charity, the Wellcome Trust, to do the research and bring you the most definitive comedy show ever about dying.

But then I noticed one detail: Timandra Harkness. I’ve never seen her perform, but it’s a distinctive name and one I knew I recognised, and I just worked out whence: in 2004 she helped publicise ”the formula for the perfect joke” in order to promote her show. The formula was

x = (fl + n^o) ÷ p

where f is “the funniness of the punchline”, l is “the length of the buildup”, p is “the number of puns”, and just in case this seemed a bit too reasonable, n is “the amount someone falls over” and o is “the ouch factor”. Science often throws up unexpected results, and here we learn that because War and Peace has very high values for both l and n, and a very low p value, it is in fact provably hysterical (although my preferred formula x = f doesn’t throw up this anomaly). This is just an advert posing as bullshit posing as maths posing as science.

I wholeheartedly agree that the simplistic “+6 months” reporting of health stories is annoying and I’d love to see a show that poked fun at it in a clever way, but frankly I don’t for a second believe that Timandra Harkness is the person to do it. Partly this is because once you sell your (and science’s) credibility in this way, I think you forfeit your right to “get sick of reading ill-founded stories about [science]“, but mostly it’s because I agree with Nicholas Parsons that

The formula has obviously been thought up by somebody with no sense of humour.

No, I like my comedy to be by people with a sense of humour.

The Church of England have launched a rather silly new website called sayoneforme.com. The site mostly consists of a big friendly green box into which you type a prayer. Then you click the button underneath, which I swear is marked ‘Amen’. A cynic might (and did) suggest that for all the difference it would make this might simply delete the text and say God’s read it, but instead the prayer is emailed to a selection of bishops who will pass it on to God for you if you’re too lazy to pray manually or if perhaps you don’t know how.

There’s also a page of submitted prayers, so we can find out what Anglicans feel is worthy of God’s time but not theirs. (To be fair, God has more.) There’s also a rather worrying amount of personally identifiable information in these prayers, for example at least one full name alongside a description of the person’s problems, which seems pretty inappropriate to me.

I pray for Andrew – that he may find meaning and purpose in his life, and peace which passes all understanding.

The first thing that struck me as odd was that people pray in text-speak.

i love you jesus
keep me surrounded you
fill me wz ur holy spirit
let me know about you -ur ways -ur service
i need u
i love you jesus

It just seems rude to me. There’s even some all in capitals, as if that will help God hear it.

we pray for simon our vicar on his move. please set us the righr peauson to be our right vicar.

I do get annoyed when I mean to type “R” but instead type “AU”.

World peace is a common theme:

O God almighty I pray for all the countries with wars to settle.

Dear god,

please stop the wars from all around the world and let there be peace. please keep my family and my pets safe.

Dear God

Thank you for life and other people so i can make friends.And thank you for famlies if we didn’t have them i don’t know what will happen and please end war

Amen

Please stop all wars

dear god
please put a end to war
please make us give up somthing for lent
thankyou for making me

I think the biggest prayer was this one, although it is at least helpfully divided up into four sub-tasks for God’s convenience:

Our Lord in Heaven.
Please:
1- Give Peace for all the world.
2- Give health for all sick people.
3- Give work for all jobless people.
4- Let us love you, because you loved us first.

This is how democracy works in the Information Age. I don’t know if God is going to get away with not ending all wars now.

I thought this one especially sweet:

Dear God

Thank you for food. Thank you for animals. Thank you for birds that sing beautifully. I really appreciate all you have given us .

Amen

It reads like they just bumped into God in the office or whatever and it occurred to them they never really said thankyou properly. “Look, God, mate, I know I don’t tell you often but I thought you should know, we all really appreciate the way you created the universe like that. I mean, we use it all the time. Seriously, good work on that one.”

dear lord
sorry for leaving litter on your beautiful earth.

To discover how honest homeopaths are, here is a passage from the Society of Homeopaths’ website, edited for accuracy:

Homeopathy simply explained: What is Homeopathy?

Homeopathy is an effective system of healing which assists the natural tendency of the body to heal itself. It recognises that symptoms of ill health are expressions of disharmony within the whole person and that it is the patient who needs treatment not the disease.

In 1796, a German doctor, Samuel Hahnemann, discovered a different approach to the cure of the sick which he called homeopathy (from the Greek words meaning ’similar suffering’). Like Hippocrates two thousand years earlier, he realised there were two ways of treating ill health: the way of opposites, most commonly used by conventional medicine and the way of similars.

Hahnemann discovered that diluting and succussing (shaking) remedies, which homeopaths call potentisation, not only produced fewer side effects but also produced better results. Homeopathic remedies are drawn from the natural world and prescribed on the principle of treating “like with like” or the way of similars.

How does it work?

Scientists cannot yet explain the precise mechanism of action for homeopathy but there is published evidence of its efficacy. It is believed that homeopathic remedies work by stimulating the body’s own healing abilities and that this stimulus assists your own system to clear itself of any expressions of imbalance. For more details on research evidence, please see the Society’s website at www.homeopathy-soh.org.

That’s not too bad. I’ve crossed out very little by homeopathic dilution standards.

A theme I’ve heard a lot about from alternative medicine types is “choice”. Homeopaths in particular are extremely keen that everyone be given a choice between ‘conventional’ and homeopathic medicine. Choice is, of course, a good thing. People should have a choice wherever possible. But the way alternative medicine practitioners use the word is disingenuous at best.

I’m going to skip over the argument for choice within the NHS, as I think that’s more to do with entitlement issues and the persecution complex fringe groups always adopt when their absurd privileges are taken away — hence every ‘attack on Christianity’ news report you’ve ever read or the endless ‘put the football on the BBC’ petitions on the 10 Downing Street website. The problem with ‘choice’ as an argument for providing alternative remedies is that their practitioners are intent on taking away any choice you may have.

A particularly gutsy Deal Or No Deal contestant may find themselves offered the swap with only the 1p and £250,000 boxes in play. Their dilemma, essentially, is between the prize in box 4 and the prize in box 17. One of them is life-changing money, the other won’t cover their bus fare if they live down the road. If they call it wrong, we wouldn’t incredulously ask them why anyone would want 1p instead of £250,000. They were never given a meaningful choice.

Both extremes of the ‘choice’ argument can agree on one thing: homeopathy and evidence-based medicine do not both work. One of them cures diseases, and the other is a waste of time and money. A patient given a choice between homeopathy and real medicine is in the same position as the Deal Or No Deal contestant above: they want the medicine that will cure their disease, but they don’t know which box it’s in. The patient has no meaningful choice until they’re told which medicine works (at which point they still have no meaningful choice since one option just seems silly).

An uninformed choice is no choice at all, so the people pushing for consumer choice are the skeptics who work to disseminate evidence of efficacy or lack thereof, to expose quacks and to debunk media scare stories. They are giving people the information which enables them to make a choice. Homeopaths are effectively arguing that we are ‘anti-choice’ because we want to give people information that will make the choice so easy it will cease to exist. I think they are anti-choice because they deprive people of information that makes the choice meaningful — and often give out misinformation that makes the answer to their dilemma both obvious and wrong. When they die of a treatable condition, will the homeopath stand up in court and say ‘this is what he chose’?

Nobody is arguing that consumers should have a choice between conventional business deals and Nigerian princes who e-mail them opportunities.