illuminating science

Some of the hysteric and extreme claims about global warming are also a symptom of pagan emptiness, of Western fear when confronted by the immense and basically uncontrollable forces of nature. Belief in a benign God who is master of the universe has a steadying psychological effect, although it is no guarantee of Utopia, no guarantee that the continuing climate and geographic changes will be benign. In the past pagans sacrificed animals and even humans in vain attempts to placate capricious and cruel gods. Today they demand a reduction in carbon dioxide emissions.

This utter clap-trap is from Cardinal Pell! Or Dr Pell, as he has a PhD. (In Church history.) So naturally, he’s an expert on global warming…In which CO2 reductions are comparable to human sacrifices.

Can people with power (I’m also talking to you, Michael Crichton) please stick to their own areas of expertise? Or at least accurately represent global scientific consensus?

Synopsis: A recent journal article claims (literally) that second guessing ourselves gives better accuracy. I think this is wrong, and that what they’re seeing is just statistics. I’d like some opinions on this!

A recent paper in the journal Psychological Science (and much publicised by The Economist in an easier to digest article) makes some interesting claims. Basically the story goes that if you ask two people to estimate something (like the number of jelly beans in a jar, or the percentage of world airports in the USA) then taking two people’s guesses and averaging them gives you a better estimate than either alone (on average). It’s called the wisdom of crowds; extend it to a hundred people, and up to a point, the group guesses get better.

Fair enough, I could believe this, I think (more specifically, the group will average towards the “group bias”, and you’re assuming this is a “good” guess. I digress…) But the new paper goes one step further: it suggests that even one person can improve their guess by making two guesses and averaging them, improving accuracy by 10 percent. The article’s authors suggest:

Although people assume that their first guess about a matter of fact exhausts the best information available to them, a forced second guess contributes additional information, such that the average of two guesses is better than either guess alone. This observed benefit of averaging multiple responses from the same person suggests that responses made by a subject are sampled from an internal probability distribution, rather than deterministically selected on the basis of all the knowledge a subject has.

Translation: we don’t come up with one best guess straight off; instead, each “guess” comes from a range of possible values our brain has computed. Furthermore, they note that a delay of three weeks between the first and second guess improves the average, presumably by making the guesses more “independent”.

But something about this bugged me, so I did a little computational experiment myself: Generate a random number (between 0.0 and 1000.0, fractions allowed) which is the “right” answer and generate two more random numbers which are my guesses (also between 0.0 and 1000.0). Then, look at the difference between the first guess and the “correct” answer, and between the average of my two guesses and the “correct” answer. Repeat.

So to be clear: I’m randomly choosing the correct answer, and then I’m randomly making two guesses with no information other than a lower and upper bound. This would be perfectly reasonable for questions like the airport percentage above (which was mentioned in the article) where you know the answer is between 0-100. I did 1200 tests (in Excel; it’s not enough for the averages to be absolutely constant, but it doesn’t change the qualitative results.)

The results: On average, the first guess was off by 330 (which I’m sure you could argue theoretically, too). But for the average (mean) of my two guesses, I was only off by 290 - this is a 10% better guess than before! Here’s a summary:

Notice the averages are in about the right place; my data is pretty random, and yet simply taking the average gets me closer.

I’ve also included there the root mean square errors (RMSE), which were discussed in the paper [Disclaimer: I don’t really have a stats background: for the RMSE I took the difference between each guess and the corresponding correct answer, squared each difference and added the results, then averaged this sum and took the square root. I hope that’s right…] Unfortunately, I don’t know exactly the data numbers and ranges used in the article, so I’m not quite sure how to compare them directly, but the percentage changes are what’s important, I think, and they fit nicely with the paper’s predictions (of between 5-15%).

Obviously, I made some assumptions, in particular that no person had the faintest clue what the “right” answer should be. But that’s not ridiculous, and it shouldn’t be hard to redo the data with a normal distribution of guesses around the mean; I’d expect it to give the same result, but the conclusion is now trivial (average two deliberately normally distributed guesses, and you’re going to get closer to the mean, on average ).

I also did a couple of trials where I fixed the “correct answer” to the same thing for every person. If the correct answer was 0 (out of 1000), then, as you’d expect, either a single or an averaged guess both produced the same average deviation, 500. Interestingly, however, their RMSE were quite different, and the averaged guess again produced a 6% better guess by this metric. Same for a guess of 1000. Why? Averaging the two numbers produces a lower standard deviation around the average (500); the RMSE weights big differences more, so the values further away from 0 (or 1000, respectively) contribute much more, even allowing for those corresponding closer values. (Does that make sense?) So RMSE might not be a great measure here.

What about if we take 500 as the average? Then the effect is even more pronounced - the mean guess has a lower standard deviation, is closer to 500 on average, and contributes much more. 250 or 750 were similar, and I’d expect this to be true for the whole range.

In conclusion, I would argue that any benefit seen in this study is simply from statistics, not from some innate feature of our brain’s estimating abilities. The only thing they did get right is that the time delay probably allows the second guess to be more “random” which seems to be useful, on average!

Thoughts? If this makes sense, I’m going to write a rebuttal/similar, but I’d love some feedback first (particularly if I’m completely wrong and/or have missed something obvious!) The preprint article is missing a key figure, but I don’t think I’ve misunderstood or missed anything important (except for their actual data values). All comments welcome!

Addendum: I finally did some simple analytical calculations - when both guesses and the answer are chosen randomly and independently from 0-1000, the RMSE of one guess should be 410, compared to 355 for two averaged guesses, just like the simulations predict! I’ve also checked that the average absolute differences for one guess should be 1000/3, which looks right, but I haven’t yet slogged through the maths for the average guess case (does anyone know a shortcut for analytical expectation values of absolute values?!)

Addendum #2: I’ve now done the RMSE case for the absolute difference (I’m so slow sometimes…)  and I predict 333 for the single guess or 291 for the averaged guess - right on the money! Thanks to Tim for useful comments about triangular probability distributions!

I was reading about the Salvation Army today, and was quite shocked to discover that, in the US at least, religious organisations are exempt from many of the civil rights laws if such laws would violate the “creed” of the religion. In particular, whether religious groups must obey laws preventing discrimination against homosexuals or requiring paying of benefits to same sex partners. This is from an old New York Times article, but still relevant:

There is no federal law barring discrimination against gays and lesbians, and there are provisions in federal law that exempt religious groups from civil rights requirements that violate their creeds. But 12 states and more than 100 cities and counties have laws to protect gays. At issue is whether religious groups administering social programs with public money in those places should be — or are — bound by those laws.

Furthermore, as a religious group, despite being a billion-dollar multinational organisation, the Salvation Army is exempt from various reporting requirements that apply to all other charities.

I’m just sayin’, a rational person looking at these sort of arrangements would really start to question the special status given to religion and religious groups in today’s society. Not that I’m saying there should be religious groups (well, not in this post) but they should have to live by the same laws as everyone else. Surely that’s reasonable?

In other news, Heinz pulled an ad today which showed two men kissing, because:

…viewers complained to the Advertising Standards Authority that it was “offensive” and “inappropriate to see two men kissing”.

Other complaints include that the ad was “unsuitable to be seen by children” and that it raised the difficult problem of parents having to discuss the issue of same-sex relationships with younger viewers.

Gah.

From a really good high school textbook, “New Century Senior Physics”, comes this choice quote on astrology:

Astrology slowly became the mumbo-jumbo side of sky watching, and was relegated to the irratioinal, non-sceintific and hoaxers club together with pyramid poewr, clairvoyance, ESP, water divining, flat earth theory, numerology, faxes from the dead, Feng Shui, Tarot cards, Bermuda Triangle, runes, UFOs, levitation, Philadelphia experiment, faces on the Moon and Elvis sightings, to name just a few.

Astrology has stagnated in the pre-scientific theoryies of thousands of years ago.  It ahas no testable hypotheses, no statistically reliable evidence of past successes, no research program, no predictive power that can be tested by experiment.  Astrologers make many extravagant claims of success bt they have never stood up to rigorous scientific scrutiny.  In short - astrology is an article of faith, of pseudo-scientific hocus-pocus and righly belongs in the comic section of the newspaper.

Awwwwwwesome.

The Australian Medical Association has just released guidelines which define binge drinking as four standard drinks per night.

This is pretty tight - an average bottle of wine is about seven standard drinks, so under the new guidelines, if two of you order a bottle of wine over dinner you are flying awfully close to the sun. (Assuming you are lucky enough to have a partner to share the wine with - otherwise, you’re in real trouble.) And if one of you drinks more than your fair share, then you’re binging.

I’m not certain how to respond to this. I’m not a heavy drinker for the most part, and I do think that many people drink too. (Even without a degree in medicine, it’s hard to imagine that drinking to the point of passing out is good for your body…) But is four drinks (per night) really excessive? I haven’t seen any discussion of the medical reasons (and Wikipedia just talks about bladder ruptures!) There’s nothing in the news stories so far, and I think it’s something that really needs to be put out there. Otherwise, this could run the risk of being portrayed as scare tactics in the media. From the AMA’s national president:

“The definition of binge drinking is something that perhaps hasn’t been brought down to the level of four drinks per night, four standard drinks per night,” she said.

“I think many Australians will be reflecting on their habits at home and wonder whether we are binge drinking on a very regular basis.”

Dr Capolingua says this could make people think twice about how much they are drinking.

The fact that we need to bring drinking to people’s attention isn’t a medical argument. Sure, it worked for me - I don’t think of myself as a heavy drinker, but I would on occasion have four or five drinks over an evening. (”Am I really binge drinking even on that? Yikes!”) But I can’t help but think this weakens the stigma (however slight…) attached to “binge drinking” Similar to something I’ve often seen around roadworks: on a 60k/h road, many people will obey a 40km/hr roadworks sign, but ignore a 20km/hr sign as just too low, and travel at their regular speed!

I’ll be interested to see the commercial media’s response, and the general community feeling. I suspect, though, that it’s not going to do good things for the AMA’s reputation.

Here’s an interesting story about a group of animal rights activists attempting to get a chimpanzee declared a human in an Austrian court of law.

Animal rights activist and teacher Paula Stibbe…wants the chimpanzee, named Matthew Hiasl Pan, declared a person. That way, Stibbe says she can become the primate’s legal guardian if the bankrupt animal sanctuary where Matthew lives closes.

Although this court case is really just an attempt to get around legal obstacles, it does raise a fascinating point, and one which has been around for a while - what is a human? Chimpanzees are the closest relatives of humans, sharing about 94% of our DNA. They can use tools, show altruism, have been taught sign language and been able to communicate, albeit only roughly and with debatable grasp of grammar. Young chimps even outperform college students on memory tests (which I spoke about on the radio recently!)

If you say that a certain level of competency is required, then what about babies, or small children? The next step is usually to talk about potential, in that a baby has potential to become much more, whereas a chimp doesn’t. But what about people with disabilities, particularly severe disabilities? And so on.

There’s the other side too:

If Matthew the chimp were declared a person, scientists foresee it would open a messy can of worms.

“In general, I don’t think that it’s a good idea to grant chimpanzees legal human rights,” [said John Mitani, a primate behavioral ecologist at the University of Michigan] “Chimpanzees are well-known to kill each other. What would we do to perpetrators of those ‘crimes?’”

That’s a neat question. Could a chimp plead diminished responsibility/capacity? But if that will always apply to a chimp, surely they don’t deserve to be classed as human? But what about those humans who do make this defence? And so on.

Very similar arguments come up a lot in spiritual discussions (e.g., whether animals have souls), in making the case for or against abortion, and broader questions of ethics such as euthanasia. It also ties nicely into the broader question of the definition of “life” and “intelligent life” - but that’s for another post!

What do you think? If this were being decided by jury, how would you vote and why? If you were to invite animals into the Human Clan, who would they be? Is the plot of The Bee Movie going to become a reality?!

It was a perfect landing, perfect touchdown and aligned perfectly to maximise the sunlight received by the solar arrays, and on perfectly flat groun (only 1/4 of a degree tilt!).

When the mission commander (I think that was hit title!) was asked by the interview  “Could it have possibly gone any better” he said:
“Not in my wildest dreams. I’m in shock…never even in rehearsal did it go this well.”

“[after] 5 years…it is [such a relief]. … We never knew for sure. We have the best team in the world…I can’t be more proud of them than I am now.”

Peter Smith, the principal investigator, said “I was right to be optimistic. This team performed perfectly. Did you see that thing just zoom down and touch?”

I was only watching and I was tense! Of course, they’re not completely out of the woods - they’ve still got to deploy the various pieces of equipment and sensors, in particular the solar arrays, but the hardest part was a success! We won’t know for about an hour and a half what happens next - so keep checking NASA for updates!

…but there is no way I could handle the stress that these guys are in.  They’re aiming for a tiny spot of just 20km x 60km on a planet that takes 15 minutes for the light to reach us that is shooting around the sun AND rotating. After hitting the atmosphere, they release a parachute to slow down, but then ditch the parachute, dropping at 120mph, before the thrusters fire, lowering the lander to the surface at a gently 5mph. And all this in just 7 minutes.  Worst of all, because it takes the signal 15 minutes to reach Earth, the whole landing will be over before we even hear about it - so everything is automated.

After a 10 month journey, these guys must be really quite stressed! EDL (entry-descent-landing) will be starting soon - connectivity has been established! Go and watch it live!

The Pheonix Mars landing is going to be heading in for a touchdown real soon. The mission scientists have passed up making any corrections to its trajectories tonight, as everything seems to be on course, giving them just one more chance tomorrow to line it up right. A dust storm was over the landing site recently, but should have moved on by the time its due to land. Should be exciting!

You can, I think, watch the landing live by going here and clicking the “SPACE.com’s NASA TV feed” link! It’ll be landing at midnight GMT Sunday, or around 10am Aussie Monday, but stuff will be happening an hour and a half before that! Exciting!

Adding my voice to the masses: Scientolgoy is not a religion - it’s a cult. It was created by - wait for it - science fiction author L. Ron Hubbard. If that’s not enough, a quick read of the Wikipedia article should convince all but the most die hard Tom Cruise fans.

Their heavy handed approach to protesters and critics is infamous, with the most recent event being a teenager charged under the UK Public Order Act which prohibits signs which have representations or words which are threatening, abusive or insulting. His sign? ‘Scientology is not a religion, it is a dangerous cult.’ Fortunately, today the Crown Prosecutors ruled there was no case, and the sign was “not abusive or insulting and there is no offensiveness (as opposed to criticism), neither in the idea expressed nor in the mode of expression.” Thank goodness for that…with the slightly dubious relationship between London police and Scientology, I think this would have been an exceedingly bad piece of PR.

Bottom line? If you know anyone who’s even tempted by Scientology - please try and talk some sense into them, or failing that, give them a few slaps across the head (I’m there’s an exemption in the criminal code, justifiable assault, etc). Perhaps just get them to watch the Chaser segment…the best bits start at one minute in!

Recently, I’ve been pondering dating odds. As you get older, more and more people are in relationships - sure, some fail, but eventually some people get it right and are removed from the dating pool. Does that mean that your chances go down? Or does a smaller pool of singles actually improve your odds?

While I might discuss that deep (and potentially depressing) question another day, it lead to me pondering another question: what fraction of a people are in relationships? In particular, what would a graph of the percentage of people in a relationship at different ages look like? A logical guess might be something like this:

Figure 1

No one dates for ages less than about 10 (I hope!) Then the percentage slowly increases as relationships slowly stick before eventually plateauing out after age 60, say. (Let’s ignore death. For now.)

Thinking more, though, I wondered whether there would be more features to the graph - specific points where the percentage rises faster or slower or where, on average, people are actually breaking up more than they are getting together, so that we would see an actual dip.

I had two ideas: one such time might be after high school - perhaps relationships peak in Year 12 (age 17), then slowly fail as people grow apart, move, go to University, etc. Anecdotal evidence suggests that a lot of high school relationships fail after 5-7 years, which might mean a dip around age 23-25. Secondly, you could conceive a dip at around age 40-50 in the “mid life crisis” phase. A new graph might then look like this:

Figure 2

Of course, it might be that even if these effects were real, they could be too small to notice when averaged over enough people. What I wanted to do was to test this with some real data, which is tricky. The Australian Census records marital status, but only as Single/Married/Divorced (or De Facto through Dwelling information questions). That’s not enough for want I want though.

Then, I stumbled upon a blog post (inspired by yet another post) that looked at the demographics of Facebook members. Turns out, this data is made available to potential advertisers - and so pretending to be interested in advertising my next party to 3 million Australians, I started gathering data about males and females in Australia and their relationship status. I’ll give you the results first, then talk caveats (of which there are many).

I looked up males and females in Australia on 21/05/08, who listed their relationship status as either “Single”, “In a Relationship”, “Engaged” or “Married”. (Anyone who selected nothing or “It’s complicated” are not included; see below for a discussion.) There are markedly more women than men on Facebook:

Figure 3

Yes, I went with the stereotypical colours - don’t hold it against me! There’s a pretty decent sample size up to age 40, and even up to age 50 isn’t bad, so I hoped to be able to pull some decent stats out. To compare ages, I looked at the percentage of men and women at each age listed as in a relationship. Let’s look at the women first:

Figure 4

The shaded red area is the percentage of women who are listed as not single for each age, and the lines show how relationships, engagements and marriages contribute to that. First of all, I was roughly right in my overall shape - it starts at low (though not zero - but we’re starting at age 13!), increases, then roughly plateaus (although you also can’t trust the last 10 years or so: small numbers = large errors).

Also nice is that the peaks in the separate types of relationships are sequential: relationships peak at around 22, engagements at 27 and marriages from 35 onwards. Of course, you can’t naively assume that the individuals of that first relationship peak end up in the marriage column, but it does neatly reflect the different stages of life and love (awwww).

My hoped-for post-high-school dip hasn’t appeared (unless you really squint at the red/blue interface around age 24 - it’s the right spot, but I don’t think it’s a significant feature). But what has appeared is a clear dip around the late-30s, early-40s. Short of doing proper stats, it looks significant, and is much larger than I would have expected. There may be other effects in play, which I’ll discuss below, but perhaps we’re seeing at least a partial effect due to real divorces? Especially if you remember that there’s still a base line increase due to new marriages.

Let’s look at the men quickly before we move on to further discussion:

Figure 5

Again we have roughly the same peaks, and relationships, engagements and marriage are in the right order. Although less pronounced, I think you can see a distinct drop off in marriages (or, at least, of FB members) - worst case it’s roughly flat from age 37-45, which translates to a net divorce rate. (There’s also that tantalising hint of a feature around age 24…nah, surely not…)

It’s also interesting to compare the two:

Figure 6

We see that women are about three years behind men in both total relationships and marriage, so men are probably marrying women around 3 years younger than them (either that, or there’s a few guys who are serious cradle snatcher sand are throwing off the stats!) Oddly, the number of women dating looks larger on these plots - could it be an illusion, caused by scaling things percentage wise? Nope - of those who list their relationships status, 68% of all women are in a relationship, compared only 54% of men. While some of these are going to be same-sex partnerships or marriages, it should affect both about the same (unless I’ve unearthed an incredible statistic and lesbians are far more common than gays!) The answer may lie in those who didn’t list their relationship, as I’ll talk about below.

Oh, and just quickly - Facebook lumps all data for over 65s into the one category (oh, the discrimination!) That means numbers are higher and the data is better, and we see a dramatic drop in marriages and a rise in relationships. If it’s real, then the interpretation of the former is a little morbid. The latter, however, could be sweet - even lifelong bachelors are finding love, if not marriage!

What are some problems with this data? First of all, it’s not a truly random sample: it’s people on Facebook. On the other hand, “everyone’s” on FB these days, so it’s becoming increasingly good. Still, perhaps the people who are joining, particularly older people, are of a particular demographic. Are there alternate interpretations of the data in this light?

For instance, let’s try explaining the marriage dip at age 40: what if more single than married people are joining around that age? Perhaps those who are married and are that age have families that take up their time; they’ll only join when their kids have left home, around age 50-60. Or perhaps singles are lonelier and so are more likely to sign up. I could argue for the opposite too: what if people with kids are actually more likely to join, through kid pressure? Hard to say, but I have to feel that both effects are relatively small, and the drop from 85% in relationships to 75% could be enough to warrant a divorce style explanation.  I’m investigating this further…

Another problem is that not everyone lists their Facebook relationship status. In fact, only about 40% of men and 30% of women who do (I think we can all guess the reason for the latter). Are people more likely to list one type of status over another? If you’re single, you might not want everyone to know. Or maybe you do, hoping to attract attention. Equally, most people in a relationship want to shout it to the world (disgusting, isn’t it?) - but after changing your status back to single for the first time, many people decide to list nothing. And then there’s those who simply have privacy concerns, and don’t make it available. How can we tell? If a higher portion of single/non-single people are hiding it, you’d expect there to be some correlation between those not listing and the relevant status. So let’s see the graph for men (the female version is just scaled):

It’s almost flat, with just a slight increase in privacy levels as people get older, which is probably to be expected. So I can’t for certain say that there’s not a massive number of married people aged between 40-50 hiding in there, but it seems unlikely.

And of course there’s dozens of other possibilities. Some people, particularly girls, list themselves as being married to their best friend. (Dollars to donuts we can actually see that peak around age 13-17 for girls in the graphs above). There might be other reasons why people of a given age and relationship status don’t list it on FB that could skew the results, but hopefully the broad strokes are here. Also, some people don’t make their birth year public - but Facebook still knows it and might include it in the data; I’m not sure.

So, conclusion: we can use Facebook (is there nothing it can’t do?) to investigate relationships through the ages (ha!). The graph looks roughly like you’d expect (or I’d expect; take your pick), with about 80% of people ultimately reporting themselves as being in relationships. Age 40 really does seem to be a bad time for marriages, but apparently at least some of them recover (either that or those 10% give up and never find true love again!) And women are going for the older man, as pop culture would suggest.

I’m currently repeating for the USA with its larger population to see whether the stats look similar, and I’m gathering some Census data on marriage rates to compare all this too. Hopefully over the weekend I’ll post that! Oh, and of course these plots don”t mean that in 20 years time we’ll have the same demographics - I suspect that by the time I’m 40, a lot less people will be marrying. The neat question, however, will be whether that helps or hinders the total relationship percentage! May this post survive until that time for comparison…

I haven’t done thorough stats on this or anything like that, so if anyone wants the data I’ve gathered, drop me a line. Any feedback or suggestions are always welcome!

Like (no doubt) everyone else with even the remotest interest in astronomy, I’ve just got to blog about this: in January, scientists caught a supernova actually exploding! In particular, they caught the initial burst of X-rays as the star blows itself apart, which are emitted hours or even days before the visible brightening of the star that we would normally detect.

What’s most awesome is that this was purely by chance - scientists studying a supernova in another galaxy had their telescopes pointed at just the right spot when it went off. The astronomer, Alicia Soderberg, immediately called up other telescopes around the world. Many of these ditched their planned observations (no doubt to the despair of those astronomers who had patiently waited for their turn at the scope!) and took detailed measurements. We’ve now got the most complete picture of a supernova ever - and who knows what that will lead to once all the data has been analysed!

Head over to <a “http://www.badastronomy.com/bablog/2008/05/21/birth-cry-of-a-supernova/”>Bad Astronomy</a> for a good overview of the whole story!

I was just reading a Facebook post in a Christian group by someone named Billy Joyce. It’s a carbon copy of countless of ignorant people, sadly most of them religious. Here’s what he said:

Recently, astronomers discovered an “old star” (100 billion years old apparently) that was giving birth to “new planets”…this is what a scientist had to say:

“We currently understand planet formation to occur around stars when they are very young…As such, we would never expect a star to undergo planet formation late in its life as the necessary conditions are not present.”

Now a statement like this leads me to believe that their knowledge is only speculation to begin with…obviously the conclusions that they had previously come to were just blown to bits by nature itself. I wonder how many millions of dollars we’ve paid these scientists as a collectivity [sic] to come to the “accurate conclusions” they’ve come to in various fields. And when you look at the overall benefit to mankind in these things, one must wonder just why it’s done at all.

It’s this very thing which drives me crazy - that’s the whole point of science. We don’t know everything, nor do we scientists ever claim to. As countless people before me have said - theories in science are almost always evolving. New observations are either fitted into the existing framework or we develop new theories which do include and explain these observations. Scientists love it when discoveries disprove old theories - it often means there’s a whole new area of science to explore, with who knows what results.

And even then, theories are rarely “blown to bits”. Instead, we realise that our existing theories are only part of the picture. Einstein’s Theory of Relativity didn’t disprove Newton’s theories of motion. Instead, they showed us that Newton’s laws are the “low speed” approximation to a bigger theory. Newton was perfectly right - unless you happen to be going near the speed of light! I’m sure our theories of planet formation will evolve accordingly.

As for “the overall benefit to mankind” - How about antibiotics and the countless other medicines? Chemotherapy? The internet? Solar power? And sure, maybe understanding planet formation doesn’t feed the hungry but it’s part of learning how the universe works, and from that who knows what we’ll discover! (Lasers were initially a scientific novelty - now look at them!) As for evolution - how dramatically did it change our understanding of life on Earth! But Billy, if you’d prefer not to use your internet, TV, car or medicines - feel free!

But this is the sort of thing that religion so often blinds people - the fact that the universe is an amazing, incredible place regardless of whether or not a God exists, and that science is helping us to appreciate and utilise the beauty of it.

Not a loaded question, but pure curiosity: How many lives has the Bible saved over the last 200 years, compared to advances in science over the same period? (And how could you estimate either?)

If you’ve never heard this question, you’re in for an experience. This (along with the Monty Hall problem) has got to be the most controversial problem in physics, ever. Seriously. Check out these discussions. It gets seriously aggressive!

So what gets people so impassioned? Here’s the problem:

A plane is standing on a runway that can move (some sort of conveyor belt). The plane moves in one direction, while the conveyor moves in the opposite direction. This conveyor has a control system that tracks the plane speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction). Can the plane take off?

Or, a better phrasing is this:

A plane is standing on a runway that can move. The plane moves in one direction, while the conveyor moves in the opposite direction at the plane’s take off speed. Can the plane take off?

Stop and think about it. Then, read on

My first answer was…no. My (incorrect!) thinking was that it’s the speed of the air over the plane wings that provides the lift for a plane to fly. Hence if you were on a backwards moving conveyor belt, so that you weren’t moving relative to the air, there would never be any lift no matter how fast you went and you could never take off.

But I “misread” the question - I’m right in part - we’ll all agree that if a plane is not moving relative to the air, then it cannot take off. (It’s the motion of air over the wings that gives it lift.) But what this question is asking is really this: Can a conveyor belt stop a plane from moving and accelerating forwards through the air? Or, another way, can a plane on a conveyor belt move forward through the air, no matter how fast the belt is moving?

The answer is yes - it can and will.

Let’s explain this three times -first, with facts, second with physics, then finally building up a logical argument with more details. I’m using ideas from a variety of sources, including Straight Dope, doesn’t depend on speed, for all intents and purposes.)

So, finally, to our plane. The wheels on a plane are only used for rolling or braking - they’re not “powered” in anyway, just like a rollerblade. Instead, a plane is able to accelerate quite independently of the ground (e.g., in mid air!), by using its engines or a propeller. No matter how fast the conveyor belt is moving, I can use a small amount of my thrust to overcome the friction there (just like the roller blades), and the rest goes into accelerating the plane. That means that the plane can and will start to accelerate forwards, eventually reaching take off speed. Again, in terms of forces, the only forces acting (horizontally) on the plane are the thrust from the engines and a tiny bit of friction from the imperfect wheels. It must move forward, by the laws of physics, and so will take off.

Just remember, that people who say a stationary plane can’t take off are absolutely right! But that’s not the key to this question - it’s whether a moving conveyor belt can stop a plane. And, it turns out, it can’t. This is really tough to get your head around at least in part because the problem is badly worded. Both sides have valid points, you’ve just got to agree on the problem. (In particular, the phrasing that the “belt moves at the same but opposite speed as the plane” - as the plane compared to what? Bad question!)

And the final words, of course, comes from Mythbusters who showed the plane can take off. It’s not a perfect experiment, but the basic idea is correct and shows the correct physics. (A moving tarp is a pretty good approximation to a conveyor belt - even if you can feel the ground through it, that shouldn’t change the friction much! The ground is still “moving”.)

I hope that helps clear things up!

In a recent discussion about education, this YouTube video came up: Math Education: An Inconvenient Truth. It’s a look at some of the curricula used in American schools, and asks the question: what should students be expected to know at the end of Year 5? In particular, should we teach the “standard” methods for doing multiplication and division (the usual multiplication (”carry the 3″ etc) and the usual long division) or are students would be better off learning more “intuitive” methods? In some sense it’s a battle between speed, complexity and understanding.

(At this point, you really should watch the video, but read on regardless!)

The argument (according to the curricula authors) against the tried-and-true methods is that although most of us can “do” them (eventually) it can take a while to learn and not everyone understands why these methods work - the mathematical insight may be lost to the algorithm.

Instead, they suggest using more “intuitive” methods. One option for multiplication is the way most people do maths in their head, except on paper. Using their example, to multiply 26 x 31, you write it as 20×31+5×31+1×31. Then you can quickly work out 10×31=310, and double and halve it to get 20x and 5x. Finally, you add it all together and you’re done. It’s good because it’s very clear what you’re actually doing - what multiplication actually means, something which can easily get obscured in the traditional method. But I would have to think it would also be slower on paper - and probably more prone to making mistakes.

A compromise is the “partial products” method, where you do keep track of what you’re multiplying (e.g., in 26×31 you don’t multiply 2 by 3, but 20 by 30.) Finally, there’s the “lattice method” (which I read about when I was much younger in a fantastic coffee table book “Oddities”), which is very cool from a geek perspective, and useless otherwise.

So what should be taught? Certainly, some of these methods are ridiculous, but the basic idea isn’t. One Big Issue is calculators (I think there’s a whole separate post there). Most mathematicians go apoplectic when this comes up, but I think there’s points on both sides. You could argue, why bother teaching multiplication at all if a calculator can Just Do It? Realistically, I don’t often multiply by hand. Aside from arguments like “you won’t always have a calculator” (which is still important (think shopping!) but I don’t feel key here) in maths you need to develop your skills and, if you like, intuition for how things go together, and how to approach questions. Problems arise when students assume every problem can be solved just by sticking it into the calculator (and this gets “worse” with graphics calculators!) - as soon as a problem is out of the ordinary, I’ve watched students spend more time hunting for a possible equation solver in their calculator than it would have taken to solve by hand!

I can’t provide data, only anecdotes, but I’d think that if you never learned how to multiply, you’d find the more complex skills which build on the basic ideas much harder. And for just the sheer number of times you need to multiply, and for how much of other maths it underlies, it’s just such a valuable skill.

What about intuitive vs algorithmic approaches? I think the word “intuitive” is a bad choice, actually - really what they’re advocating is “guess and check” methods (”10 13’s fit into 200, subtract them off and we’re left with 70. At least one 13 fits in 70, etc) It helps build that deep understanding of how maths works, but I’d argue the method itself really isn’t “intuitive” - just frustrating after you understand the principles. Interestingly, when I tutor I always emphasise understanding rather than doing - but at the same time, I encourage students to follow procedures (e.g., for differentiation) at the expense of quicker “guess and check” shortcuts, because it drastically reduces errors. (Again, another post I think).

Again, I think multiplication is important enough to justify the proper algorithm. Division, though, I’m less certain on. I’ve learned long division, only ever used short division, and even that I use only rarely these days. I’d be tempted to say the guess-and-check understanding of division might be sufficient.

And, of course, all these arguments extend to other areas of school as well. I don’t remember most of what I learned in primary school - names of explorers, poems, etc. But was the “learning how to learn” more important than the content itself? (I generally have little interest in games like Trivial Pursuit, preferring games that require skill than can be developed rather than knowledge that you either have or you don’t. I guess I feel the same about school )

So I ask again, what do you think should be taught in primary school?

So, it’s been quite a while since my last post, partially due to travel, partially due to business, and partially due to rethinking what this blog should really be doing.

I’ve decided that there are already enough people commenting on science, and I can’t really add anything. But more and more, I’m interested in the perception of science, science education and just neat science problems that don’t necessarily have any application but are still cool

So that’s what I’m going to swing this blog towards - and I hope it will be all the more interesting because of it.

So, I’ve jumped on the hot/instant ice bandwagon. This is the stuff that’s found in those instant heat packs - you know, the ones where you click the metal disc inside, and the liquid pad turns solid and heats up. The actual chemical involved is sodium acetate, which apparently is completely non toxic (and is actually used as a food additive!)

The gist is that you can dissolve more of the powder in hot water than in cold (just like dissolving sugar or salt - try dissolving as much as you can in a cup of cold water, then add some more, microwave and stir. It’ll all go in!) Then when it cools down, that extra dissolved powder wants to come out and solidify. But this requires a trigger to get things started - a crystal, a sharp knock, something. That lets you do all sorts of fun things (like the video shown above!) You can see the tower I made in my photo here. (You can also see - a mixture of corn flour and water (which makes a slime like mixture), some out of date eggs which I was trying to crush in my fist (you can’t with one hand), and some cream (which was for cocktails while I worked ) )

Unfortunately, I can’t quite get it right - either I haven’t dissolved enough powder, and the mixture won’t solidify when cooled and triggered. Or, I’ve added too much and it solidifies prematurely. But if at first you don’t succeed, try, try and try again! I’ll post my final recipe when I’m done!

This is faintly creepy - a cat that can predict deaths in a hospital. It’s not quite like a feline Grim (ala Harry Potter) where the cat turns up and they just die - rather that the cat somehow senses when they’re almost ready to go and will curl up with them in bed. Apparently, they now call the patient’s family if the cat starts purring at the door, and it has given some families time to say goodbye they wouldn’t have otherwise had! The most likely explanation is some change in either the scent or sound of the patient (e.g., relaxed breathing) which the cat can detect, but it’s quite fascinating nevertheless.

(Of course, reading it, I couldn’t help but at least consider which way the causality runs here. It’s the old problem - correlation doesn’t imply causation. It could be the cat visits them because he senses they’re dying; but it could also be the cat, for example, aggravates their sinuses and tips them over the edge! I think that’s pretty unlikely though!)

Have you seen the incredible Water Powered Clock? Amazingly, it’s a clock that runs entirely on water! That’s right, just add water - that’s all you need! There’s also a water powered calculator and soon our cars, planes and computers will all run on water! Fantastic!

Not convinced?

I can’t really imagine how water could act as a fuel directly, and their explanation that “The internal converter extracts electrons from the fluid molecules and provides a steady stream of electricity to generate power for the calculator.” is vague to say the least.

I can only assume that it works like an ordinary battery and has something like zinc and copper electrodes that, in the presence of water, are slowly corroding and freeing electrons to power the calculator. If this is the case, the calculator would be powered by nothing more than a built in battery, using water as an electrolyte, and will eventually stop working. You wouldn’t be “extract[ing] electrons from the fluid molecules”, and to say that it is “earth friendly” and “powered by most any liquid” is misleading to say the least, and pseuodoscience at the worst - not at all up to the usual standards of Steve Spangler Science! (Which just has really cool stuff!)

In the interest of upholding my scientific dignity (and when a bit of googling didn’t immediately turn up better explanations) I’ve rattled off an email to Steve Spangler Science, and we’ll see what happens!

My life is over.

The PhDComics guy, George Chan, is coming to Australia in September. And I’m planning to be away, travelling around the Northern Territory doing science shows. I mean, the latter is good, but I’ve been wanting to see him for YEARS! *sigh*

Apparently he’s going to be at UQ on the 20th of September. If you’re a Brisbane person, definitely worth checking out. If you’re in the USA, just invite him!!!