Category Archives: Science

The interesting implications of our theory of gravity…

Cosmology, Mathematics, Physics, Relativity, Science, , , , , , , , , ,

The evidence is now pretty strong that Gravity is just a symptom of ‘curved’ space time.

While it’s cool to have gravity all figured out, like so many matters in science, the answer raises even more interesting questions.

Like what is the nature of the curvature? Well, people (including me) are still trying to figure this out. In the meantime it is a good pastime to pontificate about the implications of curved space time. Here are two of my most recent theories/perspectives…

Perspective 1: Trees and apples switch places…

Each mass has a ‘destined path’, a path it will follow if left to its own devices. Just as Newton suggested in his First Law of Motion, things only change velocity when experiencing a net force.

However, he thought that gravity was a ‘force’ that made apples drop, however, the new theory of gravity suggests the apple was stationary – it was the tree and the meadow that were accelerating (upwards), a result of being pushed by the ground.

It lets us think of falling objects as ‘free from force’, and obeying Newton’s First Law.

Now, switch gears. Think what would happen if you could walk through solid things like walls. You may think it useful, but it would certainly cause some inconvenience, as you would presumable fall through the floor and plunge into the Earth’s molten core. You would fall past the centre and then start slowing; you would then briefly surface on the other side of the Earth, only to fall again. You would thus oscillate on some sort of sine wave. This is your ‘destined path’, the straight line through space time that your mass and location intend for you, where you to follow Newton #1. It is simply all the floor tiles and rocks preventing you from going straight in space-time. You are thus constantly being pushed, and thus curving off that path, thanks to the force of the floor. Lucky thing really.

Perspective 2: Slow time really is a drag…

A gravitational field can also be thought of as a gradient in the speed of time. It is possible (to me at least) that rather than supposing space-time is curved, it may well be that it simply varies in ‘density’. How? Well if time passes at different speeds in different places, that can be thought of as a density difference.

Now, we know that even when standing still, we are still plunging ahead – through space-time – in the direction of time. However,  thanks to Earth’s gravity, time is going slower down at your feet, they are sluggish, stuck in the mud. Now if you have a pair of wheels on a fixed axle, what happens if your right wheel gets stuck in the mud? It slows and you turn to the right… and in the just the same way, your body is trying to ‘turn’ downwards toward your feet – the gravity you feel!

When I first thought of this model, I was smug and pleased with myself. Until I found someone else[1] had already used it to accurately model planetary orbits. Read about it here – they have shown that waves (and therefore particles) will curve for the above reason combined with Fermat’s Principle. Bastards! 😉

 

Refs:

[1] Landau, LD; Lifshitz, EM (1975). The Classical Theory of Fields (Course of Theoretical Physics, Vol. 2) (revised 4th English ed.). New York: Pergamon Press. pp. pp. 299–309. ISBN 978-0-08-018176-9

Winning the toss

Mathematics, Science, Sports, , , , , , ,

WARNING: Please do not even try to read this unless you are cricket fan. If you are not it will only irritate you 😉 thx.

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Test Cricket: Australia vs. South Africa: 6 tosses to ZERO, nada, nought. Time for a change in the rules.

by Jarrod Hart

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Winning the toss in cricket can be a very significant advantage, and lead to unfairness. Let me explain…

Firstly, I am going to admit that I am an avid cricket fan. And being a nerd too, this makes me doubly susceptible to a love affair with sports statistics.

I probably learnt most of my maths skills working out how many runs Graeme Pollock required to improve his season’s average, or calculating the run rate required by Clive Rice’s Transvaal team to win the Benson & Hedges night series final at the Wanderers.

So what is my problem with the toss?

In many sports there are environmental factors that skew the game – the sun shining in your eye when you serve, the dew on the putting green, the wind behind Jonny Wilkinson, and so on.

A cricket pitch is no different. Being composed of sand and grass, it is not wholly predictable – it is also prone to evolve over time.

It can therefore be a big advantage to bat first, or perhaps to bat second. The skilled captain can often tell what the pitch will do from looking at it. To make things fair, a coin toss is used to see who gets to choose who goes first. Fine. Over the course of years, all teams will win some and lose some. However, with test matches taking five days each, the teams only play each other once every few years, so the ‘fairness’ may take a generation to arrive. 

The stats are clear. Winning the toss helps. Get the latest stats from wikipedia; at the time of writing 34.7% of toss winners had won the match. 30.8% of toss losers had won. The remainder draw/tie.

Some people will still say, oh, that’s not too big an effect, less than, say, the home advantage in football. Yes the numbers aren’t too dramatic, but what no-one seems to be pointing out is that that 3.9% difference is actually coming from a somewhat bigger difference in a smaller subset of the matches.

For example, many cricket tests are one-sided. That is to say, the favourite wins. In cricket upsets are fairly rare (rarer than in football for example). Draws yes, but complete reversals are not that common. This means that there have been lots of outclassed teams winning the toss (statistically, even the most outclassed team win the toss half the time). They have of course, mostly lost.

Secondly, there have been matches where the pitch really was constant. That is to say the toss didn’t help.

So we are left only with the matches between evenly matched teams on pitches that change. The 3.9% positive toss effect must be a stronger effect coming from this subset of the results.

I also have anecdotal evidence (all scientists, wince now). I have often watched a match, where the first team has scored 600 of a flat pitch, and then seen the second team face a ball that suddenly stays low or cuts around. We have recently seen some almighty thrashings, some by an innings plus. These by teams that were, just before the match, considered fairly equal.

Now we come to the present time. The #1 and #2 teams in the world have been locked in battle for several months. I am of course referring to the ongoing test series between South Africa and Australia. And Australia have just won their sixth toss in a row. They have won the last three matches, on ‘evolving’ pitches, and of course I am bitter, of course I am looking for excuses. But I am rational enough to see unfairness when it strikes.

I was not going to write about it. I knew it would come over as whining. Until a friend pointed out a simple solution: they could have one toss at the start of the series and then alternate the choices for the remaining tests, thereby preventing one team heaping the unfairness too high.

Today’s sixth win in a row for Australia was too much. We need a change in the rules. The South Africans have lost their #1 ranking to the toss, and it stinks.

The last 6 tests:

Test no. 1899 Toss won by Australia, match by SA (In Australia)

Test no. 1902  Toss won by Australia, match by SA (In Australia)

Test no. 1904  Toss won by Australia, match by Australia  (In Australia)

Test no. 1910 Toss won by Australia,  match by Australia (In SA)

Test no. 1913  Toss won by Australia,  match by Australia (In SA)

Test no. 1916 Yes, Toss won by Australia,  match ongoing (In SA)

Foot-note: Being a cricket stats nerd, it was of course sad news to hear that Bill Frindall, a peerless cricket analyst had died. He acted as the eye of a the nerd-storm that has been raging for years, about which most of the world was blissfully unaware. His death has left us all without bearing, little squalls in the night.  CricInfo is not not quite the same. Yes, it’s rammed full of passionate staff, many of whom are nerds and scholars of the game, but it seems to lack the Frindall touch. I ask you this: who will care about this problem with the toss in this new world order? Bill would have.

The Economics of Advertising Warfare

Economics, Science, The scientific method, , , , ,

Picture the scene. Acme Corp’s toothpaste business AcmeDent is a profitable enterprise; and so is that of their biggest rival Ace.

One day, however, they hire a new marketing and sales manager, let’s call him Bob. He is ambitious and full of ideas – ready to shatter preconceptions, break the mold, think outside of the box, etc, etc.

After a few days in the office he realises that the market is saturated. People are just not going to start brushing at lunchtime. The only thing for it is to increase market share. He calls a team meeting.

“We either have to increase sales or increase our margins. We have already cut ourselves to the bone cost-wise, and increasing price will lose market share. If we cut prices, we lose market share – so it looks like stale-mate.” But Bob, being new, felt this was old fashioned reasoning. Surely we could do something to get market share? “Any ideas?”, he asks.

The room is quiet. No one wants to say anything risky in front of the new boss. Looking around at his team, his eyes settle on Sheila, the head of brand management. “What are you doing to get market share?”

Now Sheila wanted Bob’s job. She’s not is a good mood, but knows to be cautious. “Well Bob, as you will know from the report I prepared for you, our advertising budget is tight; your predecessor seemed to think we just needed to match Ace’s spend.”

“What? Why?!” Bob sits up. He can smell an opportunity.

“Don’t ask me, I asked for more. He was very conservative.” There’s a murmur around the table. They all know Sheila is being polite. Before being headhunted, Bob’s predecessor had a reputation for being tighter than duck’s arse.

A few weeks later, the new ad campaign cranks into life. Bob is surprised by how much it cost, but he knows 10% more market share will make it more than worth while. He starts to study his sales figures with care. Will it work?

The end of the quarter looms. What will the results show? Bob reads the business news – Ace’s chairman has made some comments. They are very critical and accuse Acme of “destroying the market”.

“Ha!” Bob exclaims out loud. Excellent, they are hurting.

The results roll in. They are good. 12% additional market share, mostly taken from Ace. No wonder they’re moaning.

That night, he sees the new TV ad from Ace. He has to admit it’s good.

“Why didn’t we think of that?” he booms to Sheila the next morning. “It’s a great idea.”

Sheila is unruffled. “We did think of it; we just thought it would be too expensive.”

“Hell!”, Bob is on a roll with the benefit of hindsight, “we’ve seen that advertising can gain us market share – of course it’s worth it. What you can do if I double your budget?”

“Well…”

Ace’s campaign works and Acme loses most of their new-found market share. The next month brings Acme’s bigger and better campaign – tying together TV, print, competitions, star endorsements, the whole shebang. Again is works like a charm. Market share is back up.

—

Freshly sun-tanned from two weeks on the Keys, Bob is feeling pretty pleased with himself at the AGM. The CEO will surely make a point of congratulating him on a job well done. He is getting on too, and will surely be eyeing up replacements.

The meeting starts well and soon enough they came to the the financial performance of AcmeDent toothpaste.

“Bob,” the CEO starts, “what the hell is going on here?”

Bob is taken aback by the look of displeasure on the CEO’s face. Oh, well he has a reputation for being grumpy, maybe this is him having a joke. “Well, you see, we have increased market share by 10% this year, our revenues are at an all time high…”. He searched the CEO’s still stony face.

“But what about profits? What are they?”

“Well, you see, this year we made significant investments, so it doesn’t look great, but rest assured, next year…”

“Investments?”

“Yes, we invested in major advertising campaigns…”

The CEO is shaking his head slowly.

Bob is suddenly feeling a nervous. “Well, we had to spend money to get the market share, but now we’ve got it, we will see a profit next year.” That should calm him down.

“But what about Ace’s latest trick? While you were away, they’ve started a new fad amongst teenagers for luminous teeth or something.”

“Well sir, it is a bit of an arms race…”

“A race to where exactly?”, the CEO looks very serious now.

“Well…”

“Bob, can’t you see, they have to match our advertising spend to protect their business. All you’ve done is pissed both company’s profits down the plughole.”

The CEO leans over to his assistant, “How much to get the other guy back?” he whispers.

Gravity explained in 761 words

Cosmology, Education, Mathematics, Physics, Relativity, Science, Science communication, The scientific method, Things Explained, , , , , , , ,

People seem to be harbouring the impression that there is no good theory of Gravity yet. I asked a few friends – most thought Newton had explained it, but couldn’t explain it themselves. This is rather sad, 80-odd years after a darn good theory was proposed.

Of course there is still some controvery and the odd contradiction with other beloved theories, but the heart of the General Theory of Relativity really does a great job of explaining gravity and it is really wonderfully beautiful, and can be roughly explained without recourse to jargon and equations.

This is a theory that’s just so darn elegant, it looks, smells and tastes right – once you get it. Of course, the ‘taste’ of a theory doesn’t hold much water; for a theory to survive it needs to make testable predictions (this one does) and needs to survive all manner of logical challenges (so-far-so-good for this one too).

This is not a theory that needs to remain the exclusive domain of physicists, so for my own personal development as a scientist and writer, I thought I might try an exercise in explaining what gravity is – according to the general theory of relativity.

For some reason, my wife thinks this is strange behaviour!

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The story really got started when Einstien realised that someone in an accelerating  spaceship would experience forces indistinguishable from the gravity felt back on Earth. 

He or she could drop things and they would fall to the floor (assuming the spaceship is accellerating upwards)  just as they would fall on earth.

So perhaps that’s all gravity is… some sort of accelleration? Let’s see.

In the spaceship, it’s clear to us that the objects would appear to fall to the floor, but in reality, it is the floor of the spaceship that is rushing up towards the objects – this explains why things fall at the same speed whether heavy or light, matching Galileo’s own test results when he dropped various things, supposedly from the leaning tower of Pisa. It further implies that things will ‘fall’ even if they have no mass at all… such as light beams.

The thought experiment goes thus: Consider if you had a laser-beam shining across the spaceship control room; it would curve slightly downwards, because the light hitting the opposite wall would have been emitted a little time ago, when the spaceship was a little way back, and going a bit slower (remember, its accellerating).

We know the light is not bending, it is just that the source is accellerating, resulting in a curved beam. Imagine a machine-gun spraying bullets across a field – as you swing the gun back and forth the bullets may form curved streams of bullets, but each individual bullet still goes straight.

So Einstein suggested that perhaps light beams will bend in this same way here on earth under a gravitational field. Now Newton’s theory of gravity says light beams may also bend if they have ‘mass’, but the mass of light is a dodgy concept at best (it has inertia but no rest mass, but that’s a whole different blog posting). Anyway, even it it does have mass, it would bend differently from what Einstien predicted. So the race was on to see how much gravity could bend light…

This bending of light prediction was proven by a fellow called Eddington who showed that during a solar eclipse, light from distant stars was indeed bent as it passed near the sun, and by exactly the predicted angle.

Einstein went further though, suggested that light beams on Earth are, just like on the spaceship, really travelling straight, and only appear to bend, and that this can be so if space-time itself is curved. They are going straight, but in curved space.

We know that the shortest distance between two points is a straight line, but if that line is on a curved surface, supposedly straight lines can do strange things – like looping back on themselves. Think of the equator. This model therefore allows things like planets to travel in straight lines around the sun (yes, you read right).

The model has been tested and shown to work, and gives good predictions for planetary motion.

So what can we take home from all this?

Well mainly, if this model is right, we need to let it sink in that gravity may not be a force at all, but an illusion, like the centrifugal ‘force’ you experience when you drive around a corner.

Secondly, it is an open invitation to think about curved space and its marvellous implications!

Extrapolating your way

Education, In the media, Mathematics, Science, Skepticism, The scientific method, , , , , , , ,

There is a very powerful scientific reasoning tool that I use, that, it occurs to me, I wasn’t actually taught… the simple art of extrapolation.

Most people have a pretty good idea of what extrapolating is – its where you look at a trend and predict what will happen if that trend persists. 

For example, if I said it took me 6 months to save £500, I can use extrapolation to predict how long it will take me to save £2000; its something we do all the time – yesterday I was driving down from Bristol, I could count off the the miles, and knowing the distance, I could predict if I would make it for dinner (I didn’t).

Scientists use this too. A good example is the way we can calculate the temperature of “absolute zero” by looking at the volume of a balloon as you heat it up. If you had a balloon at 25C, and you heat it to about 55C its volume would increase by about 10%. What does that tell us? It tells if we cooled it, it would eventually have no volume – and that this would happen at around -275C (-273.15C actually) – absolute zero.

Of course, the method relies upon assumptions – usually the assumption that the trend will continue in the same way (people often use the term “linear” to represent relationships that form straight lines when plotted on a graph).

What if the relationship is non-linear? For example, if little James is 5 feet tall when he is 10, how tall will he be when he is 20? Clearly he won’t be 10ft tall – that is because the relationship between height and age is “non-linear”.

Most of us are smart enough to extrapolate without knowing the jargon, but when the relationships get complicated a bit of maths and jargon can help.

For example, if we want to examine the population of bacteria in a petri dish, or the spread of a virus (or a rumour) through a population, our mental arithmetic is not always up to it. Luckily, some scientists have realised even these complex affairs have some predictability and although “non-linear”, they can still be modelled – graphs can be plotted and extrapolations made.

If this interests you, I refer you to books on epidemiology; I will move onto another sort of extrapolation – one used to check people’s theories by identifying ‘impossible’ extrapolations.

Let’s say, for example, that the want to predict  how the obesity epidemic will progress in the coming decades. If the media says obesity in a certain group increased from 14-24% between 1994 and 2004, and then goes on to predict that obesity will therefore reach 34% by 2014, does this withstand scrutiny?

Never mind that the definition of obesity may be faulty (BMI), never mind that they are extrapoliting from 2 data points – let’s rather ask if the linear trend is justifiable. This can be done by extrapolating the prediction to try to break it. 

If the model is right, obesity will go on increasing and soon enough 100% (or more!) of the population will be obese. This is clearly wrong – obesity is not likely to get everyone – vast swaths of the population are likely to be immunised to some extent against obesity due to active lifestyles and good dietary educations, or perhaps its in their genes, the lucky things. 

The truth will of course be more complex – the first group to become obese will be the most vulnerable, so an increase from 14-24% may incorporate that group, but each successively 10% will be harder fought.  All this is enough to suggest the predictions made for 2014 are doubtful, and those that go further are downright shameless. But it doesn’t stop them…

I am sure you can think of other suspicious trend-based predictions, like those for peak-oil or global warming. They could do with some improvements, so get to it!

 

The trouble with academia…

Science, ,

I have had enough exposure to scientific academia (6 years full time, and now 6 years as an industrial PhD supervisor) to have seriously lost faith. Some of the issues well put by Jonathan Katz, a physicist in his article Don’t become a scientist.

Perhaps ‘lost faith’ is too kind. “Fed up with”, is perhaps more precise. Perhaps I just want to whine. The complaints I would add to Dr Katz are the following opinions I have come across:

  1. The assumption that unless you are a professor at a tedious university, you have no intellect.
  2. The idea that unless your ideas are published in a the ‘preferred’ peer reviewed journal, they are not worth bothering with.
  3. The idea that research with some practical use is somehow inferior.
  4. The idea that anyone deserves to get public money to ponder their theories without a feeling a gratitude and indeed an obligation to pay this kindness back.

Perhaps I am just envious and wish I was a don at Oxford… 😉

Information: what exactly is it?

Education, Mathematics, Physics, Science, Science communication, Things Explained, ,

I was walking to the tennis courts in Battersea Park a few years back, when I heard something on my Walkman radio. It stuck with me for years, and until tonight I haven’t followed up on it, read about it or written about it. Though I have told everyone at my work, which has resulted, as usual, in groans about how nerdy I am (and genuine amazement at how I could spend valuable time pondering these things).

What I heard was a very short anecdote about someone who wrote a little regarded paper in the 1940’s (see ref below) in which he made an attempt to define a ‘measure’ for information. Although I never read any more about it (until today), what I heard was enough to set me thinking…

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Now, if you know lots about this subject then bear with me. Those readers who don’t know what he came up with: I challenge you to this question:

  • what contains more information, a phone-number, a ringtone or a photo?

Are they even comparable?

Bits & Bytes…

In this computer age, we already have some clues. We know that text doesn’t use up much disk space, and that photos & video can fill up the memory stick much quicker.

But what about ZIP files? These are a hint that file-size is not a very accurate measure of information content.

So what is a megabyte? Is it just so many transistors on a microchip? Happily, its not, its something much more intuitive and satisfying.

Information: what is it?

If you go to Wikipedia and try to look up Information Theory, within a few seconds you are overrun with jargon and difficult concepts like Entropy; I hope to avoid that.

Let’s rather think about 20 questions. 20 Questions is the game where you have 20 questions to home in on the ‘secret’ word/phrase/person/etc. The key, however, is that the questions need to elicit a yes/no response.

To define information simply: the more questions you need in order to identify a ‘piece of information’, the more information content is embodied in that piece of information (and its context).

This helps us to answer questions like: “How much information is in my telephone number?”

Let’s play 20 questions on this one. How would you design your questions? (Let’s assume we know it has 7 digits)

You could attack it digit by digit: “is the first digit ‘0’? Is the first digit ‘1’? Then changing to the next digit when you get a yes. If the number is 7 digits long, this may take up 70 questions (though in fact if you think a little you will never need more than 9 per digit, and on average you’ll only need about 5 per digit – averaging ~35 in total).

But can you do better? What is the optimum strategy?

Well let’s break down the problem. How many questions do we really need per digit?

We know that there are 10 choices. You could take pot luck, and you could get the right number first time, or you might get it the 9th time (if you get it wrong 9 times, you don’t need a 10th question). However, this strategy will need on average 5 questions.

What about the divide and conquer method? Is it less than 5? If yes, you have halved the options from 10 to 5. Is it less than three? Now you have either 2 or 3 options left. So you will need 3 or 4 questions, depending on your luck, to ID the number.

Aside for nerds: Note now that if your number system only allowed 8 options (the so-called octal system), you would always be able to get to the answer in 3. If you had 16 options (hexadecimal), you would always need 4.

For the decimal system, you could do a few hundred random digits, and find out that you need, on average 3.3219… questions. This is the same as asking “how many times do you need to halve the options until no more than one option remains?’

Aside 2 for nerds : The mathematicians amongst you will have spotted that 23.3219 = 10

Now, we could use 4 questions (I don’t know how to ask 0.32 questions) on each of the 7 digits, and get the phone number, and we will have improved from 35 questions (though variable) to a certain 28 questions.

But we could take the entire number with the divide and conquer method. There are 107  (100 million) options (assuming you can have any number of leading zeroes). How many times would you need to halve that?

1. 50 00o 000
2. 25 000 000
3. ….
…
22. 2.38…
23. 1.19…
24. 0.59…

So we only needed 24 questions. Note that calculators (and MS Excel) have a shortcut to calculate this sort of thing: log2(107) = ~23.25…

OK, so we have played 20 questions. Why? How is the number of questions significant? Because it is actually the accepted measure of information content! This is the famous ‘bit‘ of information. Your 7 digit number contains about 24 bits of information!

Epilogue

As you play with concept, you will quickly see that the amount of information in a number (say the number 42), depends hugely on the number of possible numbers the number could have been. If it could have been literally any number (an infinite set) then, technically speaking, it contains infinite information (see, I’ve proven the number 42 is all-knowing!).

But the numbers we use daily all have context, without context they have no practical use. Any system that may, as part of its working, require ‘any’ number from an infinite set would be unworkable, so this doesn’t crop up often.

Computer programmers are constantly under pressure to ‘dimension’ their variables to the smallest size they can get away with. And once a variable is dimensioned, the number of bits available for its storage is set, and it doesn’t matter what number you store in that variable, it will always require all those bits, because it is the number of possibilities that define the information content of a number, not the size of the number itself.

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I hope that was of interest! Please let me know if I’ve made any errors in my analysis – I do tend to write very late at night 😉

References:

1.  Claude Shannon, “A Mathematical Theory of Communication” 1948

Analogies not equations, please!

Education, Mathematics, Physics, Science, Science communication, The scientific method, , ,

Have you ever noticed how equations look far more complicated and hard to understand than the concept they represent?

I sometimes get myself stuck having to read other people’s work (it’s the ‘peer review process’) and when I first read it, I am often utterly confused, like a person stumbling around a dark room they’ve never been in before. However, because I am expected to make intelligible commentary, I soldier on until I understand what is being said.

Once you understand something, it is hard to remember what you felt like before you understood it. How did that equation look the first time you saw it? I have been thinking about this…

Let’s consider ‘equations’ – a common part of many technical documents. I have found that I always overestimate how clever or useful the equations really are when I first see them. So what does this mean?

It means that using equations to help teach people we risk turning them off by giving them the impression that the work is harder than it is.

Let me give an example:

Maxwell’s wave equations. These are considered (rightly) to be an cornerstone of physics, as they model the behaviour of waves in the inter-related electric and magnetic fields. When I first read them, they were ‘greek’ to me, literally. Here’s a small one:

maxwell-faraday-equation

Obviously, you need to know more to understand what they are about. You need to know what each symbol represents – and you need to know what the operators (the × in this case) actually do. For anyone who has not specifically studied maths at university would then need to backtrack quite far, because in this case the ‘×’ is not the ‘×’ most folks know and love, its the ‘cross product’ which applies to vectors. That even leaves most science graduates cold, draining the joy of discovery for a few hours or days while you go away to learn (or remember) what the heck that means.

But is it all worth it? Is the complexity of partial differential equations and matrix multiplication really required in order to understand what the equation is describing?

Of course not!

So why are equations always wheeled out to ‘explain’ phenomena? This is a failure of teaching. Of science communication. Surely concepts can be explained much better by the use of anecdotes, metaphors & illustrations?

Scientists working at the bleeding edge of science have to be very precise in their logic, and when communicating with one another, equations are undoubtedly very efficient ways to describe hypotheses. And so, while they are good ways for experts to relate, they make it harder for newbies to “break in”, and are dreadful teaching tools.

The Maxwell equations really just describe how waves propagate in a medium – and really its just the full 3-d version of waves in a slinky, or ripples in a pond. The equations, while drawing on complex (and difficult) maths, are describing something the human brain already has an intuitive grip on, because we’ve seen it!

I’m not suggesting we could do away with equations – they are valuable in the predictions they make for those who already understand what they represent – I am just suggesting that equations should be de-emphasised, and only dragged out when the student starts to feel the need to describe the phenomenon mathematically.

So my message to all university lecturers and text-book writers is: describe a phenomenon with the use of analogy, please!

Dumbing down?

Education, In the media, Science, , , , , ,

This is my first ever blog post. Ra-ra and all that, let’s get to the subject matter.

Yes, its going to be one of those repositories for all those thoughts I probably vastly overvalue when I first conceive of them. But as I cannot be objective and they may actually serve some purpose, I might as well pop them on-line.

Topic of today? UK exam scores. Why? I just read some other blog on the subject: http://www.badscience.net/2007/08/calling-all-science-teachers/ and have some feelings on the matter.

I am not particularly qualified to comment on the education system, so I beg of you don’t listen to my ‘opinion’, but rather follow my logic…

Many people have suggested, and most recently in the public eye, Dr Goldacre in his excellent book “bad science”, that exam standards may be dropping in the UK.

I’d like to analyse this statement for the general case (i.e. any population of which a subset write an annual exam in which the questions do not repeat). Let’s try to frame the question of their ease in a less emotive logical statement…

Let’s say we have data that show the pass rate is gradually moving up year-on-year.

This must mean that one or more of the following is true:
i) the population is getting genetically smarter
ii) the population is increasing well prepared by its environment (parents, teachers, peers, the internet, etc.)
iii) the subset of people in doing the test has changed
iv) the questions are becoming better correlated to what people know
v) or last, the test questions are getting gradually ‘easier’ (or the marking more generous)

There may be more, but don’t want the extreme complexity to cloud my (eventual) point.

Now each of these statements is hard to prove without more data – and the only data we seem to have is the test scores (although we do have the tests themselves which may prove useful).

It may well be that people are getting smarter – but we might use some science to tackle that – for example you could argue that evolution cannot work this fast (and I personally doubt that nerdyness is particularly good survival and seduction tool).

But the environment is certainly changing, the subset doing the tests may be drifting, schooling techniques are being constantly refined and the correlation between what’s interesting (celebrities, MMR vaccines) and what’s examined is also hard to pin down.

I would say there is more than enough vagueness to ensure that no-one, no matter how well qualified, could answer the question “are we dumbing down” with any conviction.

However, there is a “but”.

The examiners can set the difficulty of each fresh test to be whatever they want (in theory). They could make it easy and let everyone get A’s, or they could make them so hard that only the brightest “X” percent get an A. Yet what we see, year on year, are slight improvements.

There are (at least) two hypotheses as to what the examiners are doing:
a) they are aiming to make the questions identical in difficulty to the last year, despite the full knowledge that this strategy has, to date, resulted in a gradual trend toward better marks.
b) they are deliberately aiming to get just slightly better results than last year due to some “incentive”

As the examiners for all the subjects are probably a fairly independently minded bunch and as there is no evidence for it, there are good reasons to doubt the latter hypothesis. Occam’s razor would surely favour the former, though we can’t be sure.

So where does that leave us?

We can’t suddenly make the tests harder, thus lowering the number of A grades to what they were years back – that would be unfair, and would mean that future young people will actually have to know more and work harder than their colleagues from the present time to get an A.

Why not simply rank the scores, then place predetermined fractions into each grade? This, incidentally, is what (I believe) was done when I went to school, which was essential as we had several different regional exam boards with different exams, so rankings rather than absolute results were felt more comparable. Isn’t this how IQ tests scores work? This would mean, incidentally, that by definition, exam/IQ scores for a population simply couldn’t increase with time.

Perhaps most attractive is the option to leave things as they are in the UK, and ignore the media circus. After all, what does their opinion matter?