Tag Archives: hypothesis

Evolution in the toilet bowl

No, this blog is not about how evolution theory is going down the toilet, crushed in the cold grip of reason by The Discovery Institute.

This blog is about how toilet bowls can be used to show speciation forces at work [speciation – the birth of new species].

You see, I have just recently moved to the US, and have noticed the toilets here exhibit characteristics different to their UK and European cousins. Most specifically, US toilets are filled far higher with water and the water surface is greatly increased in diameter. Furthermore, the flush-handles in the US are more often on the left, rather than on the right as they are in the UK.

How can it be in such a small and networked world, such a speciation could occur and indeed survive?


A short stroll on the ‘net does not reveal much about how Americans came to prefer deep water, so I will have a guess. Presumably some big brand (like American Standard) was strongly dominant and the flagship model offered deeper water –  perhaps to prevent skid-marks, or maybe to ensure ‘complete submersion’. As this brand was so strong it was copied, and became the standard. Time passed, and now the average american might turn their nose up at the European low-level option (or indeed the interesting Asian options).

Question: When a European sees an American toilet, are they amazed at its superiority?

No. People don’t like change – and the deep American version is probably not actually any better. For example, the chance of urine splashing on the seat (or on one’s rear for those sitting) is increased, and so therefore, if anything, I would say the ‘deep dish’ is inferior.

So what does this say about evolution? It shows how a contraption, in different environments, will evolve to become different. But more interesting (to me at least) is that Americans and Europeans are not really significantly different and thus the pressures at play were really rather random. It is not as it American toilets have evolved to be stronger because Americans are larger (that would be no surprise) –  this ‘depth’ evolution is different – and very real, but the result of an almost random mutation (of the water depth) that is perhaps not any fitter, just different, and it has survived, despite its weaknesses, due to its isolation across the pond.

What I am saying is that in replicating systems, things will drift apart (there is a natural divergence) on a fast time scale, and the survival of a trait is on a longer time scale. Perhaps in 200 years time we will see no more deep toilets, but right now we have a new species.

Thus I propose you may actually get speciation from drift alone without fitness actually being tested.


So will a device that gently catches one’s emissions and silently whisks them away, instantly, with no splashing, odour, mess or need to flush will supplant the lot? No, because it will probably be expensive, and this cost pressure will always ensure room in the ‘ecosystem’ for multiple solutions – the “two planks over a ditch’ option will always be around because it is so cheap and simple.


Anyway,  next time you go, think about what the toilet might teach us about the subtler aspects of evolution by selection. It’s valuable thinking time after all!  🙂


Epilogue: an aside on valves…

There are obviously several competing technologies for the flush valve, and none has proven clearly superior; so the fact that the US does not (in my short experience) have a very high penetration of the siphon valve (‘claimed’ by Thomas Crapper), does not surprise me. It is indeed much more leak-proof than the popular ‘flapper’ valve, but more complex and thus prone to breakdown. However, the newly popular half-flush siphon valve, which can be easily retrofitted looks to be a clear leap in its evolution. Competition is hot though, and heading to the US, we will wait with bated breath to see which technology wins out 😉

Some references:

http://www.toiletology.com/ – some history

http://en.wikipedia.org/wiki/Thomas_Crapper – the famous inventor of certain improvements

Environmental pressures are a new force in the future evolution of the toilet. First we had the dual flush, now we have the “No Mix” toilet that keeps 1’s and 2’s apart for tailored treatment! http://www.sciencedaily.com/releases/2010/03/100310134258.htm

The Apple Mac: It’s a religion…

It has been explained by writers better than I how our minds are wired in a way that makes them vulnerable to religion.

Whether it is our desire to feel secure or have simple and complete explanations for natural phenomena or simply because we enjoy the social scene at church, there is no doubting the power of the effect. Even in modern times, entire lives, indeed entire civilizations are devoted to the superstitious concept of supernatural Gods.

Although L. Ron Hubbard may have started a religion while knowing it was all a sham, most religions did not need such deliberate action. Our innate need to have faith in things has allowed religious concepts to emerge and evolve freely in our communities as far back as records go.

So why do I bring that up?

It occurred to me today while pondering why people are so defensive about Apple Mac computers – I realised that their behaviour had much in common with religious ‘zeal’.

Then it occurred to me how much the success of Apple relies on perception and conception. If it was just about getting the fastest computer, you would not buy a Mac. If it was about buying something that has wide compatibility, you would not buy a Mac. If it was about cost, you certainly would not buy a Mac.

Some might argue that Macs are more intuitive and ‘easy to use’. These are people whose idea of computing is buying a shiny box, plugging it in and doing exactly what they are expected to do. They are people who just accept it when they are told they need to buy a new printer. Or worse, they blame the printer – what a crappy printer, not compatible! These are people who do not need to set up a complex network, or run a database server.

Anyone who has a Powerbook G4 that cost several grand and is not actually compatible with the latest OSX release, yet needs that OSX release in order to actually work, and still hugs and caresses the machine as it it were a newborn baby while defending its honour and wanting to spend another several grand on a newer shinier one, is, in my opinion, dabbling in a cult.

OK, before you write me off as some sort of anti-mac fanatic, I will admit they are beautiful.

Moving swiftly on, I think it is worth analysing Apple’s success.

How does a company that controls the details of their products so completely compete with a product (the PC) that is made by hundreds of companies all constantly competing, innovating, coming and going, rising and falling? The modular design of the PC allows almost anyone to buy all the bits and assemble the machine themselves; with so many companies making monitors and keyboards and hard drives, some will make bad (fatal) decisions and die, some will make good decisions and thrive and if there are enough upstarts to keep up the supply, the consumer will only ever see the winners, even if their victory was a flook, it was a victory none the less.

You could say that PC is the computer you get from natural selection (survival of the fittest), the Mac is the the computer you get when you try to control the evolution (unnatural selection).

Now a company that tries to make everything itself can capture the value chain, sure, but as it is only one company, it cannot make even one fatal decision, and thus needs to be a little more cautious. This means it is doomed to always lag slightly on the performance vs value curve – so what does it do?

Easy, get the consumer to accept poor value. Make up for performance by buying in high quality technologies (lcd screens, hard disks, etc), and make the customer pay the premium. Then focus on marketing.

Marketing is the art of making people want something. It is unnecessary for products people need.

So what happened at Apple?

Apple, perhaps by good luck, became perceived as a David vs the Goliaths of IBM and Microsoft. For some reason (was it deliberate?) Apple computers gained traction in music recording and graphic design, and gained a sort of bohemian chic that is rather impressive considering that it is essentially “Big Business” and, like most companies, designed to make money.

Clever partnerships, and particularly the inspired partnership with Adobe (think Acrobat PDF’s, think PhotoShop) strengthened their position with journalists, publishers and illustrators establishing the Mac as the creative profession’s computer of choice.

This turned out to be a good thing, as the naughties have been the most art friendly decade yet, as popular culture has come to resent things like ‘work’ and ‘industry’, and a certain sections of society have come to view activities like sport as trivial and meaningless when compared to the value and depth in culture, poetry, good food, yoga, spiritualism and so on.

In other words, the artists have moved up in the world.

Some of the more switched on folk will realise that brands like Gucci/Armani/Christian Dior or Ferrari/Porche/Aston Martin  or Rolex/Michel Herbelin/Patek Philippe are based entirely on massaging the egos of their customers, and in the last case, they probably don’t even keep better time than a black plastic Casio.

But not many of the arty crowd have realised that Apple is using their independent nature against them. The Mac user seems to be infected with the idea that in using a Mac they are somehow being beneficent to the world, will somehow be more creative, they they are part of some loving brotherhood that has exclusive access to the truth and the light.

This is because, by accident or design, the Apple brand has been developed to find that part of our mind that wants to believe and wants to belong, and is easily dazzled; the brand is acting like a religion.


Apple’s alliance with artists continues with U2 and the Black Eyes Peas, both highly credible symbols of free-thinking modernism. But I want you to ask yourself: what is free thinking about this computer company? I’m not sure, but I suspect the only free-thinking thing about Apple is its association with icons of the free-thinking world. It is just an electronics company for Pete’s sake. Like Sony, like Samsung, like Nokia.

If you believe there is any more to it than that, then you are welcome to pay for it.


PS: Besides the defunct G4 in the drawer, there is also an iPod classic in my home. I like it. I like to hold it. Mmm.

Is the Earth like a fractal?

Have you ever spent any time looking at the Mandelbrot set? I don’t mean a cursory glance, I mean really contemplated it?

Mandelbrot set

The Mandelbrot set. The horizontal axis is the number line,

And I don’t even mean the fancy coloured versions, just the straight black-and-white one (see image on right)?

It is really far more interesting than it looks…


At first glance it just looks like a prickly pear gone wrong, so what is so interesting?

Well, remember this graph shows a set, that is to say it divides numbers into two groups, those inside the set, and those outside.

You could easily create such a set with circle – you can define the co-ordinates inside the circle is ‘in’ the set and that which is outside the circle outside the set. Such a set can be defined in a sentence: it is all points c less than the distance r from the origin.

The Mandelbrot set is just the same – a shape that divides space into two regions – in the image, the black area shows the numbers in the set, and the white area show the numbers out of the set. The only difference from a circle is that the Mandelbrot shape is more wiggly.

It equation is not much longer to define:

It is all numbers c, where if you square the number, then add the number, then square the result and add the number again, then repeat, it does not tend to infinity.

So zero is in the set, if you square it, then add it, it is still zero.

How about 1? No, it will run off: 1,2,3, 4, …

-1, on the other hand, squared, is 1, then added, goes to zero, where it will get stuck: -1, 0,0,0…

Figuring out the contents of the set is however complicated. Bloody complicated. Infinitely complicated in fact, and one of the marvels of the mathematical world.

To get a feeling exactly how complex this set is, take a look at some animations in which you zoom in on the perimeter; you can google “fractal dive” for more…

Mandelbrot Zoom Animation

You can choose what part of the set to zoom into yourself, if you want, here: http://www.h-schmidt.net/MandelApplet/mandelapplet.html

It seems that one simple sentence has been able to define an infinitely complex boundary, and begs some interesting questions: have we created a sort of universe? What is the information content of this set?

It makes my head hurt.


The area of specific interest to me, is the relationship between the platonic ‘world of maths’ and the real world; so are there parallels between such complexity in the world of numbers and the real world?

Clearly fractals sometimes have similarity to things in the real world – such as crystals, feathers and broccoli florets. We see many reminders of complex structure in the real world, and it brings me to think of the earth as a sort of giant 3-d fractal – where the solid matter is ‘in the set’ and the gas of the atmosphere and the vacuum of space is “out of the set”.

We can see that the interface, the earth’s surface, also has complex structure, including such things as crystal caves or the lining of your lungs – and like with the Mandelbrot, we also seem able to zoom in to many levels.

However, just as there are no perfect spheres in the real world, there are no perfect fractals, and it seems that the structure falls apart once we get to subatomic levels of zoom (or does it?)

Some part’s of the earth’s interface are fractal-like due to the iterative nature of their construction (tree growth, crystal growth, sea-shells, etc.), and you can see that a simple rule of “branching” in a plant can make a complex shape. However, some of the complexity, specifically organic and bio-chemistry, still seem different (to me anyway).


Krzysztof Marczak Mandelbulb

Krzysztof Marczak's Mandelbulb rendering

Now it turns out that my idea of the earth as a fractal with its skin as a complex interface can be more closely matched to the newly invented (discovered?) “Mandelbulb”, the amazing 3-d set. The interesting story of their development is told by one of their key developers, Daniel White, here.

The Mandelbulb is amazing because, as with many other fractals, you can zoom in and see ever more fascinating detail, and with incredible variation, and if you zoom into it continuously it would not be unlike zooming in on planet earth using Google Earth.

This excellent video below shows the idea of zooming into the Earth off well  (it seems to be derived from a book I happen to have called “Powers of Ten“).

So of course, you can do a similar trick on the Mandelbulb:

Enough said!

The Statistics of Fear

By all rights we should be rather scared of cars. We should regard them in much the same way we would regard a tarantula on the bedsheets or a short stroll on a tightrope. Yet we aren’t. Curious. Cars kill far more people than lava flows, piranhas or anthrax.

Perhaps they are too new for evolution to equip us?

Now if we look into the stats you realise we should be even more terrified of crap food, and the word “sedentary” should be a glare-inducing swear-word. If our bodies knew what was good for them, we would get grouchy after a day without a vigorous walk, and start shaking weakly after two. Sugar, so long sweet, should soon evolve to be utterly disgusting. Not soon enough for some.

Unproven medicine : an alternative name for alternative medicine

“Alternative and complimentary therapies”. They sound so nice. So warm and fuzzy. Surely they augment the cold clinical scientific approach to regular medicine, and have a more holistic approach catering to the soul and spirit as well as the flesh?

I argue not. Hear out my logic…

Any treatment that has proven to provide reliable benefit, is automatically added to the canon of ‘western’ medicine. Therefore the only treatments left available for ‘alternative’ to claim, are those that are unproven, or worse, treatments known to be actively harmful.

Promoters of alternative medicine will argue that western medicine is still woefully weak, and not tuned into holistic and spiritual matters and that such things defy proof. This is clearly claptrap. If you do a well designed double-blind, placebo-controlled test of an ‘alternative therapy’ and the outcomes are no better than for the placebo, then the participants who got the treatment are no better off, spirit or no spirit.

I personally prefer the sort of benefits that can be detected!

How did this situation come to pass, where unproven medications have such a grip?

I think there are three main ingredients:

  1. People make money from other people’s fear (in both western and alternative medicine) and that causes folks on both sides to hide or twist the facts – and also erodes the public’s trust.
  2. The fact that complimentary medicines do actually offer benefits – the well-known benefit of care and attention and also the benefit of the placebo effect – muddies the waters.
  3. It is however the human weakness of putting far too much value on anecdotal evidence that assures the future of unproven medicine.

I think that people who understand this do a disservice to our communities by giving this bad medicine the label ‘alternative’ or ‘complimentary’, so I would like to propose the term ‘unproven medicine’. I would however welcome some more lyrical suggestions!

The interesting implications of our theory of gravity…

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! 😉



[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

Race track pondering…

I have not personally ever raced cars. Of course I fancy my driving skills, and, like most people, am sure I am better than average, but only half of us can be right…

But watching the Shanghai Grand Prix this morning, I had a thought. Now this thought may be well known to race drivers the world over, but in all my years of listening to Murray Walker and his colleagues I never heard them discussing this. So perhaps the thought is highly original and clever. Or perhaps its thoroughly wrong!

So this is it: the racetrack can be divided into two parts, the parts that are engine (acceleration) limited (i.e. where the pedal is to the metal) and parts that are ‘grip’ limited (accelerating/braking or lateral/turning or a combination thereof).

I spent the afternoon playing with the kids, but when I should have been preparing to catch one or other at the end of a death defying flying fox manoeuvre, I found myself trying to think of exceptions to my hypothesis.

What about the approach to a corner, before you start turning, I thought? When driving round town, I commonly coast into corners with my foot off the pedal, and no G-forces to speak of. But then in a race, would you coast, even for a moment?

I think not, you would keep your foot flat until the last second then hit the brakes, with ‘coasting’ only lasting as long as it takes to move your foot 6 inches.

So ‘late braking’ is not just braking late, it’s pushing at the boundary that exists between two parts of the track.

This concept should let driver know when to just put the foot flat (and relax!) because the engine limited boundary is fairly safe – it simply can’t be exceeded, whereas the grip limit, if exceeded, will end badly. 

It should also guide the racetrack designer, they know grip limited sections are more stressful, and that the transitions from one limit to the other are ‘interesting’. 

Now, half way though the movie version of Roald Dahl’s “The Witches”, I realised my hypothesis needed a big tweak. Racetracks also have bumps, debris, oil slicks and sometimes rain. Not to mention, those other pesky cars. These all mean either limit could suddenly apply at almost any time, any place on the track. So the division of the track would never be precise, only a guideline.

However, I restate the hypothesis: one limit should always apply, if it doesn’t, you could be going faster…

Someone please shoot his down..

The scientific method defined (well hypothesised at any rate)

I recently realised that the jury is out on exactly what science and the scientific method are (or should be, at least).

Some would say that science is the endeavour to understand the world, answer the “how” behind the ocean tides, rainbows or seed germination. So the scientific method is any way we might do this. Sounds reasonable to me.

However, some would say that science is the business of ‘facts’ or ‘truth’ and proofs. We do experiments to ‘prove’ our hypothesis. This is the definition I would like to take issue with.

Theories and facts confused…

I get really agitated when I hear people say that evolution is a ‘fact’. Not because I’m a  nutty young earth creationist (I’m not), because no-one has yet furnished a proof. But, you may argue, there’s loads of evidence, its clearly a fact.

But evidence is not the same as proof.

Even if something is 99.999% sure, it is still not sure.

I think the trouble comes because people are never taught that those ‘theorems’ and ‘proofs’ they learned in maths class are not quite the same as the theories and evidence in the scientific method.

So is maths a science? Well, yes, sort of. But while it can deal with real things, like counting sheep, it actually deals with a sort of imaginary world (the so-called Platonic ‘world of ideas’). The whole of maths is a mental construct with no known (‘proven’) basis is reality. But nonsense, you say, of course there are numbers in the real world! Well so there are, but there are no proofs!

Proofs are only possible is a fully ‘understood’ world, and because the world of maths is underpinned by a set of axioms, it is, more or less, ‘understood’. But the real world in which we live is not like that. We don’t understand how the brain works, we don’t know how many dimensions there are, we don’t even know if there is a god.

So does that mean we don’t know anything? The media (and opponents of science) use this uncertainty to undermine science. “You can’t prove there is no God, because there is!” Hey presto, a proof of God.

No, science and the scientific method doesn’t do proofs and facts. So what does it do?

Let’s consider the old chestnut, evolution. People had a book that explained the marvellous spectrum of life, from the caterpillar to the jellyfish. This was good enough for many years. But some clever folks started to question why God would bother to make different tortoises on different islands, and why He would go to all the trouble of putting dinosaur bones in certain rocks and why he would disguise their uranium-lead isotopes to make them look millions of years old.

So a theory was proposed (Darwin’s natural selection) that explained the incredible story of species and, for good measure, predicted that humans are apes, which went down well in the church.

Since then, loads and loads of observations have been made that confirm the theory (with the odd tweak). Its a theory that would have been easy to disprove. If it was wrong, some animals that couldn’t have logically been explained by the theory would have cropped up. But they haven’t.

But all this evidence is not proof. And the lack of a disproof isn’t a proof.

The same is true for all accepted theories. The sun and the moon are thought to cause the tides. If that a fact?

If you ask a scientist, even a good one, he/she may well say yes, its a fact. Because it is so darn likely to be right. Because there is no good alternative theory. Because non-one is disputing it. Because the maths is just so neat. Because the theory can make predictions. All good reasons to accept a theory. But they do not make it fact.

So we do know ‘stuff’, plenty of stuff, facts to all intents and purposes, but not strictly facts in the sense of logical proof.

So what is the scientific method, then?

Science is the system of theories and hypotheses about the nature of reality that have not yet been disproven and which are ranked by the weight of evidence in their favour.

It is like a model of the world that we are ever refining, chucking out wrong theories, refining the ones that work. The scientific method is that refinement process. Well that is my hypothesis. The truth may be altogether different!