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Humans are the only species that cooks its food.
We’re also the cleverest species on the planet.
These observations prompt some people to ask “Did cooking make us clever or are we clever because we cook?”
You don’t have to be too clever to realise that that’s a spurious coupling of cause and effect.
You could equally well make the observation that we are the only species that wears clothes. Do clothes make us clever?
I’m going to have to be careful here, because I’m sorely tempted to now devise a theory that does indeed link the wearing of clothing with the development of the intellect. However, as I write this I’m wearing a rather uncomfortable shirt that’s stifling my brain’s ability to concentrate, so I won’t bother.
Actually, I probably would argue that wearing clothes helped us to develop our mental capabilities, because clothing helped to put us into a comfortable zone in which we could concentrate on other things than keeping warm.
As a consequence of clothes we didn’t have to spend all of our time huddled over the camp fire anymore.
But then, camp fires were probably very important for the development of our intellects too.
After all, we’re the only species on the planet that uses fire. There must be something in that.
What do we do when we sit in front of a fire? We stare into the flames and get lost in abstract thought. The very immateriality and strangeness of the fire encourages contemplation.
Fires also encourage cooking, which brings me back to where I meant to be at the beginning of this post.
Does cooking (or wearing clothes or using fires for that matter) promote increased intelligence?
We cook and we’re intelligent. Are they linked?
It’d seem that the obvious link would be that cooking provided a simple boost to a process that was under way already. We had to be a bit intelligent to be able to cook in the first place, but then once we’d cracked the whole business of slow roasting (or whatever type of cooking we started with – and I bet it wasn’t boiling because we didn’t have any saucepans or indeed containers of any sort back then) it freed up a lot of time that we could then spend doing other things, like the washing up.
That washing up reference was a joke of course, because as I said there were no pans in those days, just sticks. Which would probably simply been thrown onto the fire to help cook the next course. What we actually did was sit around doing nothing. Which, as you may know, is when people have all their best ideas.
It’s possible however that there may be a stronger link between cooking and intelligence than the straightforward link of cooking making our lifestyles more conducive to thought.
Before the advent of cooking, the human race was intelligent enough to be able to use basic tools and to tame fire (because without either of those there’d be no cooking). That’s quite intelligent, but not intelligent enough to put a space probe into orbit round Saturn. We had to get to that stage though, otherwise we’d have got no further.
Once we’d developed the use of tools something interesting happened to us. The fossil record seems to show that about 300,000 years after the first significant use of tools we’d evolved noticeably larger brains.
It’s postulated that by using tools such as spears and primitive cutting implements our earlier, smaller-brained ancestors could eat more meat. The digestion of meat required less energy than did vegetables, so as a result there was a surplus of energy that was diverted into powering the energy-hungry brain. The appendix shrank and the brain expanded. In modern humans the brain demands about 20-25% of the body’s energy.
There’s also the possibility that meat contains brain-enhancing nutrients that are unavailable in plant matter. There is some evidence, for instance, that the compound known as creatine which is found in animal tissue and is commonly used as a muscle booster by athletes may increase mental ability. It’s the sort of substance that’s nowadays given the name of super food (by food company marketing departments). The name creatine comes from the Greek kreas (flesh) and its similarity to the word creative is purely coincidental, I think, even if the substance does turn out to boost creativity in some way.
In parallel to the development of tools the related acquisition of cooking skills may have had a highly beneficial influence on the brain. It’s possible that cooking, by breaking down the chemical constituents of food, makes digestion easier and more efficient, thus again allowing energy to be diverted away from food processing and into brain-building.
Food for thought indeed.
Raw vegetable food faddists take note.
Part of this post (the second part) is an extract from my book, which you can see at the top of the right hand column. Or here.
This post was prompted by a forthcoming edition of the BBC programme Horizon, Did Cooking Make Us Human?
A book that’s worth reading on the subject of evolution and food is Catching Fire: How Cooking Made Us Human by Richard Wrangham of Harvard University
Take a look at the two photographs above.
The top one shows a word that’s upside down and that’s indented into a surface.
The bottom one shows a word that’s the right way up and that’s raised above the surface.
Okay, I know you’re not stupid. You realise that they are both the same photograph, with the top one upside down. (It’s a detail of a traditional red British post box by the way.)
But you’re not clever enough to see the word on the top photo as being anything other than indented, are you? Even though you know that it’s raised.
The reason for this is quite straightforward. It’s all to do with the lighting. In our everyday world objects are normally lit from above – because the sun shines in the sky and not out of the ground. In the case of the top photograph the lighting effectively comes from below. However, we don’t interpret it like that, due to the simple fact that being lit from below is a very unusual way for objects to be lit. We assume that the light in the photo is coming from above, as usual. In that case, the bright highlights and the shadows on the letters could only be where they are if the surface is indented – so that’s what we interpret it as.
What can we learn from this observation? We learn, amongst other things, that we tend to see what we expect to see. And we learn that we interpret things so that they fit in with our experiences and our expectations. This isn’t such a bad thing quite a lot of the time. In fact it’s a good thing. If we didn’t do it we’d have to go around analysing absolutely everything from first principles as though we’d never experienced anything before. We’d never get anything done. But the tendency can be an impediment when we try to make sense of things that are slightly beyond the realms of normal day to day existence – it has implications beyond such mundane things as upside down photographs.
David Eagleman, a neuroscientist at Baylor College of Medicine, Houston, Texas, has written a book called SUM: Forty Tales from the Afterlives.
It’s a work of fiction, being made up of forty descriptions of alternative versions of the afterlife: all the product of Mr Eagleman’s fertile imagination.
I mention the book partly because it sounds very interesting (I’ll be ordering a copy as soon as I’ve finished writing this article), and partly because it sounds as though it’s got an uncannily similar structure and purpose to a work of fiction that I wrote myself.
The work of mine to which I refer was written in the 1990s, over a dozen years ago. I sent it round to a few literary agents at the time but none of them were interested. Either it wasn’t a very fashionable subject back then - it predates the current explosion in interest in religion and atheism - or it just wasn’t not very good. To this day it remains unpublished. Here’s a (slightly updated) sample from the book so that you can decide on its merits or otherwise for yourself.
The Concept Behind the Book
The premise of the book is the conceit that although the world appears to be becoming an increasingly uniform place in terms of culture, with the mass media disseminating fewer and fewer ideas to more and more people, each community or town on the planet has its own unique belief system and set of myths that are fully functioning just below the surface comformity. These beliefs and myths have been preserved for many hundreds of years, since the time that communities were isolated islands of habitation in a world in which travel was extremely difficult and communication was even harder, allowing each community to develop its own concepts independently and unhindered. They are deeply held convictions that to this day go unnoticed by the casual outside observer (or even by generations of relatively recent incomers to the community).
My book is a portrayal of the hidden belief systems adopted by communities within the British Isles, because that’s where I live and where I have had an opportunity to investigate the phenomenon. Exactly the same hidden belief structure can be found in every community in the world – including your own.
Here’s an example if such a belief.
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Chesterfield
At some unknown time in the depths of the dark ages the people of Chesterfield in Derbyshire conceived a new theory to explain the observation that when an animal dies its flesh decomposes and disappears from its body, leaving only the underlying scaffolding of bones that held the creature together.
They observed that the flesh of a dead animal mysteriously transmuted from solid meat and muscle into a seething mass of wriggling, squirming maggots.
Rather than seeing the maggots as scavengers on the dead flesh, the people decided that they were a new manifestation of the dead creature itself. The creature had metamorphosed into a new form and had been reborn.
The people realised that any rebirth must be a progression, because life is nothing if it isn’t a journey forwards to an unknown but better place.
Thus maggots, being the creatures of rebirth and therefore the next manifestation en route to that better place, must be superior to the creature from which they were born.
Today you’re most likely to see maggots when you come across road kill or when you enter a fishing tackle shop, but in the middle ages, when all death was a closer companion to life, the population were familiar with something else that turned into maggots if it wasn’t buried soon enough.
Human bodies.
The inhabitants of Chesterfield concluded that because a person can transform into maggots after death this must mean that maggots are spiritually superior beings to people.
What’s more, maggots don’t remain maggots for long. In their turn they are transformed into yet another creature – a creature that, because it’s the result of yet another level of rebirth, must be an even higher life form than maggots.
Flies.
If maggots are spiritually one level higher than humans, then it stands to reason that flies must be two. Flies must be truly transcendent beings.
The flies of which I talk are the same flies that buzz around your living room on a hot summer’s day irritating you. They irritate not because they are irritating in themselves, but because you are irritable. Your irritability is a sure sign that you are a lower and less enlightened life form than the flies.
Because the true nature of flies has long been known to the people of Chesterfield, to this day flies are welcomed into people’s homes as honoured quests.
At mealtimes special food is often placed on the dinner table to attract flies to share meals with the inhabitants of a household. (Perhaps the fly that comes to the table today will be the reincarnation of a dear but dead relative.)
It is considered a great privilege indeed if a fly should choose to land on your plate while you’re actually eating from it. The larger the fly the better. Bluebottles are particularly venerated, not only because of their large size but also due to their iridescent colouring which is seen as a sure sign of their transcendent nature.
Should a person be lucky enough to have a fly alight on their own plate of food the fly is allowed to sample the dish at its leisure, coating the food with its digestive secretions as it does so (Flies don’t have mouths, only tubes. In order to ingest nutrients they first have to discharge digestive juices onto the food in order to turn it to a liquid which they can then suck up). Only once the fly has flown away can the person finally take the food into his or her own mouth and eat the freshly consecrated dish.
People in Chesterfield often die of food poisoning, and thus soon turn into flies themselves.
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Links: David Eagleman
In the lecture by Daniel Dennett featured in the previous post there’s a section about recognising language.
He discusses the manner in which we understand language by recognising the discrete packages of sound of which it’s composed.
To illustrate this, Dennett asked the audience to repeat after him an expression: “Mundify the epigastrium.” You may not know what it means, but you can make out the words and you can repeat them back (as the audience did, more or less). This is possible because the words are made up of phonemes (the smallest segments of standardised sound that are put together to form words in any particular language). Dennett then asked the audience to repeat after him a random string of odd sounds. It was impossible. This was because the audience didn’t have “the norms for correction of those sounds.” They just couldn’t get a handle on them.
Another illustration of the phenomenon of recognising the discrete packets of sound that make up words is the process that occurs when you learn a foreign language (Dennett didn’t actually mention this in his lecture - I’m adding it on my own initiative).
Some years ago I started to learn French. At the beginning of the endeavour whenever I heard any French being spoken it sounded like nothing more than a meaningless cascade of undifferentiated sound. How could anyone understand it? Over the years and with increasing familiarity with the sound structure of the language those amorphous sounds gradually crystallised into clearly differentiated words (even though I still don’t understand what half of them mean).
Because of the fact that language is composed of discrete packages of sound it’s possible to compensate for minor inaccuracies in the transmission of those sounds by mentally comparing the perceived sound with the expected, or probable, sound. You put this compensation into action every time you hear someone who has an unfamiliar accent.
The phenomenon occurs when trying to understand the written word too.
Dennett gave an example of this correction in his lecture. Here it is in this illustration.
This is the well known “optical illusion” consisting of the words “THE CAT” with malformed letters H and A.
With its modified H and A this wording looks slightly more like a contrived effect than it actually is. It looks slightly contrived because the letters are printed - and there are no printed letters that look like that H and A.
However, the phenomenon that you are observing - the correction in your head of letters to their proper form - is one that happens every time you read someone’s handwriting. Especially if you’re reading bad handwriting.
Here are the words as handwriting.
The effect is more or less the same. We recognise the intended letters immediately, due to their context, just as we recognise mispronounced or unusually pronounced spoken words due to their context.
But look at the following words. There’s ‘THE CAT’ on the top line - but what’s that word below it?
It’s HAT.
But can you read it as such? Probably not.
The H and the A suddenly start looking worryingly like made up letters. There just isn’t enough context for the H and the A to be interpreted correctly. You probably decide that it’s the word AT with an extra A at the beginning.
Let’s give the word more cues by putting it in the context of a sentence. Here’s the title of a well-known children’s book.
Mmm. It still doesn’t look very convincing. What’s more, I suspect that the confusion over the H and A in HAT is creating a sort of contagion whereby the other Hs and As start to look shaky, but that’s another subject.
So it looks as though there’s a limit to the ratio of properly formed letters and malformed letters beyond which corrective interpretation breaks down.
It’s not simply a matter of the letters having to be framed within words (The H and A in THE CAT each being nicely bracketed by the T & E and C & T). Look at the expression THAT HAT, below.
It’s nonsense.
The problem is probably simply the preponderance of malformed letters. You just can’t get a handle on them. You scan backwards and forwards over the words and you can’t make any order out of them.
Scanning and order - important aspects of the process of understanding written words. But possibly in a more complicated way than you initially assume. To illustrate this, try reading the following sentence.
Algtohuh pcraialclty all of the wdors taht cpoosme tihs stecnene are jebumld you can plrbobay udetanrnsd waht it syas.
It reads: Although practically all of the words that compose this sentence are jumbled you can probably understand what it says.
It’s thought that this interesting phenomenon occurs because you don’t read words from left to right, letter by letter in order, but that you scan the words very rapidly, taking in the whole content at once. I assume that the words also have to be in the context of a meaningful sentence which gives clues as to the probable word that’s intended. I say this because individual words that are jumbled up are just anagrams - and I’m useless at anagrams (or amganars as tehy are smeometis claled). In similar vein, that phrase ’smeometis claled’ doesn’t easily translate into ’sometimes called’ in my opinion - maybe it’s too close to looking like real words itself, so it throws you off.
Here’s a youtube lecture by Daniel Dennett entitled Darwin and the Evolution of “Why?”
Darwin and the Evolution of Why: Daniel Dennett
In my opinion the lecture doesn’t actually explain the reason behind the existence of “Why?” (Why not?), but it’s a very interesting lecture anyway.
The lecture was delivered on October 23rd 2009 in Oslo. It’s approximately an hour long, followed by 30 minutes of questions. Recorded by Richard Norton. The shaky camerawork at the beginning soon settles down.
Daniel C. Dennett is Professor of Philosophy at Tufts University, USA, where he is also the co-director of the Center for Cognitive Studies.
Dennett has authored several bestselling books, including “Darwin’s Dangerous Idea” and “Freedom Evolves”. His most recent book is “Breaking the Spell, Religion as a Natural Phenomenon”.
Last night’s tv featured an episode of the science programme Horizon, entitles Who’s Afraid of a Big Black Hole?
The programme featured a posse of eminent physics brains such as the ubiquitous Michio Kaku (who by the way should really get his hair cut - he’s starting to look far too image conscious) and Lawrence Krauss (featured in my previous post). These big brains were all saying things like “Black holes - weird!” and “Black holes - mind-boggling!”. It was easy to get the impression that the scientists were hamming it up for the cameras to some extent, and that their contributions were then edited to create even more of a Wow! factor. Such is the nature of popular science programmes.
That’s not a problem of course. In fact it’s probably essential in order to grab the attention of the easily distracted amongst the viewing population, which is most of us.
There is a problem with black holes though.
They are indeed weird and mind-boggling.
But then, what isn’t? Everything in the universe is weird and mind-boggling. It’s just because we’re so familiar with some of it, like tables and chairs and trees and rivers, that we don’t notice.
Remember the saying:
“We only tend to think that reality is weird when we contemplate its extremes,
such as the core of the atom
or the edge of the universe.
But the place is actually weird all the way through.”
Whenever black holes are described in the popular press or popular science literature the emphasis is always on their extraordinary gravitational pull (which is created as a result of their stupendous mass - the fact that they consist of the amount of matter in a star compressed to the size of a pinhead, or smaller). This gravitational pull means that anything that gets sucked into a black hole disappears from our universe due to the fact that even light cannot escape from its clutches. Impressive stuff, true. And scary sounding.
(A black hole is created when a star runs out of fuel and stops generating heat. It was this heat that made the star expand into a glowing sphere - once the heat’s gone the force of gravity that holds the star together is the only force at work, and the star is pulled inwards into an ever tighter ball.)
After the programme someone mentioned to me “What I don’t understand is - why doesn’t the whole universe just get sucked into these black holes, they’re so powerful?” A good question, and a quite understandable one due to the huge amount of hyperbole that surrounds black holes.
Here’s my explanation.
When a star collapses from the size of a star to the size of a pinhead the matter in it becomes compressed and more concentrated (to put it mildly). It doesn’t gain any mass.
For instance, look at the sun. The sun has a mass of 2 nonillion kilograms (2 followed by thirty zeros kilograms). If the sun were to collapse to the size of a pinhead that pinhead would also have a mass of 2 nonillion kilograms.
To take a more earthly example, if you take a big football-sized ball of fluffy cotton wool and scrunch it up so that it’s a dense little golfball size it doesn’t get mysteriously heavier when you scrunch it. It just gets denser, with the strands of cotton wool closer together. So it is with the star that’s compressed to the size of a pinhead. The atoms get closer together (and then the subatomic particles get closer together, and so on).
If the sun were to shrink to the size of a pinhead, and thus become a black hole, what effect would this have on the earth? You may think “Oh my God, we’ll be sucked into it, because that’s what black holes do. We’re all doomed!”
However, you’ve actually got nothing to worry about, you’ll be pleased to hear (For the purposes of this illustration I’m ignoring the inconvenient fact that before the sun can turn into a black hole the earth will inevitably have already been destroyed by other solar activity).
Here’s why there’s nothing to make you lose any sleep.
The earth is in a stable orbit around the sun. The characteristics of this orbit (the distance from the sun: the speed of the orbit) are determined by the gravitational pull of the sun on the earth, which is related to the sun’s mass (2 nonillion kilograms, remember: you don’t have to remember exactly what a nonillion is though). It’s the sun’s mass that’s important, not its size. As long as there’s a 2 nonillion kilogram object at the centre of the solar system we’ll keep orbiting it quite happily. It doesn’t matter whether that object is the size of the sun or the size of a pinhead.
The popular press often gives the impression that once a black hole’s been created it starts hoovering up matter from the rest of the universe willy-nilly, due to its immense gravitational pull, eventually consuming the whole place.
However a black hole doesn’t hoover up the universe any more than a planet hoovers up the universe. Meteors fall to earth never to escape just as objects fall into black holes never to escape. A black hole only hoovers up stuff that’s within its sphere of influence, which is no different to that of the star from which it was formed. To be sucked into a black hole an object has to be quite close to it. If it’s a reasonable distance away from the black hole, the black hole is just like any other massive object as far as its gravitational attraction goes.
Whenever black holes are mentioned there’s almost inevitably a mention of ‘What would happen if you fell into a black hole?’. Well, you’d be annihilated of course. But what do you expect? Remember however that a black hole used to be a star - a large object - that has shrunk to a ridiculously small size. To get close enough to a black hole for it to be a problem for you you’d have to get really close to the black hole - closer to it than the original radius of the star from which it was formed. If the black hole were still a star rather than a black hole you’d be inside the star, so you’d be annihilated anyway. Which is worse? Being pulled apart by the gravity of a black hole or being fried by the heat of a star? But do we worry about being annihilated by stars? Not really. They’re just too familiar.
And they’re shiny and twinkly.
Not black.
Or holes.
One of the chapters of my book about the way that we see our place in the universe (see the column on the right) is about the idea that the universe is essentially composed of nothing at all – despite its obvious solidity (in places at least). It’s about the way that nothing can give rise to something. The chapter is titled Nothing Matters (which is meant to be a pun by the way).
Here’s a very entertaining lecture by theoretical physicist Lawrence Krauss which deals nicely with aspects of this subject. (Should you only want to dip into the lecture briefly the most relevant quote is about 40 minutes in. Should you not want to dip in at all, the quote is, in truncated form, [The universe] has zero total energy, and it could have begun from nothing…which answers the question…’Why is there something rather than nothing?’.)
Lecture: A Universe From Nothing
About Lawrence Krauss
 Lawrence Krauss, theoretical physicist
People are intrigued by dreams.
What on earth are they? Why do we have them? What do they mean? (There we go again, trying to find meaning in things that we don’t understand.)
My own personal feeling is that they are relatively mundane things, made fascinating by little more than the bizarre juxtaposition of the events that (seem to) occur in them. In this respect they are a little like those children’s picture books that have pages cut into sections allowing you to compose strange and exotic creatures out of quotidian life-forms.
However, some people take them extremely seriously.
I recall hearing a Jungian therapist talking about dreams on the radio, and she was convinced of their importance. She was asked if she herself had had any particularly meaningful and life-changing dreams, and bizarrely (considering the importance that she attributed to them) she could recall but one.
She described it.
She was on the moon and in front of her was the Eiffel Tower. That’s a great dream image - the Eiffel Tower on the moon.
She didn’t just leave it at that though – as an interesting juxtaposition of two disparate objects – she interpreted it. The Eiffel Tower represented humanity’s hubristic impulse to construct edifices – not just follies such as the tower itself, but other follies such as bridges, motorways and skyscrapers – while the bleak lunar landscape represented the barren and wasted state that we are visiting upon the earth due to our enterprises in folly building.
As a result of the dream she resolved to devote more time to working towards averting the looming environmental catastrophe that we are engineering. This is a very laudable resolution of course, with which I have no objection, and which is far better than the other one that she could have extracted from the dream, that it would be a great idea to build replica Eiffel Towers on the moon.
It seems obvious to me that she took this dream to be particularly meaningful simply because her chosen interpretation of it resonated perfectly with an issue that was preoccupying her at the time. People see what they want to see in things.
You could interpret the children’s picture book figure above in just the same way. It could illustrate, for instance, the fact that people (represented by the human head) are capable of dominating the air (due to the insect wings) and the water and the earth (due to the bird’s webbed feet that can be used for walking or swimming). So far the interpretation’s looking good. But look more closely at the figure and a worrying factor creeps into the analysis. The ‘creature’ is segmented in such a way that none of the segments carries reproductive organs (It is a children’s illustration after all). The interpretation seems to point to the fact that this figure is doomed to oblivion. The creature has so much potential, but so little future.
I made that interpretation up as I went along, as you can probably tell, but it just shows how anyone can extract meaning out of nothing.
You may in fact say that my interpretation is wrong, because there is indeed just about enough room for some reproductive organs to be squeezed in there somewhere.
You’re right. Just like everyone else I ignore factors that don’t fit in with my theory. Otherwise I just wouldn’t have a theory, and where would I be then?
I’t’s always been my intention to mention something about dreams and our attitudes to them on these pages.
I’ll do that in my next post, but in the meantime, by way of a taster, here’s an example of a dream that I had myself a few months ago.
I’m prompted to recount it due to the recent news that Barack Obama has been awarded the Nobel Peace Prize.
In the dream I found myself attending a large political conference of some sort (Not something I’d normally do). I wasn’t in the actual sitting down and listening to speeches part of the conference fortunately: I was at a peripheral reception, with lots of people milling around chatting.
I was part of a small group of three or four people who were clustered together and who seemed to be concentrating our attention on a head of broccoli that one of our number was grasping.
The broccoli was organic: we knew this because it had a label attached to it that told us so. The label was plastic and seemed to be somehow embedded in the thick stalk of the broccoli. (It struck me that the plastic label, which was quite substantial - being about the size and thickness of a large wrist watch minus the strap - was a little excessive and against the ethos of the low-waste organic movement, but that’s by-the-by.)
The problem was, we couldn’t work out how to remove the label.
As we gazed impotently at the broccoli and the offending label a tall figure appeared out of the crowd to see what our problem was.
It was Barack Obama.
We explained our dilemma to him and he listened patiently and with great understanding.
Taking the head of broccoli in one hand he explained that if you held the label just so and gave it a slight twist it would detach itself from the vegetable. He removed the label effortlessly and with considerable grace.
He handed the broccoli back to one of our party. We thanked him and he disappeared back into the crowd, no doubt to seek out other people who were in need of help.
Is there no end to the good things that we think this man is capable of?
If anyone else has had dreams about Barack Obama I’d love to hear about them.
 Cartoon: The Book of Disillusionment It’s been some time since I added one of my cartoons (due to technical problems of my own making), however here’s one to be going on with.
On the subject of numbers, here’s a mathematical joke.
There are 10 types of people in the world: those who understand binary and those who don’t.
This joke can be extended. There are 10 types of people in the world: those who get this joke and those who don’t.
I suppose the ones who don’t get it can be divided into 10 categories too: those who don’t understand binary (and thus don’t stand a chance of getting it) and those who do understand binary but who don’t have a sense of humour.
If you’re one of the people who gets the joke, do you have a smug sense of self-satisfaction about the fact? Don’t worry, that’s nothing to feel guilty about. It’s all part of the whole business of humour, and is one of the reasons why humour is so satisfying.
If you don’t get the joke because you don’t understand binary, here’s a quick explanation of what binary is.
In our everyday numbering system there are ten individual digits: 0,1,2,3,4,5,6,7,8,and 9.
When you’re counting, once you’ve reached 9 you extend the sequence by starting all over again with the same numbers, but adding a digit in front of them to signify that you’re on a new sequence - so you get 10 to 19. Then you extend the sequence again, to 20 and 29 and so on.
There’s no particular mathematical reason why numbers go up to nine and then start repeating. We use that system essentially because we’ve got ten fingers. This system is based on ten digits (zero and the numbers one to nine), and it’s described as being to the base ten.
We could just as easily use a system in which the only digits are 0,1,2,3,4 and 5. In this case, once you’ve counted up to the number 5 you can’t simply go on to the number 6 as you can in the ten digit system - because there isn’t one. Instead, because you’ve run out of digits, you have to extend the sequence just as you did after reaching 9 with the ten digit system - by starting the sequence again with an extra digit in front of it. So you have to go back to the figure zero and precede it with a one. This number is written as “10″, but it isn’t the number ten in the familiar ten digit system, even though it looks like it: here it represents the number six. (In this six digit system the number ten is written as a one followed by a four, or “14″.)
That example of a numbering system had six digits, but you can equally have a system that only has TWO digits. While the six digit system lacked the digits 6, 7, 8 and 9, the two digit system lacks ALL OF THEM except for zero and one. While with the six digit system you had to start a new sequence after the number five (because there is no number six), with the two digit system you have to start a new sequence after the number one (because there is no number two). The number two is therefore written as a zero preceded by a one - as “10″.
This two digit system is what we refer to as the binary system (binary meaning two).
So, the number “10″ in the binary system is the same number as the 2 in our normal, ten digit system.
The number “10″ in the joke is actually the binary way of representing the number 2. That’s the core of the joke.
Having waded through this explanation you probably won’t suddenly find the joke hilariously funny, because an essential part of the enjoyment of a joke is the satisfaction of “getting it”. But at least you’re now prepared for the next binary joke that comes along. I’ve been told that there are 101101 of them - rather thin on the ground in other words.
Binary is the numbering system that is used in computers and other electronic equipment - because electronic equipment can only ‘recognise’ two states with which to build up numbers: on or off. (While we have ten fingers with which to do it.)
I recently received one of those emails that contains an incredible mathematical formula which magically calculates your age by starting with a totally unrelated number.
Here’s the formula (in the wording from the email).
1: First of all, pick the number of times a week that you would like to have chocolate (more than once but less than 10)
2: Multiply this number by 2 (just to be bold)
3: Add 5
4: Multiply it by 50 — I’ll wait while you get the calculator
5: If you have already had your birthday this year add 1759 .. If you haven’t, add 1758
6: Now subtract the four digit year that you were born
You should have a three digit number
The first digit of this was your original number (i.e., how many times you want to have chocolate each week)
The next two numbers are YOUR AGE! (Oh YES, it is!!!!!)
THIS IS THE ONLY YEAR (2009) IT WILL EVER WORK, SO SPREAD IT AROUND WHILE IT LASTS.
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Is that amazing?
If you think that it is, think again.
The arithmetic is ludicrously basic, but is wrapped up in a way that disguises this fact.
I’ll go through the arithmetic in a moment, if you’re at all interested - however, the main reason that I’m featuring this magical calculation here is because it’s a very good example of something that’s incredibly simple but that people mistake for being just plain incredible (and even inexplicable).
It follows a pattern that is common to many seemingly inexplicable phenomena (such as magic tricks). The power behind such phenomena lies in no small part in the fact that not only do people mistake them as being mysterious, but they actively like them to be mysterious. They deliberately look no further than the surface. After all, who wants a simple explanation when you can go “Wow!” instead?
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Here’s the arithmetic of the calculation.
1: Pick the number of times a week that you would like to have chocolate
Let’s say 6
2: Multiply this number by 2
6 x 2 = 12
3: Add 5
That’s 12 + 5 (I’ll leave these two numbers separate rather than adding them together right now - you’ll see why in a moment)
4: Multiply it by 50
I’ll multiply the 12 and the 5 from the previous step individually, which gives us 600 + 250
5: If you have already had your birthday this year add 1759
That gives 600 + 250 from the previous step, plus 1759. I’ll add the 1759 to the 250 now, keeping the 600 separate. 1759 + 250 = 2009. That gives 600 + 2009
6: Now subtract the four digit year that you were born
I’ll subtract the year of my birth, which is 1952, from the number 2009. That gives me 57
I’ve ended up with the number 600 + 57.
I’ll now finally add the two numbers together, which gives me 657.
Now, the formula states that, amazingly “The first digit of this was your original number (i.e., how many times you want to have chocolate each week). The next two numbers are YOUR AGE! (Oh YES, it is!!!!!).
It’s true: I started with the number 6, and my age is 57.
How amazing is that?
One of the tricks in this formula is that it makes you think that the number that you started with, for the amount of chocolate, is significant in calculating your age. It isn’t. In my example above I kept the chocolate part of the equation separate to the age part. The chocolate part is the part on the left of the + sign (so at step 3 above, where I got 12 + 5, the 12 is the chocolate part and the 5 the age part).
Looking more closely at the chocolate part of the equation here’s what you’ve been asked to do.
Think up a number
Multiply it by 2
Then multiply it by 50
That’s just a disguised way of saying “Think up a number and multiply it by 100″
In my case it was 6 x 100, which is 600
Think up a number, multiply it by 100, and hey presto, the first digit is the same as the number you first thought of!! No mystery there I’m afraid.
Now for the age part of the equation
Again, a simple bit of disguise obscures the incredible simplicity of the arithmetic
You’re asked to start with the number 5 (Step 3).
Then multiply it by 50
This gives 250
Then add 1759
This gives 2009. This just happens to be this year’s date (at the time of writing).
Then subtract the year of your birth.
Which, of course, gives you your age.
The trick here is that the number 2009 never appears as such in the equation, having been arrived at by a simple process of multiplying or adding other numbers. If you’d been asked directly to subtract your birth year from this number the arithmetic would be transparent.
“Imagine someone holding forth on biology whose only knowledge of the subject is the Book of British Birds, and you have a rough idea of what it feels like to read Richard Dawkins on theology.”
This is a much quoted line from Terry Eagleton’s review of the God Delusion by Richard Dawkins.
It deploys a common accusation that’s made against atheists in general: that their knowledge of theology is so superficial that it renders their arguments worthless. This line of attack as an attempt to neutralise atheism should be used with care, as I suspect that quite a few atheists, including Dawkins, do indeed have a very respectable understanding of the philosophies underpinning theology - thus making this particular argument against them worthless itself and showing the argument up for the petty barricade-building that it is.
What’s more, the argument can be turned round. It has to be taken into account that, due to the fact that there are only twenty four hours in a day in which to study anything at all, anyone who’s totally immersed in any one subject must be have an impoverished knowledge of others. The consequence of this is that anyone who has found the time to become fully conversant with all aspects of theology will be sadly lacking in knowledge of other subjects, such as the biology that Eagleton mentions. And a deep knowledge of other subjects, such as biology and all other sciences, is surely essential in order to put theology into perspective. The upshot of this is that an expert on theology is thus rendered unqualified to speak on theology. Following my reading of Eagleton’s argument at any rate.
Eagleton’s declaration of Dawkins’ lack of knowledge prompts the following question: how much knowledge of theology do you actually need in order to form an opinion on its veracity?
To answer this it may be an idea to reframe the question in Eagleton’s own entertainingly rhetorical style.
How much theology (or biology) do you have to know to realise that the Book of British Mythological Creatures is a work of fantasy?
While on holiday in Ireland recently I came across a press cutting stating that the 2009 Templeton Prize had been won by Bernard d’Espagnat of the University of Paris Sud. The cutting stated that he’s a Professor of Theatrical Physics.
Is this proof that the Templeton Prize is all about suspension of disbelief?
The prize is awarded annually to a person who has, to quote from the prize’s website “devoted their talents to expanding our vision of ultimate purpose and reality”. The prize “celebrates … the quest for progress in humanity’s efforts to comprehend the many and diverse manifestations of the Divine”.
Unfortunately I can’t name and shame the newspaper that was responsible for this humorous editorial slip, as the cutting was too small (It was accompanying an art exhibition that included work by the artist who illuminates the Templeton Prize’s certificates).
More about the Templeton Prize
With the 400th anniversary of Galileo’s use of the telescope upon us (along with the 400th anniversary of the use of the telescope by other, less well known individuals such as Thomas Harriot, as mentioned in my previous post), here’s a rarely commented upon point about the way in which the telescope transformed our view of the cosmos.
It’s taken from my book, Where Are We, What Are We, Why Are We?, which you can see in the column to the right.
One of the most remarkable, though little remarked upon, aspects of the story of Galileo (and the other telescope users) is that the things that they saw through their instruments – the sight of which changed forever the way we see the universe – are things that are just beyond the range of unaided human vision. If our eyes were capable of seeing with only a smidgen more detail we’d be able to see the craters on the Moon and the satellites of Jupiter just by looking at them (The Jovian satellites are of a brightness where they are actually teetering on the edge of visibility to the naked eye, although the glare from the planet itself contributes to making seeing them well-nigh impossible). I would speculate that a hawk, with its hunter’s eye, or even more so an owl, with its excellent night vision, can see the craters on the Moon and possibly the satellites of Jupiter (if they can get around the glare problem) quite easily just by glancing casually at them. But they know not the implications of what they see.
Think how different the history of our awareness of our place in the universe may have been if we’d only had very slightly better eyesight.
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