Why I don’t like pie

This morning, as I was fumbling with the three digit number lock for my bike and as I later read some tweets about Valentine cancelling itself out this year (14-2-12=0), I was reminded how much numbers matter in our lives.

For me, however, this has always been the source of much frustration. Indeed, if it had been invented back then, I’m sure I would have been diagnosed as a child with at least a mild form of dyscalculia. I remember having to sit through hours and hours of extra math lessons just to be able to do basic sums and even today I struggle. Honestly, I cannot do something like 15+7 immediately. I have to split it up in 15+5 and 20+2. I’m also notoriously bad at mixing up stuff like 97 and 79, thanks partly to the confusing Dutch system of saying zevenennegentig and negenenzeventig. (Even as I wrote this down I noticed that I had confused them).

Later on my dyscalculia developed into a very apathetic relationship to numbers in general. For instance, for someone who likes history it didn’t help, I’m profoundly uninterested in dates. I always needed a little trick just to remember them, like 1798 for the French Revolution. But the Battle of Marathon (490 BC) or the one at Actium (31 BC), two of the most iconic dates of Ancient History – a subject I took at university –, will be forgotten almost as I’m writing this down.

The trouble is numbers don’t mean anything to me. Which is a pain in the ass. I mean, there are phone numbers to remember, credit card codes, locks, birthdays, licence plates (I think mine ends in 927 but honestly, I’m not sure), and so forth. So every so often I get into trouble. Like that morning this summer when I woke up, turned on my cell phone and realised I had suddenly forgotten my PIN code. So I tried once, I tried twice and I tried three times… And then you need a PUK code, in the middle of France, in a hotel, at 6 o’clock in the morning. At which point you yell something that rhymes with PUK…

It has always puzzled me why I am so bad with numbers. The only explanation I can think of is that there are too few numbers. Indeed, there’s only 0,1,2,3,4,5,6,7,8,9 and all the rest are combinations of those signs (I have no place in my life for i, e, or π). At least with things and feelings and places and people there are loads of words! And I’ve never had any trouble remember those.

But with numbers, it’s all the same to me. When I use words there is a certain darkness to black and a certain brightness to white (try it, don’t you agree?), but there’s no Constantinopleness to 1453 (The Fall of Constantinople, in my world also dated 1345 or 1354) and 3,14 has nothing to do with pie for me.

Which reminds me. When I was thirteen, I went to a summer camp in Switzerland where one of the guides was an engineer. He was fascinated with numbers and one day even boasted: ‘I can recite π up to 100 digits after the 3!’. At which point a friend of mine, nowadays a paratrooper and in the army’s special forces, replied: ‘So?’.

Quite.

Quantum of doubt

When I was a teenager, I hated physics. And I sucked at it too. I remember one time having to calculate the amount of air pressure within a sealed water bottle. Triumphantly I quickly wrote down: 0. Because, I reckoned, since there is a cap on the bottle, that prevents the pressure from the outside air getting into the bottle. Of course, I was wrong. But I remember sharply - yes, with all the sharpness you can expect from a 14-year-old boy who was publicly laughed at by his alcoholic physics teacher for that answer - that no one bothered to explain why I was wrong. I just sucked at physics (like I sucked at geography or musical education) and that was that.

Today I know that I didn’t hate physics because I sucked at it, but because nothing we were ever taught in high school physics was interesting enough for me to want to try and be better at it. Indeed, for our class (that got only one hour of physics a week) the most interesting chapters were dropped with the message ‘You guys won’t understand this anyway’. And so physics became a kind of applied mathematics. All I remember us doing was calculating things like how quickly a drop of water falling from a cloud would hit the ground (remember F_z?). For someone like me, who was basically only interested in stories and therefore forever looking for the why behind everything, it was torture. Because no one ever talked about the whys. Physics, from the Greek word for ‘the things of nature’, should be about explaining how and why our physical world behaves the way it does. But we never heard anything about that. I guess if you asked our teachers they would have said that that was way too difficult for us.

Yet one year ago, probably almost to the day in fact, I was waiting with Fred for a Japanese train to arrive (Japanese trains are never late, so we must have been early) and I was listening to him explaining Einstein’s relativity theory and I realised that, when properly explained, even the most fundamental physics are not difficult at all. With ever growing eyes and ears and even brain, it seemed, I suddenly understood why distance and time are ultimately relative. I still rank that very moment firmly within the top five of interesting insights I’ve ever had. For one, because Einstein’s discovery is mind-blowing, but also because I realised then and there that physics can be interesting. In fact, it’s probably the most interesting thing there is.

Now yesterday evening I had another ‘physical’ experience, so to say, while watching the BBC documentary ‘A Night with the Stars’ (watch it here on YouTube). In the program, Manchester University physics professor Brian Cox explained the rudimentary elements of quantum theory which accounts for just about everything, so it seems. It answers questions like why it is that even though atoms consist of more than 99,9% empty space, you don’t fall through your chair while reading this. Or why it is when I rub my hands, every atom in the universe instantly changes ever so slightly (something to do with energy levels of electrons). Or why you can put something in a box, preferably a rather small one, wait a while (okay, a rather long while) and have a reasonable chance that whatever you put in the box will not be there anymore when you open it. Fascinating stuff, really, discovered by mostly young researchers who must have had a brain running on kerosene.

In fact, the longer I watched the documentary, the more I started thinking about these geniuses of quantum theory, people like Max Planck, Wolfgang Pauli or Werner Heisenberg, and the amazing discoveries they made. And I must confess that suddenly I was insanely jealous of them.

Indeed, being in academic research myself (but about literature for God’s sake!) I suddenly felt like an imposter. Really, I asked myself, has any scholar in the humanities ever produced anything as staggeringly true as the Heisenberg uncertainty principle (pun not intended)?

I mean, just look at it. Even if you don’t understand it (like me), you have to realise one thing. This is a mathematical formula, which means that it is universally true: always and everywhere, for every fucking particle in the whole Goddamn universe!

Indeed, nothing we scholars in the humanities will ever put down about anything, no matter how hard we research it and how much we think about it, will be able to boast a fraction of the value Heisenberg’s discovery. And that’s a bit of a blow. Especially since no one in humanities and particularly in my small field seems to care very much about this.

Sure, we can’t all be Nobel Prize winners and research in the humanities is fundamentally different to physics, but what annoys me is that lately it seems no one around me is truly trying to push the boundaries of what we know anymore. Academic research should be about formulating, testing and refining hypotheses in an open, but ever critical environment. Yet lately, it seems that a lot of what I see in my small field boils down to formulating clichés, testing the limits of everyone’s patience, refining the art of looking smart in a self-important, but ever empty environment.

After all, we might have been the people who invented the names ‘alpha’ and ‘beta sciences’, but after yesterday, I’m having real doubts about the value judgement seemingly implied in this alphabetical order. Because I seriously ask myself: is what I’m doing as good (for lack of a better term) as what a physicist does?

Truth be told: I’m not so sure anymore…

Mrs. Robinson

Research is a fascinating thing. Only today I read on The New Scientist that after additional observations our beloved neutrinos seem to continue their quarky behaviour and might after all be able to travel faster than the speed of light (story here). If it were true (and I still think we need to be careful), it would be a jaw-dropping finding.

Just think about it. We’re able to send people to the moon, soon even to Mars. We can operate on people’s brain while they are awake. We are about to replace solar panels with a kind of ink that contains silicium nano solar cells, which means that we can print energy cells on paper! And still we do not fully understand one of the most basic things in the world: how fast stuff can move. Just imagine what we’ll be able to do once we do understand it!

And this, dear reader, is why it’s such a privilege to be part of the group of people that can contribute to our understanding of things - even if, in Fred and Fred’s case, that involves questions about stuff which might seem much more trivial than the behaviour of neutrinos. Moreover, it is also the reason why scientists and scholars should take their job as serious as they possible can. But regrettably they do not always do so. A year or two ago, I was shocked to hear that a philosophy professor, whom at one point I was very close to working with for a year, had been fired for plagiarizing on a massive scale. And lately, there seem to be more and more cases of the same deontological tomfoolery. Only recently there was the case of a sociology professor who made up his own research data (story here, on Wikipedia no less!) and yesterday I read about a cardiology professor doing something similar (story here). And it baffles me. If you truly believe in your sacred - and yes, that's the word for me - mission as a researcher, namely to discover new information about ourselves and the world we live in, how can you then knowingly spread false information? It's beyond me.

Anyway, I'm on this high horse because today I was confronted with some bad research myself. No cases of plagiarism or anything as bad as that, but still. The last week I have been working my way through pages and pages of Latin correspondence between Erasmus and one of his Frisian acquaintances, since I have been invited to speak about the topic at the end of the month. Now when doing research I like to form my own opinion about a subject before reading papers by others that involve the same or a similar topic. Just to be objective, you know. So this morning I finally started looking at some of the articles I had gathered. One of them, by a certain Mrs. Robinson, was published in 2004 in a journal that has an IT-B ranking (with IT-A being the highest possible, think Nature or Science) and discusses some of the aforementioned correspondence while tackling a different issue. Now just imagine my jaw dropping when I discovered that not one of Mrs. Robinson's statements, not one, about these documents is correct. Apparently she misunderstood them, all of them. And so the world is left with just a little bit more false information. Here's to you, Mrs. Robinson!

On her online cv (where she also proudly posted an online version of the paper horribilis) I read that Mrs. Robinson (a PhD in classics by the way) is also an artist. God bless you, please, Mrs. Robinson - but stick to art in the future, will you? At least that doesn't have anything to do with the truth.

Koo-koo-ka-fucking-choo, Mrs. Robinson.

Centenary

This really is our one hundredth blogpost. What started as (and, as you will soon see, with) a joke has now officially become a collection of 100 reflections, rants and rhetorical ramblings. Apart from the embedded pictures and youtube video's, this amounts to more or less 200 kilobytes of information.

And yet, we have chosen to wait with the fuzz until we reach number 111. The question is of course: why? First of all, despite the fact that people celebrating anniversaries seem to have a natural liking towards multiples of five, any number is interesting. This can even be proved mathematically. For when do we call a number interesting?

Or just skip the number, and let's talk people instead: when do we say someone is interesting? When they have this one particular property that sets them apart from the others, right? Some sort of characterization that renders them unique. Well, the same thing applies to numbers. Two for example, is an interesting number, as this is the only even prime number. Which - pun alert - makes it the oddest one amongst the prime numbers...

Suppose now there exist numbers which are not interesting. Or downright boring, to make it worse. Wouldn't it then be quite interesting for a number to be called the first boring number? Agreed, it doesn't sound as nice as being a perfect number (like 6, because it is the sum of its own proper divisors, since 6 = 1 + 2 + 3), but it would still be a pretty interesting property. However, this very argument undermines the concept of being a boring number. Which therefore means that any number is interesting.

There are even websites and books listing numbers, and the reason why they are interesting. Here's a nice example. And it explains why we choose the number 111, as this is the smallest possible magic constant of a (3x3)-magic square containing distinct primes. And if that doesn't ring a bell, nevermind: only eleven to go...

Googolplexiglass

Every once in a while, we all need big numbers to properly express ourselves - right? Because you have to repeat yourself for the gazillionth time, because you don't feel like packing the whole fucking shitload of stuff into boxes, because someone has been working on your nerves for you don't know how long.

Next time, you may want to use the word 'googolplex', which is a really big number. Interestingly big in fact, which is why I will devote a rather nerdy blurb to it. The term was cornered by a nine-year-old (Milton Sirotta), who meant to define 'a number which is equal to one, followed by writing zeroes until you get tired'. His uncle, Edward Kasner, then formalized this definition, 'because different people get tired at different moments'. No shit, Sherlock.

But how do you define googolplex? Let us first consider an analogy: we all learned at kindergarten that 10 to the power 2 is 100. Which can be written as the number 1 followed by 2 zeroes. Which is not that much, unless you feel like using it as the number of times you had to read the previous sentence before it made sense to you. However, if we would consider the number 10 to the power 100, that would already be much more. Although you could still write this number explicitly. Agreed, it's not exactly the most exciting thing to do, but one could easily do this in less than a minute. Or write it in words, because 10 to the power 100 is called googol.

Now imagine writing down a number which is defined as 10 to the power googol. That means: the number 1 followed by googol zeroes. For some strange reason, this sounds doable, doesn't it? Boring as hell, surely, but doable. The thing is, this number is so huge that it is physically impossible to write down. First of all, assuming that you can write two digits per second, it would take you more than 10 to the power 92 years. Which is way more than the estimated age of our universe. Secondly, assuming that you would write one digit per atom - too small to read, by the way - you wouldn't even have enough space to write the zeroes down. Even if you would zoom down to Planck spaces - the smallest physically measurable volumes - you would still not have enough space for all the digits. Leave alone ink and pens...

So next time you need a really big number to express yourself, I've got one word for you: googolplex. Always nice to get a blank stare from people, politely nodding and checking their iPhone's Wiki-page when you proudly walk away.

The Ig Nobel Prizes

You might have read about them in the paper today, but obviously there is only one source that you can trust on a topic like this: your faithful Fred and Fred. If ever something was right up our alley, it’s the Ig Nobel Prizes.

In case you missed it: the Ig Nobel Prizes (a pun on ignoble and Nobel) are awarded each year in October for ten unusual or trivial achievements in scientific research. The stated aim of the prizes is to ‘first make people laugh, and then make them think’.

Yesterday the 21st award ceremony took place at Harvard University, and a Leuven professor was on the receiving end. Indeed, Luk Warlop, together with a number of colleagues, received the prize for demonstrating that people make better decisions about some kinds of things – but worse decisions about other kinds of things – when they have a strong urge to urinate.

Funny, innit? And it gets even better if you remember that the Ig Nobel Prizes are almost always presented (by genuine Nobel laureates, by the way!) to actual researchers who have been labouring for years on extraordinarily difficult, but seemingly trivial or absurd topics. Just imagine what some academics apply themselves to. Here’s a small sample of the prizes over the years:

• Literature (1995): David B. Busch and James R. Starling, for their research report, ‘Rectal Foreign Bodies: Case Reports and a Comprehensive Review of the World’s Literature’. The citations include reports of, among other items: seven light bulbs; a knife sharpener; two flashlights; a wire spring; a snuff box; an oil can with potato stopper; eleven different forms of fruits, vegetables and other foodstuffs; a jeweller’s saw; a frozen pig's tail; a tin cup; a beer glass; and one patient's remarkable ensemble collection consisting of spectacles, a suitcase key, a tobacco pouch and a magazine.
• Chemistry (1998): Jacques Benveniste, for his homeopathic discovery that not only does water have memory, but that the information can be transmitted over telephone lines and the Internet.
• Physics (2000): Andre Geim and Michael Berry, for using magnets to levitate a frog. Geim later shared the 2010 Nobel Prize in physics for his research on graphene, the first time anyone has been awarded both the Ig Nobel and (real) Nobel Prizes.
• Physics (2001): David Schmidt, for his partial explanation of the shower-curtain effect: a shower curtain tends to billow inwards while a shower is being taken.
• Biology (2003): C.W. Moeliker, for documenting the first scientifically recorded case of homosexual necrophilia in the mallard duck.
• Economics (2005): Gauri Nanda, for inventing Clocky, an alarm clock that runs away and hides, repeatedly, thus ensuring that people get out of bed, and thus theoretically adding many productive hours to the workday.
• Mathematics (2006): Nic Svenson and Piers Barnes, for calculating the number of photographs that must be taken to (almost) ensure that nobody in a group photo will have their eyes closed.
• Medicine (2010): Simon Rietveld, for discovering that symptoms of asthma can be treated with a roller coaster ride.

Now say for yourself: surely it’s any academics dream to receive an Ig Nobel Prize one day? Therefore we from Fred and Fred are already hard at work for next year’s edition. Just imagine the possibilities…

• Cosmology (2012): Fred and Fred, for proving the possibility that parallel universes exist in which even numbers cannot be divided by 2.
• Linguistics (2012): Fred and Fred, for their study ‘Fly, Feel and Fall’, a list of 1,000 words which become very funny when pronounced with a Japanese accent (which turns every f into an h and every l into an r).
• Marketing (2012): Fred and Fred, for definitively disproving that cleaning products which feature animals (ducks, frogs, bears, etcetera) clean better than those which do not.
• Philosophy (2012): Fred and Fred, for (the title of) their paper ‘Does Existentialism Really Exist?’.
• Sports Science (2012): Fred and Fred, for discovering the constant h, representing the relation between the size of the ball and the size of the hole (basketball, snooker, golf, …).
• Medicine (2012): Fred and Fred, for their decennia-long research ‘Is it really impossible to lick your own elbow?’.
• Communication (2012): Fred and Fred, for talking for a whole night about the infinite monkey theorem, which states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type the complete works of William Shakespeare.

Fingers crossed!

PhD peculiarities

Last Sunday Fred came over to my place and we had a healthy discussion about stuff only Freds can have discussions about. The matter at hand was Latin alliteration and assonance and its relation to independent and conditional probability. But rest assured, I won’t bother you with the details…

However, at some point in the conversation a strange fait divers came up, which I am sad to say I can’t recall anymore. What I do remember is that I could proudly refer Fred to the passage in my PhD thesis where said fait divers was mentioned. Which reminded me how much strange stuff there actually is in my PhD! For a thesis about one year (1598) of a humanist's correspondence, there sure is a lot of unexpected information in there. Only recently, for instance, I told my friend E. about the fact the Romans collected taxes on pee (the urinae vectigal) as it could be used in the leather industry…

Indeed, this is only one titbit of the gazillion strange little pieces of information contained in the 911 pages of PhD I worked on from 2003 to 2009 (yes, I had no life then, thank you). As I was able to do so by your hard-earned tax-euros, I thought it only fair to give you a small sample of such PhD peculiarities.

My PhD will inform you about:

1. The precise name of the Roman gladiator who fought wearing a helmet without any openings for the eyes and who therefore competed completely blind (Andabata).
2. The way the 1598 peace talks between the Spanish and the French at Vervins almost didn’t start because of a row about the exact formation in which the different diplomats would be seated during the negotiations.
3. The different sources and opinions about the life span of the Phoenix, the mythical bird that rises from its own ashes (500 or 1000 years depending on whether you believe the Greek or the Roman tradition).
4. The title of a book in which you can check what the weather was like in the Low Countries (Belgium and The Netherlands) from 1000 AD to the year 2000 (J. Buisman, Duizend jaar weer, wind en water in de Lage Landen, Franeker, 2000).
5. The fact that the Greeks seem to have been more afraid of the sea than the Romans. (If you don't believe me, see De Saint-Denis, Le Rôle de la Mer dans la Poésie Latine, pp. 300-302).
6. The differential diagnosis (yes you know this term from House MD) for an oedema (which can be caused by anything from small bruises to serious infections, heart failure, nefrotic syndrome (kidney failure) or non-Hodgkin’s lymphoma (cancer of the lymphatic system).
7. The fact that Spa water was already sold in bottles in 1598.
8. The mathematical problem of the quadratura circuli, the challenge of constructing a square with the same area as a given circle by using only a finite number of steps with compass and straightedge (it took people until 1882 to realise that it’s actually impossible).
9. Who brought the tulip to Europe, who popularized its cultivation, and when the Dutch tulpomania reached its zenith (Augerius Busbecquius, Carolus Clusius and the 1630s)
10. The phrase: “Can I have another gin-tonic?” in Modern Greek (και άλλο τζιν τόνικ)
11. A lengthy discussion of the correct surname of Thomas Rhediger (Rhedigerus, Redingerus, Rehdiger, Rudinger, Rudiger, Rüdiger, Rediger, Redinger or Rehdiger?)
12. The fact that horridula virtus (‘the hard virtue’) is a strange expression because the adjective horridulus is usually employed in Latin in connection with nipples.
13. That Pliny the Elder knows a plant that will give you difficulties peeing, which is strangely called chamaeleon (see Plin., hist. nat., 22, 18, 21)
14. Some considerations on why the Persian imperial messengers called Peichi (Peykān-i Hāsṣṣa) could have carried a small axe and a flask of perfume with them (perhaps the perfume was a gift, emergency payment or just good manners when they had travelled for miles on end to deliver the message?)
15. That the 41st abbot of the Benedictine monastery of Liessies near Avesnes was a naughty man because he drank and partied at the monastery.

Phew! And still the papers are saying that university education in Belgium needs to be of ‘more general’ interest.
Of course, this wouldn’t be a blog on Fred and Fred if there weren’t a little twist to it. Of the aforementioned fifteen peculiarities, one is not really mentioned in my PhD. Can you spot which one ? It’s number -1000+8371-7359 (just a calculation as a spoiler alert…). But mind you that’s only because I struck it out at the last minute. It’s still the God honest truth!

PS: if ever you would feel the need to learn more about which plants cause difficulties peeing or about Latin adjectives usually associated with boobies, you can read the full version of my PhD through this link. Enjoy!

Quarky behaviour

Let's be honest, if this isn't our first blogpost you are reading, the word 'nerd' must already have crossed your mind. On several occasions, I guess. Not that either one of the Freds considers this to be an insult. As a matter of fact, 'writings having a touch of nerdiness' was more or less what we had in mind when we came up with the idea to start a blog. Right from the beginning.

But does anyone know what a nerd really is? My dictionary says: an unstylish, unattractive or socially inept person, slavishly devoted to intellectual or academic pursuits. I cannot speak for myself, but I can definitely say that the other Fred does not qualify as a genuine nerd if this is the definition. Don't get me wrong, he enjoys intellectual and academic pursuits, but that's it.

The thing with definitions is that they are like wedding shoes' laces: way too rigid to be useful. It might be easier to think of a list of easy questions which may help you to determine your degree of nerdiness.

Who is your idol?

Now this would definitely be my giveaway. Albert Einstein. I do have a back-up answer, every once in a while it's just easier to say Mike Patton, but my idol is a physicist. I read more books on Einstein than an average family can handle in a lifetime, I sign my emails with one of his quotes and I have at least one ex-girlfriend who will happily admit she fell in love with me the day I (successfully) explained to her what the special theory of relativity exactly says.

Why am I sharing this? Well, I guess you all saw the news this week. An international team of scientists said on Thursday they have recorded sub-atomic particles travelling faster than light. Neutrinos, to be more precise, arriving 60 nanoseconds earlier than predicted. A nanosecond, people, that is one billionth of a second. Compared to this unit of time, a blink of an eye takes ages. And yet, according to connoisseurs, this is a finding that could overturn one of Einstein's long-accepted fundamental laws of the universe.

Just in case you feel this burning desire to send Fred (or Fred) an email, with the question 'How do you feel about this discovery, that could imply that Einstein was wrong?', here's an answer: this will not affect my adoration. Fred makes mistakes too. Usually having effects lasting a wee bit longer.

Too bad they focused on neutrinos by the way. I would have loved to see my train arrive a few nanoseconds earlier than expected. Although I am not sure I would have noticed, I'd probably be blinking my eyes...

Hyperproblems

Everyone knows what squares are, right?

Imagine you have an infinitely large kitchen. If that doesn't really make sense to you, imagine a kitchen which is larger than the largest kitchen you can think of.

And now repeat that.

Suppose also that the kitchen floor needs to be tiled, with an infinite collection of equal squares. Wait, their colours may vary. But not their size: they must all have the same area. No matter how hard you will (or - more likely - will not) try, you will always end up with a kitchen floor in which every square has at least one complete edge in common with one of its neighbours.

Can you see that?

Either your kitchen floor ends up looking like a chessboard (see the picture above) – in which every square only shares complete edges, one with each of the neighbouring tiles – or it ends up like a kind of deranged chessboard, in which every row is slightly translated with respect to the neighbouring rows. Which still means that every square has two complete edges in common with its neighbours.

The upshot is that these are the only possibilities. Any other arrangement will have 'holes', which cannot be filled up with the tiles at your disposal, as they're all equally big. Think of the kitchen floor: if you try anything different from what I just described, you'll have to start breaking and cutting tiles, to fit them into the holes you created.

(the sound of a rusty rattling brain)

You still here?

Good.

Infinitely large kitchens: way too much dishes to be washed, an infinitely large cupboard underneath the kitchen sink – most likely housing an infinite collection of plastic bags – and a huge fridge.

Bigger than any fridge you can think of.

Suppose this fridge needs to be filled with an infinite amount of identical cubes. Yes, you may put different things in these boxes and they may have different colours, but they must have equal measures. Do you see it coming? No matter how hard you try, you will always end up with a configuration in which every cube has at least one complete square in common with one of its neighbours.

Either they are perfectly stacked, so that each cube shares its six squares with the neighbouring boxes (up, down, left, right, in front and behind), or you start messing around with the layers of boxes. At worst, each cube has only two squares in common with direct neighbours in one direction. Can you still picture that?

(the sound of people thinking "Where the hell is this going?")

Proceed with caution now, as this is the point where a stretched mind might end up being a strained one. Because you can repeat this idea in any dimension. 'Hypercubes?', you're asking. Yups. Hypercubes.

I will introduce you to the secrets and delights of higher-dimensional objects in a future post. As for today – and the sake of not making this post (or your coffee break) too long – you'll have to believe my word: you can define the analogue of squares and cubes in 17 dimensions. Or 85, if that suits you better. And infinitely large 17-dimensional kitchen floors need to be tiled too. The only difference however, is that hyperfloor tilings in 17 dimensions behave rather peculiarly: 17-dimensional tiles can be rearranged in such a way that each of these tiles has absolutely zero “complete sides” in common with its neighbours. Only pieces of "sides".

An abstract sense of freedom, envied by squares and cubes.

In case you're having a hard time trying to picture this: don't. It's impossible for our human brain to actually picture this, unless you're willing to trust your mathematical abstraction skills.

The weirdest thing of all, is the following: the tiling property which holds for squares and cubes holds in dimensions 4, 5 and 6 too. It does not hold in any dimension bigger than or equal to 8. Which leaves one case, right? Well, the case of 7 dimensions is still a highly non-trivial mathematical problem. People still don't know how hyperfloors in 7 dimensions behave.

(all together now)

Who cares?

Mathematicians.

Yes, they are strange people.

Never content with partial answers, always looking for problems which may or may not be in need of a solution, unable to rest before all details are completely comprehended, categorized and classified. And even if they succeed, that merely brings them back to square one.

Cube one.

Hypercube one.

You get the picture...

Definitions

One of the hardest things about my job as a professional mathematician is trying to come up with the correct definitions. And I am not talking about the boldfaced ones, silently introducing the arrival of a theorem like the text message "You've got plans for tonight? Fancy a beer or two?" portending a mind-numbing hangover. I am talking about the actual definition of my job.

Be it on a reception of a friend who finally found a job, toasting to the arrival of a new rat in the race, at the airport, anxiously awaiting the arrival of your bag, on a party, hastily downing a beer or two until the buzz in your brain is big enough to safely ignore the first chapters from the unwritten textbook on 'Social Engineering', or at the Christmas table, spending a stiff first night with your parents-in-law, there's always this one particular moment - usually marking the ending of a silence which would otherwise become even more awkward - in which someone ignites the dreaded conversation:

-"So, what do you do for a living?".

-"Errr, I'm a mathematician."

This may seem like a perfectly harmless opener to you, but it is nothing less than the socializing mathematician's nightmare. Either you get a puzzled face blankly staring at you ("A mathematician? Not wearing glasses? Having a beer?"), often followed by an almost robotic "Oh, how interesting!" and two eyes nervously scanning the place for the nearest exit, or you get an overly enthousiastic "Oh, so that means we're colleagues! What are you working on?". The latter scenario results in me scanning the room for the nearest exit - I meet enough mathematicians at work, no need to do so outside our habitat - the former in trying to steer away from the subject.

Not that I don't like to talk about mathematics though, it's just that people's attitude towards mathematicians is rather polarized. For some strange reason, meeting a math-whizz evokes either scientofobic laughter in people, or an almost pious admiration - as if we are Chosen Ones, spending our devout lives staring at codes that need to be cracked. When someone tells me he's very good in reciting sentences backwards, I feel absolutely no urge to apologize myself for the fact that I can't. But when I tell people I'm a mathematician, things are different: "Oh, mathematics. Sorry, I've never been too good in that." Underlined with the compassionate look I try to keep for special occasions, like a blind colleague telling me his wife left him when she heard he has testicular cancer.

Next time you meet a mathematician, people, there's no need to be so humble. We're lucky bastards after all, being able to do a job which consists of doing things we're good at. Staring at an equation holding on to its solutions like a lioness guarding her cubs, slurping coffee all day long (which is actually Paul Erdos' definition: 'a mathematician is a machine turning coffee into theorems'), locking ourselves into our brain, playing a formal game of beauty. Next time, please proceed as follows:

-"So, what do you do for a living?".

-"Errr, I'm a mathematician."

- "Pft, big deal. Can you say that backwards, by the way? I met a guy who can do that in a second, he's amazing!"

Definition:

A mathematician is like an IKEA closet: always a few screws loose, but put them in any living room and they will perfectly blend in with the wallpaper.

Algebra of Guilt

Sure, I don't like mondays is a phrase that's used too often. Especially when you consider the tragic story behind that beautiful song. But still, today was one of those days... Again.

In fact, I actually tried to amuse myself in the train by calculating the shittiness of stuff that happened today. Of course, I only engaged in this truly breath-taking mirth because I was bored as hell thanks to another horror show of my good friends NMBS & NS.

So my first exercise was to think about train delays and how to calculate their influence on your day. So I came up with value d, which is the time it actually takes you to get to work divided by the amount of time your commute usually takes. The higher d (especially d > 1), the more reason you have to complain. In my case, today d = 442 / 330. I then tried to refine the equation, by splitting up this total value d in d at any given point in time: d(t). So I could then calculate how much shittier delays get as you progress through your commute.

Anyway that's where it ended, as I'm pretty sure the math was getting dodgy there (it's not really right I know), and moreover, I couldn't find any other interesting values. I tried some stuff with m, which is text messages received minus text messages sent (ideally your value should be positive), but that wasn't much fun either.

But while I was thinking about shitty stuff to count and ways to calculate its effect, I started thinking of other things that proved more difficult to count. Like how many times I had genuinely said hello to someone today (zero). Or how often I had thought about my citytrip next weekend (zero). Or the amount in euros (zero) I had given to that guy who came up to me in Antwerp Central Station at the end of my 'shitty' day, asking if I could spare something for the homeless.

I even knew his name, for fuck's sake, and I'm sure he recognized me as well from all those years ago...

As one mathematician once said: Sometimes it is useful to know how large your zero is.

Random blurbs

In information science and communication theory, randomness or noise is often described as irrelevant, meaningless data. A fairly simple description, but it raises interesting questions. What is meaningless, and what do you mean by irrelevant? Being absolutely no stranger to alcohol and what it can do to the human brain - ranging from making you put your (double) tongue into a completely stranger's mouth to having a groundbreaking insight of cosmic proportions, I feel rather tempted to wave this description away as absolute nonsense. But then again, what is randomness?

I was being confronted with this rather erhm... irrelevant issue a few days ago, during my last lecture for biologists. I had to write down something arbitrarily on the blackboard, but the harder I tried to generate random numbers, the more I realized how non-random my example actually became. And I guess we all have the same reflex with respect to these matters: so-called random number sequences cannot have too many repetitions, and should not include obvious combinations like 1234 or 666, isn't it? But where does that leave you?

I mean, does the following sequence look random to you?

3064464030121369

Probably not, right? Very correct, you might have recognized the conjectured dimension of a module associated with the free commutative Moufang loop with 23 generators. Anyway, my point being that sometimes it is difficult to believe that things are just random. And this applies to real life as well, as we (Fred and myself) once again experienced this weekend: our flight from Prague to Brussels was delayed, and this lead to missing the last train from the airport back to Ghent. By two lousy minutes, I guess delayed trains are never to your advantage. However, we did realize that there was a tiny chance that we could get home, taking a taxi from the airport to the Central train station in Brussels where we might still catch the train coming from the airport. In poker lingo: the backdoor flush draw to the nuts.

And guess what, on our way to the official taxi stand - where you are supposed to queue and wait for a yellow cab - we bumped into a shady driver addressing us with a coincidental "Voulez vous un taxi?". For exactly one nano-second, which is more or less the time it takes an average person to notice that the word 'Eyjafjallajokull' contains a spelling mistake, we felt a bit uneasy. Was this not too fishy? One exchanged look later, a classical "I don't know about you but I am fucking tired and need a bed"-look, we decided to go for it and roll the coaster. Which is not just a funny way of putting it: apart from loops, it really felt like a roller coaster ride. With one hand underneath his seat, "Damned, where's my fucking telephone?", our taxi driver zigzagged us through the city and delivered us to our (almost) final destination in (no) time where we safely boarded our train. There was even enough time left for a snack from a vending machine, and the realization that Brussels central station is where randomly weird people meet on a Sunday evening.

And then again, when are people considered to be weird?

(de)Constructivism

According to popular belief, academics are incapable of talking about anything that is not related to (their) work. This is probably one of the reasons why I decided to participate in Fred's idea to start a shared blog, hereby hoping to disprove this assertion.

However, my problem with starting something - be it a blog, a book or a conversation with the person sitting next to me on the train - is that I always end up spending way too much time thinking about the first words. Even these very lines were concocted a few minutes ago, while I was having a shower.
Somehow, this reminds me of my youth. More than once, I got my collection of Caran d'Ache pencils from the cupboard because I felt like drawing something, only to end up staring at an empty page, basically begging my mom for inspiration.
- "Mom, you have to tell me what to draw."
- "Okay, how about a helicopter?"
- "No, that's too difficult."
- "A tiger then?"
- "That is a good idea, but I have no orange crayons."
This exchange of random subjects and lousy excuses usually went on for a few more minutes, until either we converged to the classical solution - a car, to be parked on the fridge - or I got tired and decided to build something with my collection of Lego. Which, of course, often resulted in me repeating my question - mutatis mutandis.


I preferred Lego to crayons though as the act of erasing was a lot easier. And part of the fun. Whereas my own creations often survived a while, most of the demolishing happened once the friends who came over to play were on their way back home. For some strange reason, they never understood that Lego bricks are not meant to be randomly connected or assembled. There is a colour code to be respected: once you start using red bricks for example, you have to stick to this choice until you run out of red ones. And then comes the tricky part: you now have to switch from one colour to another, in the most symmetric way possible.


Once my friend asked me why I'd destroyed the helicopter he had constructed the week before. Well, it could have been a tiger too, I can't remember what my mom had answered to his question. Back then, I didn't know how to explain why I'd did so. This weekend however, I realized there's an easy metaphor.
So L., just in case you bump into this blog, listen carefully: think of my Lego bricks as mathematical axioms, and of your construction as a mathematical theorem. Even though you did prove the theorem, anyone who is but vaguely familiar with basic mathematics will tell you that even logical constructs - or, to translate into abstract words, your Lego designs - are prone to being as aesthetic as possible. You do prefer a clever argument over a lengthy calculation, even though this means you will have to sit down and think for a while - don't you? Well, in retrotort, that is why I broke your stuff into pieces.