Poll: The Results

I have been planning to review the results of the polls on my blog for some time, and it seems I have finally gotten around to it. Needlesstosay the turnout has been rather poor. Which is surprising, because 100% of respondents said they vote in polls. Extrapolating that result shows that everybody votes in polls. I guess just not on my blog. Here are the highlights of what we have learnt:

• Judas Iscariot is the people's favourite disciple, however he only got 50% of the vote and doesn't have an overall majority. He needs to form a coalition with any of Simon Peter, James or Bartholomew.
• Amy Pond is the best
• Ainsley Harriot is the sexiest TV chef.
• Robots are our masters
• All sorts of people like cryptic crosswords.
• Absence makes the heart grow fonder

AH was delighted to hear he was voted sexiest chef on TV.

There will now be a change of tack with regards to the polls. I think instead of trying to garner people's opinions on topics I shall ask simple questions with factual answers. You have no reason not to vote now.

Solar Panels

Here is a quick thing that has pissed me off.

I just saw this story on the TV about something to do with financial incentives to install solar panels. I could go back and read it properly, but I doubt I will. While watching, I think, "great, there is a scheme to encourage people to get solar panels, and consequently save energy [and the environment]". But the story quickly turns out to be about how some people are worried about the future of the [solar panel installing] industry. Oh no, some people might loose their jobs! *gasp* Surely they are missing the bigger picture? All those suits they were interviewing should be putting saving the planet as their highest priority and not making money.

Look, here is a house with some solar panels on the roof.

In other news, my exciting TV schedule seems to be winding down. Congratulations to Ash Mair on winning Masterchef: The Professionals. Of course the real winner is the food (or Michel's beard). Greg makes some hilarious noises and Michel makes some hilarious expressions; it really is entertaining viewing. Also congratulations to Harry Judd and his professional partner Aliona Vilani. I would have liked to see Jason Donovan win, but Harry was probably the better dancer.

There has been some sort of comedy show on Saturday evenings. In between Brucie's stand-up slots they play music. There may be some dancing or something going on, but I don't pay that much attention.

This means I have more time for other things. Like being bored. Or maybe, just maybe, working on my blog. I an idea for a series (two) of posts. We will have to see...

Polar Bear Christmas

Can somebody please explain to me what polar bears have to do with Christmas. I totally get that in parts of the northern hemisphere the celebration of Christ's birth happens to fall in the season of winter. So it is natural to associate wintry things with Christmas. E.g. snow, robins and holly with red berries. (Of course the holly is there all year round, but the berries only come out in winter)

What I don't get is polar bears. They don't migrate south into New York state in winter, or anywhere else. So why do we see so many pictures of them cheesing it up for X-mas?

If you want to put this lovable creature in your garden this Christmas then you are a deranged maniac. But the good news is you can totally buy it from Walmart. (Out of stock at time of writing.) Not only that, but America's friendliest supermarket has generously discounted it from $54.00 to $53.93. That is a hugemongous 0.13% saving, after all, this is the season of good will.

Additive Number Theory is Hard

.. for example nobody has published a (correct) proof of the Goldbach conjecture that claims every even number is the sum of two primes. Maybe this isn't actually additive number theory as it concerns the addition of prime numbers, and prime numbers are the building blocks of multiplicative number theory.

But let me tell you a couple of interesting results I found recently on the internet.

Question:
Suppose I want to add some numbers and get a specified total. How many ways are there to do this?

Let's see how many ways there are to add up to 4. You have 1+1+1+1, 1+1+2, 1+3, 2+2 and 4. That makes five ways to add up to 4. Amazing. It makes sense to restrict ourselves to using positive integers, and to ignore the order of the summands. Adding up numbers like this to get a total of n is called a partition of n. So we get to say there are 5 partitions of 4.

Let's define a function!

p(n) = The number of partitions of n.

Simple aye? Here are the first few values. Notice how it grows rather quickly.

n	p(n)
1	1
2	2
3	3
4	5
5	7
6	11
7	15
8	22
9	30
10	42
11	56
12	77
13	101
14	135
15	176
16	231
17	297
17	297
18	385
19	490
20	627

This is the partition function and encodes the answer to the above question. Of course it is still hard to evaluate p(n) for a given n, so we are no closer to answering the above question. But you have to feel that by learning about this function, we are making progress.

If you restrict in some way the numbers you can use to get to your specified total, (e.g. primes or squares) then you can do some interesting maths...

Every positive whole number can be written as the sum of four squares. (The four squares theorem)

Now we know a few technical words I can share the interesting result I found.

If n = 5k+4 then p(n) is divisible by 5.
If n = 7k+5 then p(n) is divisible by 7.
If n = 11k+6 then p(n) is divisible by 11.

It seems crazy to me that the divisibility of the number of partitions of n should be related to n like this. Check them for yourself using the table I helpfully provided. The sequence of numbers in the right hand column is one that naturally turns up all over the place and people love to spot patterns in apparent randomness. I strongly suspect that the ancient Greeks or whoever had seen that these results hold for all the values they could check, but were unable to prove them in general.

These results are attributed to Ramanujan, an Indian mathematician whose genius was so unlike anything before or since that you can't help but regard him as a bit mad. His works are dense with the most complicated formulas and I am always bewildered at how he discovered them.

Rhubarb: Part 2

It seems customary these days to begin my post by explaining why it is so long since the last post. However I can't imagine anybody is eagerly waiting for an update on Coughing Fit. The explanation is simple; I have been putting more of my spare time into other things recently. Like watching all the cookery shows on TV at the moment.

Today I finally got to do some gardening. Which is a relief, because I was on the verge of missing my opportunity to get lots of tasks done before winter really prevents gardening. This morning was one of those rare occasions when the weather and my family responsibilities simultaneously allowed me to get in the garden. I seized the moment and made sure I got everything done I needed.

There are still lots of leaves left on the trees, but I got most of the ones on the ground. If I don't get a chance to collect leaves again this year I don't think it will be too bad. But more importantly I moved project rhubarb along a bit. Having cleared a suitable space last time, today I continued to prepare the ground. I mixed loads of home made compost into the clay and rocks. I also removed a few rocks. The soil gets a little better everytime I go out there. As instructed in my rhubarb book, I stuck a whole load of compost into some deep holes and marked the spots ready for spring.

Not only that, but today was one of those very rare occasions when I do some gardening that isn't just weeding and tidying - I planted some things. I had three peonies to plant - can't wait to find out what they look like when they grow. They were just weird bits of twigs when I opened the bag. I hope I put them in the right way up. After that I started the knee-destroying job of planting enough bulbs to keep the Dutch economy going a little longer.Well, perhaps not that many. There were 65. The idea is that you randomly toss them over the site and then plant them wherever they fall. The first part of that is much more fun than the second.

At first glance this may appear very similar to my previous photo of the site. However now it actually contains three peonies, which are virtually invisibly at this stage. And a stick indicating where to plant rhubarb.

After al that work I was tired and dirty and reckoned I deserved a little rest. So I treated myself to a luxury lunch of Heinz smoky BBQ beans on toast. Which was pretty good. Perhaps the second best BBQ type beans I have ever had. The best was at a BBQ earlier this year: some people who I didn't know did them properly, cooking bacon and onions and things. They were nice.

Beans on toast: A meal fit for a king

Something to look forward to

Not just lots of rhubarb crumble. I have made a couple of discoveries this week, which might possibly brighten my life a bit over the coming months.

Since getting back from america, I have had a renewed enthusiasm for playing the piano. And I have changed the way I play in two ways, both motivated by my desire to amaze people with my fingers (and emotional swaying) should I ever get chance to play the piano to my friends. I plan to play music people will like (aka popular music) and, I plan to play it at any opportunity. This means learning some pop songs, and also, learning them so well that I can play them with no sheet music or aide-memoires whilst drunk.

This is not an easy task, and I have never been very good at memorising music. But with enough effort it might be possible. The hard part is remembering which songs I can remember. I think I am allowed to make a note of that in my phone. But I still have to learn some pop songs. I have been spending some time in the evenings in the last couple of weeks watching videos explaining how to play particular songs.  The frustrating thing is that it is often 18 hours or so later before I can actually play the piano. It is quite a memory challenge to watch a video tutorial and then try to play the piece so much later. I have so far failed to get anything more than the main hook for a few songs.

But then I made a real discovery. A professional pianist who "gives" away sheet music of the pop-songs she plays. (Turns out that gives means you are required to make a donation, but whatever.) So I am totally going to get a few and see if I can learn them. Also, watching all her videos made me realise that I don't object to keyboards (and digital pianos) as much as I used to.

Vika Yermolyeva getting a good sway on.

In a completely unrelated turn of events I started listening to my first ever podcast today. Not entirely sure when I am going to get to listen to it, but now I can get clued up on the weekends NFL fixtures before they happen. It features my favourite ever sports-pundit (it's not a long list): Mike Carlson.

Win a trip to Krispy-Kreme (cash value £10). Be the first to correctly comment with what Mike and I have in common. I will give you a clue, it isn't our taste in shirts. 

Another upcoming treat to look forward to is the new season of Masterchef: The Professionals. Featuring beard enthusiast Michel Roux Jnr and his dim-witted sidekick Greg Wallace, it is actually quite entertaining. It also has Monica Galetti in it, who glares at the contestants until they start crying. Masterchef random quote generator says:

There's no place in Masterchef for pink food. There's no place in the world for pink food.

Another poll about food

Am now back from a recent trip stateside. Which, in part, is responsible for the lack of blogging in recent weeks. I got to do both those things that Americans love to do: work hand and impose democracy on a far away country. Only kidding, the two things I am thinking of that Americans love to do are eat far too much and watch TV. I got to eat lots and lots, and I also watched a small amount of TV. Sometimes I even got to combine the two by watching TV whilst eating. Not only that, but on at least one occasion when I wasn't eating, I was watching the food network in my room.

Which reminded my of Rachel Ray.

Rachel Ray. Like really, what are you going to keep in those pockets?

Who is actually some sort of celebrity chef, who totally has a TV show and writes cookbooks and things. I like this acticle about her, particularly the sentence, "Objects derive meaning from their context".

Food shows are vaguely educational right? Although perhaps for TV purposes they get classed as entertainment. But the the thing that grinds my gears about Ray (or Rachel Ray as people like to call her) is that she can't decide how to pronounce endive. Every single time she mentions the vegetable she says "en-dive or on-deev" and makes a failed little joke out of it. I strongly feel she is supposed to be the authority on this recipe she is presenting, but she seems to be admitting her own ignorance. Just pick one and stick to it woman, people will follow you. And if someone writes it to complain about your pronunciation, then you can sit back and smile, smug in the knowledge that they are a tool, and you are far better looking and wealthier than the people that watch your show.

We all know sex and food make a great combination. And I think we should have a poll on the topic. Another celebrity chef who who likes to combine the two is Nigella.

I was about to try and write some words to express my thoughts on the her, but instead I will unashamedly quote from this blog.

When she leaned over to stir the batter for a chocolate cheesecake I swear I could see the cameraman waging a Herculean internal war to remain professional and not fill the screen with her magnificent breasts, and as my own febrile lust reached the boiling point Nigella pulled her wooden spoon from the creamy, russet mixture, trailing a thick bolus of sweetness to her slowly-parting lips and orgasmically sighed “Mmmmmm…” with unbridled sensuality, later punctuated with an equally erotic and drawn-out “Yuuuuuuum.”

I remember seeing a photo of Ainsley wearing nothing but a bunch of grapes. The internet seems incapable of finding this photo for me again, and so I am unable to share it with you. It will just have to remain a happy memory. It is also the sole reason why I think he deserves a spot in the poll.

Giada de Laurentiis is another american who, like Ray, clearly got a job on TV for her culinary knowledge and skills. Sophie Dahl on the other hand is some sort of ex-model who likes food. The rest are just in the poll to make up numbers.

What's on TV

Filling the hole left by Thomasina Miers is a new cookery show on Channel 5. The "Real Food Family Cook Off" features well known foodies Matt Dawson, Lisa Faulkner and Anton du Beke. (Fair enough it does have Ainsley Harriot).

Celebrity slapper Matt Dawson MBE had a successful rugby career but has spent the subsequent years faffing around trying to keep his face on TV. He tried dancing and cooking, and now he is trying hosting a food show. If A Question of Sport was Shooting Stars, then Matt Dawson would be Jack Dee.

Anton du Beke is quoted as saying that he can turn anybody into a great dancer. He was also in another cooking show, "Step up to the Plate" with Lloyd Grossman.

Lisa Faulkner used to be a model or some shit. They say don't trust skinny chefs, I guess that might extend to commentary on cookery shows by skeletor.

However, this latest competition based show pales into insignificance next to Monday's "gripping" final of Antiques Master. Unfortunately, I was rooting for the lady specializing in antique tiles, who didn't make it to the final.

Celebrity lesbian Sandi Toksvig was an obvious choice to host  Antiques Master

A Note on the Nature of the Universe

Made a discovery this week and I feel it is my duty to share it with the world in the hope that others don't make the same mistake I did.

I had just finished cleaning up after dinner and made a cup of tea, and I knew that a little later on that evening we would be having plum crumble and custard. I figured I would do some preparation and start the custard, then I could sit down for an hour and all I had to do later was press "start" on the microwave. So I mixed the custard powder and sugar and milk and left it in the microwave. Then I could settle down with my tea and not move for a while.

Later I put the second part of my plan into action and turned the microwave on. However things didn't work out quite like I had planned. For it seems that in the hour I was sat watching TV the custard has settled. So when I first checked to see how it was getting on, it was all runny at the top, and proper solid and messed up at the bottom. Perhaps the best thing to do in this situation would have been to scrap it and start again. But I was so looking forward to not having to bend over to get the ingredients out of the cupboard, that I just made the best of what I had. It tasted alright, but it wasn't the lovely velvety custard I was expecting.

Keep this in mind though... The plan might have worked if I had stirred it just before starting to cook it.

Rhubarb: Part 1

A friend of a friend has an allotment that he shares with this man...

Somehow, I ended up with some rhubarb in my house a few nights ago. And yesterday I made it into a crumble. This experience reminded me how much I like rhubarb, and how I haven't cooked with it for years and years. Like 10 years probably. My parents had some and I used to love eating it. I would pull it, and "top and tail it" and cook with it. I remember having great fun cutting the leaves off with my very sharp knife. I liked to cut the leaves off in one motion, if the knife got stuck and I had to have a second cut then I was very disappointed.

A Plan is Formed

All these thoughts made me really want to grow my own rhubarb. I seem to remember my dad giving me the impression that it was difficult to get it established, but when it was going it would last for ever. That sort of put me off, but no longer. I am going to grow some, and it is going to be fricking awesome. I selected the most suitable part of my garden and got to work straight away the very next day. There were a couple of problems which presented themselves immediately.

• It is completely the wrong time of year for planting rhubarb.
• There is a giant bush of some sort in the way.
• The soil in that area is rubbish. Full of clay and rocks.

However, these three problems sort of work together to give, what I hope will be, a good outcome. I need to improve the quality of the soil, and by the time I have done that it will be march and I can plant away. And the first thing I want to do to improve the soil is get rid of that bush what is sucking all the nutrients out of the clay and rocks.

I never remember to take the "before" photo. So, instead of a "before" and "after", I can present you with a "during" and a "during".

The stump gets the first round, but I'll be back.

This is an artist's impression of what my garden will look like when Project Rhubarb is complete.  As you can tell I am also planning to add a peony. The artist didn't know what a peony looks like, so he added a nebulous green bush with some colourful dots on it.

A Tale Spanning Three Centuries

I spent a fun afternoon at war with the bush. It's hard work replacing a moderately acceptable bush with empty soil soon to be filled with weeds. The task of excavating the giant rootball was made slightly more interesting by the discovery of a Victorian coin. When it was all cleaned up it turns out to be a penny from 1889.

Difficult to believe, I know, but my kitchen work surfaces aren't actually marble. Instead they are MDF with a clever marble-effect surface.

Speed Cameras

I really struggle to understand how people can complain about speed cameras. Firstly, and most importantly they reduce death and injury. That should be all that needs to be said on the matter.

However, people do complain about them, and some people intentionally damage them. So perhaps we should say more about them...

The way I see it, complaining about speed cameras is tantamount to admitting that you drive too fast. Everybody thinks they are driving safely and don't like to be told otherwise. (The only people who don't think they are driving safely are involved in some sort of high speed chase and no amount of cameras or speed limits will change the way they are driving.) But of course, they are wrong, which is why there are so many accidents and deaths and injuries.

The second argument against speed cameras is that councils are using them to make money. Like that is a bad thing? I really don't have any problem at all with councils making money from speed cameras, if they didn't get money that way they would have to do it some other way. Do you think these people would happily accept an increase in their council tax if it meant no speeding fines? Do you think it would change how they drive? I think it is a good idea to make money from people who speed - it is like a tax on stupid people (people that aren't me).

Here is a little story about road safety that makes me a little angry, and doesn't involve a speed camera. I'm going to make up the details because I don't know them, in fact the story may not be true at all...
A guy made a bet with his friends that he could drive from Penistone to Barnsley in 10 minutes. It goes without saying that this is a stupid and dangerous thing to do. So he set off and was bombing along the A628 at 80 or 90 mph. He lost control of his car and killed himself and probably some other people. The speed limit on that road was 60 mph at the time. The council or the police or whoever investigated and the speed limit on that stretch of road was reduced to 50 mph.

Like, as if that is going to make any difference at all? I think it stands to reason that this man would have given as much notice to a 50mph speed limit sign as a 60mph sign as he took part in his driving challenge. But consequently everybody has to drive that little bit slower on that road these days...

Final Thoughts
Speed cameras reduce deaths and injuries. Even death and injury to stupid people.

Taco

Just been watching Mexican Food Made Simple with chef Thomasina Miers. I like shows about food, and this definitely ticks the box. I couldn't help but notice that every recipe she cooks he describes as "my favourite". Makes me think that she isn't being entirely genuine and is over-egging her descriptions.

However the best thing about the show is that she keeps saying the word "Oaxaca". Which is a funny word. I was enjoying how she kept slipping it in at every opportunity and repeated the sounds: wa - ha - ca. I have since discovered her motive for her comical overuse of this place name; it is also the name of her chain of restaurants in London. Perhaps she is trying to implant the name in people's minds so that she gets more business in these difficult economic times.

What is information?

So, apparently we live in the information age. But I have never found a satisfactory answer to the question: What is information? I think it is fine to not know at this time. If you went back in time to the iron age (for example) and asked the people there, "what is iron?" they would not hesitate in showing you lots of examples of iron and how they manipulate it. Now we feel we have a better understanding of iron than the people did in the iron age. We know about chemistry and stuff and how atomic properties determine the macroscopic characteristics of iron.

Similarly if you ask about information now, people are very quick to start talking about binary data and the internet and stuff. But there is a lot more to it than that.

\begin{interlude}But first, an example rant on the topic of information in the modern world: Advances in data technology has devalued music. That is not to say that modern music is any less good than it has been in the past. But rather, that as a currency it is worth less. Record companies made shedloads promoting their artists and we all bought their records and the artists enjoyed wealth and fame. But now we can (in principle) all enjoy their music for very little money now that we don't have to produce physical discs any more. I can just re-arrange a few gazillion particles inside my ATX tower (or my phone) and be listening to a hardcore trance mash-up before you can say, "Amy Winehouse". No self-respecting group of greedy music industry CEOs want you to stop giving them money (they wear cowboy hats you know) so we had all that kerfuffle about piracy and stuff. But surely it is an unmaintainable situation. We can't support the cocaine habits of all these people when information (binary data) is so cheep and easy to copy and transport. I suspect in the long run it will be a good thing for music; it will become artistic again, and have less of a mass-produced factory feel to it.\end{interlude}

If you look in a dictionary to find out what information is, you will quickly find there are two separate concepts which share the same word, just to keep things interesting. One is the binary data we all know and love, but there is the unrelated concept of knowledge and meaning. So you can say we live in an age of manipulating binary data, where we can store it and move it in great quantities, but I think we are still struggling to work out what information is. That is a deep philosophical problem.

I wanted to share a link to a factoid I acquired at some stage; the amount of data transmitted over the internet is about 1 exabyte a month. However when looking for said factoid I immediately ran into the problem has been getting me riled up and motivated this post. And that is that you can't measure some things in bytes. Instead of finding what I was looking for, I found a paragraph about how much space it would take to store all the words ever spoken by people, ever. Estimates range from 5 exabytes, to 42 zettabytes depending on if you store it in text or a digitised sound recording. But what are you actually storing? If you record it as text then you are loosing a lot of hesitations and inflections which surely contribute to the intended meaning. And even if you record all the sounds, you loose gestures and expressions.

Sure, you can take all the words ever spoken, and digitize them somehow so that it takes up lots of bytes. You can even undo the process and recover large parts of the intended meaning. But I think it is impossible to do that without loosing some of the intended meaning. And if the process is not completely reversible, what have you got stored in your bytes?

Check out this link, it makes me sad. These are the kind of people who tell you how many bytes it takes to store a person. I really don't see how you can do that when we are still struggling to understand what a person is, with unresolved questions like the mind-body dichotomy. I for one believe that I am not simply the product of electrical impulses in my brain – that I do not exist inside my cranium.

Digital information seems to be stored in specific locations. By this I mean that if you opened up your phone or your hard drive and looked at it hard enough, it is possible to say "this bit of information is stored in this physical location". I expect there are technical reasons why the preceding sentences aren't entirely true, but I am sure the premise is sound. On the other hand, I know all the words to "De Colores" and I strongly believe if you were to dissect my brain you could not say that the first instance of the word "colours" was contained in any specific location. Moreover, I believe it would be possible to remove any individual portion of my brain without affecting my memory in the slightest.. However, like all the best theories, this is completely untestable. You could never be sure you hadn't just removed a part of my brain that has nothing to do with memory.

Even if the things I know are somehow contained in my head (which I am prepared to accept is not the case), then I feel it is likely that each quantum of knowledge is equally distributed over a wide region.

Is information even quantizable? Computer says, "no". It seems nobody has thought to ask this question before. We try quantize everything we can (my favourite is the phonon) and the world is making lots of money out of binary data, so why stop to ask this question?

The concept of steganography is quite interesting and not completely unrelated to what I am trying to say in my post. It is the "art and science" of hiding one message inside another. People get all mathematical about it, looking for redundant bytes inside a file, working out how much extra information you can hide in there (measured in bytes of course) and worrying about the statistical likelihood of different patterns occurring and stuff. Which is great, I like mathematics and shit.

But surely there is another way to do it. Surely it is possible for somebody to say something, but given the correct context and background knowledge it can mean something quite different. I can't deny that the first type of steganography appears in my blog, but I think there is more of this second type.

Check out this topical story. It seems everybody is at it, although 8 billion-to-one is surely an over-estimate. Like how many words (or paragraphs) start with a K? A quick glance through my post reveals zero. And people always do rubbish maths when producing statistics for popular consuption. Sure the chance of 7 random letters spelling that particular word is 26⁷, but what about all the other combintations of 7 letters which could be considered "meaningful".

Final thoughts

Perhaps this image sums up the point I am trying to make, and like my favourite book (and potentially my blog) can be interpreted on several levels. Is it a sequence of 71552 bits of binary data? Maybe it is a picture of an American themed race-track? Maybe it is the numeral zero? Can we attach meanings to any of these interpretations, and how many bytes of information are you actually gaining when you look at it? I like to think that should the right person receive a tiny (in terms of bytes) message then they could attach to it vasts amounts of information.

Pizza

Just finished three days off work, which gave me some time to chill and relax at home. You can believe that at your peril. I did, however, get to go to Pizza Hut. Everybody loves their all you can eat buffet lunch. However, it was a little disappointing this time. The salad bar was missing one key ingredient - lettuce. They tried to make up for this with two types of chillies. Not only that, but they have removed my favourite ingredient, beetroot, from their salad bar. I haven't seen it there for years, I guess it is gone for good.

After my trip to the salad bar I tucked into the pizzas and pastas. I like their white and green pasta; I think their philosophy is, "if it's green and a vegetable, then put it in". Cos it has spinach, broccoli and peas. Lovely. 

I have to admit I was a little disappointed with the size of this slice of pizza.

And just one more thing, while I am in full on rage mode: no toilet seat!

I'm such a fool sometimes. On Monday I cleaned the car for only the forth time in two years of ownership. This turned out to be a mistake, cos on Tuesday I parked it next to the grass while the guy was driving his lawnmower all over it. Consequently it is now covered in bits of grass. Then on Wednesday I took it to a farm with all the mud and fun that entails. I figure things may have worked out better if I had done them in a different order.

A lovely hill I saw the other day.

In the interest of balance, I should point out that I like Pizza Hut and will definitely go back there. Remember, other disappointing pizza themed eateries are available.

Elevenses

Today I was faced with that perennial problem that has confronted Englishmen throughout the centuries: What to have with my tea as a mid-morning snack. Today I went a bit crazy and chose something that I very much doubt Brunel had when he took 10 minutes out from designing bridges.

"What is this stuff?" you may ask. I know I did. Apparently it is some giant breakthrough in material science: Spreadable marshmallow.

You put it on toast.

It looks like some futuristic goo that wouldn't be out of place  falling out of tubes in Portal 2.

The finished product; looks so yummy.

I took the plunge and had a couple of bites...

... then a couple more.

All gone. It actually does feel and taste like marshmallow. Weird.

High pressure

Just been watching The Great British Weather on the BBC and felt I really should express the rage it caused me in the most public way I know how. (Hence this post...)

They seemed to assume that because I was British I wanted it to be hot and sunny. And then proceeded to tell me about all the places in the world where it is uncomfortably hot and how the sun is dangerous. I already knew that, which why I don't want it to be hot and sunny.

I already knew that it used to be fashionable to be pale, but that changed when the working classes moved from the fields to the factories. They failed to explain why so many people find it desirable to be tanned. I did learn that 59% of people in Liverpool use fake tan 5 times a year (or was it a month, I forget).

I really don't understand the appeal of heat. It just makes it difficult or uncomfortable to do simple tasks, like get where you are going, or cut the grass, or sleep. And I don't understand people's desire for tanned skin. I once knew a perfectly normal woman who was worrying about getting some fake tan before she went on holiday, with the justification,

"I can't possibly go sunbathing if I am all pale."

In other news, I had a productive day on Sunday. I did some gardening, and did all the usual things like make meals. I had a potter round the park with the family where I got to watch a few overs of cricket. Not only that, but I baked scones. The circle ones are regular scones with sultanas. The triangle ones are cheese. A jot of mustard makes them extra special.

New book

Yay, my new book has arrived. Let me tell you a little about it. I call it the bible according to Conway. Which is wrong in many different ways. I am (obviously) mixing two ideas: the Gospel according to X, and the Bible. Not only that, but this book isn't written by Conway - he only co-authored it. But, like the Bible, it is a collection of many different pieces all together in one hardback volume. It contains lots of lists and data on the best known results in many unsolved problems, some of which are already out of date. (Most notably, the status of the face-centred-cubic packing has changed from "the densest lattice packing and probably the best packing" to "the densest packing". But it's a great book and I am going to enjoy reading it.

It has already reminded me of the kissing number problem. In three dimensions you can fit 12 identical spheres around another sphere of the same size so that they all touch it. You can't do the same with 13 spheres touching the central one. This second fact has been suspected for centuries, but it wasn't proved until 1953. And the proof is quite simple, once you have developed your spherical geometry toolkit. I am tempted to look it up again.

This is Conway from the 70's (I suppose). When I did maths talks, I liked to use colourful props to distract from my lack of preparation. I am fairly certain that is an Escher on his shirt, surely used as a distraction from his hair. Nice beard though.

Best Thing Since Sliced Bread

SATA is one of those occasions when a new technology comes along that is better than its predecessor in every possible way. For those not in the know, SATA is the thing that is replacing (some of) those massive ribbon cables that inhabit computer cases. It is faster, and importantly smaller, meaning that air circulates more easily and computers run cooler. I am quite a fan.

And the little connectors are much easier to maniuplate than the huge ones on IDE cables.

I had no problems fitting my new hard drive, but it hasn't cured my BSoD like I expected.

Spring Greens


I discovered a new vegetable this week. Little did I know that I was eating it out of season, I guess the clue was in the name.

So many options how to cook them.

Lasagna

Made a lasagna the other day. Not bad for a first attempt, if I do say so myself. It all got eaten, so it passes the first test I suppose.

In my dim and distant past Sunday was the best day for food cos we got two main meals. A regular Sunday lunch, and then in the evening we had lasagna accompanied by chips and peas. Then we usually got cheesecake with an incredibly hard base. It was a fun challenge to cut through it (using a spoon) and keep it on your plate.

Anyway, I believe it is a controversial topic, so I would like to draw your attention to the poll about what to have with lasagna. If you want to go for "other please specify" then why not comment on this post?

Evgeny Lebedev

All of this noise about phone-hacking and invasion of privacy seems to have distracted us away from two very important points. I think it is time I reiterated those points lest they be forgotten.

1. It is the function of the media to criticise the government and the authorities.
2. Nobody gives a shit who Ryan Giggs* sleeps with.

I had to be reminded of this by Evgeny Lebedev when he was interviewed on the TV the other day. Sometimes it takes an outside perspective to see things clearly. This man used to work for [own] newspapers in Russia where the press is not so free. He explained how in Russia, journalists have been murdered for writing unfavourable articles about certain people. Our press can write whatever shite they want, and we are one of the least corrupt countries in the world**. These two facts and not-unconnected.

If a newspaper taps some phones and discovers that a businessman is making a large "donation" to the government in exchange for a change to the law, and then exposes the thing. Then that is a victory for Britain. If they tap some phones and discover that some dude wot is occasionally on TV is sleeping with some woman nobody has ever heard of, then the newspapers are just pandering to their readers' base interests. They are just trying to make money and are forgetting point 1 above.

In case you missed it, I think injunctions and super-injunctions are a bad idea. Perhaps RG could have had more success and spent less money by just having a few people assassinated.

Why-aye pet! With this false beard and amazing Russian accent, nobody will ever suspect  I am secretly controlling the media for the purposes of keeping me and the other one on TV.

* Or Andrew Marr.
** Why the fuck is Mugabe still in power?

Scarborough

Not been to Scarborough for a while, so it was good to take the family there yesterday. We had only been there 10 minutes and we had walked into a "candy & novelty" shop. My wife had waved a lollipop at me shaped like a naked female torso, and my son had waved a lollipop at me shaped like a cock and balls.

What I don't understand, is why Scarborough isn't full of all kinds of terrible diseases. I think it has all the things you need to make disease. It is full of nasty fat people who, when the aren't smoking, are stuffing a burger or an ice-cream into their face. There is discarded food all over stinking in the sun. And the whole place is covered in sea-gull droppings. And after 6 hours parked there, so was my car. There are obviously loads of people bringing their germs in to the town then distributing new ones around the country. Why aren't these disgusting slobs poorly?

I saw some walking miracle in the morning who was eating shrimps out of a polystyrene cup. Fair enough I thought, it looks gross, but I am all for fresh local produce. But later on I saw them shutting up the seafood snack stall (between the burger stall and the ice-cream/doughnut stall) and they were covering all their prawns and crab sticks and stuff with cling-film. Thereby destroying all my picture of fresh local produce.

On my entrance to one of the public toilets I was passed my a man sweeping black slurry out of the toilets. Good thing I had put my disposable flip-flops on, and had changed out of my best work-shoes. (See, that's me being positive.)

Scarborough castle, from the north.

The day promised to be really nice in the morning, so we went preparing for scorchio. I should have known better, and it clouded over in the afternoon. And before you know it, I was half a mile out into the north sea with no jacket, and no shoes. I was a bit chilly. Still, it was an interesting setting to learn that the town had coped perfectly well after European law-makers has stopped the local fisherman from going out and raping the oceans everyday.

There is a new addition right in the middle of this picture.

Nice little Italian-style restaurant on the waterfront. It's got a veranda and lots of views.

Before we left to come home we went to Ask for dinner. I was a little hesitant, as my previous experiences with that chain have been medium to poor, due to the slow service. But I needn't have worried - it was fine. It is definitely a welcome new addition to the town, I am not sure what occupied that prime piece of land before. It is right in the middle of the waterfront with great views and they must surely get lots of passing trade. It is like a beacon of cleanliness in a sea of shit. The food was good, but the best bit was that I could use a clean bathroom to wash my hands before I ate. I don't really understand why places like that pretend to be more Italian that then really are. Maybe all those waiters and waitresses really are Italian, or maybe they are faking. I neither know nor care. But it was really refreshing when I walked into a Pizza Express in London and the waiter said,

"Good afternoon luv, I'll be your waiter. My name's Gary."

"Seasonal produce at its best" with Greg Wallace

I had to share this example of "celebrities" endorsing food ranges. Who wouldn't want to buy some value potato wedges with this inane slapper gurning at you?

The making of

It seems a requirement these days, that whenever somebody makes a film or TV show, they also have to make a documentary explaining how challenging it was to make the film or TV show. Following in that tradition I will explain the angst that I went through to demonstrate the strength of 2 pi.

I put a lot of effort into that post about pi. Maybe you noticed. Even so, I bet it is riddled with typos and mistakes. I put in many hours that I could have chosen to spend playing Starcraft.

It was clear to me when I was doing my Ph.D. that a typical mathematician spends 20% of their time working on content and 80% making their work look pretty. I don't have the time or effort to make my internet maths look pretty, and the result was, as with all things, a compromise. I figured it would be a good idea to hunt around for a sensible and quick way to get the maths in my blog looking good. I am not sure I have found it yet.

Let me rant about some of the choices I was faced with and the frustrations I had as I prepared to educate the world about 2π. Mathematicians write real maths in LaTeX. Which is good at what it does, which is typesetting. I have done a bit of LaTeX in my time, and almost without thinking, started getting it all installed so I could prepare my thoughts. But then I paused and considered, "How am I actually going to do this?".

I hunted around the internet for things to convert my LaTeX into HTML. There are some things that will do it for you, but very few of them are maintained. I was amazed how many broken links and webpages from 2002 I found. And things only written on linux that I can't even uncompress without getting some extra software. Maybe that is not the way you want to do it then. But I did find a good discussion on precisely the problem I was facing: how to display maths on the internet. It pointed out that HTML does not do typesetting. (I had chosen to forget this.) Instead it lets the browser decide how to lay out text, with (ideally) just a few hints from HTML tags. This makes it incredibly difficult to get good looking formulas actually encoded into HTML.

Then it occurred to me that I had spent hours reading wikipedia to remind myself about the Reimann zeta function, and I had been staring at a good example of how to do maths online. Their solution is to make each formula an image. Which is quite a lot of work unless you have some clever tool to do it for you (which I don't). And in the end that is what I did for all the big equations. Which took me some time.

So, I get all my post written with images in it and stuff and I press "preview". And it looked rubbish.

The whole thing was about "pi" so I really needed every "pi" on the page to look nice. But for some reason google have decided to use different fonts in the blog composer to the actual blog. The pi in the preview looked more like two T's next to each other. I made the decision to change the font of the whole thing to something that I hope will have nice curly pis on most browsers. But that completely messed up all the line spacing and makes that post completely inconsistent with the rest of my blogs. I still feel it was the right decision. It would be wrong to spend all my time faffing around turning every last symbol into an image when I could be having fun. And it would also be wrong to have people read "Why 2TT is better than TT", they would be like "huh?".

That was all fairly dry and boring. So here are some photos of a knitted hat to lighten things up.

Why 2pi is better than pi

1  My opinions


1.1  2π is better than π


I spent an enjoyable few years studying maths. And during that time I kept seeing "2π" in formulas. I came to the conclusion that it is wrong that π has a special name and a symbol, and that 2π should have those privileges instead.


I didn't take it much further than that. Occasionally I would tell people my feelings on this issue in the pub, cos in those days I got to discuss maths in the pub all the time. I certainly didn't go on a massive internet crusade to do anything about it. Then years later, it was pointed out to me that this is not a new idea. And there is indeed a whole lot of people who agree with me. Check it out.


Today is the day when people stop what they are doing and remember "2π". Because in some countries the date looks like "6 . 28", which is the start of the decimal representation of this interesting value. Of course, the day is all rubbish, because some people like to write "28 . 6 . 2011". And there is nothing special about the decimal system either. Whereas the value is some magical intangible object which is completely independent of how we represent it in physical form.

Two pies

1.2 Why is it better?


Well, think about this. The circumference of a circle is πD where D is the diameter. Who uses diameters anymore? (Apart from midwives) Whereas, the circumference is also 2πr where r is the radius. And everybody likes to use radii. The above website will give you lots of information on the topic, so I am not going to bother. But in short, it boils down to the fact whenever you see a a 2π you have gone all the way around a circle. And when you see π you have gone half way, or magicked a half into your equation by some other means. (For example integrating - see below!)


2  Some maths


2.1  Area of a circle


Let's start with the junior school example, the formula for the area of a circle.

How do you derive this? How do you work out any area? You integrate! We want to integrate the constant function 1 over the inside of a circle of radius r, a region henceforth known as B_r for ball. The natural choice is to use polar coordinates, and changing to polar coordinates a sneaky r appears in the integrand.

2.2  Gaussian Distribution

Everybody's favourite probability distribution: the Gaussian distribution. If we take the "standard" one, then it has this formula:

What's that I see? A 2π. How does that get there. Well, being a probability distribution, the Gaussian has the property that

Looking at this another way, you might spot that the area under the curve

(1)

is actually √{2π}. Without going into too much detail, this 2π appears in the same way as the previous example, by integrating around a circle. It turns out that y(x) is very difficult to integrate, but if you square it and change to polar coordinates again, you end up trying to integrate

which, bizarrely, is possible. But not very interesting.


2.3  Stirling's approximation


Stirling's approximation gives you an approximation to the factorial function for large values. Here it is:

So you started by multiplying a few integers together and you end up with a 2π appearing in your maths. What!?! I did a little digging to see how this happens, and it is actually the same as the previous example, you need to evaluate the same integral integral (1). Perhaps it is not so incredible then?


2.4  Bernoulli numbers and the Reimann zeta function


The Reimann zeta function is an interesting thing, and people have written whole books on it. I just want to look at one of its many interesting properties. We only need to worry about the value of the zeta function for positive even integers, and for those values you can express the zeta function using this formula.

When you think about the zeta function at s = 2, you find you are summing the reciprocals of the squares. It's quite fun to work out the value of this sum, but I will just tell you.

Look at that, it's got π in it. Why? No idea. Let's try the same thing with s = 4.

That has a π⁴ in it. So one naturally senses a pattern forming after just two of these equations. And indeed, there is a pattern, it is usually written like this.

(2)

Where B_n are the Bernoulli numbers. Here are the first few...

If this is the first time you have seen the Bernoulli numbers then you might want to take (2) as their definition. Then you could incorporate the factor of 2²ⁿ into B_2n and you are left with a formula involving π and not 2π. However that would be a daft thing to do. The Bernoulli numbers turn up all over mathematics and most of the time, they aren't next to any pis, so you can't use them to sneakily try to change from π to 2π or back again. The appearance of 2π in this formula is pretty strong evidence that we have given a name and symbol to the wrong value.


2.5  The reduced Planck's constant


A little bit of history of physics now. Way back at the turn of the 20th century, before people had "invented" quantum mechanics, Max Planck discovered a relationship between energy and the frequency of some light and invented a new constant h to put in his equation. This came to be known as Planck's constant. Over the years, as quantum mechanics developed, physicists decided that it was better to measure the frequency of light, not in Hertz (cycles per second), but in radians. With the effect that everything gets multiplied by 2π. They found that h / 2π appeared all over their work, so invented a new constant

so that things looked neater. Even physicists want their work to look pretty.