Sound and Fury

I bought a mint plant a while ago. I called it Hendrix. It sits on my desk, to the left of my laptop. It’s probably not the best place in terms of light and whatnot, but my room is pretty small so there isn’t much choice. I water it regularly and it is growing well. It brightens up my room and gives me an almost limitless supply of mint leaves to chew on when I need something to fiddle with. I think Hendrix has done wonders for my state of mind. I feel calmer, more relaxes despite the threatening onset of exam doom. Also, I’m much more minty fresh.

I wish I could stop websites resizing my browser. It’s really annoying. Damn you stupid websites.

This is ridiculous. Productive day I’ve been having, watching videos on youtube…

My friend Tom explained how there are uncountably many mltiplicative subsets of the natural numbers;

CONSIDER the countably infinite set of prime numbers, and its uncountable power set. By taking a relevant element of that power set you can generate any multiplicative subset you want; additionally since prime factorisations are unique, distinct elements will generate distinct multiplicative subsets, hence you have a 1-1 correspondence with an uncountable set.

QED!

So there we go.

“Vert” should be another tog, I’ll come up with a definition later I suppose.

OK, here’s some terminology; a multiplicative subset of the natural numbers is one where if i and j are both in it then so is i.j. An additive subset is one where if i and j are in it then so is i+j. Obviously all additive and multiplicative subsets of the naturals have infinite cardinality. They are all elements of the power set of the natural numbers.

Apparently, there are uncountably many multiplicative subsets of the natural numbers. I’m not entirely convinced. There are at least countably many, since {the numbers greater than n} form a countably infinite family of multiplicative subsets. There are only countably many additive subsets of the naturals, however. Additive implies multiplicative since multiplication is just iterated addition. A multiplicative subset is a member of the power set of N. But there are uncountably many M-sets, so there must be a bijection between P(N) and M-sets. But there are infinitely many subsets of N that are not multiplicative…In fact for any M-set there is an infinite family of subsets which are not multiplicative. (i.e. for some set M, any set of the form M\{x} where x is in M and x=i.j some i,j in M) Are there really only countably many non-multiplicative subsets of N? I know infinity is thoroughly weird, but I’m having trouble with this.

The easiest explanation is that my Symbolic Logic notes are faulty. I’ll email Mr. Dude about that later…

In other news that question I was pondering a while ago about the set of all circles with a given arc as a chord has been solved! Well, we think that the answer is that the only parts of the plane not in the set are points on a line which is an extension of the chord.

Speaking of maths problems I’ve pondered before I realised that there are several other ways to define the sierpinski gasket, some of which were mentioned in a talk Ian Stewart gave at a maths society event last term… I’ll write some more about that later, right now it’s Simpsons O’clock!

So, we were talking about duffel coats on the way back from campus, and then we got on to talking about how toggle is a great word and deserves to mean something better than this. Then, after some random tangent we ended up talking about what the words “inflect, deflect, reflect and genuflect” have in common. We decided some kind of generalisation would lead to a new word, something like this;

• Flect: to distort or alter the motion or direction of something, normally something non-physical

This idea of generalising similar sounding words and creating new words in much the same way as mathematical generalisation works was such a good idea that it deserved a new word; to toggle.

• Toggle: to extract the similarity in meaning from words of similar sounds and to coin a new word with that meaning with that sound

With this word coined, we realised that togs (the word formed by a toggling) are everywhere. “ology” “ism” and so on. Great.

On another note, I’ve decided that I should stop calling my knot theory revision “revision”, because most of this stuff is new to me. So I should call it knot theory vision. There’s no sense in which it is re-vision… But if I went round saying “I’m going to do some maths vision” people would think I’m a weirdo… Not that I’m not a weirdo…

So here is something I came across which I thought was cool. But I had to hit myself when it made me think of Kuhn’s idea of paradigm shifts and his disagreements with Popper… Must stop thinking about courses I have completed the assessment for… Must concentrate on Knot Theory. Need to understand rational tangles and how they’re the same as 4 plats, 2-bridge knots and daisy chains…

In other news I bought a mint plant. He is called Hendrix. Have I mentioned him already? He lives in my room, but I might move him kitchenwards so that he gets more light. But then I’ll forget to water him more often. Sigh. I don’t know how much water to give him either… I just kind of randomly apportion him some water whenever I feel like it. I should probably read up on how to care for my new buddy, but that’s just another displacement activity to avoid work…

Speaking of avoiding work, I’m going to catch up with xkcd now…

Haiku Circus is
My new favourite website
It makes me chuckle

Peep Show and Have I Got News For You were both funny. But not in that order. Peep Show was on after HIGNFY was. Anyway. I might be out tomorrow and miss all the campy goodness of Eurovision. That would be a crying shame. I’ll have to trawl YouTube for the highlights.

I found a googlewhack today. I think it was “groupoidification periphery” Although by writing about it here it will probably cease to be a Googlewhack. Still, groupoidification is my favourite word today. It will probably be word of the week…

Another “favourite” of mine is today’s favourite fact; Tony Blair dated Mary Harron who went on to direct American Psycho. Now that is a pretty awesome fact.

Here are a couple more pointless holiday ideas!

• Only reply to direct questions day
• Respond in a different medium to the one you were addressed in day (So ring up to answer emails, write down the answer to verbally asked questions etc…)
• Finish every sentence with the word “underpants” day underpants
• Blink as little as possible day
• Wink at strangers day
• Speak only in internet memes day (So basically all you can do is ask for cheeseburgers, inform people as to the state of their base, what you’re doing to their dudes and tell people how it is in Soviet Russia)
• Walk like an Egyptian day

OK, that’s enough.

I splashed out on the ability to edit my CSS on this blog, but then decided I don’t have time to work it all out. I should be studying… One day I will get round to it. But wordpress deserve some money off me, I suppose. I use their bandwidth and whatnot…

Other things I have spent money on recently include;

• A ludicrously over-engineered umbrella (it was raining and we hopped into Black’s and all they had was uber hiking stylee umbrellas…)
• A sexy watch (actually pretty cheap)
• Jimi Hendrix CD. Because I didn’t have one.
• Japanese food for me and the ladyfriend. Was very tasty. Much recommended.

And now I should probably get back to some revision, before it’s time for Friday night telly. HIGNFY and Peep Show, Oh yeah! The only time there is something on TV that isn’t shit

Eurovision tomorrow! Is everybody excited? I hope I get to watch it. It would be a shame to miss the most gaudy tasteless camp night of television of the year…

My keyboard is buggered. I need to do something about that. It keeps just not recognising  keystrokes, and sometimes my computer decides I am holding down the the “i” key or the “left” key… Quite annoying. Need to fix that somehow…

Well done John Higgins, the new snooker world champion! Well done Mark Selby as well. The last few frames of the final were great. I didn’t see much of the earlier sessions of the final, though they sounded pretty one sided one way or the other.

I thought of another holiday; Narrate your own life day.

My Farside calendar is telling me that today is “Early May Bank Holiday” and I was thinking that that is a stupid holiday. (It should be called “stay at home and watch the snooker world championships final on BBC2 day”) Bank Holidays are stupid. What’s the point? You get a day off work and everything is shut. Great. They should stagger these holidays; banks get Monday off, supermarkets get Tuesday and so on. That means that on any one day, most stuff will be open and everyone gets a day off. Hooray! Then I thought that every day should be something special on the calendar. Like tomorrow. Tomorrow is just the 8th of May. Tuesday. Nothing special. Poor little eighth of May. So I started thinking up new holidays to sprinkle on the little “nothing” days, in the vein of Talk like a pirate day and Steak and a blowjob day I have thought up some other holidays;

• Give everyone you meet a 13amp fuse day
• Greet people with an annoyingly loud yelp day
• Eat nothing but carrots day
• Speak only in sentences with a prime number of words in them day
• Wear something purple for me day
• Speak only in song lyrics days
• Speak only in film quotes day
• Dress like a wurzel day
• Physically abuse a 4×4 driver day
• Set alight to a smoker day (July 1st)
• International “not a holiday” day

OK, so some of these aren’t as snappy as “Christmas” or “Easter” but whatever.

On a lighter note, the golden mean is 1+(1/ 1+(1/ 1+(1/ 1+(1/ 1+(1/ 1+(1/ 1+(1/ …

A while ago, during the Easter holiday when I was all on my own in the house I watched Casino. While I was watching it I made a spreadsheet of the birth dates and death dates of a lot of important mathematicians and philosophers of the long 19th century. The list expanded a bit over the next few days and I recently added a few scientists who sprang to mind and covered a similar period and I published it here. If anyone has any suggestions for people to add I would appreciate it. I should add some important enlightenment type figures; Rousseau, Voltaire and so forth…

I basically wanted to have more of an idea of who was living when. The way my philosophy courses were taught meant that we studied philosophers pretty much chronologically until Kant, and after that it went crazy. We did Schopenhauer then Nietzsche (and Sartre and Wittgenstein but I didn’t do either of those courses) then we skipped back and did some Hegel (writing before Schopenhauer) then Marx. Marx I could place approximately in a historical context, and I learned that Hegel was in his late teens at the time of the French revolution. So I thought it would be cool to collect some more information on who was around when. At the same time I was doing a course on the history of maths which was more accurately a course on 19th century analysis. So a lot of these guys were around at the same time as the philosophers I was studying. The actual idea to sit down and sort this list out was prompted by my discovering that Bertrand Russell didn’t die until 1970 and Popper was around in 1994 (one of my lecturers David Miller wrote papers with him.)

And so the list is here. Hooray!  If anyone has any suggestions as to how to make this information into a sexy timeline type dealy, I would be interested in hearing from you! Also taking suggestions for important dates that need including, French Revolution, the Terror,  Declaration of Independence of the U.S. etc…