Wednesday, December 17, 2008

All Burnt Out

Today I am exhausted. There is no other way to describe me. I am one of them stupid people who have the habit of 'wanting to put my foot into everything'.

It was the student Galois Group lecture today, which although I didn't understand parts of, was very well delivered and the turnout was equally great. I did something to make sure that we had a good turnout, which I will mention in a minute, but the lecture was a fantastic way to end the semester. During the lecture I also took back what I said about TGG in my previous post, for these Wednesdays are honestly worth it. As I have said on numerous occasions, I only wish that I could spend more time trying to take the Galois Group further. (Well at the moment I do spend 98% of my time on TGG, so the other 2% would definitely do some good!)

You see the final week of term is always a dodgy time for a lecture, and considering the fact that I have been shirking my responsibilities for the past week or so, I was worried about the attendance. (The student was very keen on a big audience you see). The lecture was titled Maths and Philosophy, and a natural part of me wanted to advertise in the Philosophy department, but I just never got round to it. However last Thursday, by chance I bumped into a lecturer from Manchester who I had spoken to briefly during the Philosophy workshop organised by Professor Borovik, and he gave me his email address as he was in a rush. I emailed him and asked him if he could advertise the lecture amongst students in his department and that seemed to have done the trick!

The lecture finished at 1:45pm which sent me into a mini-panic, as if we had all started piling out of the room, the refreshments would not have been set out - my friends normally get started at 1:45pm! What I didn't know was that the student had intentionally finished early as he had expected lots of questions. The following fifteen minutes were indeed filled with questions and discussions, which made me deduce that the lecture was more of a philosophical one than a mathematical one! I honestly felt a lot of the philosophical jargon go over my head, but as the student said, the idea is that I now read up more into this topic, which I will (eventually!).

Dr. E kindly did the conclusions etc. and he pointed out the fact that a lot of Physicists and "third floor" people of our building had ventured down for the lecture, which was nice to see. You see if I had the other 2% of time and effort, then I could work harder whilst advertising these lectures and always get 50+ attendance. I got lucky this time round (i.e. the powers that be feel sorry for me!) but the lectures are not just for the maths department - they're for everyone who is interested by what will be said! I just wish that I could find the time to get the stupid website online so everything was more accessible.

Indeed, I wish for a lot of things. I can't recall mentioning this on my blog before, but if I had another me, life would be complicatingly simpler!

Today I am unable to stand on my feet at the moment, as for the past week or so my food intake dramatically decreased, due to my stupid immune system playing up. I've been feeling slightly better so I have wanted to stuff my face with whatever I can get my hands on, but my body disagrees with this. Today I had to skip breakfast, so I have only eaten an apple, a wispa, a jaffa cake, some pringles and drank two cups of tea. That explains my exhaustion as today I have also ran more times than I can count. I had to run in the morning to make sure I wasn't late, and then I had to run to get the milk, and then I had to run when I saw Jerry and .... and yes I actually do run, as opposed to walking fast. Don't get me wrong, I love sprinting, but the stupid adrenaline kick that I get on Wednesday makes me feel invincible which doesn't help! I honestly don't know how I managed to stay standing today.

You see straight after the lecture at 2pm, I had this meeting to attend which I ended up going slightly late to. I "sit" on various committees in the Maths department and this happens to have its uses (note - I did say I am one of them 'gits' who like to dabble my hands into everything..). Initially, perhaps naively, I only actually volunteered as I thought that by doing so I could put forward the case of TGG, so the people who sit on comfy chairs above us would take it seriously. Yes that was very naive of me, but I enjoy these meetings (at times!) so everything is good. The Galois Group has actually benefited, but I think I have personally benefited too.

Today the meeting went past 4:15pm (hence my tiredness!) and parts of it did drag. You always have your "nap time" in meetings and towards the end I had mine but it was a nice nap, as 'Peter' who was sat opposite me did something that amused me. I sat chuckling to myself, not as discreetly as I would have liked, but there you have it!

Anyway - I digress. Two days left till freedom/doomsday/exams! More on that later, but I got the time to sit at the computer so I thought I would type whatever randomness came to mind, and to thank all the people who have made an effort to attend Galois Group lectures this semester, and who have helped to keep me sane! Thank you. :) If you have any feedback on how things went this semester, and how I can improve, please do let me know. I value any constructive feedback.

Monday, December 15, 2008

Mathematics and Philosophy - Student Galois Group lecture (and "Cheer up Beans!")

I feel kinda bad that I'm only blogging at the moment, in order to get any readers out there to attend the Galois Group lectures! (So I've added some snippets after my invitation for you to attend this Wednesday.) Please do come, as this student has gone solo and wants as many people attending as possible (and so do I!):

Dear All,

The last Galois Group lecture of the semester - Mathematics and Philosophy (see abstract below) - will be given by third year Mathematics student, on Wednesday 17th December 2008 in the Alan Turing Building room G.205 at 1:10-2pm, which you are all invited to attend.

Please show your support to the student lecturing, and find yourselves in room G.205 this Wednesday! All you have to do is turn up, and of course stay for the free refreshments at the end.

If you have any queries or questions please feel free to contact Dr. M.D Coleman or myself. I hope to see you this Wednesday,

Kind regards, Beans...

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Wednesday 17th December 2008 at 1:10-2pm
Alan Turing Building, room G.205

Student

Abstract: Mathematics and philosophy - How do these subjects differ?

Can we pose philosophical questions mathematically in order to come to conclusive answers?

This lecture will examine various philosophers', physicists' and mathematicians' relatively recent attempts and successes at answering bold philosophical and often seemingly ambiguous questions.

The lecture will look at the paradoxes of self referential statements such as "I am a liar", including the possibility of time travel, philosophically, physically and (most importantly!) mathematically.

The lecture will mainly explore Max Tegmark's mathematical formalization of a theory by David Lewis that states "every logically consistent universe exists" and its implications for philosophy and physics. I will try to explain how this can characterise the notion of objectivity which is essentially Group theoretic.

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Truth be told I have been quite ill since Friday week 10, and this morning I nearly fainted on my way into University! I really wasn't well enough to attend University as I had been throwing up over the weekend, but already I have missed more than 10 lectures of the semester and am still copying up notes, so I had no choice but to attend. The woman who asked me if I was okay in the morning, whilst I was commuting, advised me to go straight back home. A part of me wished that I had.

Anyway - it's the last week of term, and I have to grin and bare it. Dr. Coleman even told me to cheer up today, but I am too bloody depressed to cheer up! You know what it's like with me - I haven't been studying and then I feel cack, so I can't do anything anyway, which just makes things even worse. I have to make sure though, that I don't crack, as I nearly did when talking to Dr. C earlier today. I don't think I'm destined to be a proper Mathematician, but just one of them text book mathematicians, who learn stuff to pass exams.

I am considering a possible merger with Mathsoc for The Galois Group, albeit reluctantly, but I feel boxed in by my ambitions and my studies. Honestly speaking, an epsilon part of me, very deep down, wishes that The Galois Group also belonged to the empty set. At least then I could actually imagining graduating with a decent degree - the best I can get.

I can't describe the sensations I'm feeling in any more detail. A big part of me is wishing that I had taken this year out and interrupted my studies, just so I could take a break from it all. However, as everyone had pointed out to me, that wouldn't have necessarily solved things.

I have perhaps pushed myself too much and am feeling very tired about everything. Weirdly, a William Shakespeare quote just came to mind: It is not in the stars to hold our destiny, but in ourselves. Sigh. Would you believe me if I told you that the Maths is absolutely amazing this semester? and I exaggerate not! I think this is another reason as to why I've been quite down - I can't really explore the Maths and get it into my head, as I just haven't been able to find the time (or health for the past week or so!).

We have four weeks over Christmas which isn't really enough, but I am told that there were some survivors on the Titanic... \{lame} (but hey that cracked a smile!)

Anyway - I feel that I should have blogged more this semester, because in it's strange way, it helps. (Well I feel slightly better now....) It's quite funny (in a not so funny way) how I started this semester, and how it is ending. I will shut up now, but once again, please do try to attend the student Galois Group lecture on Wednesday. Thank you.

Thursday, December 04, 2008

The Empty Set

As I have previously mentioned, I am now allowed to use the computers in the Brian Hartley (BH) room for “Galois Group” business (i.e. to make and print posters, and to use TeXnic centre). However, on the door to the Brian Hartley room, in big massive writing, it says: “Only for Staff and Postgraduate Students”.

Yesterday as I conversed with Dr. Coleman, he, as always, commented “that I wasn’t allowed inside the BH room”. I once again explained how I am now “allowed” to use the room (which isn’t “all that” if I may say so myself!) but then I had a better idea.

Previously I have, perhaps naively, defined myself as infinity (amongst many other names!), but yesterday I did something radical. I boldly stated to Dr. Coleman that I now define myself as the empty set!

If I remember correctly, from the epsilon mathematical knowledge that I have, the empty set is contained in every set. Hence the “problem” of me being allowed in the Brian Hartley room is no longer a problem! Yes – I feel that at this stage (in my small moment of glory!) someone is going to come along and say “but…”. Well to any “butters” out there, please go easy on me…

Now being the empty set means that I have certain “cool” properties, which I won’t make a big hoohaa out of. (Don’t want to upset the locals…)! But the main thing is that I don’t have to justify why I should be using a certain room.

Sadly though, one property of the empty set which I am currently feeling is “being empty”. Hollow.

This is one of them weird coincidences in life, so don’t think that ever since I became the empty set I actually lost all matter inside of me! (Although that would be interesting as where would the things inside of me have then gone?)

Inevitably with change there is a lot of friction. However I am now stressed beyond belief and I’m not able to deal with this friction appropriately. I just keep on losing my cool. I do feel like I’m going to topple over the edge soon, and it’s a damn lucky thing that I can’t remember much about toppling objects from Mechanics 2 (college), otherwise who knows what rubbish I would have forced down your throats!

My studies are my biggest stress because I am not studying. For this I obviously blame the Galois Group and then I stop caring about it, and not giving it 100%. Now this means I have two parts of me which are falling apart – hence the emptiness. Professor Dold said to me on the postgraduate open day, that he can see me being anything in life (if you follow me). That is a very sad thing for it reminds me that I perhaps won’t ever get to do what I want, but I can do anything else.

The third year is full of different pressures. You want the best degree that you are capable of and you also want to know what to do next. What to do after you graduate. I’m failing at both instances, for although I want a lot of things they are sadly out of reach at the moment. The scary thing is that I can no longer say “I hope to do a fourth year” for I am not a second year student anymore, with such luxuries. The distance factor which was the reason for the bubble I lived in, has now popped.

I should be making the next batch of posters now, but my hearts not in it so I’m not. Instead, here I am trying to do the impossible – organise my internal chaos.

The way things stand I am failing in all departments. I feel empty. Alone. Don’t get your tissues out just now, but there is no one who will ever be able to understand what makes me tick in the way I do. No one knows why I want to do four years, and do a PhD. And on the other hand, no one understands why I want to accomplish something bigger and better in life, which I haven’t blogged about.

I am very na├»ve – I confess. And I have a very unrealistic idea about life and indeed I have always had unrealistic aspirations of things, people and myself. I sometimes used to tease my ickle cousins with sweets. To get them to come to me I would wave a packet of sweets in front of them (which they obviously couldn’t eat) and then once I had them in my clutches, the sweets swiftly went out of sight! If the child was a persistent one, he would start whinging for the sweets and I would have to do something. If however it wasn’t persistent, I would distract it by perhaps making funny faces and changing the scenery. (Yes – I have a big bag of tricks I’m afraid!)

The same thing is happening to me now. The possibilities that lie ahead of me are cruelly waving at me to come forward. But which sweets do I prefer? And most importantly, which sweets will actually be given to me, and not quickly hidden? Yes – I do over think this perhaps, but as I said, there is much that I can’t make you understand. (I can’t claim to understanding everything properly myself).

Can I juggle a PhD/four years and “this other thing”? Some people say yes and others say no. Gah. In this emptiness all I do is fall. It reminds me of a Doctor Who episode where there is this big dark pit which the Doctor is attempting to enter. He ends up just letting go and surprisingly has a soft landing. I have landed yet so I wouldn’t know.

Since I have started my third year, my vocabulary of mathematical terms has increased. I can no longer say “measure” in a normal sentence (!) and indeed now the gluing lemma in Topology came to mind! I desperately hope that the gluing lemma can be applied to the empty set…

Anyway, enough of this mumbo jumbo now. A part of me knows that I shouldn’t be sacrificing my studies, but I have become too overwhelmed with how much work I have got to do now. It is this sense of been overwhelmed that causes me to panic. The maths is quite hard as well, and four weeks over the Christmas holidays will not be enough to “learn and understand” the maths. Then the likes of me want to do a PhD…

Monday, December 01, 2008

Lecture for The Galois Group by Dr. Peter Eccles

Hello hello hello.

Yes - I have finally found time to blog, but first let me advertise the next Galois Group lecture, lest I find myself out of time! Dr. Eccles is no longer Dr. Eccles in my dictionary. He has demanded that I replace Dr. Eccles with Peter! Now as you can imagine I find this quite strange, but Dr. E - well what he doesn't know can't hurt him, and he doesn't know about my blog so I can write Dr. E here if I want to! - seems to be beating me at my own game though. Every time I use Dr. E in an email or person, he replies with a ridiculous formal "substitution" of my name! He doesn't know that Beans has no surname. Pfft. Anyway - it is indeed quite strange to be addressed in such a formal manner, so I have been quite quick in editing my dictionary.

Because of this fiasco I have decided to give every single individual lecturer, who I talk to on a regular basis, the option to substitute "Dr. Z" with their first name! Does that sound better? Pfft again... ANYWAY - times running out so without further ado:

I warmly invite you to attend Dr. Eccles* lecture this Wednesday 3rd December 2008 at 1:10pm in the Alan Turing Building, room G.205 (see abstract/title below). Please do make an even bigger effort to attend, as Dr. Eccles has been a fantastic supporter of The Galois Group from day one and has attended all but one lectures. A fine record indeed! He is a wonderful lecturer and a funny guy too, but if you ask him he'll claim that his "lecture will be boring" (something I learnt when I asked him to "sell his lecture during a topology lecture!). It definitely won't be boring and I will try my best not to embarrass him whilst introducing him.... MUHAHAHAHA :D

See you on Wednesday.

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Wednesday 3rd December 2008 at 1:10-2pm
Alan Turing Building, room G.205

Peter Eccles

Abstract - From Perspective to the Projective Plane

During the fifteenth century artists made significant advances in the use of perspective in order to give an impression of depth in their pictures. Leon Battista Alberti wrote the first text on this subject in 1435. I will describe his method for drawing a square tiled pavement and illustrate it using a photograph of the Alan Turing Building taken by Nick Higham.

Alberti's work led to questions about what geometrical features different views of the same object might have in common. The answer to this question was provided by Girard Desargues in 1639 with the introduction of projective geometry. In this, additional 'points at infinity' are added to the Euclidean plane so that any pair of straight lines in the plane meet at a unique point (which is a point at infinity if the lines are parallel). This feature is observed when viewing straight railway lines going into the distance: they appear to meet at a point at infinity. I will give an example of how Desargues was able to unify certain disparate results in Euclidean geometry, by observing that they are all special cases of a single result in projective geometry.

In more modern times, topologists have studied the projective plane as a single object in its own right. In 1902, Werner Boy constructed a model of the projective plane in three dimensional Euclidean space. I will describe one method for constructing this model. I will also
mention some unsolved problems relating to models of this type.

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Free refreshments are available at the end and for further information or any queries please feel free to contact Dr. M.D Coleman or myself.

* I don't know where the bloody apostrophe is meant to go - humbug!