This blog is a record of my mathematical journey - a mathologue, I suppose - which I have now begun in earnest. Although this is my first entry, I have already been on the journey since 2006. But this is no matter, because the last three years have been mainly a preparation - the metaphysical tying of my mathematical shoelaces for a race with Achilles and the tortoise, as it were; but more on Achilles soon.
My journey of discovery - for that is what I now know the study of mathematics to be - began as an experiment and a challenge. I always believed myself to be an 'arts student', and had no interest in mathematics. Indeed, I did poorly in maths at school and was proud to say whenever anyone raised the topic of mathematics, 'there are three types of mathematicians: those that can count and those that can't.' I actually still like to say that now when people raise their eyebrows in disbelief at my mathematical studies. (Honestly - and perhaps this is because I have always been more the literary type - people look at me as if I am a Martian when I tell them I am studying mathematics).
It all began with Russian, which, when I began my Russian studies at university in 1988, was a type of Martian. Russians were unknowable and so much Cold War mystique had been built up around them. Anyway, I began studying the Russian language and found I had a facility for language, which, however, I still believe was down to hard work combined with an enjoyment for the subject.
Some years later I completed a Master of Arts in International Relations. This was a course work Masters and one of the subjects was International Relations Theory. This subject exposed me to philosophy. I then came across a book called Sophie's World (Amazon US).
I was then absorbed with philosophy - Democritus, Plato, Satre, Foucault and Slavoj Zizek (one of the great modern cultural philosphers, see in particular Welcome to the Desert of the Real (Amazon UK).
Anyway, I had a definite love of knowledge, hence philosophy, and, then popular science such as The Matter Myth (Amazon CA), which then led me to read many other popular science books and finally a book called The Language of Mathematics (Amazon FR). (Note: I did not read any Science Fiction in my spare time as it is generally appallingly written! But I am an avid fan of SciFi shows such as Firefly even though they have made no more, ta ma da! [WARNING to Amercicans: the previous link will lead you to a website that explains that this Chinese phrase is a swear word, which words, of course, are more dangerous than guns!])
Anyway, I am finally getting to the nub of the matter: to wit, I thought that if mathematics was a language, and as I was good at language - and looking for an intellectual challenge - then perhaps, if I approached mathematics as I would a new language, then I could penetrate this arcane field of knowledge and glimpse the beauty of which so many mathematicians have spoken.
And so I Iined up with Achilles and the tortoise (see Zeno's Paradox of Achilles and the Tortoise). I went back to the basics and re-learned the 'alphabet' of mathematics. From Roman numerals, fractions, percentages, decimals, basic algebra, long division - which for some reason had been unfathomable when I was young - and then onwards through high school maths. I then took a bridging course in advanced high school mathematics at my local university so that I could fulfil the prerequisites for taking undergraduate mathematics.
Even though I have convinced myself that mathematics is indeed a language, it is also something else, something more than language which enables you to see things differently; although a language does this too, I suppose, by giving you an insight into another culture, another way of thinking. Anyway, the experiment and the challenge continued, but I thought it might all end with calculus. Believe me when I tell you that to mere mathematical mortals gazing upon the mountain of mathematics, 'calculus' is a daunting arete, but an arete that must be negotiated if one is to find the path to higher level mathematics.
But I did negotiate this arete - at least the early part - and came away with a good grade, but with a few bumps and bruises from integration and trigonometric identities. Still, it was, and is, exhilarating.
And now I am embarked on my first semester of university undergraduate mathematics (one maths subject through distance learning - I still have to work to eat!): MTH101. It's week five and I am taking notes on inverse trigonometric functions.
I am excited and feel as if I have finally set out on my great trek up the mountain, having trained on the lesser slopes these last three years. I believe I am fairly well equipped with the mathematical prerequisites.
In some respects I feel like I am on a journey as a limit at infinity (hence the title of the blog): I am, in a way, a function defined on some interval - along with Achilles and the tortoise, of course - and if I can take x (the knowledge I hope to gain) sufficiently large, then I can get very, very close to the limit at infinity. And perhaps getting close to this limit will help me to see those beautiful views of which so many speak. And if I am exceptionally lucky, and my experiment does not fail, I may even glimpse a new view, such as a way to unlock the secrets of the Navier-Stokes equations, for example! That, at least, is my grand goal; in the interim, I must content myself with making it to the base camp of my mountain and not dwell on the cloud-covered tops. And this means understanding implicit differentiation, but more on my troubles there in the next blog.
