It is finally a relatively lull week. I've managed to complete a programming (hacking) lab early, and since my room mate has kindly requested that I not work too late tonight because he needs a proper rest for the calculus test tomorrow at about 7.30 in the morning, I'm not going to be doing any more homework for the night.
Which is fairly liberating. To be able to just sit back and relax in the darkness (oh, how I miss the darkness!) and just relish in the good music that I have on my headphones, while my hard drives and cooling fans spin with a silent hum. The night air is somewhat fresh after the light rain that started in the evening; a really wonderful way to spend the night. Oh how I long for that special someone to actually be next to me, and the two of us, sitting in the light rain under the dark sky, on top of a field with the sweet smell of dew in the air, huddling close together, enjoying each other's warmth as the small droplets of rain fall pitter-patter ever so slowly on and around us. And our heads will be touching, in the way that lovers do, and we keep our eyes closed and concentrate on each other's rhythmic breathing. It would be a timeless night, where at that moment, time would seem to have stood still, and there were only two people in the whole world (us).
Mmmm... a sweet dream indeed. A dream that may or may not come true, depending somewhat on what I do, and what fate has in store for me.
But I digress [as usual]. As this semester draws on, I realise that I am actually learning more new stuff than ever before, particularly on the way with which truth is being pursued in terms of the application of logic. Logic itself is a strange beast—it starts off as being a symbol manipulation game, but as the number and type of axioms and rules of inference increase, the logistical system starts to take on a life on its own, where its syntax and semantics are intertwined to the point that it becomes devilishly hard to determine which is which within the system itself. This is a most wonderful way to think about how things are constructed in the real world. The study of logic itself has taught me something that I had slowly come to suspect; while everything that can be derived from the axioms can be derived with only the axioms, but with the proving of more general forms of axiom schemas, it makes the proof much simpler to comprehend, much like how we use mathematical induction to prove certain properties without going back to old school Peano arithmetic. This whole idea is one that seems inane, but has really deep metaphysical impact. Derived rules of inferences are very useful because we do not need to be bogged down by the mechanical intricacies to "make it work".
With that information in mind, I kind of feel a bit put-off by folks who keep claiming that "you can always prove everything from the axioms, so the derived rules of inference are useless". I mean, hell yeah, you can prove everything from the axioms and the primitive rule of inference, but do you know how long it will take you if those are all that you can use? Idealism without being grounded in reality is useless, as is being completely utilitarian without any ideals to look up to. What's the point of doing a proof if all it involves is a whole bunch of mechanical symbolic manipulations (which the computer beats us in doing hands down), and not the overall insight that we are most interested in?
Okay... it is actually getting late (it's 1 am, and even though I like the dark, I'm feeling the strain/tiredness from all the hacking earlier), and so I'm gonna crash out.
Until next time.
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