In order not to run out of ideas for this blog, I’ve decided to write several posts about Great Ideas :-D. These are things I have read, thought, or somehow learned, and they may or may not have stunned me the moment I learned them, but forever after they have ceaselessly shaped all that I think, do, and believe. I mean, this is a Grad Blog 🙂 ,and these ideas are why I’m in grad school, they’re what keeps me unreasonably happy from day to day despite the fact that I live in a tiny windowless basement apartment with three cats. The cats are a member of the Great Ideas (in another post).
If you have Great Ideas (and I know you do – hell, you are in, or about to come to, graduate school!) – share them here! If you disagree with me – please bombard away.
Without ado, in no order whatsoever, and exhibiting my perfectly honest bias to science and Western thought:
1) Newton and the classical physicists – The Universe is knowable by a finite human mind; all the phenomena in the universe are condensable into a small set of laws. So few laws, in fact, that the stars move through the same laws that make an apple drop.
This idea is staggeringly big. It’s not obvious at all that the stars do the same thing as an apple does, and if every event is governed by its own law, if every time causality was invoked a new rule must be created, then there are acts of creation at every moment of existence. A God must then be around at all times – not only the Prime Mover, but the Mover, period. With this idea, however, we merely need a Law-giver. The observation that the human mind, so finite in scope, could potentially comprehend nature – (nearly) ALL of it – so boggles and baffles the mind that it becomes immediately natural to think of ourselves as gods. A deterministic near atheism (which nothing in modern science has broken) is almost the immediate logical result. Staggering, I tell you. Of course they weren’t the first, many ancients had faith in the power of Reason, but the classical physicists are the one who made the real purchase with what had always been a theoretical potential.
Clockwork universe, courtesy of http://www.gadgetvenue.com/grand-orrery-mechanical-clockwork-universe-11281509/
2) Darwin and the theory of selection – Selection is the only creative force in the universe. It is sufficient for all the wonders of the world.
Wow. After years of studying evolution I still have trouble wrapping my head around this one. Take three ingredients, random change, inheritance of random change, and differential survival based on that random change – and you can create meaningful novelty. The novelty came out of the randomness, the meaning came from the fact that the bad ones died. By selection I don’t just mean natural selection, of course, there’s also sexual selection, random selection (drift), all sorts. But this is the first and, a hundred fifty years afterwards, the only mechanistic theory of creativity. The only other creative force around is God. All innovation, cultural, biological, in literature or in the genome, if it is to find a mechanistic, non-mysterious explanation, can only find it in the theory of selection. There is no other creative power in nature.
3) Turing – the Universal Turing Machine (UTM) is the most powerful machine in the universe, and it’s a simple machine.
The above isn’t strictly true – a computer scientist can slaughter me here. There are parallel UTM’s, oracle’d up UTM’s, and it’s not clear if UTM’s can do things as fast as possible. But all those caveats done and said, it remains true that all the computational devices in the universe, once they are capable of what a UTM can (Turing-complete, in the jargon), then they all are equivalent, in a profound sense. The basic idea is that a very simple machine, with an infinitely long tape, a moving pencil and eraser, can execute every and any algorithm – and the amazing thing is, lots of systems are capable of becoming a UTM (e.g. Conway’s Game of Life). As far as we know, that means a UTM can essentially replace the universe – so you can write a set of rules and run the UTM such that the entire universe, including you, me, and this blog, runs in the UTM. In some sense, it means if we understand the UTM, we understand everything, in another sense, it means that if a system is UTM-capable, it is everything.
It leads immediately to the analogy that the mind is a computer. Whether that is true, and whether that is important, are the most important questions in the theory of mind today (at least for me :-P).
Courtesy of http://pmb.livejournal.com/72363.html, by Peter Boothe
4) Godel – the Incompleteness Theorem
The importance of this is debatable, but even in its most minimal form it sets hard limits on knowledge – all knowledge. What the Incompleteness Theorem says is that any Turing-complete system (see above) – that is, any system that deduces results from a basic set of axioms using a powerful enough logic, is either incomplete or contradictory. If the system is incomplete, then there are true statements within the system that one can never prove from the axioms. If a system can prove every true statement within it, then the system contains a contradiction. Remember, Newton gave us the hope that the Universe is precisely such a formal system, and this hope is still burning bright today in the physicists’ search for a Theory of Everything. Awesome, I know.
The basic idea is that in any powerful enough logical system, one can construct the statement “this statement is false”. Either we reach a contradiction here (whether it’s true or false), or else we cannot decide it (incomplete). What does that tell us about the universe? Human intelligence? We don’t know.
Stay tuned for more next week! See anything inaccurate? Anything blatantly wrong? Disagree? Can’t understand something because I was being obtuse? Let me know 🙂