|Moor Xu on 2013 Pi Day|
|peterthedestroyer on 2013 Pi Day|
|Against the “R… on Contest Math|
|The Ram on Putnam vs USAMO|
|pi on Analysis of the 24 Game|
- 47,082 hits
I used to think that I like physics, almost as much as mathematics. But as time has gone on, this idea has changed, and I no longer see physics in such a positive light. What changed?
In the past, I saw (theoretical) physics as being a wonderfully powerful tool to explain the real world. Progress in physics seemed to give better understandings of our universe and better understandings of reality. Since then, I’ve become disillusioned with the way (theoretical) physics is done.
The physical theories that are currently in existence are incapable of modeling all physical phenomena, and some theories are even inconsistent (electromagnetism and point charges, for example). This is disappointing, but it shows that there is work that needs to be done. The ultimate goal of theoretical physics is to obtain a “theory of everything” that models the entire universe perfectly. Such a goal must remove inconsistencies and must not leave any holes. Though many people are working toward this ideal, it is not clear that it can ever be obtained. Indeed, progress in physics over the past few centuries has made improvements that supposedly come closer to approximating such a perfect theory. However, even as progress has been made, the ultimate goal still remains as distant as ever.
In fact, even if physics did reach a theory of everything, it is not possible for physicists to show that this is actually the case. As an example, consider the state of physics in the late nineteenth century. At the time, physicists thought that they were about to find a perfect model of the universe, one in which nothing is left unexplained. Then Einstein’s theory of relativity came along and shattered this view of the world. What if relativity had not been discovered? Would we now be learning that physics is no longer in need of research? Even if the ultimate goal could be achieved, there would be no way of ever showing that it has been achieved. Physics can never yield absolute certainty.
What is much worse is a consideration from pure mathematical logic. Gödel’s Incompleteness Thoerem states that any reasonable logical system must be either inconsistent or incomplete. Assuming that the goal of physicists is to find a logical system to model the behavior of our universe, we see that no such “theory of everything” can be both consistent and complete: The ultimate goal of theoretical physics is actually unobtainable. This goal is simply an ideal that we can move toward but never reach.
After these considerations, I find theoretical physics to be unsatisfying. The inconclusive nature of physical theories is deeply disturbing, and suggests that instead of being some sort of powerful tool, the study of theoretical physics is just an endless modeling problem. I’m happier with applied physics, where people are not even attempting to move toward any such ideal. In the end, though, I think I’ll stick with mathematics: a world that deals in certainties and has no relationship with reality.
Orwell wrote in 1984 that “Freedom is the freedom to say that two plus two make four.” In the context of the story, it’s clear what this means: The Party wants people to follow the principles of doublethink and believe whatever the Party proclaims, regardless of actual truth; thus, the ability to say that two plus two make four represents freedom of thought.
We can look at this quotation differently, however. The vast majority of people believe that two plus two equals four, and anyone who seriously believes that two plus two equals five is considered uneducated or even insane. Therefore, in our society, we are often not free to say whatever we want. Though our thoughts cannot be monitored and are still held private, there are limits on what we can express to the outside world. Indeed, in order to be accepted in society, we have to abandon some of the ideals of freedom of expression. It’s all part of the mob mentality that holds society together.
Freedom is the freedom to say that two plus two make five.
In the end the Party would announce that two and two made five, and you would have to believe it. It was inevitable that they should make that claim sooner or later: the logic of their position demanded it. Not merely the validity of experience, but the very existence of external reality, was tacitly denied by their philosophy. The heresy of heresies was common sense. And what was terrifying was not that they would kill you for thinking otherwise, but that they might be right. For, after all, how do we know that two and two make four? Or that the force of gravity works? Or that the past is unchangeable? If both the past and the external world exist only in the mind, and if the mind itself is controllable—what then?
This leads to some interesting questions that I haven’t yet been able to resolve. Orwell suggests that we can’t know if two plus two is actually four or five or pi, and he never gives any explanation or indication for why we might know such a thing. So that’s left as an open question to ponder: How can we be sure that two plus two equals anything at all? From that perspective, how can we be sure of anything? Is there any truth at all? I’m not sure, but I haven’t seen any reason to believe that truth might exist.
I’ll write more when I have time to organize my thoughts.
As everyone should know by now, yesterday was Pi Day (March 14), the most important holiday of the year. Pi Day is a day to celebrate the amazing properties of the number , and every year on 3/14, at 1:59:26, every competent person must spend 53 to 58 seconds reciting 97 digits of pi.
What do you get when you write 3.14 on a sheet of paper and hold it up to a mirror? Try it and see! It’s a sign from the gods of mathematics.
This year, there was a government conspiracy to cheat Americans out of an hour of this most glorious of holidays. Daylight saving time means that we skipped the hour from 2am to 3am. This is simply unacceptable, and provides further evidence of the incompetence and complete failure of democratically elected government. We must try to recover from this lost hour of Pi Day, and here is what I suggest we do: We shall celebrate from 1am to 2am on November 7, when we get this hour back. We will not allow our government to take away our right to Pi Day!
I do have some intelligent posts planned, but Pi Day is simply too much fun.
I was told some time ago that I should create a blog. At the time, I said that I would think about it, and I’ve procrastinated for so long now that I can’t remember who to blame for the suggestion. In any case, after some thought, I decided that I’d try blog writing; however, I never found a good opportunity to counteract inertia and feel motivated enough to write something. It seemed like the momentous occasion of the birth of my blog needed to happen on a special day. And indeed, today is a special day; in fact, today is Pi Day, the most important day of the year!
This blog will contain my thoughts on various topics that I find interesting. Given that I’m not necessarily a very interesting person, I don’t promise to update this daily, or even weekly. I’ll write something when I feel like I have something to say. When I don’t have any interesting thoughts, I’d prefer to stay quiet than to spew out boring verbose nonsense, so if I disappear from blogging, you may assume that I’m just suppressing my boring thoughts and keeping them from infecting others.
Feel free to comment and discuss anything that I post, as your comments would likely provide the motivation for me to continue writing and updating. It’s no fun to type up thought provoking ideas when nobody is around to hear them.
Happy Pi Day!