So I had nostalgia for some old games like Lemmings and SimTower, but unfortunately, the Mac version of these games were only available for Mac OS 9. Being on an intel Mac with Leopard, it wasn’t possible to run these programs immediately. So I spent a good deal of yesterday and today trying to get an emulation of Mac OS 9 to work on my Macbook.
Sheepshaver is an open-source solution that emulates a PowerPC to run Mac OS 9 on an intel Mac, but like many open-source apps, they don’t make it easy. I had to track down various Macintosh ROM files of old PowerPCs, and also fiddle with a preference file in Terminal. o_O yikes! Nevertheless, I was successful, and I feel smarter for having done it. Here are some screenshots:
The legendary Mac OS 9 booting inside Leopard!
Mac OS 9 and Mac OS X side-by-side.
I even got Internet to work inside this thing.
If there is one area of mathematics I do not enjoy, it is combinatorics. Whenever people start saying things like “n choose k, but divide by two because you double counted,” it goes right over my head. I can’t quite put my finger on it, but there is something really hard about counting arguments for me.
I would have dismissed combinatorics outright as being petty and stupid (perhaps unfairly) if it had not been for my Topology seminar last semester. In studying simplicial homology, I learned that at the heart of space, there is something fundamentally combinatorial about it. You see, simplices (which are in essence n-dimensional generalizations of triangles) are defined and dealt with in a purely combinatorial fashion. And yet, this reveals something deep and fundamental about the nature of space.
The moral of the story is that combinatorics is very fundamental. It seems to crop up in nearly every branch of mathematics. And yet, it seems to be the only area that category theory has not swept under the rug as being a “trivial application” of category theory.
I wonder if there is a way to formalize and abstract counting arguments in a category-theoretic fashion? (I think Yoneda’s lemma is already hinting at this.)
P.S. Sorry about the exceptionally nerdy post. Not every post is like this, I promise.
As you can see, the visual style of this blog is much more streamlined and professional now. I really like the clean and simple look of this new theme.
But there are improvements to things you cannot see as well. The WordPress backbone has been upgraded to the latest version, and the sidebar has been completely widgetized! Now, I no longer have to create my custom sidebar (with the twitter updates and all) every time I change my theme.
Neat.
Troops dug burial pits in this quake-shattered town and black smoke poured from crematorium chimneys elsewhere in central China as priorities began shifting Thursday from the hunt for survivors to dealing with the dead. Officials said the final toll could more than double to 50,000.
-The Associated Press
I am convinced that the reason for such fatalities in the chinese earthquake is due to widespread practice of constructing buildings too quickly and carelessly. I have been generally very suspicious of whether China is actually becoming a first-world nation, or it’s just really good PR. I hear stories from my parents about how Koreans always check trade shipments (like sea products) from China because they are notorious for stuffing cargos of Crab shipments with blocks of lead (to increase weight). And then I hear about poisoned toys shipping to America.
I think the Chinese are trying too hard to seem like a first-world nation without actually doing the hard work. Most of the nation is still in poverty, and there is massive corruption in their government. Plus, from what I can gather about the general culture of the Chinese people, image and PR gets priority over actually improving the country itself. (This is actually generally true for Asian culture, maybe except the Japanese. But I think the Chinese have it the worst.)
I can just imagine the Chinese constructing these large cities as quickly as possible, with very little safety standards in place. And now, their carelessness and borderline deception has come to bite their own ass – in the form of 50,000 casualties. Of course, the flip side is that the world’s sympathies will be with them – right on time for the Olympics. Couldn’t have wished for a better PR outcome, especially on the heels of the Tibetan protests.
I have observed something very curious about studying mathematics. Ideas that seem very complicated and hard-to-grasp at first seem to make much more sense a day or two later, even if I haven’t done any additional studying. For example, when I first read about simplicial homology, it was very confusing and frustrating. But the very next day, everything just clicked, and it all made sense. It is somewhat difficult to describe how this change happened, but nevertheless I felt very comfortable with the material after sleeping on it.
There are two possible explanations for this, and I have seen different mathematicians arguing for both. The first possibility is that you just get used to the material. As the famous saying goes, “You don’t ever learn mathematics, you just get used to it.” While that quote seemed somewhat crazy to me 2 years ago, now I know why such an aphorism exists. There really is a process that most math students go through, where even very complicated ideas suddenly become very comfortable after a day or two. Proponents of this theory would hold that, where as upon first learning one is concerned with the reasons and justifications for the new ideas and theorems, one begins to shift focus on the results themselves rather than the reasons for them as comfort settles in. And by shifting focus to the “what” rather than the “why”, the topic seems “easier”.
The second explanation is that your subconscious works out details while you are sleeping, hence you have really understood the material better the next day, even if you haven’t deliberately studied. Apparently Poincare was a big proponent of this idea, and hence he never worked on problems for more than short spurts at a time. I think I have also read somewhere that Einstein was sleeping almost 14 hours a day when he was working on Relativity.
I think both explanations are plausible, and a little of both are probably true. One thing is for sure: cramming for math doesn’t work. And studying for extended periods of time also doesn’t work. Frequent breaks are needed to solidify the material, which is exactly what I am doing right now. 
The Swarthmore Christian Fellowship held a meeting today, where three of its members gave a personal testimony about God in their lives. I attended out of curiosity.
As I suspected, the talks themselves were incredibly personal and moving – but also lacking in evidence. Everytime a speaker used the word “God”, you could have replaced it with “aspiration”, “motivation” or something similar. In other words, while the emotions they were feeling were genuine, they are also identically available to the nonbeliever- except with the knowledge of truth that it’s only the workings of our very complicated psychology, not anything supernatural.
At times, I wanted to get up and ask point-blank “Do you believe that Jesus was literally born from a Virgin?” Afterall, isn’t that one of the most important aspects to being a Christian? And I suspect that their true beliefs about this is a complicated amalgam of wishy-washy, poetic, metaphorical certainty and faith. But in the end, it is a perfectly plain question with a perfectly plain answer- either Jesus of Nazareth was born from a virgin, or he was not.
One thing that struck me greatly was the kindness and candor of the people there. I have been aware of the very pleasant, but sometimes saccharine, kindness of Christians, but it struck me in a new way when I experienced it myself. It is all very pleasant and nice, and made me realize that many stay faithful for the wonderful community more than anything else.
But all that nice atmosphere, kind generosity, and genuine emotions have no bearing on objective reality. For that, we must turn to dispassionate testing and observation. I think the biggest “flaw” many modern American Christians have is mixing emotional conviction with truth. Just because you “feel” something doesn’t mean it’s true. It must be verified independently.
In the end though, these people are pretty harmless. Unfortunately, the same can’t be said for the religious in other parts of the world.
In my ever-ongoing efforts to combat procrastination, I have been observing how other efficient and productive people deal with stress and fatigue, if they ever encounter any at all. I have made some very interesting discoveries.
First, there appear to be a cultural difference of work ethic between Americans(that is, predominantly white academics types) and Koreans (including Korean-Americans). This difference is very subtle on some levels, but also vastly different on other levels. And this difference of work ethic is what leads to the apparent academic success of most Asian Americans in their teenage years. Interestingly enough, this work ethic that drives Asian teenagers to success is also what ultimately leads to their demise later on in life (most likely in college).
Put simply, there is a brutal efficiency and simple-mindedness with which Americans do work. There is an emotional detachment to performing the daily commitments that allows them to apply themselves day-in and day- out with comparatively less stress. The opposite is true for Asian-Americans. They tend to invest a lot of “mental energy” into even the most routine tasks. Every task is an emotional event, for good or for worse. This leads to better outcome at first, but also leads to quick burn-outs. It also results in initial greater physical productivity at the cost of greater mental stress.
This cultural difference permeates every fabric of the two societies. One of the most common conceits in Korean TV Soap operas is the story of the Underdog, who devotes his entire life to a certain craft, like brewing wine or studying law, sacrificing everything along the way, including his family, friends, and whatever else, and ultimately ends up as the CEO of a wine company, or a highly successful international lawyer. Implicit in all this is the exceedingly high mental investment into his goals. What I’m trying to say is, Koreans tend to have a “All-in or not worth doing” mentality. What do Americans say? “Take it easy, man.”
The end result is almost exactly the opposite of what one would expect. Where as in the Korean TV shows the “all-in” mentality leads to great success, in reality it leads to burn outs and failure due to too much stress. On the other hand, the American mentality of “Take it easy” actually takes you pretty far. Performing daily tasks with a somewhat emotional detachment allows one to be more productive with less stress.
My lesson from all this is that I’m going to try to “Take it easy.” But the trick is to only “take it easy” mentally and emotionally, while still applying myself physically with emotional detachment. In other words, perform tasks out of habit rather than out of necessity. This seems to be the best approach to maximizing productivity.
In my relatively short experience in academia, I have noticed one trend that tends to separate those in the Natural Sciences and those who are not. As in anything else, there are exceptions, but it seems to me that those with first-hand experience in the quantitative sciences understand that Science just might be the best tool we have in figuring out some of the most intractable questions for human kind – What is the meaning of life? Why are we here? Is there a God? etc.. On the other hand, those without experience in the quantitative sciences seem to think that the Natural Sciences are simply cold, hard facts – with no inspiration or spirit, and is doomed to explain only the nitty-gritty facts with numbers and charts. This is simply not true. Perhaps the most important contribution by Science to humanity is its ability to give definite, concrete answers to the questions philosophers and humanists have only been able to ponder about.
While those philosophical questions may seem simply rhetorical and un-answerable anyways, they are actually quite tractable and answerable through rigorous experimentation and logical deduction. Take the question “Is there a God?” for example. This is, in essence, a scientific hypothesis, because a world without God is observably a different universe than one with a God. (This is, of course, assuming that your definition of “God” is sufficient to yield such observable differences. If your definition of God is not as strong, than certainly it is not the belief of mainstream Christianity, Judaism, or Islam, hence of less concern.)
Of course some of these questions have already begun to be answered. The question “Why are we here?” was answered definitely by Darwin – we are here because of evolution. Now, I understand that some people mean more than that when they ask “Why are we here?”. But such pseudo-philosophical waxing is BS. The only meaningful interpretation of the question “Why are we here?” is to literally answer it with brute facts. Of course, another mistake many make is that such a brute fact-based answer is either demeaning or uncomfortable. Well, even if it were, that has no bearing on the veracity of the answer. And I don’t think it’s all that demeaning to begin with. In fact, it’s awe-inspiring that we could be here as a product of such a beautiful and elegant process like evolution. And those who claim otherwise apparently lack the imagination to grasp the austere beauty of the intricate and elegant universe around us.
We all know how much Microsoft copies from Apple. But did you know that Apple copies just as much from Microsoft? The following is a list of some features that appeared on Windows first.
1. Multiple User Log-ins and fast user switching
2. Internet browser-style file browsing with forward/back buttons
3. Window minimizing
4. Keyboard Shortcut to Application quitting (Ctrl+Alt+Del vs. Apple+Option+Esc)
5. Right mouse click
6. Running applications shown at the bottom of the screen
7. “Desktop” folder in a “home” directory to reflect files placed on the desktop
The more Microsoft and Apple copy from each other, the better it is for consumers.
The orientability of a manifold is a mathematical notion that is seemingly abstract and far-removed from reality. It is an issue dealt with in Topology, a modern branch of mathematics that studies properties of space. But in fact, it is one of the reasons why you and I could exist as living beings.
You see, the biochemical molecules that are responsible for sustaining life, amino acids for example, are chiral molecules. This means they have handed-ness. Chemists refer to them as enantiomers. For example, L-Leucine is different from D-Leucine in that they are mirror images of each other. And if you tried to take L-Leucine and rotate it around in space until it looked like D-Leucine, you couldn’t do it. They are mirror-images. And the difference is profound. Certain pharmaceutical drugs cure diseases in one enatiomeric form. Its mirror image could kill you. Indeed, that was exactly the reason why Thalidomide, which was originally designed to cure morning sickness, led to babies being born with no legs or arms. They used the wrong mirror-image form of the drug.
What does this have to do with the orientabiity of manifolds? Well, the mere fact that mirror images of things exist in nature that are not identical (have different chemical effects, for that matter) means that space is orientable. If space were a non-orientable manifold, this distinction would not exist.
Now, we are not actually certain if space is orientable or not. If it was not orientable, an astronaut could travel far into space and come back to earth to find that he is the mirror image of what he used to be! He would find his Heart on the opposite side of his body, and that mole on his left side of his chin would now be on the right! And if L-Leucine had traveled the same path that the astronaut had, it would have turned into D-Leucine! But not one know if such a thing is possible, hence we do not know if space is orientable or non-orientable. But, at least such a phenomenon does not occur nearby earth. Otherwise, we would have to fear for our lives to accidentally travel an orientation-reversing path somewhere in space!
