First, I moved out of residence and thus no longer had a whiteboard on my door. Then, Facebook changed its format to hide a person's information unless someone took the time to check. I thought my plan for going all the way through the Oxford Dictionary of Quotations and writing out my favourite quotations was doomed... until I remembered that I have this thing called a blog, and some people actually read it. So, without further rambling, I will begin with this week's set of quotations, starting once again back at A.
"If you want to be adored by your peers and have standing ovations wherever you go - live to be over ninety." - George Abbott, American director, producer, and dramatist, 1887-1995
"Power tends to corrupt, and absolute power corrupts absolutely." - Lord Acton, British historian, 1834-1902
"Do not put such unlimited power into the hands of the husbands. Remember all men would be tyrants if they could." - Abigail Adams in a letter to her husband, John Adams, 1744-1818
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Tuesday, September 30, 2008
Friday, September 26, 2008
McCain: How does he get away with these things?
I am very much confused how the presidential race remains as close as it is. When saying things like "Yippee" or implying a pivotal role in the development of the internet can sink a campaign, how the hell has McCain remained a contender? I remember about a month ago reading a piece on his ten biggest gaffs in a single week in which there was video footage of him joking about finally managing to kill off the Iranians thanks to increased cigarette exports to Iran and another in which he talked extensively on the dangerous situation along the Iraq-Pakistan border, and now today his campaign blatantly jumped the gun in declaring victory in a debate that hadn't even happened yet. It just baffles me...
Political Science Review: Aristotle and Cicero
I realised I ought to keep going with the political science reviews before I get too involved in my stuff this year and forget. I decided to cover both Aristotle and Cicero in one post since, to be honest, I didn't actually read most of Cicero. His text happened to come up during a particularly busy part of the summer, and I just never got around to getting back to it. However, one interesting thing my TA told me about with Cicero's On Obligation (which is the text we were reading) is that it used to be one of the most widely read pieces of historical political theory up until about a hundred years ago. Then, for whatever reason, it began to decline in popularity. It isn't even usually included in the list of texts for the course I took, but my professor used to be a classics professor and he liked it. Also, there is a line which will take on some significance in the next installment of Political Science Review, and that is: "wrong may be done, then, in either of two ways, that is, by force or by fraud, both are bestial: fraud seems to belong to the cunning fox, force to the lion; both are wholly unworthy of man..."
Anyway, after my confession of not actually reading Cicero, I will hop back to Aristotle's Politics, which was the next text after Plato's Republic. Do you remember how I said that I did not really like Plato? Well, after starting Aristotle, I missed Plato. A lot of my dislike for Aristotle is from my modern perspective of being sensitive to subjects like slavery and misogyny, but there were other issues I found unresolved. The most important one was that Aristotle defined politics as the defining characteristic of man, and citizens as the most important members of a city as they practiced politics together as equals. However, when he defined the three 'good' governments (monarchy, aristocracy, and constitutional government), he stated a clear preference for absolute monarchy provided the ruler was a wise and good one well above all his peers. Leaving out the missing information of who should be the judge of the ruler's wisdom and goodness, such a stance begs the question of who is doing the political deliberations that makes life in a city good? I'm not sure I expressed that clearly, but if it doesn't make sense, someone can call me on it in the comments. Basically, I don't think Aristotle has much to offer other than an interesting historical perspective.
Before I disparage the ancient thinkers too much, however, I should note that one thing I found interesting was virtually all of them thought that it was most appropriate that only the educated citizenry ought to have political power. While I know any sort of check on political power (in other words, the right to vote) is wildly open to abuse in terms of marginalizing a portion of a population, at the same time I think it is an important thing that should not be dismissed out of hand simply due to fear of oppression. There are many things that could be used in the wrong hands for oppressive power (such as a police force or an army), but at the same time not having them is worse. I should probably devote a post solely to this topic if I decide to pursue the thought process further, but I would be interested to see if anyone has strong feelings on the matter as it stands.
Anyway, after my confession of not actually reading Cicero, I will hop back to Aristotle's Politics, which was the next text after Plato's Republic. Do you remember how I said that I did not really like Plato? Well, after starting Aristotle, I missed Plato. A lot of my dislike for Aristotle is from my modern perspective of being sensitive to subjects like slavery and misogyny, but there were other issues I found unresolved. The most important one was that Aristotle defined politics as the defining characteristic of man, and citizens as the most important members of a city as they practiced politics together as equals. However, when he defined the three 'good' governments (monarchy, aristocracy, and constitutional government), he stated a clear preference for absolute monarchy provided the ruler was a wise and good one well above all his peers. Leaving out the missing information of who should be the judge of the ruler's wisdom and goodness, such a stance begs the question of who is doing the political deliberations that makes life in a city good? I'm not sure I expressed that clearly, but if it doesn't make sense, someone can call me on it in the comments. Basically, I don't think Aristotle has much to offer other than an interesting historical perspective.
Before I disparage the ancient thinkers too much, however, I should note that one thing I found interesting was virtually all of them thought that it was most appropriate that only the educated citizenry ought to have political power. While I know any sort of check on political power (in other words, the right to vote) is wildly open to abuse in terms of marginalizing a portion of a population, at the same time I think it is an important thing that should not be dismissed out of hand simply due to fear of oppression. There are many things that could be used in the wrong hands for oppressive power (such as a police force or an army), but at the same time not having them is worse. I should probably devote a post solely to this topic if I decide to pursue the thought process further, but I would be interested to see if anyone has strong feelings on the matter as it stands.
Saturday, September 20, 2008
UTIAS
This past Tuesday I took a trip out to UTIAS to see a former professor of mine (and now fourth-year project supervisor, but more on that later). What does such a fancy acronym like UTIAS stand for, you might ask? It is the University of Toronto Institute for Aerospace Studies. Even though I am no longer in Aerospace Engineering, I still have very fond thoughts for UTIAS. I find the building very inspiring. The whole place has an ambience of intellectual excitement and scientific daring that makes me want to do something profound (while it is invigorating, that feeling alone, unfortunately, does not actually yield something profound... at least not yet). Unfortunately, UTIAS is rather difficult to get to, being an awkward 22km away from the University of Toronto main campus and not on a subway line (instead it is a rather long subway trip to the end of the line, and then a further bus ride from there). If you poke around the website for a while, you might see them claim that it is only a 30-45 minute commute by transit from the main campus to UTIAS, and you might think, "for a city the size of Toronto, that's not so bad". Well, I don't think that whoever wrote that part of the website actually took the trip from main campus to UTIAS by transit. The subway trip alone is 45 minutes, and that is assuming your train actually goes all the way to Downsview (the last station) and doesn't instead dump you at Wilson (the second to last stop, where my train for some reason decided it was as far north as it needed to go). Then, assuming you have perfect timing and manage to snag the bus just before it leaves the station, you have another 15-30 minutes (depending on traffic).
Anyway, aside from being hard to get to, you also cannot just show up and waltz about the place. Unlike the main campus, where very few places are locked up, you cannot access the main building without a key card or without buzzing the front desk and signing in. However, if you have a legitimate reason to be there, the institute is very nice. There are a ping-pong and pool table in the cafeteria, a very nice lounge, lots of offices, and even more fancy pictures of space and spacecraft (some real, others rather fanciful... although I haven't yet seen a picture of any of the various incarnations of Enterprise, I wouldn't be surprised if there is one somewhere in the building). Also, I'm not quite sure what it is, but the entire place exudes an ambience of the 50s-70s, when lots of money was spent on scientific endeavours and being a scientist was seen as important, daunting, and wonderful (this is how I still see science, but it doesn't seem to be a normal view. Of course, this is probably just a romanticized view of the Cold War era I have garnered through movies like October Sky).
While I know it would be disruptive for those working at UTIAS, I wish they offered public tours. Between the wind tunnels, the Mars dome, the giant flight simulators, the micro satellite lab, and all the other research areas, I think UTIAS would be a wonderful outing for a family visiting Toronto. So, if you are visiting Toronto and are interested in aerospace, try sending someone at UTIAS an email and ask if you can have a tour. You never know, if you sound excited enough they might let you in.
Anyway, aside from being hard to get to, you also cannot just show up and waltz about the place. Unlike the main campus, where very few places are locked up, you cannot access the main building without a key card or without buzzing the front desk and signing in. However, if you have a legitimate reason to be there, the institute is very nice. There are a ping-pong and pool table in the cafeteria, a very nice lounge, lots of offices, and even more fancy pictures of space and spacecraft (some real, others rather fanciful... although I haven't yet seen a picture of any of the various incarnations of Enterprise, I wouldn't be surprised if there is one somewhere in the building). Also, I'm not quite sure what it is, but the entire place exudes an ambience of the 50s-70s, when lots of money was spent on scientific endeavours and being a scientist was seen as important, daunting, and wonderful (this is how I still see science, but it doesn't seem to be a normal view. Of course, this is probably just a romanticized view of the Cold War era I have garnered through movies like October Sky).
While I know it would be disruptive for those working at UTIAS, I wish they offered public tours. Between the wind tunnels, the Mars dome, the giant flight simulators, the micro satellite lab, and all the other research areas, I think UTIAS would be a wonderful outing for a family visiting Toronto. So, if you are visiting Toronto and are interested in aerospace, try sending someone at UTIAS an email and ask if you can have a tour. You never know, if you sound excited enough they might let you in.
Sunday, September 14, 2008
Game Review: Diplomacy, Part III: End Game Analysis
After many months, I figure it is time I finished my rudimentary analysis of the game Diplomacy. For reference, here are links to Part I (game description) and Part II (opening and mid-game analysis).
To briefly recap, the second stage of the game occurs when all (or at least most) of the neutral supply centres have been occupied by one of the seven major powers. Most players are on nearly equal footing in terms of military size, and the number of players means cooperation with at least one or two others is necessary to overcome an opponent (even though the game is zero-sum in terms of any progress made by one player is at the expense of another). The third and final stage of the game is difficult to concretely separate from the second, but it basically happens when some players begin to lose badly and others expand their military to impressive sizes of ten or more units. At this point one or two players may even be eliminated from the game. While in my experience this seems to happen most often to either Germany or Austria-Hungary (being in the centre is an unfortunate place to be), it doesn't always. Russia makes a large and tempting target, and a Russian leader lacking vigilance might find himself victim of a disastrous invasion from the north through Scandinavia, Finland, and the Barents Sea, or from the south (especially if the Turks manage to get a fleet in the Black Sea). Even Great Britain, which is notoriously difficult to invade (but, at the same time, notoriously difficult to expand from) can be defeated, especially if France and Germany team up and devote some resources to developing their fleets. If enemy ships manage to enter the English Channel and the North Sea, the British are in a lot of trouble.
Regardless of who has found their fortunes dwindling and their dreams of European dominance shattered, as the dust settles the remaining juggernauts begin to face the same predicament that spurred the first round of wars: to expand their empires, they need a target to conquer. The difference at this point, however, is that interactions between players are now often more complicated. Many turns have gone by in an alliance against a foe, but with that foe gone, players begin to wonder how long the alliance will continue. Additionally, those doing exceptionally well at this point begin to grow cocky; victory is looking more assured, as their militaries are now three to four times as powerful as they originally began. It is hard to give much analysis for this part of the game, since the situation is virtually impossible to predict. This is also the part of the game that I have the hardest time with, simply because I don't like the concept of backstabbing an ally. While it very often is advantageous to strike without warning (especially if you and your ally are doing equivalently well or he is even doing better), I have a hard time emotionally with that. It might sound like I am making myself out to be a nice guy here, but I'm not entirely sure that is the case, either. It could be a remnant of chivalry that makes me feel this way, but it could also be a testosterone driven alpha-male style arrogance in which I want my foe to know that I'm coming for him and still have no way of stopping me. I like to think it's the chivalry side of things, but who knows.
Anyway, I am wandering away from the topic at hand. Often people actually don't make it this far in Diplomacy (it is an awfully long game for a single sitting), and simply stop after a player or two is eliminated (or even before if time players need to leave) and simply count up the number of supply centres under each person's control, determining rank in that manner. I hope in my ruminations on the subject I have done Diplomacy justice, and perhaps I may also manage to convince some of my readers who actually know me and have always begged off playing to give it a shot.
To briefly recap, the second stage of the game occurs when all (or at least most) of the neutral supply centres have been occupied by one of the seven major powers. Most players are on nearly equal footing in terms of military size, and the number of players means cooperation with at least one or two others is necessary to overcome an opponent (even though the game is zero-sum in terms of any progress made by one player is at the expense of another). The third and final stage of the game is difficult to concretely separate from the second, but it basically happens when some players begin to lose badly and others expand their military to impressive sizes of ten or more units. At this point one or two players may even be eliminated from the game. While in my experience this seems to happen most often to either Germany or Austria-Hungary (being in the centre is an unfortunate place to be), it doesn't always. Russia makes a large and tempting target, and a Russian leader lacking vigilance might find himself victim of a disastrous invasion from the north through Scandinavia, Finland, and the Barents Sea, or from the south (especially if the Turks manage to get a fleet in the Black Sea). Even Great Britain, which is notoriously difficult to invade (but, at the same time, notoriously difficult to expand from) can be defeated, especially if France and Germany team up and devote some resources to developing their fleets. If enemy ships manage to enter the English Channel and the North Sea, the British are in a lot of trouble.
Regardless of who has found their fortunes dwindling and their dreams of European dominance shattered, as the dust settles the remaining juggernauts begin to face the same predicament that spurred the first round of wars: to expand their empires, they need a target to conquer. The difference at this point, however, is that interactions between players are now often more complicated. Many turns have gone by in an alliance against a foe, but with that foe gone, players begin to wonder how long the alliance will continue. Additionally, those doing exceptionally well at this point begin to grow cocky; victory is looking more assured, as their militaries are now three to four times as powerful as they originally began. It is hard to give much analysis for this part of the game, since the situation is virtually impossible to predict. This is also the part of the game that I have the hardest time with, simply because I don't like the concept of backstabbing an ally. While it very often is advantageous to strike without warning (especially if you and your ally are doing equivalently well or he is even doing better), I have a hard time emotionally with that. It might sound like I am making myself out to be a nice guy here, but I'm not entirely sure that is the case, either. It could be a remnant of chivalry that makes me feel this way, but it could also be a testosterone driven alpha-male style arrogance in which I want my foe to know that I'm coming for him and still have no way of stopping me. I like to think it's the chivalry side of things, but who knows.
Anyway, I am wandering away from the topic at hand. Often people actually don't make it this far in Diplomacy (it is an awfully long game for a single sitting), and simply stop after a player or two is eliminated (or even before if time players need to leave) and simply count up the number of supply centres under each person's control, determining rank in that manner. I hope in my ruminations on the subject I have done Diplomacy justice, and perhaps I may also manage to convince some of my readers who actually know me and have always begged off playing to give it a shot.
Monday, September 8, 2008
Last Year of Undergrad
This morning my last year as an undergraduate student started. It seems like this has been a very long time coming, due to the fact that I have spent two extra years being an undergraduate thanks to losing a year in the transfer from engineering to science and the year-long internship I did while still in engineering. Anyway, in preparation for this year, I decided I would post a list of the courses I am going to be taking. It might not be interesting to anyone else, but it's interesting to me.
Computational Complexity and Computability: The name pretty much sums up what this computer science course is about. I am not particularly excited about this course, but neither am I dreading it. It should be interesting enough, and I may even be pleasantly surprised if it turns out to be engaging beyond a passing interest.
Knowledge Representation and Reasoning: This is a fourth year/graduate computer science course that I was actually signed up to take last year, but ended up switching out of due to the fact that I would be taking it at the same time as its prerequisite (which I was also taking while skipping its prerequisite). The content of this course follows fairly traditional approaches to artificial intelligence (constructing knowledge bases of known facts and using logic to reason about further facts). While I find traditional AI quite intuitive, I also think it is impractical and unwieldy when faced with large-scale problems. I am looking forward to this course quite a bit because I like what I have seen of the professor, and he co-wrote the textbook which I also like from the bits that I have read so far.
Neuroscience Laboratory: While overall self-explanatory from the title, I'm not quite sure what to expect with the details of this one. I have heard fairly unfortunate reviews about it from other students I know who have taken it, but, while I would like to focus on theoretical work, I think a practical knowledge of the laboratory is a useful thing to learn. I haven't really done much wet-lab work (really just high-school chemistry and the summer I worked at the Columbia Brewery in quality control), so I'm a little nervous about some aspects of the course.
Neuroanatomy: Also a fairly descriptive title, while I was initially thinking of not taking this course due to the fact that I tend to find the memorization of anatomy incredibly dull, I heard very good things about the course and its instructor. Also, there is a laboratory component to this course as well which should be interesting.
Linear Algebra II: I am not at all looking forward to taking this course. I know linear algebra is an important area of math, and I have been upset with myself for not learning it better in my first year of university those many years back, but that doesn't mean I enjoy it. Oh well, learning cannot always be fun, sometimes it is just necessary...
Chaos, Fractals, and Dynamics: This is my fun math course for the year. While I heard wonderful things about the professor who normally teaches it, he is unfortunately out on sabbatical for the year. I actually had my first lecture this morning, though, so I got a look at the professor who will be teaching the course. While he has an unfortunate tendency to mumble, he is interested in the material and doesn't give the impression to hate/look down upon the students he is teaching, so I'm calling that a win (I know it is stereotyping, but it seems like hatred of and/or disdain for students is a little too common in the mathematics faculty. I won't mention names, but I think of several examples).
Neuroscience I: Systems and Behaviour: A full year grad-listed physiology course, I think this should be a good one. It is taught by several of the same professors who did the motor control systems course I took last year, including the professor who I did research with this past summer. The material looks interesting and challenging.
For those who are counting, you might have noticed this is only seven courses. That is because Systems and Behaviour is a full year course, but even then I only have four courses per semester, rather than the normal full load of five. That is because I am still planning to add a project/undergraduate thesis course, I just need to finalize a professor under whom I will work. This has taken a fair bit longer than I had thought it would, mainly because almost the entire machine learning department is away on sabbatical this year (which has the added unfortunate side-effect of meaning several of the courses I had planned to take are also cancelled, as well as the remaining professors are too busy to take on a project student). Anyway, I have tentative contact with a professor in aerospace engineering (I do recognize the irony here) who does work in robotics, but we still have to find the time to meet in person rather than just through email.
EDIT: Oops, I forgot to add the other activity I am going to be doing this year. Combining my desperate need for physical activity, my dorky love of history, and my male aggressive instincts manifesting in the desire to play with weapons, I have decided to take a fencing class at the athletic centre.
Computational Complexity and Computability: The name pretty much sums up what this computer science course is about. I am not particularly excited about this course, but neither am I dreading it. It should be interesting enough, and I may even be pleasantly surprised if it turns out to be engaging beyond a passing interest.
Knowledge Representation and Reasoning: This is a fourth year/graduate computer science course that I was actually signed up to take last year, but ended up switching out of due to the fact that I would be taking it at the same time as its prerequisite (which I was also taking while skipping its prerequisite). The content of this course follows fairly traditional approaches to artificial intelligence (constructing knowledge bases of known facts and using logic to reason about further facts). While I find traditional AI quite intuitive, I also think it is impractical and unwieldy when faced with large-scale problems. I am looking forward to this course quite a bit because I like what I have seen of the professor, and he co-wrote the textbook which I also like from the bits that I have read so far.
Neuroscience Laboratory: While overall self-explanatory from the title, I'm not quite sure what to expect with the details of this one. I have heard fairly unfortunate reviews about it from other students I know who have taken it, but, while I would like to focus on theoretical work, I think a practical knowledge of the laboratory is a useful thing to learn. I haven't really done much wet-lab work (really just high-school chemistry and the summer I worked at the Columbia Brewery in quality control), so I'm a little nervous about some aspects of the course.
Neuroanatomy: Also a fairly descriptive title, while I was initially thinking of not taking this course due to the fact that I tend to find the memorization of anatomy incredibly dull, I heard very good things about the course and its instructor. Also, there is a laboratory component to this course as well which should be interesting.
Linear Algebra II: I am not at all looking forward to taking this course. I know linear algebra is an important area of math, and I have been upset with myself for not learning it better in my first year of university those many years back, but that doesn't mean I enjoy it. Oh well, learning cannot always be fun, sometimes it is just necessary...
Chaos, Fractals, and Dynamics: This is my fun math course for the year. While I heard wonderful things about the professor who normally teaches it, he is unfortunately out on sabbatical for the year. I actually had my first lecture this morning, though, so I got a look at the professor who will be teaching the course. While he has an unfortunate tendency to mumble, he is interested in the material and doesn't give the impression to hate/look down upon the students he is teaching, so I'm calling that a win (I know it is stereotyping, but it seems like hatred of and/or disdain for students is a little too common in the mathematics faculty. I won't mention names, but I think of several examples).
Neuroscience I: Systems and Behaviour: A full year grad-listed physiology course, I think this should be a good one. It is taught by several of the same professors who did the motor control systems course I took last year, including the professor who I did research with this past summer. The material looks interesting and challenging.
For those who are counting, you might have noticed this is only seven courses. That is because Systems and Behaviour is a full year course, but even then I only have four courses per semester, rather than the normal full load of five. That is because I am still planning to add a project/undergraduate thesis course, I just need to finalize a professor under whom I will work. This has taken a fair bit longer than I had thought it would, mainly because almost the entire machine learning department is away on sabbatical this year (which has the added unfortunate side-effect of meaning several of the courses I had planned to take are also cancelled, as well as the remaining professors are too busy to take on a project student). Anyway, I have tentative contact with a professor in aerospace engineering (I do recognize the irony here) who does work in robotics, but we still have to find the time to meet in person rather than just through email.
EDIT: Oops, I forgot to add the other activity I am going to be doing this year. Combining my desperate need for physical activity, my dorky love of history, and my male aggressive instincts manifesting in the desire to play with weapons, I have decided to take a fencing class at the athletic centre.
Tuesday, September 2, 2008
Political Science Review: Plato
The second political text we read was the famous text The Republic by Plato. One interesting fact about the book is that it was not titled The Republic in original Greek but rather was simply Politeia (though with Cyrillic letters), which means 'the political system'. Calling it a republic is a bit of a misnomer with our modern sense of the word, as the system of government that Plato ultimately arrives at is not very republican at all but is much more a hierarchical meritocracy. Also, for the record, I would like to point out that when I say republican I do not mean the modern travesty of a political party that exists in the United States today, but rather the notion of a government loosely defined to be run by and for the people.
While part of me recognizes that it is unfair to judge Plato's writing and arguments from my privileged perspective of modernity, I still didn't like this text very much. A large part of my dislike was that I found it frustratingly tedious to read, as it is written as a dialogue and Socrates' interlocutors simply spent most of their time making comments like "well, how could it not be?" and "of course that is how it must be so" no matter the quality of his argument. While that is simply a stylistic critique, I do have more substantive criticisms as well.
The Republic is a long book, so I won't go through all the arguments that I found weak or otherwise lacking, but will rather attempt to outline what is, in my opinion, the most significant error in the text. In 533c - 534a, Socrates argues that geometry and other sciences are only "thought", which is a lesser form of knowing than "knowledge". Knowledge apparently encompasses dialectic, which is what Plato claims his political analysis falls under, and therefore, since it is the highest and truest form of knowing, Plato is clearly correct. I found this completely hypocritical, since the reason geometry was a lesser form of knowledge was that it made use of hypotheses untouched that no account could be given of (in mathematics, these are called axioms). In other words, it is a set of facts that are taken as given. However, Plato himself (through the character of Socrates) spends the first several sections of the book making all sorts of unqualified statements which are simply accepted as fact, such as gods exist and are completely good, there is a normative morality and goodness, and there are four virtues (justice, wisdom, courage, and moderation), among other such claims. Even if the entire text was internally consistent (which I do not believe it always is), the arguments it purports are still dependent upon the claims which he simply accepts as true and given. Therefore, according to his own definitions, Plato's analysis is not knowledge but is mere thought.
While I think there are positive aspects of the text, as a whole I found the arguments unsatisfying. I have had more than one person tell me that is an exceedingly arrogant stance to take, given that Plato is considered one of the greatest thinkers to have existed, but I have a hard time with that attitude. Famous men are very often famously wrong (some of Aristotle's claims are patently ludicrous, but I will get to Aristotle next). I think The Republic is worth reading if one has the time due to its wide-ranging impact on our society, but it should be read without credulity and deference undeservedly given.
While part of me recognizes that it is unfair to judge Plato's writing and arguments from my privileged perspective of modernity, I still didn't like this text very much. A large part of my dislike was that I found it frustratingly tedious to read, as it is written as a dialogue and Socrates' interlocutors simply spent most of their time making comments like "well, how could it not be?" and "of course that is how it must be so" no matter the quality of his argument. While that is simply a stylistic critique, I do have more substantive criticisms as well.
The Republic is a long book, so I won't go through all the arguments that I found weak or otherwise lacking, but will rather attempt to outline what is, in my opinion, the most significant error in the text. In 533c - 534a, Socrates argues that geometry and other sciences are only "thought", which is a lesser form of knowing than "knowledge". Knowledge apparently encompasses dialectic, which is what Plato claims his political analysis falls under, and therefore, since it is the highest and truest form of knowing, Plato is clearly correct. I found this completely hypocritical, since the reason geometry was a lesser form of knowledge was that it made use of hypotheses untouched that no account could be given of (in mathematics, these are called axioms). In other words, it is a set of facts that are taken as given. However, Plato himself (through the character of Socrates) spends the first several sections of the book making all sorts of unqualified statements which are simply accepted as fact, such as gods exist and are completely good, there is a normative morality and goodness, and there are four virtues (justice, wisdom, courage, and moderation), among other such claims. Even if the entire text was internally consistent (which I do not believe it always is), the arguments it purports are still dependent upon the claims which he simply accepts as true and given. Therefore, according to his own definitions, Plato's analysis is not knowledge but is mere thought.
While I think there are positive aspects of the text, as a whole I found the arguments unsatisfying. I have had more than one person tell me that is an exceedingly arrogant stance to take, given that Plato is considered one of the greatest thinkers to have existed, but I have a hard time with that attitude. Famous men are very often famously wrong (some of Aristotle's claims are patently ludicrous, but I will get to Aristotle next). I think The Republic is worth reading if one has the time due to its wide-ranging impact on our society, but it should be read without credulity and deference undeservedly given.
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