The History of Computability

As part of my forays into the subjects of philosophy and empiricism, one of the things I advocated for is the idea that scientists should be more aware of the philosophical underpinnings of their respective fields. I have been meaning to do a series on the philosophical underpinnings of my own chosen field (namely, how intelligence works) for quite some time now, but in order to do that I need to lay some groundwork. One of the most important pairs of concepts for the theoretical pursuit of understanding how intelligence works is also the fundamental pair of concepts underlying computer science: computability and complexity. As I had mentioned in my Scientist Appreciation of Alan Turing, computer science is a relatively young discipline with much of its fundamental work done by Alan Turing and Alonzo Church (who I never did get around to doing a Scientist Appreciation about). These days people take the idea of a programmable electronic device for granted, but it was remarkably recent that a formal architecture to describe and discuss such devices was actually rigorously developed.

Before I get too far ahead of myself, however (and electronic computers are quite far ahead), I will begin at the turn of the 20th century. A remarkably brilliant man named David Hilbert compiled a list of 23 unsolved mathematical problems in 1900. This list in many ways served as a sketched outline to guide theoretical research for the coming century, with a number of the problems remaining unsolved even today. Although many of Hilbert’s problems are fascinating in their own right (I’m sure all of them probably are, but I don’t actually understand a few of them), the one which is relevant to the discussion at hand is his tenth problem. Hilbert's tenth problem is ordinarily written as something along the lines of

Find an algorithm to determine if a given Diophantine equation with integer coefficients has an integer solution.

However, this is not actually how Hilbert posed the problem, as the word algorithm had yet to enter useage (Webster's New World Dictionary, for example, did not include the word 'algorithm' prior to 1957). The actual original statement of the problem was something along the lines of:

Given a Diophantine equation with any number of unknown quantities and with rational integral numerical coefficients: To devise a process according to which it can be determined in a finite number of operations whether the equation is solvable in rational integers.

Before a number of my readers balk at the term 'Diophantine equation', it simply means an indeterminate polynomial equation (for example, x + y = 5 is an Diophantine equation, since there is no single assignment of values that satisfies the equation. Rather, the solution is the line x = 5 - y).

As I mentioned, at the time that Hilbert originally posed this problem the term algorithm was not in use. An algorithm is essentially a process or sequence of instructions, but with a number of specific properties (namely, that it has a finite sequence of instructions and is well defined (at no point does it reach a state in execution in which it is not clear what it is to do next)). Informally, algorithms have been around for centuries. One of the most famous (and one that is likely familiar to any computer science student) is Euclid's algorithm for determining the greatest common divisor of two numbers. However, prior to Hilbert's problems, very few people had ever attempted to analyse the notion of abstract processes. Mathematicians and scientists developed and utilized specific mathematical methods for specific problems, but, for the most part, each one was developed and investigated within the context of its application alone. What changed all of this was that people began to question whether or not there actually existed the process that Hilbert's tenth problem was asking for. The fact that some problems could be unsolvable was a fairly ground-breaking notion, and provided the impetus to explore the general notion of solvable methods.

Although the actual proof that no such algorithm exists which can solve Hilbert's tenth problem did not come about until 1970 with the publication of Yuri Matiyasevich's doctoral dissertation, the inkling that it might be unsolvable began much earlier, particularly from the field of logic with Kurt Gödel's famous incompleteness theorems. Motivated by the growing question of solvability and mathematical truth, in 1928 Hilbert proposed another, more general algorithmic challenge called the Entscheidungsproblem (decision problem). The Entscheidungsproblem takes a formal language and a mathematical statement in that language as input and outputs whether or not it is true. The problem piqued the interest of both Church and Turing, motivating the two of them to independently formalize the concept of calculability in the mid 1930s. Both Church and Turing independently showed that the Entscheidungsproblem could not be solved. The models of computation that Church and Turing each used (λ-calculus and Turing machines, respectively) were subsequently shown to be equivalent, and thus the field of computability was formed.

I will discuss the actual material of computability in the next post on this topic, but I thought an historical overview might help illustrate the motivations behind the field as well as provide a somewhat less painful introduction for those not familiar with the terms. I am not sure I was entirely successful with the latter aim, but feel free to leave any comments or send me questions via email for parts that are not clear.

Further Discourse on Demonizing Darwin

In my most recent Scientist Appreciation post on Friedrich Wöhler, I pointed out that Darwin, in my opinion, receives a disproportionate amount of discussion and demonizing by the religious right compared to other historical scientists. Regan responded to this by saying:

The biggest reason that Darwin is such a huge target is because the work he did and inspired totally invalidates the story of genesis.

Wohler's challenge to vitalism is different in the sense that there is nothing in the bible that says "And lo god created vitalism, and it was pretty neat", so it was easier to rationalize that concept into the theological worldview. The work that Darwin did and inspired can't be crammed into the bible no matter how hard you try. The bible says X happened, and the study of the processes of natural selection and evolution says Y happened. There is no possible way to reconcile the two.

I think the stranger scientist to be demonized by religion is Galileo. The bible doesn't even explicitly say the sun travels around the earth, and they still put him under house arrest until he died.

Since Regan's statements do not satisfy the quandary I meant to be presenting but are nevertheless factual and reasonable, I thought it worth writing another post on the matter to hopefully elucidate my original intent more clearly. As with most of my posts on subjects outside the realm of computational neuroscience, I have not made exhaustive study of the topics I cover here, so it is reasonably possible I am basing my discourse on incorrect information (of course, that is still possible when I am talking about computational neuroscience, just I tend to think it less likely). If you disagree with what I write, please do not hesitate to leave a comment or send me an email.

The thing is, revealed religious truths are awfully dependent on the ephemeral whims of people. Organized religions also tend to have a couple driving forces to deal with - there is both the scripture itself as well as clerical dogma. Before widespread printing of the Bible, these two forces in the Christian world were largely one and the same - Christianity was governed by one of a few theocratic hierarchies (the Catholic church in the west, and the Eastern Orthodox Church in the east). My historical knowledge of eastern Europe is weaker than my knowledge of western Europe before the 1900s, so I will primarily concentrate on the west. This merging of clerical dogma and scripture under the closed purview of the Catholic hierarchy meant that, for the most part, there was one accepted version of Christianity and alternative interpretations of the scripture (which could possibly lead to new dogmas) were not widespread (since few had access to scriptural learning) and, when they did occur, suppressed through threats of excommunication and the charge of apostasy. This situation could help explain the reaction to Galileo, as the view of Earth as the centre of the universe, while not explicitly scriptural truth, was heavily part of the clerical dogma. Given the philosophical stance of the Christian faith that humans are the favoured creation of an all-powerful god, Earth as the centre actually fits better. Combined with scriptural references like Joshua making the sun stand still, the conclusion that Earth was not the centre of the universe and rather revolved around the sun contradicted current dogmatic law based on the currently favoured interpretation of scripture. Galileo's conclusion, therefore, was, in some interpretations, contradictory to scripture, but, more importantly, was subversive to the power of the religious hierarchy. As time progressed and Galileo's view of the solar system became more and more undeniable, the religious dogma gradually shifted to accommodate. The story of Joshua was recast either to 'metaphor' or interpreted as the miracle of the Earth halting its rotation and orbit rather than the sun halting its motion, and the clerical dogma avoided comment on the issue before finally apologizing for Galileo's treatment a couple decades ago when someone must have realised they were still remiss in that regard. Of course, one reason the Catholic church is usually so slow to apologize or admit wrongdoing for anything is because, technically, their head guy is supposed to be divinely inspired by an omnipotent and timeless all-powerful being. As their god's agent on Earth, the pope should infallible (at least once he becomes pope). Admitting mistaken persecution of a brilliant scientist because his claims were deemed wrong makes the infallibility of a divinely inspired leader a little harder to argue.

Moving past Galileo and back to the time period of Darwin and Wöhler, however, schisms within the world of Christianity had been amplified by the translation of the Bible into many languages as well as widespread availability of printed material and an increase in literacy. Although there was still a certain amount of power concentrated in clerical hierarchies, there happened to be more of them now that the Church of England existed along with other Protestant branches like Lutheranism, and that division weakened their overall power. As was pointed out by Andrew, Darwin did not operate in a vacuum. Geology and paleontology were being developed by pioneering scientists like Georges Cuvier and James Sutton. Darwin was not the scientist who first developed the idea that extinct species had once lived on Earth without any evidence of mankind in a period of time far further in the past than one could feasibly trace the Biblical story. What he did was develop a theory that elegantly explained the appearane of the biological rule based on these observations as well as zoological observations in his current day. I would argue that it was the scientists who developed the fields of paleontology and geology who more directly contradicted the Biblical story of genesis.

Thus, the manner in which Darwin's work contradicts Biblical creationism must be seen more as a philosophical contradiction rather than a direct one, in which evolution can be seen as a naturalistic mechanism to explain the distribution and form of extant species. This explanation weakens the need for a divine explanation for the form of modern life, although it says nothing about the origin of life. Before vitalism had been demonstrated incorrect and we were able to generate organic substances from inorganic subtrates, an avenue for theological retreat remained widely open. By recasting genesis as a metaphor and enfolding evolution into "god's plan", the divine origin of life was much more easily defensible when there was no known natural mechanism for going from inorganic to organic. Without the abandonment of vitalism, theistic evolution is a much more viable outlook (although I would contend that one still has to answer how a benevolent and all-powerful god would deign to rely on such a largely unforgiving and unpleasant mechanism).

Evolution, it would seem, largely attacked the dogmatic idea of immutable forms, while the disproof of vitalism greatly weakens the idea of a divine origin for life. Both are aspects of the Biblical creation story, which is why I thought Wöhler's work also undermined religious dogma in a similar manner to Darwin's.

Scientist Appreciation: Friedrich Wöhler

One thing that confuses me about Charles Darwin is just how greatly he is demonized by anti-science groups (primarily the fanatically religious). After all, while Darwin did make profound contributions to the field of biology, he is not the only scientist to help expand our knowledge of the natural world into an area that was formerly staunchly under the purview of theology. One other such scientist was Friedrich Wöhler, a German chemist from the nineteenth century.

Though he spent much of his younger days working in various institutions throughout Germany (and even briefly in Stockholm), he spent the final portion of his professional life working in Göttingen (which is why his statue now graces one of the town's squares). Among a copious output of work that included the isolation of aluminium, titanium, and several other elements, Wöhler also began the field of organic chemistry through the synthesis of urea without the aid of a living cell. This turned the idea of a 'vital force' required for generating organic compounds on its head, and brought the exploration of biological organisms within the sights of the physical sciences. In modern terms, he helped spark the development of organic chemistry and thus the related fields of biochemistry, molecular biology, molecular biophysics, and bioengineering.

Of course, Wöhler's singular demonstration of the synthesis of an organic compound did not fully discredit vitalism, but it got things started. Now, the idea of a vital force unique to living beings has been virtually abandoned (outside of a few caveats which I will soon be discussing). What I find strange is that the acceptance of the physical and chemical basis for our bodies has been, for the most part, complete. The previously widespread set of beliefs in various life forces has retreated entirely into the form of an incorporeal and undetectable soul or New Age woo of some indefinable energy that can be somehow helped (expensively) by interior decorating consultations or dubious and mildly unpleasant physical interventions. This retreat, too, has been performed without reference to the historical shift in our perception of life and its constituent parts. There is no demonizing of Wöhler, or false stories of recanting on his deathbed. In actuality, Wöhler is pretty much a ghost in the public mind. Outside of those who study chemistry or have an interest in the history of science, his name barely registers. While part of that may be that chemical synthesis is slightly more direct to demonstrate, as we have seen with the shifting goal-posts of the many incarnations of creationism, scientific demonstration is not actually the point.

I don't really have an answer for this difference in the way history has treated the two scientists, but I do have an appreciation for Friedrich Wöhler's contributions to science. His initial synthesis of urea may have been an accident, but it was no less ground-breaking.

Scientist Appreciation: Felix Klein

As some of you may have guessed by my post from earlier today, I have my suitcases and I am back in business. With so many famous scientists and mathematicians steeping Göttingen in history, I have decided it is time to ressurrect my Scientist Appreciation posts. Every time I find something named after a famous scientist or mathematician (and I have my camera with me), I will thus get a photograph and say a few things about the emminent fellow. Of course, I should therefore change the label perhaps to Mathematician Appreciation for fellows like Felix Klein, but I hope their memory will not be too tarnished if I place them under the label of 'Scientist' for the sake of reducing clutter on my sidebar (and for brand recognition...).

Felix Klein is actually someone who I mostly knew of thanks to my girlfriend. With her extensive interest in geometry and group theory, Felix Klein is a massively famous figure to her. A little bit of research on Wikipedia and he seems awfully impressive to me as well. Mathematically, he was exceptionally important in the founding of group theory and the relation of geometry to other areas of mathematics (I only have a vague understanding of the appropriate terms here, so to avoid wildly embarrassing my girlfriend and any other mathies who might be reading this, I will refrain from going into too much detail). What makes Felix Klein extra exceptional, though, is he was also exceedingly important as a facilitator of the scientific enterprise as a whole.

While serving as a young professor in Munich, he taught courses to Adolf Hurwitz, Carl Runge, and Max Planck (among others, but those three I have directly encountered in memorable ways within my own studies). After a brief stint in Leipzig, Klein moved to Göttingen where he worked to rebuild the city's prominence in the world of mathematics. To that end, he managed to fenagle Hilbert away from Königsberg, guide the mathematics journal Mathematische Annalen to become one of the best in the world, and begin allowing women to study in Göttingen. Perhaps even more widely impacting than his administrative and leadership roles in Göttingen itself, Klein also began to advocate for the adaption of calculus instruction in secondary schools, a practice gradually adopted in many countries even outside Germany.

So, whether you are a devoted mathematician or simply a dabbler like myself, you should take a moment to appreciate the endeavours of one Felix Klein. If you want more detail on the man, have a look at his Wikipedia article.

"In a garb of black, we must pay respect to the colour we're born to mourn"

It came to my attention a couple days ago that there has been a sad loss this past week. Dave Arneson, one of the creators of Dungeons and Dragons, passed away. With Gary Gygax's death having happened only last year, it would seem an era of geek gaming has come to an end.

The Exploits of Lincoln and Darwin Are Not Comparable

I have complained about people conflating these two historical figures before due to the irrelevant coincidence that they were born on the same day, which is perhaps why it isn't surprising that on today, their birthdays, people continue to make stupid American-centric swipes at Darwin. I found that post kind of randomly, and it irked me. As I mentioned in the comment I left there, Google and Wikipedia are both internationally available websites with a vested interest in world-wide applicability. However, I suppose if you fail to realise (or willfully ignore) the profound effect evolutionary theory has had on our understanding of biology (and therefore medical science, agriculture, ecology, and many other areas which contribute to the welfare of humanity worldwide), then it might be possible to construe honouring the 200th anniversary of Darwin's birth as somehow being an insult to the memory of Abraham Lincoln. Otherwise, I see no basis for such a conclusion.

Scientist Appreciation: Alan Turing

I had my Computational Complexity and Computability course tonight, and on the way home while slogging through the snow I wondered how I could work a post around the rather fascinating course material. Then I realised it gave me a perfect excuse to resurrect one of my favourite series on this blog which sadly fell the wayside: Scientist Appreciation! So, since he is so central to the subject of computability, this installment of Scientist Appreciation is devoted to Alan Turing.

Alan Turing had an unfortunately short life, but prior to his untimely death at the age of 41 he completed works and earned prestige which would make most academics inwardly weep with envy. His work helped form the theoretical foundation of computer science while he also goes down in engineering history as helping to construct one of the first true computers. Additionally, he gained popular fame as a code breaker during World War II working to counter the infamous Enigma machine as well as having his name become widely known in the realm of both artificial intelligence and science fiction through his proposition of the Turing Test for intelligence. While he is probably more popularly famous for his cryptography and the Turing Test, the rest of this post will focus on his theoretical framing of the notion of computability.

The true power (as well as the beauty and frustration) of mathematics is its elegant rigour and formal set of rules. If you truly want to know the properties of something, find a way to frame it mathematically and probe the results. Thus, when people were trying to understand the concept of an algorithm and determine just what sort of problems were computable, Turing created the eponymous concept of the Turing Machine (TM for short). In its regular formulation, a TM can be envisioned as an assembly line with a computational head positioned above a sheet of some sort (paper, perhaps) which can be both read and written to by the head. This sheet extends to infinity to the right, but has an ending to the left (from which the input is written). In each computational step, the head reads in an input from one position on the sheet, changes its internal state, has the option of writing over the current sheet's position, and then moves either to the left or the right (if it tries to move left in the initial position it stays where it is). This might sound like an awkward and plodding kind of computational machine to have, but there are some really fascinating things which can be shown about them. I don't know if there is any interest, so I won't go into detail now, but if any of my readers want me to give examples of some interesting problems with TMs let me know in the comments (or send me an email, if you have my email address). The thing is, I think I might just enjoy this because it is the kind of mathematics that comes the most naturally to me (as naturally as I think any university level math can come to a non-genius). Even if no one cares, I might not be able to restrain myself after I talk about Church in the next Scientist Appreciation and tie his work in with Turing's.

Anyway, my laptop is really acting up tonight, so I'm going to end this post here and hope my computer doesn't die (it also means I haven't proof-read this, so I hope it isn't too abysmal. Of course, I could always save as a draft and publish tomorrow, but what would be the fun in that?). In conclusion, Alan Turing made an amazing account of himself for his short life, and his early death was a tragedy for mathematics and computer science.

Political Science Review: Hobbes

This will probably be my last post in the Political Science Review series. While we also read Locke, I ended up not getting past his early stuff. While it was interesting, particularly in relation to Aristotle's opening as they both discussed the role and organization of the family, I am not sure I remember enough of it to really do it justice. So, if you are interested in Locke you'll just have to read his stuff yourself, and I will end my sojourn into political science with a review of Hobbes' Leviathan.

Hobbes was an interesting thinker. While Leviathan is a rather difficult text to slog through (mostly owing to it being written in English used several centuries ago), his ideas and thinking quite impressed me all the way to chapter 19, at which point it seemed to all fall apart. Not to get ahead of myself, though, let me start at the beginning. Hobbes begins by discussing the nature of man, going so far as to look briefly at sensory perceptions and how a person knows what he knows. While his neuroscience is stifled a little by 17th century science, some of his basic ideas are interesting and, taken together, form a coherent, logical context for his later political analysis. He paints a rather dismal picture of mankind, though, in many ways accepting a similar view to Machiavelli on the nature of man as violently selfish and greedy. The main difference between Hobbes and Machiavelli, though, is Machiavelli stressed greed and desire for glory as the primary drives of men, while Hobbes emphasized fear (specifically of a violent death).

Given that Hobbes was a much more careful, academic, and theoretical thinker than Machiavelli, where Machiavelli dove straight into political discourse on realistic situations, Hobbes carefully defines his terms and thoughts about human nature. Probably the most important one Hobbes outlines is his definition of the state of nature, or state of war (they are the same thing for Hobbes) in which there is no government. This is essentially anarchy and, according to Hobbes, is an absolutely horrible, terrible state where people butcher each other and steal without qualms. He says, for example, than in the absence of a political authority, "every man is enemy to every man..." (13.9). Though Hobbes admits that there are other driving forces in the quarrels of men and the reasons they agree to live in peace, he emphasizes fear as the greatest of them all.

What is rather interesting about Hobbes' analysis, though, is he abandons the common normative views on morality and instead defines them in a rigid and clear manner. This has huge ramifications for his later thought, particularly justice, which he defines as, "injustice is no other than the not performance of covenant. And whatsoever is not unjust, is just" (15.2). Importantly, though, Hobbes makes the caveat that if either party has legitimate fear that the other party will not follow through with their part of the covenant, that nullifies said agreement. Thus, "before the names of just and unjust can have place, there must be some coercive power to compel men equally to the performance of their covenants, by the terror of some punishment greater than the benefit they expect by the breach of their covenant... such power there is none before the erection of a commonwealth" (15.3). Hobbes therefore places fear as the root of the political power of a state, as it must enforce the political agreement undertaken by its citizens through fear of what it means to breach that agreement. Since he also points out that without some form of state there can be no outside coercive force, he subtly hints at what he later makes more explicit: there is no legitimacy for personal morality, but rather what the state dictates takes precedence. The explicit statement of such totalitarian thought comes much later, however, so at this point (chapter 15) I didn't notice the dictatorial undertones and was still rather impressed.

Taking the idea that the agreements which allow for civilized life cannot exist without a central government to enforce them, Hobbes begins to discuss how such a government should appear. It is at this point, in my opinion, that his analysis veers off the course or rationality and into the realm of 'where the hell did this come from?', if you will excuse my break in style. For, while Machiavelli made the, in my opinion true, statement "there is no doubt the public interest is never a guiding principle except in republics", Hobbes states (seemingly completely out of nowhere and not at all supported by reality), "in monarchy the private interest is the same with public" (Discourses pg. 166, 19.4). Hobbes even seems to contradict himself at several points very shortly after, first when he explains that any successful state institution must be essentially immortal or it would fall and need to be rebuilt with each generation, thereby returning its citizens to the horrors of anarchy in each interim. This requirement, as Hobbes aptly points out, means that such an institution must be designed without taking into account the natures of the men occupying it, something which a monarchy clearly fails to do. Likewise, as Hobbes even admits, a monarchy has an extremely high risk of failure at the death of each monarch.

Despite the drawbacks of a monarchy, however, Hobbes continues to argue in favour of one, with his specific description growing increasingly despotic. His main reason seems to be that, within the monarch's lifetime, a state run by a single powerful individual is the least open to civil strife and internal division, thereby minimizing the chance of a catastrophic meltdown into anarchy and civil war. Hobbes spends several chapters addressing (in my mind, inadequately) some of the drawbacks of a monarchy, particularly in the dangers of the monarch blatantly trampling on what we in our modern political outlook would recognize as the civil rights of the state's citizens, particularly in the case of their property rights. Recognizing that not all subjects can be expected to understand that revolt against the government will lead to anarchy which, no matter how terrible the government is, will be much worse, Hobbes states "the grounds of [the monarch's] rights... need to be diligently and truly taught..." (30.4). This struck me as an exceedingly weak argument in which Hobbes ensnared himself in his own rhetorical trap. If anarchy is such a terrible state that any government, no matter how bad, is better and proper education of that fact can make such a government stable through the citizens' fear of anarchy, then this could be used for any government and all the hoops Hobbes jumped through earlier to explain why a monarchy was the best form of government for its stability comes to naught. Education can make any government stable by playing upon the fears of its populace, which leaves the only reason for a monarchy being Hobbes' empty statement that a monarch has his interests aligned with those of the people.

Thus, I found myself unfortunately dissatisfied with Hobbes' political analysis towards the end of his text. I still think the first eighteen chapters were well developed, however, and it was especially interesting to read his thoughts on the fundamental nature of why a government needed to exist. Though I disagree with the initial theological underpinnings of the beginning of Locke's work, I think once he finishes quoting scripture to beat back the arguments of some contemporary of his, he gives a more approachable and, in the end, less flawed portrayal of the nature of government than Hobbes. Locke is also easier to read, being a little more contemporary, but if you have a lot of time to kill, reading Hobbes first will help give some grounding for Locke's work.

Also, this post was a little condensed to make it into an approachable blog post for easy perusal rather than into a daunting block of text which no one would want to read. If you find Hobbesian thought interesting, however, I am somewhat proud of my final essay in the political science course in which I compared Machiavelli and Hobbes on their analysis of the nature of man and how it leads to their formations of what a civil authority should be like. The essay focuses on Hobbes but uses Machiavelli as a backdrop with which to compare (and, since I agree more with Machiavelli's analysis, poke holes). If you want, you can contact me or leave a comment and I can send you my essay (though I will be wildly shocked if anyone takes me up on this offer).

One final note - the references. Except where noted that I was taking quotations from Machiavelli's Discourses, all quotations are given from my version of Leviathan in the format [chapter].[paragraph number].

Political Science Review: Machiavelli

Out of all of the works we read over the summer, Machiavelli's were my favourite. Not necessarily because I agreed with him, but because he recognized that politics is a dirty business that doesn't necessarily have an absolute answer. While everyone else (aside from Thucydides) seemed to think that he had developed the definitive treatise on the proper manner of government, Machiavelli recognized that perhaps there might be better minds than his who would come to different conclusions, but he nevertheless strove to write texts that would be useful to people living in the real world rather than in some ideal world where men acted as they ought to, and not as they actually do.

We read most of both The Prince and The Discourses. While The Prince seems to be his most famous work (I think that is simply due to the fact that it is the most shocking of the two in its blatant sociopathy), I found The Discourses to be far more insightful and penetrating. It was also where I think Machiavelli found some redemption, as he displayed himself to care about the lives and security of the citizenry and not just the welfare of a ruler. He was one of the first political theorists to recognize that there is a certain degree of wisdom amongst the entire populace of a country, and not just in an aristocratic elite (of course, the suffrage of the masses was something that I have always been raised to see as the correct and best form of governance, and it was an apriori assumption that I believe this course challenged the most for me). The need for a balanced institution was argued for by Machiavelli both eloquently and rationally. He took great pains to back up his claims by using historical precedence as well as a degree of psychological pessimism that was both enlightening and depressing.

I am getting ahead of myself, however. Perhaps I was simply initially set in favour of Machiavelli because of his rejection of the political theories of all those thinkers who we had previously read who I found to be so logically lacking (Plato, Aristotle, and Cicero). As promised, do you remember Cicero's statement: "fraud seems to belong to the cunning fox, force to the lion; both are wholly unworthy of man..."? Machiavelli has a direct allusion to that when he states in regards to the qualities a prince must have, "One must therefore be a fox to recognize traps, and a lion to frighten wolves." I do not think that is my entire reason for enjoying Machiavelli's works, though.

I think I will end this review, therefore, in saying that I greatly recommend reading Machiavelli's works. While they are in many ways depressing and cynical, they are realistic and rationally laid out. I think in many ways it is unfair that Machiavelli's name has become associated almost exclusively with negative connotations of underhanded power grabbing and backstabbing, for there is a lot more to his texts than an advocacy for brutality and deceit. Of course, that said, I think I will end with a choice quotation from The Prince that displays the clear sociopathic psychology that so characterizes this particular work.

"Whenever you have to kill someone, make sure you have a suitable excuse and an obvious reason; but, above all else, keep your hands off other people's property; for men are quicker to forget the death of thier father than the loss of their inheritance."

Quotations - A New Regular Post

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

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.

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.

Political Science Review: Thucydides

Monday night marked the end of my required social science credit. I had my final exam for POL200Y1 - Political Theory. I actually quite enjoyed the course, though I discovered that I hold some of the most famous thinkers in history in contempt. Perhaps that is a mark of extreme arrogance on my part, but I suppose I'll have to live with it. I have been meaning to write some thoughts about the course for a while, and so I decided that over the next little while I will try to give a brief review of the works that I read from each of the authors we looked at: Thucydides, Plato, Aristotle, Cicero, Machiavelli, Hobbes, and Locke (in chronological order).

Thucydides was a slightly odd first choice of author, as he is the only author whose text we looked at was not specifically a political text, but was rather historical. However, his text had many political overtones, as he directly states early on that the point of his history is to look at the nature of man, for men cannot know their nature without understanding their history. The specific history explored by Thucydides is the Peloponnesian War. A more complete history of the details of the war can be found on Wikipedia. Though containing political points, Thucydides is primarily a critic. He offers no concept of how things should be fixed, he simply points out some of the failures of political systems at the time.

The war itself was mainly between Sparta and Athens, though it involved virtually all of Greece as the other city-states became drawn in on one side or the other. I think one of the most interesting parts of Thucydides is also at the very beginning just after he outlines his motivations for writing the history based on the unchanging nature of man. He states that, though it was largely unspoken, he thinks the main cause of the war was fear of Athenian power. Sparta at the time had the most powerful land army, with their infantry being legendary for their martial prowess (this was is only a few decades after the war against Xerxes and his Persians). Athens, however, is the primary naval power as well as one of the richest Greek cities. It also has the largest population and one of the first true democracies.

The text mostly consists of speeches and dialogues. This at first seems fairly strange in a historical text, but once you get used to the style it is pretty interesting. One of the most striking characteristics of the text was the strong parallel I saw between the Athenians and the United States of America. Athens, like the United States now, was a powerful imperial state with a distinct economic advantage over its rivals. Like the United States in the second world war, Athens served as an instrumental force in a war that was largely seen as noble and necessary for defeating a decidedly evil foe (the Persian invasion of Greece). Their success in stopping the Persians earned them a great deal of good will and respect, but also forced them into the political affairs of the whole region. The memory of the great war was now fading away, leaving those who now found themselves wronged by the imperial aspirations of Athens feeling embittered and resentful. Athens justified themselves by claiming that they had the right to elevate their standards of living through unequal treatment of subordinate city states because they were better. Theirs was a blessed way of life, more free and noble than that of their neighbours. They also made the argument that someone had to be on top, and they were better than any of the alternatives.

Anyway, I don't really have a lot to say about Thucydides other than he was interesting. If you find ancient history engaging, I would say he might be worth reading. Also, if you enjoy historical parallels to contemporary politics, he can be read in that manner quite easily. Perhaps my lack of things to say, though, might also rest in that I read him at the beginning of the summer, so many of the details are starting to fade. My discussion of the next six writers should be a little more engaging.

A note about crackers

I believe most people reading this blog have heard about the whole eucharist 'stealing' business that went on in Florida a while ago, followed by the desecration of one by PZ Myers. Up to this point I have avoided comment on this subject simply because it seemed rather absurd to me and I plan to continue with the no comment policy. This is just a quick post to mention that even Hobbes, one of the founders of modern political philosophy, pointed out multiple times throughout his seminal work Leviathan that the concept of transubstantiation was utterly ridiculous and made absolutely no sense. That was three and a half centuries ago. I have many issues with Hobbes' conclusions (he is scarily totalitarian. In fact, I think it is specifically in chapter 19 that all of Hobbes' careful ruminations shockingly lead him to the nonsensical declaration that a despotic monarch is the best form of government). Actually, I seem to have lost the original point behind this post, but I think I'll put it up anyway, because I found it to be interesting tidbit of information. Hobbes is an odd character - sometimes nearly atheistical, other times he is arguing straight from scripture. I think it might be safest to regard him in a similar manner to Jefferson, in that he was raised in a Christian society but was intellectually frustrated with the contradictory and evidentially baseless nature of many of the church's teachings.

A Stupid Argument

As I have mentioned before, the intention of this blog was never meant to be contentious or ranting. Perhaps I'm just having a belligerent couple of weeks with this Aristotle essay hanging over my head, but I was once again struck by the inane stupidity of an article today and felt the need to respond. The article compares Darwin and Lincoln and tries to decide who was the more important historical figure. It can be found here.

While the premise of the article is a little stupid, I would be willing to forgive that for the sake of generating popular interest in historical figures. However, the part that I couldn't let slide was the utter ridiculousness of the conclusion. The article concludes that Darwin was less important because Wallace also had the idea of natural selection, though less rigorously developed, so we would simply have inevitably figured out natural selection with or without Darwin. However, if you stop for a moment and consider that argument, I'm pretty sure that if Lincoln had not existed there still would have been a 16th President of the United States of America. Sure, he might not have handled things as well as Lincoln did, but that argument didn't seem to stop the author of the article thinking that Darwin wasn't so important after all.

Anyway, maybe I'm just cranky.