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Much has been written about this article. For instance: ---------------- http://www.telegraph.co.uk/technology/5273453/Fifty-years-on-CP-Snows-Two-Cultures-ar

Much has been written about this article. For instance: ---------------- http://www.telegraph.co.uk/technology/5273453/Fifty-years-on-CP-Snows-Two-Cultures-are-united-in-desperation.html http://www.telegraph.co.uk/technology/5273453/Fifty-years-on... Such was the intensity of debate that it might be supposed that these were age-old themes: but in fact, the idea of separating academic disciplines into groups known as science and humanities was no older than the 19th century. The term "scientist" was only coined in 1833, and it was not until 1882 that another Rede Lecturer, Matthew Arnold, discussed – under the title of "Literature and Science" – whether or not a classical education was still relevant in an age of great scientific and technical advance. ---------------- There are also many themes in this article that are specific to Britain in the 1950s: ---------------- Snow compared Britain unfavourably with the US and USSR, in terms of numbers of young people who remained in education to the age of 18 and above. The British system, he argued, forced children to specialise at an unusually early age, with snobbery dictating that the children would be pushed towards the "traditional culture" and the professions, rather than science and industry. Arnold was responding – with infinitely more courtesy than Leavis – to an earlier lecture by T H Huxley, known as "Darwin's Bulldog" for his rumbustious defence of evolution, who argued that science was as valid an intellectual training as the classics. It was not a popular opinion. As late as my own childhood in the Sixties, the bright boys were expected to read classics at Oxford, and the less bright steered towards the labs. ---------------- I think 2 things are worth remembering about any such debate: 1.) as a civilization becomes more advanced, the people in it tend to become more specialized. If you grew up in 1700, it was perhaps possible to read all of the classics, in literature (Homer) and medicine (Galen) and philosophy (Aristotle) and physics (Aristotle) and math (Euclid). But nowadays it is impossible to study every branch of knowledge to any meaningful depth. 2.) for all of the obvious disadvantages that come with specialization, there are also many advantages (indeed, that is why specialization exists). A modern potter has a fantastic array of choices regarding materials, which did not exist even 50 years ago. A historian today must pick a narrow speciality, as there are now many millions of documents to look through to be considered an expert -- indeed, I have a friend who has specialized in the American Civil War, and he once said "If you have only read 1,000 books about the American Civil War, then you are just an amateur." And in the old days the village blacksmith might have known how to make both a hoe and a horse hoof shoe but a modern mechanic needs to specialize regarding devices (cars? domestic machines? textile plants? telecommunications?) but then also pick a sub-specialty (if a car mechanic, then foreign or domestic? Perhaps a few particular brands). There is an economic benefit to specialization. I worry that gets forgotten when this debate comes up.

padobson 13y ago
This is great, you summed up every idea I had while reading this in a way that was far more articulate than I could have. I only have one thing to add: If there is an economic and even, possibly, a societal benefit to specialization, and The Two Cultures idea complains about the rift between the humanities and the sciences, then has someone properly updated the material to show how much more specialized society is becoming? The Wiki article talks about a possible third culture, but it seems to me you could become fairly deeply specialized in business/economics without ever needing a classical humanities education or a classical math/science education.
msluyter 13y ago
Specialization is something I often wonder about. Consider the following analogy: the sum of human knowledge is represented by a giant circle (though not necessarily perfectly circular in shape). Anything inside the circle is that which is known; anything outside is unknown. You're born in the center, and as you learn, the set of what you know extends towards the edge. As you mentioned, at some point in time, you could know all of the circle; now you can only know some subset of it. If you're a scientist or whatnot, you actively move the edge outward. My question is, will we ever reach a point where it takes so long to move from the center to the edge that we'll eventually stop making progress? In mathematics, it already takes considerable time to reach the knowledge boundary (30 years or so?) Will we reach a point where it takes greater than a lifetime? Or, is it possible to jump to the edge by skipping some foundational knowledge (could you do higher math without knowing, say, calculus, for example?) What are the risks of doing so? And ultimately, how does a complex society hang together when each person has (at most) knowledge of a tiny subset of available knowledge?
- lkrubner 13y ago
  You get at the degree to which all human knowledge is limited by the central nervous system that humans possess. There must be some finite number of axons and dendrites that can be stuffed into the cranium of a human, and even if there is a sophisticated system of compression and/or multiplexing in use, we can probably assume that a finite amount of axons and dendrites can only carry a finite amount of information. Thinking of the physical limits on human knowledge leads to a model of knowing that puts the central nervous system at the center of our our experience of the universe. There may be an absolute reality that exists outside of us, but since all of us are human (I assume) we must admit that our knowledge of that absolute reality will forever be shaped by that central nervous system. The limits of the central nervous system cause humans to look for models of reality that fit well with those limits. For instance, there is The Magical Number Seven, Plus or Minus Two: http://en.wikipedia.org/wiki/The_Magical_Number_Seven,_Plus_or_Minus_Two http://en.wikipedia.org/wiki/The_Magical_Number_Seven,_Plus_... Because of the (very very finite) limits on working memory, the human mind leans heavily on heuristics that allow simple models to stand in for the complexity of reality. No human being could easily work with a physics model that had 1 million variables: therefore we tend to look for models that have a handful of variables, yet still give us reasonably good estimates. Just yesterday there was posted to Hacker News an article about a slinky, and that article contains a good demonstration of the kind of simplifying assumptions we often make to reason about problems that are too complex to approach directly: "I decided to idealize the problem like this: the slinky is an ideal spring with mass distributed uniformly throughout. It is also a spring that can pass through itself. These assumptions make analyzing the problem easier." And of course, we often present students with problems where the difficulty of achieving perfect measurements of variables is simply assumed away. For instance in this exercise: http://www.uta.edu/ce/nsf/ret/docs/lesson-plans/reynolds08-5.pdf http://www.uta.edu/ce/nsf/ret/docs/lesson-plans/reynolds08-5... The important things to measure are: force, deflection, torque, moment of inertia, stress and strain. Often, in real life situations, engineers have no way to perfectly measure these things. Large engineering projects proceed with various methods for getting reasonable estimates: known upper and lower bounds, prototypes, isolated testing of particular connections, etc. The smartest people alive never get to the point where they really know reality, they only know estimates. I do not mean to make this point overly philosophical, I am talking about practicalities here: there may be an absolute reality that we can know directly, but when it comes to doing anything useful, we develop estimates using fairly simple models, models which are well suited to the limits of our minds. In some sense, the models we build about the world are always simplified models that make it easier for our limited central nervous systems to make estimates about the world. I just offered a physics examples of simplifying assumptions, but I could also focus on the humanities. Perhaps your life's goal is to figure out the "real" reasons why the French Revolution happened, or why Communism was so popular for so long, or why the Industrial Revolution happened -- the possibilities are as limitless as the combination of all the variables in action over the course of centuries, the psychology and biology of billions of people, and the technology that existed at the time, and the weather and the crops and the economy and the religions and the amount of sunlight reaching the earth and everything else, combining exponentially to some very large sum. You might research the issue for 40 years, but in the end, if you want to draw some useful conclusion, something that others can benefit from, something that might influence policymakers in the future, you will need to come up with a simplified model that focuses on the handful of variables that you regard as the most important. There is another model of knowing, which takes for granted the absolute reality outside of us. That model is well summarized by this XKCD comic: http://xkcd.com/435/ http://xkcd.com/435/ In that model, biology is a sub-branch of physics, which is a sub-branch of math. However, if you focus on the limits of the central nervous system as the practical limit of human knowing, then you end up with a model where physics and math (and everything else) is a sub-branch of biology, specifically, a sub-branch of neurology. Even the two models of human knowing that I describe in this post to Hacker News can be thought of as sub-branches of neurology. All human knowing is, in some sense, a clever hack of our neurology, and certainly all heuristics and models are hacks which adapt to the limits of that neurology. There is nothing wrong with simple models, so long as they allow us to get useful work done. But I think our reliance on simple models tells us why specialization is so important. If a person can study a subject for 40 years and, having read tens of thousands of documents, still distills the data down to a small handful of variables, a model that gracefully adapts to the limits of the human mind, then we must admit that it is the rare human being who goes much beyond simple models. In those cases where simple models don't work, and where there only thing that works is a model with hundreds or thousands of variables, then clearly, achieving an understanding of such models must surely be the work of a lifetime. You need to get to studying when you are 20, and you need to specialize, because when you are 50 you will still be only approaching the ideal, never quite there, only approaching it, still learning more.

padobson 13y ago

This is great, you summed up every idea I had while reading this in a way that was far more articulate than I could have. I only have one thing to add: If there is an economic and even, possibly, a societal benefit to specialization, and The Two Cultures idea complains about the rift between the humanities and the sciences, then has someone properly updated the material to show how much more specialized society is becoming? The Wiki article talks about a possible third culture, but it seems to me you could become fairly deeply specialized in business/economics without ever needing a classical humanities education or a classical math/science education.

msluyter 13y ago

Specialization is something I often wonder about. Consider the following analogy: the sum of human knowledge is represented by a giant circle (though not necessarily perfectly circular in shape). Anything inside the circle is that which is known; anything outside is unknown. You're born in the center, and as you learn, the set of what you know extends towards the edge. As you mentioned, at some point in time, you could know all of the circle; now you can only know some subset of it. If you're a scientist or whatnot, you actively move the edge outward. My question is, will we ever reach a point where it takes so long to move from the center to the edge that we'll eventually stop making progress? In mathematics, it already takes considerable time to reach the knowledge boundary (30 years or so?) Will we reach a point where it takes greater than a lifetime? Or, is it possible to jump to the edge by skipping some foundational knowledge (could you do higher math without knowing, say, calculus, for example?) What are the risks of doing so? And ultimately, how does a complex society hang together when each person has (at most) knowledge of a tiny subset of available knowledge?

lkrubner 13y ago
You get at the degree to which all human knowledge is limited by the central nervous system that humans possess. There must be some finite number of axons and dendrites that can be stuffed into the cranium of a human, and even if there is a sophisticated system of compression and/or multiplexing in use, we can probably assume that a finite amount of axons and dendrites can only carry a finite amount of information. Thinking of the physical limits on human knowledge leads to a model of knowing that puts the central nervous system at the center of our our experience of the universe. There may be an absolute reality that exists outside of us, but since all of us are human (I assume) we must admit that our knowledge of that absolute reality will forever be shaped by that central nervous system. The limits of the central nervous system cause humans to look for models of reality that fit well with those limits. For instance, there is The Magical Number Seven, Plus or Minus Two: http://en.wikipedia.org/wiki/The_Magical_Number_Seven,_Plus_or_Minus_Two http://en.wikipedia.org/wiki/The_Magical_Number_Seven,_Plus_... Because of the (very very finite) limits on working memory, the human mind leans heavily on heuristics that allow simple models to stand in for the complexity of reality. No human being could easily work with a physics model that had 1 million variables: therefore we tend to look for models that have a handful of variables, yet still give us reasonably good estimates. Just yesterday there was posted to Hacker News an article about a slinky, and that article contains a good demonstration of the kind of simplifying assumptions we often make to reason about problems that are too complex to approach directly: "I decided to idealize the problem like this: the slinky is an ideal spring with mass distributed uniformly throughout. It is also a spring that can pass through itself. These assumptions make analyzing the problem easier." And of course, we often present students with problems where the difficulty of achieving perfect measurements of variables is simply assumed away. For instance in this exercise: http://www.uta.edu/ce/nsf/ret/docs/lesson-plans/reynolds08-5.pdf http://www.uta.edu/ce/nsf/ret/docs/lesson-plans/reynolds08-5... The important things to measure are: force, deflection, torque, moment of inertia, stress and strain. Often, in real life situations, engineers have no way to perfectly measure these things. Large engineering projects proceed with various methods for getting reasonable estimates: known upper and lower bounds, prototypes, isolated testing of particular connections, etc. The smartest people alive never get to the point where they really know reality, they only know estimates. I do not mean to make this point overly philosophical, I am talking about practicalities here: there may be an absolute reality that we can know directly, but when it comes to doing anything useful, we develop estimates using fairly simple models, models which are well suited to the limits of our minds. In some sense, the models we build about the world are always simplified models that make it easier for our limited central nervous systems to make estimates about the world. I just offered a physics examples of simplifying assumptions, but I could also focus on the humanities. Perhaps your life's goal is to figure out the "real" reasons why the French Revolution happened, or why Communism was so popular for so long, or why the Industrial Revolution happened -- the possibilities are as limitless as the combination of all the variables in action over the course of centuries, the psychology and biology of billions of people, and the technology that existed at the time, and the weather and the crops and the economy and the religions and the amount of sunlight reaching the earth and everything else, combining exponentially to some very large sum. You might research the issue for 40 years, but in the end, if you want to draw some useful conclusion, something that others can benefit from, something that might influence policymakers in the future, you will need to come up with a simplified model that focuses on the handful of variables that you regard as the most important. There is another model of knowing, which takes for granted the absolute reality outside of us. That model is well summarized by this XKCD comic: http://xkcd.com/435/ http://xkcd.com/435/ In that model, biology is a sub-branch of physics, which is a sub-branch of math. However, if you focus on the limits of the central nervous system as the practical limit of human knowing, then you end up with a model where physics and math (and everything else) is a sub-branch of biology, specifically, a sub-branch of neurology. Even the two models of human knowing that I describe in this post to Hacker News can be thought of as sub-branches of neurology. All human knowing is, in some sense, a clever hack of our neurology, and certainly all heuristics and models are hacks which adapt to the limits of that neurology. There is nothing wrong with simple models, so long as they allow us to get useful work done. But I think our reliance on simple models tells us why specialization is so important. If a person can study a subject for 40 years and, having read tens of thousands of documents, still distills the data down to a small handful of variables, a model that gracefully adapts to the limits of the human mind, then we must admit that it is the rare human being who goes much beyond simple models. In those cases where simple models don't work, and where there only thing that works is a model with hundreds or thousands of variables, then clearly, achieving an understanding of such models must surely be the work of a lifetime. You need to get to studying when you are 20, and you need to specialize, because when you are 50 you will still be only approaching the ideal, never quite there, only approaching it, still learning more.