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I'd argue that, as advances are made, it becomes easier to move faster through the circle. It's not that you're skipping foundation knowledge, but you're just

I'd argue that, as advances are made, it becomes easier to move faster through the circle. It's not that you're skipping foundation knowledge, but you're just learning one core piece. Instead of learning the area under an encyclopedia of curves, you learn integral calculus and you're done. Instead of memorizing thousands of rules involving the interaction of various charged objects, you learn Maxwell's four equations and you're done. Or, you could learn geometric calculus and then only need to learn one four-symbol equation. Instead of learning thousands of different circuits to accomplish thousands of different tasks, you learn one Turing machine. Knowledge is constantly increasing, but we're also continually finding that a large amount of our previous knowledge was redundant. I once saw a great article, that I wish I could find again, list off a series of scientific laws that could all be derived from nothing but unit analysis. The circle grow larger, but our steps do as well.

mturmon 13y ago
Good point. There are algorithms for manipulating Roman numerals that used to be taught, but that no longer are. And really, little is lost. People used to practice at long algebraic exercises (e.g., trig manipulations, or tricky integrals) that are no longer considered worthwhile. Just give it to Mathematica. It's like medium-sized linear systems -- sure, you could solve it manually, but nobody does, or even remembers all the shortcuts and tricks that used to be so important. A brief and vivid essay on this is "Forget it" by the late Isaac Asimov: http://readanybooks.net/ScienceFiction/Asimov37/27283.html http://readanybooks.net/ScienceFiction/Asimov37/27283.html
judk 13y ago
That's reductionist and oversimplifying. Maxwell's equations aren't enough to solve any practical example systems in the real world, so they aren't all you need to know to understand the world.

mturmon 13y ago

Good point. There are algorithms for manipulating Roman numerals that used to be taught, but that no longer are. And really, little is lost. People used to practice at long algebraic exercises (e.g., trig manipulations, or tricky integrals) that are no longer considered worthwhile. Just give it to Mathematica. It's like medium-sized linear systems -- sure, you could solve it manually, but nobody does, or even remembers all the shortcuts and tricks that used to be so important. A brief and vivid essay on this is "Forget it" by the late Isaac Asimov: http://readanybooks.net/ScienceFiction/Asimov37/27283.html http://readanybooks.net/ScienceFiction/Asimov37/27283.html

judk 13y ago

That's reductionist and oversimplifying. Maxwell's equations aren't enough to solve any practical example systems in the real world, so they aren't all you need to know to understand the world.