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I've found that I also need to understand the historical context/impetus... I need to be shown and eventually understand why something was developed when it was

I've found that I also need to understand the historical context/impetus... I need to be shown and eventually understand why something was developed when it was developed. I need chronology of thought and ideas. For instance, learning about Gödel's theorems without having the Hilbert back-story explained. Learning about Leibniz's and Newton's calculus without learning about infinitesimals. And so on. There's generally a reason _why_ concepts are born _when_ they are born. If you think about your maths classes, sometimes you're instructed to learn a method because it is useful and because it has real-world applications but it I don't think anybody is ever first taught algebraic geometry properly, if I may use that word. I don't think kids are taught the geometry is one thing and algebra is another and that different spaces can have different metrics. Am I making sense here? Do people see what I'm trying to get at? Am I arguing for HADEPT? :) (Historical context, Analogy, Diagram, Example, Plain English explanation, and just then Technical definition)

kalid 11y ago
Great point. I find myself looking at the history of the idea when writing up a post. Did you realize negative numbers were only accepted in the late 1700s? That the Fourier Transform was originally rejected as untrue when first presented, by world-famous mathematicians even? (Yet we require students to internalize it without issue in a single lecture.) Historical context is huge. I think I'm now stuck with this ADEPT name but maybe it fits into the Plain English portion :).
- igravious 11y ago
  > Did you realize negative numbers were only accepted in the late 1700s? I did not know that! This makes total sense. I'd like to know more about that. When you think about it, only whole positive numbers make sense from a quantitative perspective. One thing, two things, three things, and so on. What's half-a-thing? Right? a half-a-thing is still just one thing, if you know what I mean. And how can no thing (nothing) be a number? And how can negative numbers be "numbers". It has always struck me that imaginary numbers are really badly named. Zero and the negative numbers are just as 'imaginary', equally unintuitive from a certain perspective. I applaud what you're doing. I think there is a metric-tonne of dogma and bad naming schemes in the standard maths curriculum. Remember in software engineering they say that naming things is one of the hardest parts of the task? I think the same applies to maths, perhaps more so.
  - kalid 11y ago
    Exactly! There's a quote from a famous mathematician at the time that the negatives "Darken the very whole doctrines of the equations". If positive is good, negative must be evil right? And how can "less than nothing" exist? I love the philosophical implications of it. Ugh, tell me about the naming. "Imaginary numbers?" How about "rotated numbers". Nobody complains "Hey, when will I ever use the second dimension?". But "imaginary numbers" are setup to be eye-rolled.
  - billbrown 11y ago
    I'd recommend "The Joy of x" by Steven Strogatz. It's full of that sort of story.

kalid 11y ago

Great point. I find myself looking at the history of the idea when writing up a post. Did you realize negative numbers were only accepted in the late 1700s? That the Fourier Transform was originally rejected as untrue when first presented, by world-famous mathematicians even? (Yet we require students to internalize it without issue in a single lecture.) Historical context is huge. I think I'm now stuck with this ADEPT name but maybe it fits into the Plain English portion :).

igravious 11y ago
> Did you realize negative numbers were only accepted in the late 1700s? I did not know that! This makes total sense. I'd like to know more about that. When you think about it, only whole positive numbers make sense from a quantitative perspective. One thing, two things, three things, and so on. What's half-a-thing? Right? a half-a-thing is still just one thing, if you know what I mean. And how can no thing (nothing) be a number? And how can negative numbers be "numbers". It has always struck me that imaginary numbers are really badly named. Zero and the negative numbers are just as 'imaginary', equally unintuitive from a certain perspective. I applaud what you're doing. I think there is a metric-tonne of dogma and bad naming schemes in the standard maths curriculum. Remember in software engineering they say that naming things is one of the hardest parts of the task? I think the same applies to maths, perhaps more so.
- kalid 11y ago
  Exactly! There's a quote from a famous mathematician at the time that the negatives "Darken the very whole doctrines of the equations". If positive is good, negative must be evil right? And how can "less than nothing" exist? I love the philosophical implications of it. Ugh, tell me about the naming. "Imaginary numbers?" How about "rotated numbers". Nobody complains "Hey, when will I ever use the second dimension?". But "imaginary numbers" are setup to be eye-rolled.
- billbrown 11y ago
  I'd recommend "The Joy of x" by Steven Strogatz. It's full of that sort of story.