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i was a physics major, too. the student in our year who was best at math had trouble with the "hand wavy" stuff we'd do. "well, this term is basically zero, so

i was a physics major, too. the student in our year who was best at math had trouble with the "hand wavy" stuff we'd do. "well, this term is basically zero, so we'll just remove it" and then she'd pull her hair in frustration, like "how can you just do that? how is it still valid?" it wasn't enough to tell her "well it still gives us the valid results" - she had to be able to interpret every portion of an expression and then make intuitive sense of it. at first i was annoyed with this habit of hers, but eventually i started doing it to. for a lot of really math-minded people, hand waviness is anathema, and physics was full of "2 + 2 = 5 for sufficiently large values of 2, so we'll just assume that to make things easier"

_pius 12y ago
"well, this term is basically zero, so we'll just remove it" and then she'd pull her hair in frustration, like "how can you just do that? how is it still valid?" I've tried to teach friends with that hangup and found it difficult. Those people weren't good at math, though. I feel like with mathematicians, you should just be able to explain with limits.
- sedachv 12y ago
  > I feel like with mathematicians, you should just be able to explain with limits. Assuming the limit exists without actually proving the sequence converges is going to produce total junk. Jaynes spent a good portion of Probability Theory illustrating this.
  - _pius 12y ago
    I'm just talking about using the concept of limits as a teaching tool, not assuming a particular limit exists.
    - sedachv 12y ago
      Yes, this is why the mathematicians are pulling their hair out! You can't just drop terms when you feel like it.
TeMPOraL 12y ago
I feel that the right approach (at least it worked for me) is to tell the matematician - "see, this term is very close to zero for all practical inputs we can see in real life (proof of which will be left as an exercise for you), so - as you can see from the structure of the equation - we can safely drop it without introducing any significant error to the end result. Yes, the result will be a little bit less accurate; no, no one will notice. And if you happen to encounter a high-energy (or whatever) problem, you can always go back and use the full equation". Explicitly accepting that each handwave introduces errors and imprecision but that sometimes those errors are below what we can measure (or care about) should be acceptable enough for a math-minded person.

_pius 12y ago

"well, this term is basically zero, so we'll just remove it" and then she'd pull her hair in frustration, like "how can you just do that? how is it still valid?" I've tried to teach friends with that hangup and found it difficult. Those people weren't good at math, though. I feel like with mathematicians, you should just be able to explain with limits.

sedachv 12y ago
> I feel like with mathematicians, you should just be able to explain with limits. Assuming the limit exists without actually proving the sequence converges is going to produce total junk. Jaynes spent a good portion of Probability Theory illustrating this.
- _pius 12y ago
  I'm just talking about using the concept of limits as a teaching tool, not assuming a particular limit exists.
  - sedachv 12y ago
    Yes, this is why the mathematicians are pulling their hair out! You can't just drop terms when you feel like it.

TeMPOraL 12y ago

I feel that the right approach (at least it worked for me) is to tell the matematician - "see, this term is very close to zero for all practical inputs we can see in real life (proof of which will be left as an exercise for you), so - as you can see from the structure of the equation - we can safely drop it without introducing any significant error to the end result. Yes, the result will be a little bit less accurate; no, no one will notice. And if you happen to encounter a high-energy (or whatever) problem, you can always go back and use the full equation". Explicitly accepting that each handwave introduces errors and imprecision but that sometimes those errors are below what we can measure (or care about) should be acceptable enough for a math-minded person.