3 ms·

I agree. My father was working in thermodynamics, and he quietly steered me from tricks to being able derive things myself. For example, in cross-multiplication

I agree. My father was working in thermodynamics, and he quietly steered me from tricks to being able derive things myself. For example, in cross-multiplication, percents, unit conversion, long division. I remember him saying: "Forget all rules about percentages. All you need to know it's like a number multiplied by 100." He also wasn't fond of mole as unit, he felt that it obscures things especially for students. Later I applied the same method myself on algebra (deriving binomial expressions), trigonometric functions (deriving constants from unit circle, other relations from the basic relations of sin(x+y)) and so on. I guess this actually applies to any field. Do not start with tricks and shortcuts until you understand and can do the deed with basic methods.

carapat_virulat 11y ago
It's still a complicated approach without proper material or teachers to orient you. There are "obvious" derivations that may be possible to produce by most people by putting a couple of hours on it, and then there are other "obvious" derivations that took hundreds of years and thousands of man-hours, and when you are learning you aren't on a position to tell them apart. Others are a bit in the middle and can be turned into the "easy" kind by making a few not-so-obvious assumptions. But that still requires a proper guidance. Even derivations itself probably contain plenty of not so obvious "tricks" that should be known to develop them. It's not so clear cut what is a trick and what are obvious assumptions from the real world. I suspect that the regular increase of IQ every generation may be related to all those hidden tricks and skills that everybody acquires at school or from general culture, but that at some point they become invisible obvious assumptions and common sense. Another easier approach may be to start with the tricks and work backwards from there to more general premises.
tome 11y ago
> I remember him saying: "Forget all rules about percentages. All you need to know it's like a number multiplied by 100." I don't remember what rules or tricks I was taught about percentages, but I do remember realising that "%" meant "/ 100" and from there everything else followed.
- asgard1024 11y ago
  I went to elementary school in Czechoslovakia, late 80s, and we learned some rules about percentages (which I believe was just a modified formula with the multiplication by 100) as a part of what you call cross-multiplication.
- SixSigma 11y ago
  But it doesn't mean / 100, it means "per 100" as described here in "The history of the percent sign" http://www.shadycharacters.co.uk/2015/03/percent-sign/ http://www.shadycharacters.co.uk/2015/03/percent-sign/
  - plonh 11y ago
    / means "per"
    - Retra 11y ago
      and × means "of"

carapat_virulat 11y ago

It's still a complicated approach without proper material or teachers to orient you. There are "obvious" derivations that may be possible to produce by most people by putting a couple of hours on it, and then there are other "obvious" derivations that took hundreds of years and thousands of man-hours, and when you are learning you aren't on a position to tell them apart. Others are a bit in the middle and can be turned into the "easy" kind by making a few not-so-obvious assumptions. But that still requires a proper guidance. Even derivations itself probably contain plenty of not so obvious "tricks" that should be known to develop them. It's not so clear cut what is a trick and what are obvious assumptions from the real world. I suspect that the regular increase of IQ every generation may be related to all those hidden tricks and skills that everybody acquires at school or from general culture, but that at some point they become invisible obvious assumptions and common sense. Another easier approach may be to start with the tricks and work backwards from there to more general premises.

tome 11y ago

> I remember him saying: "Forget all rules about percentages. All you need to know it's like a number multiplied by 100." I don't remember what rules or tricks I was taught about percentages, but I do remember realising that "%" meant "/ 100" and from there everything else followed.

asgard1024 11y ago
I went to elementary school in Czechoslovakia, late 80s, and we learned some rules about percentages (which I believe was just a modified formula with the multiplication by 100) as a part of what you call cross-multiplication.
SixSigma 11y ago
But it doesn't mean / 100, it means "per 100" as described here in "The history of the percent sign" http://www.shadycharacters.co.uk/2015/03/percent-sign/ http://www.shadycharacters.co.uk/2015/03/percent-sign/
- plonh 11y ago
  / means "per"
  - Retra 11y ago
    and × means "of"