# Are some people born good at maths?

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#### Geezer

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##### Re: Are some people born good at maths?
« Reply #50 on: 09/02/2012 16:05:37 »
but, but, but, isn't it just a "slope" which is a ratio of uppyness to alongyness?
There ain'ta no sanity clause, and there ain'ta no centrifugal force æther.

#### imatfaal

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##### Re: Are some people born good at maths?
« Reply #51 on: 09/02/2012 17:38:07 »
yes  - but when you deal with limits approaching zero or off to infinity things become very complicated - instantaneous measurements calculations etc can become very screwy .  As I tried to say and failed - it is the limit as the  change in x tends to zero.

$$\frac {dy}{dx}(x_0)= \displaystyle \lim_{h \to 0} \frac {y(x_0 +h) - y(x_0)}{h}$$

Mad mathematicians would tell you that the ratio of two infinitessimals can be anything you choose (kind of like the ration of two infinities it is not well defined).
No, AFAIK that's definitely wrong. The reason that calculus works is that the LIMIT of dy/dx as you take the deltas towards zero is (in most normal cases) completely well defined. In some case limits can take two values in different directions where the curve jumps, so the curve has to be smooth where you differentiate; trying to differentiate a fractal doesn't do anything very good!
Maybe I didnt explain well - but it is not wrong.  There is a big difference between the limit as I have it above and the ratio of two variables as they tend to zero.  dx is not the  $$\lim_{\Delta x \rightarrow 0}\Delta x$$ as this is zero.
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#### Geezer

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##### Re: Are some people born good at maths?
« Reply #52 on: 09/02/2012 17:57:35 »
yes  - but when you deal with limits approaching zero or off to infinity things become very complicated - instantaneous measurements calculations etc can become very screwy .

WHOOSH!!

I think I better stick to uppyness and alongyness.
There ain'ta no sanity clause, and there ain'ta no centrifugal force æther.

#### Geezer

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##### Re: Are some people born good at maths?
« Reply #53 on: 09/02/2012 18:46:00 »
Actually, isn't this, to some extent, what the OP was referring to?

These points are interesting to the mathematically inclined, but to the average engineer who just wants to solve a stinking problem, they might appear slightly esoteric and academic.

It's like any tool. The experts will test it to the limits and understand all of its corner-cases. The rest of us will use it like any other hammer, and, if it doesn't work, we'll get a bigger one.
There ain'ta no sanity clause, and there ain'ta no centrifugal force æther.

#### JP

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##### Re: Are some people born good at maths?
« Reply #54 on: 10/02/2012 02:43:45 »
Except there are certain rare circumstances in which the hammer will fail catastrophically, and you can only know them by understanding how the hammer was built.

You can use it without worrying too much, but sometimes...

(By the way, as a physicist I'm very guilty of using derivatives as fractions and throwing infinity around with reckless abandon.)

#### imatfaal

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##### Re: Are some people born good at maths?
« Reply #55 on: 10/02/2012 09:48:31 »
Actually, isn't this, to some extent, what the OP was referring to?

These points are interesting to the mathematically inclined, but to the average engineer who just wants to solve a stinking problem, they might appear slightly esoteric and academic.

It's like any tool. The experts will test it to the limits and understand all of its corner-cases. The rest of us will use it like any other hammer, and, if it doesn't work, we'll get a bigger one.

Almost totally agree - but with same proviso as JP.  The hard core scientists I know are all very clear on the rules and derivation of those rules and then break them almost all the time - I swear I once saw someone cancelling the ds in dy/dx
There’s no sense in being precise when you don’t even know what you’re talking about.  John Von Neumann

At the surface, we may appear as intellects, helpful people, friendly staff or protectors of the interwebs. Deep down inside, we're all trolls. CaptainPanic @ sf.n

#### Geezer

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##### Re: Are some people born good at maths?
« Reply #56 on: 11/02/2012 21:48:26 »
BTW, I posted a video in the "Fireman's Hose" topic, and I was wondering how you would figure out how to produce maximum thrust form such a device. I'm pretty sure it would take a bit of calculus.
There ain'ta no sanity clause, and there ain'ta no centrifugal force æther.

#### sasha44

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##### Re: Are some people born good at maths?
« Reply #57 on: 12/02/2012 05:23:48 »
Ha haa you guys should have seen our Applied Mathematics lecturers face when a student asked what is the use of us Biological Science students learning applied mathematics. She just said " I don't know, I only teach mathematics" :O I mean at least say you can use it to find the area of a graph!