Re: Epistemology 201: The Science of Science

From: Albert Wagner (albertwagner_at_cox.net)
Date: 03/18/05 

Date: Fri, 18 Mar 2005 10:01:15 -0600

Wolf Kirchmeir wrote:
> Albert Wagner wrote:
>
>> Wolf Kirchmeir wrote:
>>
>>> Albert Wagner wrote:
>>>
>>>> Wolf Kirchmeir wrote:
>>>>
>>>>> Albert Wagner wrote:
>>>>> [...]
>>>>>
>>>>>>
>>>>>> Actually, applied mathematics, as used in engineering is good.
>>>>>> Everything else in mathematics is pure fantasy serving no purpose
>>>>>> but to entertain mathematicians.
>>>>>
>>>>>
>>>>>
>>>>> And very often, until the math is invented by those 'orrible
>>>>> mathematikers who are merely fantasising, there isn't any math to
>>>>> apply.
>>>>
>>>>
>>>>
>>>> Don't flatter yourself. Most engineers know what the math is for,
>>>> and what in reality the math represents. Math isn't magic, after
>>>> all. Anyone competent enough in math to graduate from engineering
>>>> school could do as well as anyone posting to this NG.
>>>
>>>
>>>
>>>
>>> Here's an anecdote. In 1st year engineering, we had a course on
>>> "Materials and Processes." It was, I now realise, an excuse for the
>>> Dean to talk to us ignorant adolescents about the profession of
>>> engineering, and to reminisce, and to drop little intellectual bombs,
>>> just in case we thought that engineers knew everything (whereas those
>>> artsy-fartsies knew nothing, of course, and besides they didn't get
>>> anywhere with the nurses.) One lecture was about columns, and
>>> buckling, and how the shape of the column has more to do with its
>>> resistance to buckling than the stuff it was made of, and so on. He
>>> mentioned that the equations that described the buckling of a column
>>> were the same as the equations that describe harmonic motion, such as
>>> that of a spring. He said he had no idea why. I was very young, but
>>> this was an Aha! of the first order.
>>
>>
>>
>> What exactly /was/ your epiphany? Was it that you understood the
>> 'Why'? Or that no one needed to understand the 'Why'? And is this
>> happenstance typical or an anomaly? Who was the genius that noticed
>> that the formula could be used for column buckling? And who developed
>> the equations for harmonic motion?
>
>
> Two main insights:
>
> a) that there is a constant interplay between practical and abstract
> mathematics. Research in math is often prompted by the need to
> understand the engineering/physcis better. And ingineers/physicists
> asoften as not go looking for some math that will help them build a
> model to explain their obersvations.
> b) that engineers often did not understand why their equations worked.
> (It's likely, BTW, that the column buckling puzzle has been solved, but
> I swricvhed out fo enineering: I went into it because one of those psych
> tests told me that would be my metier, but it was wrong: I apparently
> had suitable talents, attitudes and interests, but not the patience or
> obsessiveness that makes a good engineer.)
>
> If my knowledge of the development of steam engine technology is any
> indication, a) and b) are typical: ad-hoc formulas (involving piston
> area, cylinder volume, coal quantities, etc) were developed before the
> theory of thermodynamics was developed to the point where it could be
> used to improve the technology.
>
> As I recall it, the Dean told us this anecdote as an illustration of odd
> relationships betwen different areas of engineering, that connection
> being the math.
>
> The equations for harmonic motion were developed by physicists.
>
> Point is, to claim that engineers know what the math represents is a not
> quite right. Emngineers know what they can use the math for. So do
> physicists, etc. But it is as often as not a surprise. A reminder:
> complex numbers were invented about a generation before engineers
> realised they could be used in electrical power engineering.
>
> I see no reason to suppose that any particular branch of mathematics
> must have a practical, real world interpretation. In the last century or
> so, the more common pattern is development of the math, then the
> practical application. In the early stages of the scientific and
> industrial revolution, is more commonly the other way round.
>
Thank you. The observation that the same math underlies both
phenomena is to me more significant than the actual math itself. 

-- 
"I consider it quite possible that physics cannot be based
on the field concept, i. e., on continuous structures. In that
case nothing remains of my entire castle in the air,
gravitation theory included, [and of] the rest of modern physics."
	-- Albert Einstein in a 1954 letter to Michele Besso.

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