In article <email@example.com>, Kevin Foltinek <firstname.lastname@example.org> wrote: >Alberto Moreira <email@example.com> writes:
>> "Karl M. Bunday" <"kmbunday"@yahoo.de.com.de (remove \".de\" twice to >> E-mail)> said:
>> >Kevin Foltinek wrote, in reply to my reply to MagiG
>> >> I never had difficulty learning math (and I now have a Ph.D. in math),
>> I wonder if you had a Ph.D. in a more computation-intensive >> discipline, you would still think the same way ?
>The same way as what? If I had a Ph.D. in computational astrophysics, >I would now think that I had difficulties learning math?
One of the things I work on are computational procedures. In a practical situation, knowing how to carry out arithmetic, at which I am fast and accurate, is rarely helpful. In computational astrophysics, or computational biology, or computational economics (I have worked with these people), the computations have to be automated.
>> >> My >> >> next memory of any math class is seemingly endless repetition of >> >> "2+3=__, 3*7=__". Of those two memories, the Cuisenaire is the happy >> >> one.
>> >Would it be a fair inference that the happy memory did more to >> >keep you going in your Ph.D. program than the less happy memory?
>> Yet it's the drill on 2+3=__ and 3*7=__ that matters to most of us who >> do things that are less abstract than pure math. Ability to compute, >> specially to do mental computation on the fly while studying something >> else or while in a classroom, is fundamental to learning anything that >> has any shadow of an application in real life.
>You are evidently ignorant of the wide range of applicability of >mathematics. I personally know pure math Ph.D.s who work or have >worked in finance, risk management, defense, construction, and >engineering (and those are just off the top of my head); I am also >aware of specific examples of the application of so-called "pure math" >to very concrete problems. None of these involved the ability to do >mental arithmetic; many of them involved the ability to understand the >logical and mathematical structures involved. Many of them involve >the ability to program computers to do rather complicated >computations, a skill which requires a deeper understanding of the >nature of computation than is used for mental arithmetic.
>The ability to compute is worthless unless you know what you are >computing and why you are computing it. Neither can be known without >what you call "abstract pure math".
This is so true. Quite a few who have a reasonably good intuitive understanding of some of the abstract concepts, and can use them, do not recognize that this is the case. One can understand the properties of the integers using base 2 arithmetic just as well as with base 10, if not better; the memorization and drill have been eliminated. Formulating the problem so that someone who understands how to solve problems can do so without knowing the source is the important part. This mathematical communication is the important part for non-mathematicians, provided the understanding of the concepts is present. What good is it to be able to add without knowing what numbers mean?
>> So, my question is, Kevin, how much did your dislike of computation >> channeled you into pure math as opposed into something more practical >> ?
>I did not say that I dislike computation. I specifically referred to >"seemingly endless repetition", which was obviously (in my case) >unnecessary (and, I would speculate, unhelpful for many others).
Little repetition is necessary, provided the concepts are present. All it gains is speed in imitating machines.
>If you are happy doing little more than regurgitating the addition and >multiplcation tables, fine; I, however, try to find more useful, >productive, and interesting things to do.
I agree. I use my arithmetic abilities only mainly when it saves time; with the available software, this even extends to doing manual hexadecimal arithmetic. But it only saves time.
Also, I have NOT memorized the hexadecimal tables. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Deptartment of Statistics, Purdue University firstname.lastname@example.org Phone: (765)494-6054 FAX: (765)494-0558