
Re: Structured Programming
Posted:
Mar 15, 2014 3:52 PM



On Fri, Mar 14, 2014 at 12:21 AM, GS Chandy <gs_chandy@yahoo.com> wrote:
> Kirby Urner (KU) posted Mar 14, 2014 9:41 AM ( > http://mathforum.org/kb/message.jspa?messageID=9411805)  GSC's remarks > interspersed: > >
> I do try not to stereotype things (as best I can). > > i) I had considered the cases of both 'monied', privileged individuals AND > 'poor' individuals. > > ii) I had qualified the words "monied", "poor" and "spoilt" by putting > them between single quotes, more or less to indicate that I was aware of > the stereotyping that often occurs. > > What's difficult to quantify sometimes are the nonmonetary aspects of a scenario. Maslow, as in hierarchyofneeds Maslow, advised trying to assign a monetary value to everything of considering a change in job or career or whatever. By some measures, peasants in Ladahk have it made, the perfect life style, and pushing them into apartments and office jobs is in no way a step up.[1]
http://worldgame.blogspot.com/2011/01/economicsofhappinessmoviereview.html
The point of my post was I am very wealthy in terms of having access to engineering tools that no one had anywhere until quite recently. To be able to compute (1 + 1/n)*(1 + 1/n)*(1 + 1/n)....(1 + 1/n) for n such terms, and to converge to a specific number less than three ( e < 3 ) with 300 decimal digits of accuracy... new. Some would say trivial. I'd say: in schools, we should not dismiss such powers.
Yesterday was pi Day but I was thinking about e Day.
Remember my story of that police department, unhappy at being used as "the bad guy" to scare students about the Internet, versus sharing it with police as a playground, a place to explore without driving fast while drinking and killing someone, which they get tired of seeing. Cyberia should not be a place to wall off. We should build more virtual schools there. No one need think of you as "poor" if you just send your avatar. A layer of anonymity gets added we might as well use to pedagogical / andragogical advantage.
> That said, I do believe it is fair to suggest that 'privileged people' > often do take the great good fortune of their privileges for granted, so to > speak, and often do not use their abilities effectively, i.e., they get > 'spoilt' by the privileges they enjoy, and do not really understand that > much of their privilege derives from factors way beyond their personal > competence levels. >
> probably my favorite though. Is TinTin 1%? How > about Snowy? >
This was a Belgian comic.
Well, when I was a kid I rather rarely read comics, though I was familiar > with Capt Marvel, Superman, Batman, etc. I enjoyed Mad Magazine (a bit > later, I think). However, I would not by choice spend my limited pocket > money or earned money on them; I did spend a lot on books. > > >
Here are some more recent paragraphs I think RH might agree with:
In algebra we get to ask: what would x have to be to make this equation true? x is asked to "satisfy" some equation. Later, a whole cast may be asked to bring satisfaction to a whole "system of equations". This is where our concept of "algorithm" enters in i.e. if there's a way to squeeze actual solutions from this puzzle, by turning some wheels as it were, we want to know about it.
Here I'd say computer math does not substitute for human genius in actually discovering some algorithms. The computer becomes the recording device for recording the stepbystep routines, once the beginning inputs are known, the para meters of a given equation. The computer is the new executor for the algorithm, not someone paid "to compute" i.e. we no longer hire based on mental arithmetic skills as a spreadsheet or other electronic computing context is assumed. We have been relieved of that responsibility, as far as business is concerned.
In other words, I think RH and I agree that once you have that fluency in Algebra where you understand variables may have many values substituted for them i.e. they are not constants, but more like placeholders, then you're ready to "transcribe" the algorithms you learn about in math, to the computer language you're learning to use in your computer math class.
Comprehension of the algebra, the math behind the process, including the proofs of any reliedupon theorems, gives you the confidence to translate that deep understanding into working code for storage and sharing with peers and mentors. You are likewise a consumer of other peoples code and benefit from all the hard but often fun work of transcribing algorithms into computer languages.
Conversely, those coming to a deep topic and not knowing the theorems, may start from the other end, studying the algorithms as a way to prepare ourselves to learn more of the generalizations at the core. I don't want to belittle the "tourists" anymore than I want to be dismissed or belittled just because I've strayed from my beaten path and gotten into a fresh topic area I know little or nothing about.
For example, without knowing Euler's Theorem about totients, a generalization of Fermat's socalled "little" theorem, you can still start to appreciate the power of encrypting using RSA, an algorithm. You study the algorithm as a means of climbing into the deeper math, which requires defining concepts such as "totient" in the first place.
In computer math ("CSenabled algebra"), we'll do that (teach about Euler's Theorem, about totients), and not because we think it's rocket science or super hard. Just runothemill stuff, this RSA cook book recipe, and used in every web browser, part of https protocol.[2]
Writing the code for RSA is a way to learn it. That's the approach taken in the high school math book we both think highly of, used with kids of privilege (privileged by definition, if they get to use such books): Mathematics for the Digital Age and Programming in Python.[3]
Kirby
[1] The Economics of Happiness http://worldgame.blogspot.com/2011/01/economicsofhappinessmoviereview.html
[2] RSA, what it is and where it's used: http://mathworld.wolfram.com/RSAEncryption.html http://stackoverflow.com/questions/3968095/howdoeshttpsprovidesecurity
[3] some of my own crypto stuff, by now somewhat dated: http://4dsolutions.net/ocn/crypto0.html

