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Topic: new tutor here
Replies: 151   Last Post: Jul 17, 2013 4:09 AM

 Messages: [ Previous | Next ]
 GS Chandy Posts: 8,307 From: Hyderabad, Mumbai/Bangalore, India Registered: 9/29/05
Re: new tutor here
Posted: Jun 17, 2013 1:32 AM

Joe Niederberger posted Jun 16, 2013 11:15 PM:
> R Hansen mentions:
> >...abstract analytical (non visual) thinking.
>
> This just reminds me of something. A famous computer
> scientist (not mathematician, unfortunately) once
> confessed he could never find a relation "More
> Abstract Than" on which to base a systems
> architecture on, even though CS people had talked
> about "levels of abstraction" for years prior.
> (Parnas went on to write on of the classic papers in
> the field after clearing away some built up B.S.)
>

i) Unless I misunderstand, the relationship "more abstract than" is simply a 'specification' of the relationship "more ... than" - and that is *fairly* well understood (*though probably more understanding is desirable, perhaps even required!)

ii) Is the "Parnas" you discuss "David Parnas" (https://en.wikipedia.org/wiki/David_Parnas) and the specific paper "On the Criteria To Be Used in Decomposing Systems into Modules", D.L. Parnas (Carnegie-Mellon University) (http://sunnyday.mit.edu/16.355/parnas-criteria.html ) ??

I hasten to note that I had not earlier known either of David Parnas or of his classic paper (which I am now trying to read and understand). Offhand, it strikes me that Warfield's work in systems should effectively resolve many of the issues that arise.
>
> The above strikes me as somewhat the same.
> Abstraction means to focus on some properties of
> something while disregarding others. So Euclidean
> lines and planes are already abstract. Much visual
> thinking used in mathematics would be abstract by the
> same token. Some thinking might be guided by
> algebraic manipulation of expressions -- most people
> would not call that visual thinking though the
> expression on paper are visual objects.
>
> Ultimately, mathematics often strives towards the
> "proof" as the gold standard. A proof, in the most
> rigorous sense, is a formal object in a formal
> system, which is abstract in one sense (if its tokens
> and primitives are thought to *refer* to something
> else -- the "abstraction" involved is distilling just
> those properties of that something else one wants to
> encode in the formal system.) On the other hand, if
> the system is thought of as simply a game of symbols
> and rules with no external referents, its a bit of a
> misnomer to call it abstract, as it abstracts from
> *nothing* in that case -- its just a game. The same
> could be said for algebraic systems, if we really
> view them as purely formal games. I know in
> colloquial speech people would ordinarily refer to
> any symbolic game of this type to be "abstract". But
> from a different viewpoint, they are really
> *concrete*, in that the symbols and rules are rigidly
> fixed.
>
> Most real life proofs fall are simply reviewed
> arguments that enough qualified people think could be
> turned into a formal proof if push comes to shove.
> Any kind of thinking, visual or otherwise, that leads
> to a proof (formal or not) is mathematical, abstract
> thinking, in the usual (colloquial) sense.
>
> Some people, I think, would regard expression
> manipulation as "more abstract than" thinking about
> lines and slopes and planes etc. I think I'll go with
> Parnas on that issue though.
>
> Cheers,
> Joe N
>

Yes, to much of your argument above - subject to the provisos that: a) I've not yet read David Parnas's paper and b) my note on Warfield's work above needs to be 'integrated' into whatever enhanced understanding I may obtain on reading the above-noted Parnas paper.

GSC

Date Subject Author
6/12/13 Michael Mossey
6/12/13 Wayne Bishop
6/12/13 Michael Mossey
6/13/13 Wayne Bishop
6/13/13 Dave L. Renfro
6/13/13 Joe Niederberger
6/14/13 Robert Hansen
6/14/13 Joe Niederberger
6/14/13 Robert Hansen
6/14/13 Joe Niederberger
6/14/13 Robert Hansen
6/14/13 Joe Niederberger
6/14/13 Robert Hansen
6/15/13 Louis Talman
6/14/13 Michael Mossey
6/15/13 Robert Hansen
6/14/13 GS Chandy
6/16/13 GS Chandy
6/15/13 Louis Talman
6/15/13 Joe Niederberger
6/16/13 Robert Hansen
6/15/13 Pam
6/16/13 Robert Hansen
6/15/13 Pam
6/16/13 Wayne Bishop
6/16/13 Joe Niederberger
6/16/13 Robert Hansen
6/16/13 Joe Niederberger
6/17/13 Robert Hansen
6/16/13 Michael Mossey
6/17/13 GS Chandy
6/17/13 GS Chandy
6/17/13 Pam
6/17/13 Robert Hansen
6/17/13 Pam
6/17/13 Robert Hansen
6/17/13 Pam
6/17/13 Pam
6/17/13 Joe Niederberger
6/17/13 Robert Hansen
6/17/13 Joe Niederberger
6/17/13 Joe Niederberger
6/18/13 Robert Hansen
6/17/13 GS Chandy
6/18/13 GS Chandy
6/18/13 GS Chandy
6/18/13 GS Chandy
6/18/13 Joe Niederberger
6/18/13 Robert Hansen
6/18/13 Joe Niederberger
6/18/13 Joe Niederberger
6/18/13 Robert Hansen
6/18/13 Joe Niederberger
6/18/13 Joe Niederberger
6/18/13 Robert Hansen
6/18/13 Robert Hansen
6/18/13 Joe Niederberger
6/19/13 Robert Hansen
6/19/13 Robert Hansen
6/21/13 Wayne Bishop
6/21/13 Wayne Bishop
6/19/13 Joe Niederberger
6/19/13 Robert Hansen
6/19/13 Joe Niederberger
6/19/13 Robert Hansen
6/19/13 Joe Niederberger
6/19/13 Robert Hansen
6/19/13 Joe Niederberger
6/19/13 Robert Hansen
6/19/13 Robert Hansen
6/19/13 Joe Niederberger
6/19/13 Joe Niederberger
6/19/13 Joe Niederberger
6/19/13 Robert Hansen
6/21/13 Joe Niederberger
6/21/13 Robert Hansen
6/21/13 Joe Niederberger
6/21/13 Robert Hansen
6/21/13 Joe Niederberger
6/21/13 Robert Hansen
6/21/13 Joe Niederberger
6/21/13 Joe Niederberger
6/21/13 Dave L. Renfro
6/22/13 Robert Hansen
6/22/13 Robert Hansen
6/22/13 Joe Niederberger
6/22/13 Robert Hansen
6/22/13 Robert Hansen
6/23/13 Joe Niederberger
6/23/13 Robert Hansen
6/23/13 Robert Hansen
6/23/13 Joe Niederberger
6/23/13 Robert Hansen
6/24/13 Robert Hansen
6/24/13 Joe Niederberger
6/24/13 Joe Niederberger
6/24/13 Joe Niederberger
6/25/13 GS Chandy
7/10/13 Dave L. Renfro
7/10/13 Robert Hansen
7/10/13 Joe Niederberger
7/10/13 Robert Hansen
7/10/13 Robert Hansen
7/10/13 Robert Hansen
7/11/13 Joe Niederberger
7/11/13 Robert Hansen
7/11/13 Joe Niederberger
7/11/13 Robert Hansen
7/11/13 Robert Hansen
7/11/13 GS Chandy
7/11/13 Joe Niederberger
7/11/13 Robert Hansen
7/11/13 Robert Hansen
7/11/13 Louis Talman
7/11/13 Robert Hansen
7/12/13 Wayne Bishop
7/12/13 Louis Talman
7/12/13 Wayne Bishop
7/12/13 Robert Hansen
7/12/13 Gary Tupper
7/12/13 Wayne Bishop
7/12/13 Louis Talman
7/11/13 Joe Niederberger
7/11/13 Robert Hansen
7/11/13 Joe Niederberger
7/11/13 GS Chandy
7/12/13 Wayne Bishop
7/12/13 Joe Niederberger
7/12/13 Wayne Bishop
7/12/13 GS Chandy
7/12/13 Joe Niederberger
7/13/13 Robert Hansen
7/13/13 GS Chandy
7/13/13 Joe Niederberger
7/13/13 Wayne Bishop
7/13/13 Robert Hansen
7/13/13 Robert Hansen
7/13/13 Peter Duveen
7/14/13 Joe Niederberger
7/14/13 Joe Niederberger
7/14/13 Joe Niederberger
7/14/13 Robert Hansen
7/14/13 GS Chandy
7/15/13 Wayne Bishop
7/15/13 Joe Niederberger
7/15/13 Robert Hansen
7/15/13 Peter Duveen
7/15/13 Joe Niederberger
7/16/13 GS Chandy
7/16/13 Wayne Bishop
7/16/13 GS Chandy
7/17/13 GS Chandy