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Topic: all of math is just addition and multiplication
Replies: 36   Last Post: Jun 17, 2013 6:04 PM

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GS Chandy

Posts: 7,057
From: Hyderabad, Mumbai/Bangalore, India
Registered: 9/29/05
Re: all of math is just addition and multiplication
Posted: Jun 11, 2013 4:53 PM
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Joe Niederberg posted Jun 11, 2013 6:53 PM (GSC's remarks precede and interspersed):
Several aspects of the mental models we each hold in our minds cannot be explained at all. A few aspects of the mental models can be explained in prose. A few more aspects of those mental models are explainable via p+sg than can be explained in 'pure prose'. The saying "A picture is worth a thousand words" is a prose description of a well understood phenomenon (though the 'pictures' of the saying actually referred to 'illustrations'). The 'structural graphics' of 'p+sg' provides something more than mere 'illustration'.
> GS Chandy says:
> >the story Poincare tells about how he managed 'in
> >his sleep' to resolve a particular complex problem
> >that had been troubling him - which resolution later,
> >I believe, led him to 'chaos theory'

>
> I'll say more later - but why should we expect all of
> our "computation" to be available to introspection?
>

It's not my claim at all that "all of our 'computation' is available to introspection" (or that we should expect such availability).

Part of the 'computation' that our minds do carry out (willy-nilly) is, we claim, something equivalent to what we may describe as 'structuring', some parts of which we capture in the 'structural graphics' I recommend.
>
> I've also had the wonderful experience of waking up
> with fresh new insights that led to fruitful
> accomplishment.
>

Indeed you have. What your mind has (probably) done while you were sleeping or resting is to explore the 'structure' of the problem, so that, when you awoke, the 'solution' came more or less unbidden to mind.
>
> GS Chandy says:

> >I claim that computation is definitely an 'entirely
> >natural phenomenon' - but whether it 'precedes' the
> >arrival of man, I do not know. It does seem to be
> >something that humans do explicitly. However,
> >animals, too (I believe) do 'computation': e.g. an
> >anthill is definitely based on extremely complex
> >calculations (probably more complex than those in the
> >most modern and ambitious of our skyscrapers). True,
> >those ants do not seem (in our rather limited
> >understanding of them) to compute 'explicitly'.

>
> You say "explicitly" - I might say "consciously,"
>

No. It's not just the 'conscious computation' (versus 'unconscious computation') that I am discussing. What I intended to describe is the *way* we communicate about the things we discuss.

We make things 'explicit' (to each other and, to an extent, to ourselves) by talking/or writing about those things.

Our 'intellectual training' since childhood has thus far been in 'prose': pure prose is not quite adequate to enable us to understand the 'structure' of the systems within which we need to work, of the systems we seek to design, develop, improve, etc.

As a perhaps relevant instance (of a sort), there is a fair amount of evidence that children learn to understand 'prose descriptions or prescriptions' better when those are accompanied by visual illustrations or by enabling them to work with artefacts of the things under discussion. (Check out a genuine Montessori class, for instance). Likewise, adults too can develop a deeper understanding of systems under discussion by exploring the inter-relationships between the factors within those systems - this is something done rather (even very) ineffectively via pure prose.

It is my claim (after Warfield), that exploring the 'structure' of those things we need to understand (via the 'structural graphics' he developed; other graphics are also probably possible) - such exploration via structural graphics enables us understand the 'systems' under discussion in a way that is not possible at all through 'prose' exploration or discussion - regardless how skillfully one uses prose.
>
> or
> as above, in a way available to introspection. That's
> a good distinction, but it may not (or it may!) make
> much difference in how computation proceeds in
> general, or tell us much about how to describe it or
> analyze it.
>

I suspect the above ideas you have articulated (based on mental models in your mind) would be more clearly understood by me if we were using 'p+sg'.
>
> Humans also do much computation without any
> self-awareness at all - in say, your vision system.
>

Of course. Fully accepted.

But it is NOT those computations (in, say, our vision system) that I am talking about. However, it is possible that we might draw a useful analogy here: imagine, for instance, describing something to me - say, a room in which we happened to be sitting together - if I were blindfolded. Then, if I were able to take off the blindfold, your description would carry a whole world of difference in meaning to me. Likewise, in systems, 'p+sg' very significantly enhances meaning of 'pure prose'.
>
> GS Chandy says:

> >In any case, I do have rather grave doubts about our
> >current (human) ability to understand the
> >relationship 'precedes' (in any 'systemic sense')

>
> I merely meant in the chronological sense.
>

I believe I had not expressed myself clearly. What I wanted to mean by 'systemic' was something else: I wanted to say that the 'chronological sense' of 'precedes' is generally not clearly understood when we look at any unknown system (and even when we look at systems we believe we know). We are, alas, generally not very well aware of the workings of most of the systems in which we work and play and live.

It is my claim that we're not even adequately aware of the 'structure' of the systems we ourselves design and implement! We in general understand the 'structure of systems' only quite superficially [in a 'mechanistic way']. I claim that this is, in fact, a major contributing factor to a great many of the societal issues and conflicts that we confront.

Extensive 'modeling' using the transitive relationship "CONTRIBUTES TO" could help bring about better understanding of the structure of systems of concern/interest - and thereby to develop/improve our systems. E.g.: a great many of the deficiencies of our educational systems derive from an inadequate understanding by various stakeholders in the system of the inter-relationships of the various factors in the system.

What I wanted to say was that, in any system (which we may not *know* quite thoroughly), trying to put down the 'precedence' of events/ milestones is somewhat an 'iffy' venture.

Remarkably, quite large parts of 'management' (and of the way we 'manage' our systems in general) depend to a sizable extent on PERT Charts (based on 'precedence' - explicitly or implicitly) - without us having adequately understood the underlying systems at all!

I claim that it is only AFTER we have adequately understood the 'structure' of the systems under consideration that we could perhaps think of discussing the precedence of events or milestones in them with reasonable accuracy.

For various psychological reasons related to the way we have grown from infancy, we ARE able somewhat better to understand "CONTRIBUTION" within systems.
>
> GS Chandy says (regarding music analogy):

> >At a 'broad' level, I agree entirely - though I do
> >not understand the mental models you are working from
> >in any detail.

>
> That's too bad - rather key to my whole argument.
>

Again, I must have expressed myself poorly. I had understood your argument (to the extent possible when communications are in pure prose).

What I wanted to say is that the 'mental models' we each have in our respective minds are known to ourselves (to some or a considerable extent). When we discuss anything with others, we are in fact describing those mental models we hold in our minds. It so happens that descriptions of mental models in 'pure prose' are somewhat ineffective (regardless how skillful the user of the prose). Some enhanced clarity of communicating about our mental models is possible through the use of 'p+sg' as opposed to communicating about them in 'pure prose'.
>
> The point is concepts, language, and rules can be
> formulated directly at a level appropriate to some
> given phenomenon, without starting from the "ground
> up".
>

Agreed.
>
>Chemistry, for example, made a great deal of
> progress even though at the time, in the 1700s and
> 1800s it could not really be reduced to the physics
> of the time. That needed to wait till quantum theory
> of the 20th century.
>

Agreed.

(Aside: as you've brought up the subject of chemistry, an analogy might be useful: I observe that Mendeleev's Periodic Tables in Chemistry brought about the general understanding about 'elements and their properties' by elucidating the 'structure' of how those elements are 'related'. [We're interested - or I am interested - in the 'structure of systems in general']).
>
> Here's a thought experiment, maybe it will work for
> you, maybe not. Suppose an extra-terrestrial
> intelligence examines one of our computers, and
> suppose it is a completely different technology from
> anything they've seen. Furthermore, let's grant them
> supreme knowledge and competence in measuring and
> analyzing electro-magnetic and quantum phenomenon. So
> they could see all the voltages flying around, the
> whole fantastic dance at quite a closeup and complete
> viewpoint.
>
> Now uppose they don't have a vocabulary and mental
> concepts that includes the likes of, RAM, CPU,
> register, ALU, program, etc. etc. etc. Well then,
> this intricate mechanism may be a complete mystery to
> them, even though in principle they have complete
> physical knowledge of it. Those higher level concepts
> serve as a key to unlocking the meaning of the
> device, much like a Rosetta stone. Without those
> concepts further understanding may be completely
> blocked. Its not as if complete physical knowledge
> serves as any kind of automatic gateway to obtaining
> these higher level concepts.
>
> So too with nervous systems.
>

OK - agreed.

Your example (analogy?) does not gainsay ANY of my claims about 'p+sg' serving as a useful enhancement of 'pure prose'. Nor, for that matter, does it address the issue of the 'differences' between 'human intelligence/ consciousness' and 'animal intelligence/ consciousness' (if we're interested in doing that).

I believe that, in fact, exploring this analogy in more detail may well help demonstrate that 'p+sg' is an ESSENTIAL enhancement to pure prose when we wish the better to understand 'inter-relationships of factors in a system'.

I observe that Robert Hansen has suggested that you have, in fact, "described the development of math". I believe he is mistaken.

We had earlier made a few statements about human Vs. animal intelligence/ consciousness:

In regard to 'human intelligence/consciousness' versus 'animal intelligence/consciousness', I claim that we are not today in a position to understand either of these phenomena effectively.

We ARE in a position to work towards better understanding of human intelligence/consciousness because we know - to some extent - how to 'communicate' with other human intelligences; currently, we are unable to communicate with any animal intelligence (except at extremely superficial levels, levels at which 'scientific conclusions' are unwarranted); we claim, of course, that animals do not possess 'consciousness'; they do not 'think'; and so on and so forth. In general, I believe we know too little to be able to make such claims - we can more or less accurately claim that they do not 'think as we do' - but that's about it.

I claim we could better understand human intelligence/ consciousness if we look upon it as a 'system' and then try to find out how various 'factors' may "CONTRIBUTE" to it. We can accomplish that communication between humans somewhat more effectively through the use of 'p+sg' than through the conventional prose in which we conventionally converse.

If we work towards better understanding human intelligence/ consciousness, we may some day be equipped to understand animal intelligence/consciousness (if such a phenomenon actually exists). Till we're better equipped to understand our own intelligence/ consciousness, it is nothing but that "MASTERS-OF-THE-UNIVERSE" syndrome that we humans suffer from to imagine that we can do anything more than VERY superficially describe 'animal intelligence/ consciousness'.

GSC


Message was edited by: GS Chandy


Date Subject Author
6/3/13
Read all of math is just addition and multiplication
Donald Sauter
6/4/13
Read Re: all of math is just addition and multiplication
Dave L. Renfro
6/5/13
Read Re: all of math is just addition and multiplication
Robert Hansen
6/4/13
Read Re: all of math is just addition and multiplication
kirby urner
6/5/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/5/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/6/13
Read Re: all of math is just addition and multiplication
Michael de Villiers
6/6/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/6/13
Read Re: all of math is just addition and multiplication
kirby urner
6/7/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/7/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/7/13
Read Re: all of math is just addition and multiplication
Louis Talman
6/8/13
Read Re: all of math is just addition and multiplication
Robert Hansen
6/7/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/8/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/8/13
Read Re: all of math is just addition and multiplication
GS Chandy
6/8/13
Read Re: all of math is just addition and multiplication
GS Chandy
6/8/13
Read Re: all of math is just addition and multiplication
GS Chandy
6/8/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/8/13
Read Re: all of math is just addition and multiplication
GS Chandy
6/9/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/14/13
Read Re: all of math is just addition and multiplication
kirby urner
6/9/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/10/13
Read Re: all of math is just addition and multiplication
GS Chandy
6/10/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/11/13
Read Re: all of math is just addition and multiplication
GS Chandy
6/11/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/11/13
Read Re: all of math is just addition and multiplication
Robert Hansen
6/12/13
Read Re: all of math is just addition and multiplication
GS Chandy
6/12/13
Read Re: all of math is just addition and multiplication
GS Chandy
6/12/13
Read Re: all of math is just addition and multiplication
Robert Hansen
6/12/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/13/13
Read Re: all of math is just addition and multiplication
GS Chandy
6/13/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/13/13
Read Re: all of math is just addition and multiplication
GS Chandy
6/17/13
Read Re: all of math is just addition and multiplication
Donald Sauter
6/17/13
Read Re: all of math is just addition and multiplication
Donald Sauter

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