Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 GS Chandy Posts: 8,307 From: Hyderabad, Mumbai/Bangalore, India Registered: 9/29/05
Re: all of math is just addition and multiplication
Posted: Jun 11, 2013 4:36 AM

Joe Niederberger posted Jun 10, 2013 11:04 PM (GSC's remarks precede and interspersed):

As often, I agree (but for a few reservations) with practically everything you've argued below. In order to explain those reservations adequately, I shall need to use 'prose + structural graphics' (p+sg, which I had mentioned earlier).

[This has to be done *in tandem* with you, as you raise ideas or thoughts that may come to mind - and those ideas/thoughts of yours are 'integrated' with my thoughts and ideas, and these integrated models could (perhaps) become our 'consensus' in a way.

[Currently, our discussion is using (prose) words from 'mental models' we each hold in our respective minds - and only a small part of what we wish to communicate actually goes 'across' effectively when we use pure prose. 'P+sg' could help us get things across a great deal more clearly and effectively].

Unfortunately, we do not here have the needed facilities to develop or show the needed p+sg parts of any discussion/ argument (integrating the views of different participants as they are brought up), so I shall have to do without (though I do indeed construct my own models, along with my impressions of what your models may be. In the circumstances, the understanding I have of your mental models is quite superficial). I discuss, below, as much as I can in pure prose:
> GS Chandy says:
> >I believe it is entirely counterproductive to try to
> 'compare' humans (directly or indirectly) to machines
> because it is entirely clear by now that no such
> comparison is 'meaningful' at all
>
> Doctors routinely view us as machines, and mechanical
> implants and parts are turning more of us into
> cyborgs everyday.
>

Partially true: and no doubt we shall continuingly become more and more 'cyborgean' over time - but I doubt we shall ever become 'fully cyborgs': there are some very major issues, none of which we adequately understand yet. Isaac Asimov had explored some of these issues superficially in the 'I, Robot' stories - but science proper has not yet, I believe, done any such required exploration.

Whatever, I observe that, for some quite remarkable (as yet unexplained) reason, the only truly effective doctors are those that treat their patients NOT as machines, but as human beings!! There are individuals (entirely unqualified medically or in science) who bring a lot more healing to their patients than do the most highly qualified doctors who treat their patients as machines. Scientists and doctors have not yet troubled themselves to try to explain this remarkable phenomenon (to the best of my inadequate knowledge).
>
>Its only when we approach the "I"
> (somewhere in the brain today -- not many believe it
> involves the heart anymore) that objections begin to
> mount.
>

That 'location' of the "I" as being 'seated' firmly in the brain is, I suspect, rather suspect. The "I" is - I assert - bound up in the 'whole human being' (whatever that whole might be).

The 'brain' (which we've just about begun to understand at its fringes as a physical entity) is 'associated' with something we call the 'mind' - which is not yet much understood, if it is understood at all: there are those that claim that there is no 'mind', only 'brain': I personally believe this is entirely entirely false. (This can be demonstrated using 'p+sg').

I guess it's a bit like my non-belief in God: I strongly believe there is no such 'being' or 'entity' [apart from 'nature'] - but I'm entirely unable to prove the non-existence of God. On the other hand, believers are also unable prove the existence.

To return to this mundane plane from metaphysical speculation, there is a LONG way to go before we begin to understand (at any 'usable level') the brain even as a purely physical entity - and a MUCH longer way to go before we begin to understand just how that 'immanent thing', the 'mind', is 'associated' with the brain. This part of my argument can be somewhat more effectively [to some extent] developed using p+sg. The rest of my argument requires further development of what I call -for want of a better name - 'brain+mind science'. (It is my quite strong belief [but it is currently only a belief] that the 'brain' simply cannot be understood as a purely 'physical entity' - it perhaps can be somewhat understood if we learn the associations existing between 'brain' and 'mind'.

Most of what is weak in the above argument is because I am using 'prose' where I should be using 'p+sg'; whatever else is weak is because the 'brain+mind science' I've postulated does not yet exist.
>).
>Some gurus teach that the "I" isn't the true
> self, oh well!
>

I have little faith in 'gurus' (of the conventional variety; particularly those of the ilk of Sri Sri Ravi Shanker, who by the way lives here in Bangalore). But yet I must grant that those gurus may well be verging towards a correct and meaningful statement when they teach that "the 'I' isn't the true self". I'd have more respect for them if they would also say, "I know little or nothing about the 'I'" - some of them do indeed say this in words, but generally they say it as though, underlying it all, they do in fact know ALL about the 'I'!!)
>
> But I really only brought up this bit about natural
> computing ala Denning because (1) I think its an
> interesting view that is not entirely common today,
> and (2) though I wouldn't know how to define "all of
> math" myself, it seems it never gets too far from
> something related to computation, be it numerical or
> logical or algebraic.
>

It seems to be true enough that 'math' never gets too far from 'something' related to computation; but that doesn't 'explain' (if anything can) 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' - which still has innumerable HUGE unresolved problems today. (I do not have access to my references right now, so I cannot give you more details on this and how specifically it relates to the argument I'm putting forward here).

I like to think of 'math' as being one VERY remarkable aspect embedded in the even more remarkable process of 'thinking' or 'mind' - and we know little about either 'math' or 'thought' at a 'meta'-level. What is 'math' and what is 'mind' are questions to which we really have few definitive answers today. (This fact doesn't trouble me at all: I do 'math' with some facility, just as I do think quite comfortably about 'mind' as something 'associated' with 'brain', though I know very little about the nature of such association).
>
> If computation itself is viewed as an entirely
> natural phenomenon (preceding the arrival of man),
>

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'.

In any case, I do have rather grave doubts about our current (human) ability to understand the relationship 'precedes' (in any 'systemic sense'). I believe it would benefit us very significantly to explore and better understand the relationship "contributes to" in systems (and as well as "hinders") before we attempt to work on 'precedence' in systems. [But we find innumerable managers, scientists, and Robert Hansen pontificating about PERT Charts, without any of them having adequately understood the nature of the 'precedence relationship!]

I believe a great many of the current issues and problems we (humans) are confronting today (without being able to arrive at even reasonably 'workable resolution') is precisely because most of our science and tech persists in thinking about and using 'precedence' with little understanding of how it works in complex systems - this argument too requires 'p+sg'. [I do hope to explore some of these issues in a book I've started - that book will contain plenty of 'p+sg' (though this may well be an unwise marketing strategy].
>
> then math itself appears more natural, even if man
> did/does not recognize immediately as such.
>

I claim that math IS in fact, 'entirely natural' - but in order to explain what I mean by that (and for me to understand what you may mean), we would need to slip into 'p+sg'. However, to me it seems that 'math' is something that humans do - humans are not something that math does.
>Rather
> than trying to reduce math to nearly nothing (just +
> and x), this view places it in a much grander
> context, in my estimation.
>

I whole-heartedly agree that 'math' is something MUCH more than just '+' and 'x'. That was, in fact, the underlying point I had made in my initial response to Donald Sauter at this thread.
>
> The question that the natural computing view raises
> is, what are the best concepts and language that
> should be employed to understand the complex
> information processing systems found in nature?
>

I believe Warfield's view of systems has much potential to help us understand these. My own work on Warfield's ideas has been focussed on trying to make it more readily accessible to all regardless of their background - I have succeeded to a fair extent: any high-school student can now understand AND use it to issues/problems of interest to him/her.

At some stage in the future, I might like to do this kind of application (i.e. exploring issues relating to complex information processing systems in nature). As I currently understand the matter, 'good' concepts to help us initiate a usable understanding of complex information processing systems would be "contributes to" and "hinders". These two relationships will help us construct usable working models that could take us quite far to enhance our understanding.
>
>I'll
> try an analogy - we know music hits our ears as sound
> waves. But to understand music we don't begin at the
> physical level and analyze the physical phenomenon of
> sound in all generality. Sound in general is noise -
> only certain sounds are music. To understand that we
> have concepts of rhythm, scale and harmony, and
> proceeding from there to larger structures (phrases,
> forms, etc.)
>

At a 'broad' level, I agree entirely - though I do not understand the mental models you are working from in any detail.
>
>Its about finding the right concepts and
> relations and way of talking about the phenomenon. To
> understand computing in all its natural glory,
> starting at the level of physics may be a dead end.
>

Again, I believe the 'right' concepts and relationships to help us 'deepen' our understanding of music (for instance) would have to develop from models predicated on the transitive relationship "CONTRIBUTES TO" (and its 'negative' "HINDERS").

GSC

Date Subject Author
6/3/13 Donald Sauter
6/4/13 Dave L. Renfro
6/5/13 Robert Hansen
6/4/13 kirby urner
6/5/13 Joe Niederberger
6/5/13 Joe Niederberger
6/6/13 Michael de Villiers
6/6/13 Joe Niederberger
6/6/13 kirby urner
6/7/13 Joe Niederberger
6/7/13 Joe Niederberger
6/7/13 Louis Talman
6/8/13 Robert Hansen
6/7/13 Joe Niederberger
6/8/13 Joe Niederberger
6/8/13 GS Chandy
6/8/13 GS Chandy
6/8/13 GS Chandy
6/8/13 Joe Niederberger
6/8/13 GS Chandy
6/9/13 Joe Niederberger
6/14/13 kirby urner
6/9/13 Joe Niederberger
6/10/13 GS Chandy
6/10/13 Joe Niederberger
6/11/13 GS Chandy
6/11/13 Joe Niederberger
6/11/13 Robert Hansen
6/12/13 GS Chandy
6/12/13 GS Chandy
6/12/13 Robert Hansen
6/12/13 Joe Niederberger
6/13/13 GS Chandy
6/13/13 Joe Niederberger
6/13/13 GS Chandy
6/17/13 Donald Sauter
6/17/13 Donald Sauter