On 25/01/2011 03:25, Rune Allnor wrote:
..
>> The danger in dismissing analogy is that all
>> systems of communication - including math - are based on analogy,
>
> Could you please provide refernces?
>

Try "The Semantics of Science" by Roy Harris (if you can find one; sadly 
not cheap so I have never been able to won a copy). See both Ch 3 
"Semantics and the Royal Society" and of course Ch 6, "Mathematics and 
the Language of Science". There are some online reviews here to give you 
a flavour of the book:

http://linguistlist.org/pubs/reviews/get-review.cfm?SubID=61659

http://www.pantaneto.co.uk/issue24/wawrzyniak.htm

It should be required reading (as other books by Harris such as the 
eminently affordable "Mindboggling") for anyone inclined to say "I know" 
and expect that act of communication to be received as intended.

>
> Studying an analagy is totally ridiculous.
>

On the contrary, everything we do and say is, and have to be to have 
meaning, fundamentally reocentric. Mathematics cannot escape this any 
more than any other "scientific" pursuit can. Call it a model, or an 
analogue, or a description, or a context, whatever, without it we have 
no reason to ~do~ or communicate anything. Without it the DFT is not 
"the DFT" at all, just an arbitrary strange matrix procedure, an act of 
juggling numbers, with an inverse - and  that only if you know what you 
mean by "matrix" and "inverse" and why eiterh of them might be useful. 
"Extracting information" is also meaningless without the definition of 
both "extract" and "information". If numbers need have no meaning (as is 
clearly the case for a solitary number), they contain no information to 
extract and no operation applied to them has meaning either; and 
manifestly neither does any output. Then, if some result is somehow 
"useful", that is more by blind chance than by anything more elevated.

There is a profound lesson emerging from this thread that should 
engender a certain caution and reserve in everyone - that even such a 
seemingly graven in stone thing as "The Fourier Transform" is so steeped 
in linguistic sophistry, reocentric confusion and contextual ambiguity, 
even after all these years, that any assertion that "I know", by anyone, 
itself is essentially no more than the adopting of an essentially 
unprovable position. The FT is just versatile and ambiguous enough in 
its very nature that it is no more nor less than what each person makes 
it. Like any mere number, what it is and what it means depends entirely 
on what it is used for "in the real world". A summary of selected 
features and applications is the best that can be done. Absolute 
"precision in language and semantics" is as impossible as counting all 
the integers.   At best it is a rhetorical ideal as real and meaningful 
as "world peace". At worst it is an aspect of the "language myth" that 
can only result in a total and systemic failure of communication.

I, of course, pretend ~not~ to know!

Richard Dobson

On Jan 25, 10:01&#4294967295;am, Chris Bore <chris.b...@gmail.com> wrote:
> On Jan 25, 3:25&#4294967295;am, Rune Allnor <all...@tele.ntnu.no> wrote:

> > > logic, it is very helpful to be reminded that systems of reasoning are
> > > inherently limited, and of the dangers of failing to be aware of those
> > > limitations and their effect.

> > Parrot. There is nothing in your previous writings
> > that carry any hint of you having the faintest clue
> > of the meaning or implications of the paragraph above.
>
> > Rune
>
> You really do come across as a very rude person.

What does that have to do with anything?

> And in discourse here you violate your own precepts about not assuming
> outside the domain of data presented. You have no idea of my
> background or qualifications at all, yet you permit yourself to
> generalise in the most offensive way based on your own interpretation
> of what you think I said, as to what I may or may not know or be
> competent in.

You have presented the view that studying an analogy is
equivalent to studying the 'real thing', whatever that might be.
In other words, you claim that precision in language and semantics
does not matter.

I have presented the view that you are a parrot, based on the
observation that you argue in self-contradictory ways, when
you then start referring works that warn about the limitations
of language, and take it to support your own view.

Obviously you have not understood the semantic meaning of the
words you quote - which happens to be a trait of the parrot.

Hence my use of the analogy.

Now, according to your own argument that it's OK to study the
analogy, I could now proceed arguing against you based on
your flying skills, color of plumage, nesting habits and
so on, that characterize the parrot birds.

Do you really support such views?

> If you don't understand what I say, just admit it and
> get over it, but don't try to pretend that your understanding so far
> surpasses mine that you can patronise.

I don't pretend. I know. At least what the DFT and friends
is concerned.

Rune

On Jan 25, 3:11&#4294967295;am, Rune Allnor <all...@tele.ntnu.no> wrote:
> On Jan 24, 10:35&#4294967295;am, Chris Bore <chris.b...@gmail.com> wrote:
>
>
>
> > On Jan 18, 4:43&#4294967295;am, Rune Allnor <all...@tele.ntnu.no> wrote:
>
> > > On Jan 17, 6:55&#4294967295;pm, Fred Marshall <fmarshall_xremove_the...@xacm.org>
> > > wrote:
>
> > > > On 1/15/2011 1:10 AM, Rune Allnor wrote:
>
> > > > > But of ocurse, if you are content (proud, even...?) with
> > > > > passing on your own mediocricy, then there is little I or
> > > > > anyone else can do about it.
>
> > > > > Rune
>
> > > > Rune,
>
> > > > Perhaps you're put off by the *style* of the writing.
> > > > But, I've yet to hear from you any part that is *incorrect*.
> > > > [please see the errata I posted].
> > > > Could you please be more specific? &#4294967295;I surely don't want to promulgate
> > > > notions that are mediocre or worse....
>
> > > The comment on mediocricy was aimed at Chris, not you.
> > > In retrospect I might have trimmed the post to be more
> > > clear on that particular point.
>
> > > Rune
>
> > I don't understand why you go out of your way to repeat that
> > particular point, which seems to me not to add to the debate.
>
> It clarifies that I was talking about you and no one else.
> Making sure that such statements reach the correct address
> is rather essential.
>
> Rune

You know what, this is just rude. You and others like you make it no
longer worthwhile to participate here.

No need to respond to this, I have just one final post to make in
comp.dsp and then I shan't be back.

On Jan 25, 3:25&#4294967295;am, Rune Allnor <all...@tele.ntnu.no> wrote:
> On Jan 24, 10:30&#4294967295;am, Chris Bore <chris.b...@gmail.com> wrote:
>
>
>
> > On Jan 15, 9:10&#4294967295;am, Rune Allnor <all...@tele.ntnu.no> wrote:
>
> > > On Jan 14, 10:11&#4294967295;am, Chris Bore <chris.b...@gmail.com> wrote:
>
> > > > On Jan 13, 7:31&#4294967295;pm, Fred Marshall <fmarshall_xremove_the...@xacm.org>
> > > > wrote:
>
> > > > > On 1/12/2011 6:13 PM, Rune Allnor wrote:
> > > > > ....snip.....
>
> > > > > >> Dale repeats his point about the DFT being (in my terms) an abstract
> > > > > >> thingy that is simply a mapping of N points - having nothing whatsoever
> > > > > >> to do with any imagined or real samples which may exist outside the
> > > > > >> sample regions.
>
> > > > > > I garee with Dale on this.
>
> > > > > ***And so did I Rune. &#4294967295;I just gave Dale credit for illuminating that
> > > > > viewpoint.
>
> > > > > >> &#4294967295; This is a surely a valid perspective of the FT as a
> > > > > >> *mapping* but I've not reconciled how it fits in my own perspectives.
>
> > > > > > It's the *only* perspective of the FT, in any of its
> > > > > > shades, shapes or forms.
>
> > > > > ***I'm disappointed to hear that there is only a single viewpoint or
> > > > > framework possible. &#4294967295;That seems too restrictive in human thought.
>
> > > > > >> If one takes an infinite continuous function and samples it then...
>
> > > > > > Why do you bring sampling into this? We were discussing
> > > > > > the FT up till this point, not sampling.
>
> > > > > ***If I had not intended to discuss sampling then I guess I wouldn't
> > > > > have brought it up. &#4294967295;But I did. &#4294967295;It seems obvious to me. &#4294967295;Surely if we
> > > > > can discuss abstract mathematical relationships then we can discuss the
> > > > > conversion from a particular continuous function to a discrete sequence, no?
>
> > > > > >> OK. &#4294967295;So let's start out by sampling F'(w).
>
> > > > > > Keeping in tune with your 'practical' approach: How do
> > > > > > you 'sample' F(w)? What kinds of ADCs work in frequency
> > > > > > domain?
>
> > > > > ***Perhaps there is a flaw in the fabric.... &#4294967295;Well, let's see: &#4294967295;Dale
> > > > > mentions that he worked for companies who made spectrum analyzers. &#4294967295;Many
> > > > > of those devices generate the spectrum as a continuouss function. &#4294967295;And,
> > > > > I'll bet, that some of them either started with sampled data to generate
> > > > > that continuous function. &#4294967295;And, I will assert, that if I want to
> > > > > notionally sample that continuous function then I may do it in my head
> > > > > at least. &#4294967295;The *domain* really doesn't matter. &#4294967295;Let's not take the
> > > > > notion of being practical all the way to "it must be demonstrated to
> > > > > exist physically in order to discuss it".
>
> > > > > ***What should one conclude from this comment? &#4294967295;One can compute the FT
> > > > > of a continuous function/signal or of a discrete sequence. &#4294967295;The result
> > > > > is a continous function. &#4294967295;Are we to conclude that it is somehow
> > > > > unreasonable or improper to imagine sampling this continuous function?
> > > > > Whey is that any more unreasonable than imagining sampling a time
> > > > > function?
>
> > > > > > All you have achieved is to swap a quagmire for quick sand.
>
> > > > > ***I'll leave this to others to comment on.
>
> > > > > ***What I attempted to do was:
>
> > > > > 1) create a framework for *discussion* along the lines of something that
> > > > > makes a lot of sense to me. &#4294967295;The intent was to unify related thoughts
> > > > > and to point out possible differences on the way.
>
> > > > > 2) seek constructive comments regarding what I may have left out, jumped
> > > > > over, stated really incorrectly, etc.
> > > > > I *tried* to say when things were fuzzy in my mind and did ask for help.
>
> > > > > It appears that others have agreed by citing references of similar
> > > > > discussions. &#4294967295;So far, I've not seen comments about how to improve the
> > > > > discussion I presented. &#4294967295;It seems to me that this would be useful. &#4294967295;It's
> > > > > presented in a step-by-step fashion so that any step might be dismissed
> > > > > (with rationale I'd hope) or improved or embellished on.
>
> > > > > For example, it seems like you have tried to dismiss sampling a
> > > > > continuous function in frequency. &#4294967295;I welcome that. &#4294967295;But where's the
> > > > > rationale?
>
> > > > > Fred
> > > > >> Dale repeats his point about the DFT being (in my terms) an abstract
> > > > >> thingy that is simply a mapping of N points - having nothing whatsoever
> > > > >> to do with any imagined or real samples which may exist outside the
> > > > >> sample regions.
>
> > > > Whilst I totally agree with this, I do think one can bear in mind that
> > > > 'signal' processing in many cases does intend to process a 'signal' -
> > > > which I interpret to be a real-w-rold thing.
>
> > > You might interpret that as you which, but once you do, you
> > > effectively limit yourself from exploiting efficient methods
> > > to extract information from data. Even data that originate
> > > in the Real World.
>
> > > I have more than once told the story of how I developed a
> > > passive sonar detector that worked orders of magnitude
> > > better than the usual stuff - my initial simulations
> > > indicated 10-12 dB better detection indexes - before
> > > doing any of the fancy or elaborate stuff.
>
> > > Of course, I had used *maths*, not *intuition* or *analogies*
> > > to arrive at my algorithms, which meant that none of those
> > > who ought to have had a huge interes in my results were
> > > anywhere near capable of understanding what I had done.
>
> > > But of ocurse, if you are content (proud, even...?) with
> > > passing on your own mediocricy, then there is little I or
> > > anyone else can do about it.
>
> > > Rune
>
> > I am not sure I referred to my own mediocrity or whether I was content
> > or proud to pass it on. I don't think I am competent to comment on
> > other people's mediocricy either.
>
> ...which is a hallmark of the mediocre...
>
> > Let me try to clarify what I tried to say. Signals tend to represent
> > things in the 'real' world. That means, for example, that they have
> > properties in addition to being a set of numbers.
>
> Nope, they don't. Not in the context of DSP. In the data
> domain they do. There is a significant difference between
> the sequence
>
> x[n] ={ 37.1, 36.9, 37.3, 37.0 }
>
> being interpreted as, say, body temperature readings in degree
> Celsius (in which case they are perfectly normal), or if they
> are lap times from a 10000 m speed skating race. In which case
> they are 6-7 seconds behind what is presently considered world
> class performance.
>
> But for the purposes of any algorithm one might choose to
> use to extract information, they are merely a sequence of
> numbers.
>
> > For example it may
> > be very important to know what the signal represents (volts,
> > pascals..) and to know if the set of numbers we have represents a sub-
> > set of a supposed larger set - and if there may be rules of how the
> > numbers may behave.
>
> In the context of DSP this is irrelevant.
>
> > This is context. I think in this discussion it has
> > been referred to many times, sometimes rather dismissively, as 'the
> > model' or the 'assumptions'. What I am saying is that the model, the
> > assumptions, are criticial to doing signal processing because they
> > relate the results of processing back to the thing the signal
> > represents.
>
> This is why I think your thinking is mediocre: You mix the
> mathemathical domain and the problem domain. Yes, knowing
> what the data represent is crucial when you want to interpret
> the results.
>
> It is irrelevant when you crinch the numbers.
>
> > This is not suggesting 'intuition', and I do not think I said that. It
> > is saying that the model, the assumptions, are critical to signal
> > processing and not side-issues. The math is easy - the modelling,
> > implementation, and interpretation of results, is not.
>
> DSP is merely a collection of standard maths boxes that have
> no inherent meaning. No need to bring in any models or anything
> like that.
>
> > However, I disagree with you in dismissing the value of 'analogy'.
> > Analogy is a basic way to proceed in analysis, and may be fundamental
> > to communication.
>
> It is one of the worst obstacles to reaching insight.
>
> > Modern logic and philosophy of science tends to
> > suggest that metaphor and metonym are the two fundamental modes of
> > communicating meaning (cf Jakobson). To dismiss this seems to be going
> > back to the Royal Society view in the 17th century that we could
> > 'separate the knowledge of nature from the colours of rhetoric..'
>
> They were right. Using the correct terminology is a
> pre-requisite to obtaining meaningful, precise insight.
>
> > which, like Hilbert's aim of proving math from within, was doomed to
> > fail: in this case because analogy seems to be inevitable in any human
> > system of communication.
>
> Which is why the concept of 'science' is so recent and so
> narrow - it has only been around for 2 centuries and is
> more or less limited to the Western cultural sphere (which
> is *not* the same as Western geography!)
>
> > The danger in dismissing analogy is that all
> > systems of communication - including math - are based on analogy,
>
> Could you please provide refernces?
>
> > and
> > it is highly undesirable to ignore this limitation of those systems.
>
> Studying an analagy is totally ridiculous.
>
> > There is a great deal of work available in these areas, encompassed to
> > some extent in semiotics (the science of signs) and although its
> > interdisciplinary nature does make it less accessible to those of us
> > who are used to concise formal symbolic systems like math or formal
> > logic, it is very helpful to be reminded that systems of reasoning are
> > inherently limited, and of the dangers of failing to be aware of those
> > limitations and their effect.
>
> Parrot. There is nothing in your previous writings
> that carry any hint of you having the faintest clue
> of the meaning or implications of the paragraph above.
>
> Rune

You really do come across as a very rude person.

And in discourse here you violate your own precepts about not assuming
outside the domain of data presented. You have no idea of my
background or qualifications at all, yet you permit yourself to
generalise in the most offensive way based on your own interpretation
of what you think I said, as to what I may or may not know or be
competent in. If you don't understand what I say, just admit it and
get over it, but don't try to pretend that your understanding so far
surpasses mine that you can patronise.

On Jan 25, 3:25&#4294967295;am, Rune Allnor <all...@tele.ntnu.no> wrote:
> On Jan 24, 10:30&#4294967295;am, Chris Bore <chris.b...@gmail.com> wrote:
>
>
>
> > On Jan 15, 9:10&#4294967295;am, Rune Allnor <all...@tele.ntnu.no> wrote:
>
> > > On Jan 14, 10:11&#4294967295;am, Chris Bore <chris.b...@gmail.com> wrote:
>
> > > > On Jan 13, 7:31&#4294967295;pm, Fred Marshall <fmarshall_xremove_the...@xacm.org>
> > > > wrote:
>
> > > > > On 1/12/2011 6:13 PM, Rune Allnor wrote:
> > > > > ....snip.....
>
> > > > > >> Dale repeats his point about the DFT being (in my terms) an abstract
> > > > > >> thingy that is simply a mapping of N points - having nothing whatsoever
> > > > > >> to do with any imagined or real samples which may exist outside the
> > > > > >> sample regions.
>
> > > > > > I garee with Dale on this.
>
> > > > > ***And so did I Rune. &#4294967295;I just gave Dale credit for illuminating that
> > > > > viewpoint.
>
> > > > > >> &#4294967295; This is a surely a valid perspective of the FT as a
> > > > > >> *mapping* but I've not reconciled how it fits in my own perspectives.
>
> > > > > > It's the *only* perspective of the FT, in any of its
> > > > > > shades, shapes or forms.
>
> > > > > ***I'm disappointed to hear that there is only a single viewpoint or
> > > > > framework possible. &#4294967295;That seems too restrictive in human thought.
>
> > > > > >> If one takes an infinite continuous function and samples it then...
>
> > > > > > Why do you bring sampling into this? We were discussing
> > > > > > the FT up till this point, not sampling.
>
> > > > > ***If I had not intended to discuss sampling then I guess I wouldn't
> > > > > have brought it up. &#4294967295;But I did. &#4294967295;It seems obvious to me. &#4294967295;Surely if we
> > > > > can discuss abstract mathematical relationships then we can discuss the
> > > > > conversion from a particular continuous function to a discrete sequence, no?
>
> > > > > >> OK. &#4294967295;So let's start out by sampling F'(w).
>
> > > > > > Keeping in tune with your 'practical' approach: How do
> > > > > > you 'sample' F(w)? What kinds of ADCs work in frequency
> > > > > > domain?
>
> > > > > ***Perhaps there is a flaw in the fabric.... &#4294967295;Well, let's see: &#4294967295;Dale
> > > > > mentions that he worked for companies who made spectrum analyzers. &#4294967295;Many
> > > > > of those devices generate the spectrum as a continuouss function. &#4294967295;And,
> > > > > I'll bet, that some of them either started with sampled data to generate
> > > > > that continuous function. &#4294967295;And, I will assert, that if I want to
> > > > > notionally sample that continuous function then I may do it in my head
> > > > > at least. &#4294967295;The *domain* really doesn't matter. &#4294967295;Let's not take the
> > > > > notion of being practical all the way to "it must be demonstrated to
> > > > > exist physically in order to discuss it".
>
> > > > > ***What should one conclude from this comment? &#4294967295;One can compute the FT
> > > > > of a continuous function/signal or of a discrete sequence. &#4294967295;The result
> > > > > is a continous function. &#4294967295;Are we to conclude that it is somehow
> > > > > unreasonable or improper to imagine sampling this continuous function?
> > > > > Whey is that any more unreasonable than imagining sampling a time
> > > > > function?
>
> > > > > > All you have achieved is to swap a quagmire for quick sand.
>
> > > > > ***I'll leave this to others to comment on.
>
> > > > > ***What I attempted to do was:
>
> > > > > 1) create a framework for *discussion* along the lines of something that
> > > > > makes a lot of sense to me. &#4294967295;The intent was to unify related thoughts
> > > > > and to point out possible differences on the way.
>
> > > > > 2) seek constructive comments regarding what I may have left out, jumped
> > > > > over, stated really incorrectly, etc.
> > > > > I *tried* to say when things were fuzzy in my mind and did ask for help.
>
> > > > > It appears that others have agreed by citing references of similar
> > > > > discussions. &#4294967295;So far, I've not seen comments about how to improve the
> > > > > discussion I presented. &#4294967295;It seems to me that this would be useful. &#4294967295;It's
> > > > > presented in a step-by-step fashion so that any step might be dismissed
> > > > > (with rationale I'd hope) or improved or embellished on.
>
> > > > > For example, it seems like you have tried to dismiss sampling a
> > > > > continuous function in frequency. &#4294967295;I welcome that. &#4294967295;But where's the
> > > > > rationale?
>
> > > > > Fred
> > > > >> Dale repeats his point about the DFT being (in my terms) an abstract
> > > > >> thingy that is simply a mapping of N points - having nothing whatsoever
> > > > >> to do with any imagined or real samples which may exist outside the
> > > > >> sample regions.
>
> > > > Whilst I totally agree with this, I do think one can bear in mind that
> > > > 'signal' processing in many cases does intend to process a 'signal' -
> > > > which I interpret to be a real-w-rold thing.
>
> > > You might interpret that as you which, but once you do, you
> > > effectively limit yourself from exploiting efficient methods
> > > to extract information from data. Even data that originate
> > > in the Real World.
>
> > > I have more than once told the story of how I developed a
> > > passive sonar detector that worked orders of magnitude
> > > better than the usual stuff - my initial simulations
> > > indicated 10-12 dB better detection indexes - before
> > > doing any of the fancy or elaborate stuff.
>
> > > Of course, I had used *maths*, not *intuition* or *analogies*
> > > to arrive at my algorithms, which meant that none of those
> > > who ought to have had a huge interes in my results were
> > > anywhere near capable of understanding what I had done.
>
> > > But of ocurse, if you are content (proud, even...?) with
> > > passing on your own mediocricy, then there is little I or
> > > anyone else can do about it.
>
> > > Rune
>
> > I am not sure I referred to my own mediocrity or whether I was content
> > or proud to pass it on. I don't think I am competent to comment on
> > other people's mediocricy either.
>
> ...which is a hallmark of the mediocre...
>
> > Let me try to clarify what I tried to say. Signals tend to represent
> > things in the 'real' world. That means, for example, that they have
> > properties in addition to being a set of numbers.
>
> Nope, they don't. Not in the context of DSP. In the data
> domain they do. There is a significant difference between
> the sequence
>
> x[n] ={ 37.1, 36.9, 37.3, 37.0 }
>
> being interpreted as, say, body temperature readings in degree
> Celsius (in which case they are perfectly normal), or if they
> are lap times from a 10000 m speed skating race. In which case
> they are 6-7 seconds behind what is presently considered world
> class performance.
>
> But for the purposes of any algorithm one might choose to
> use to extract information, they are merely a sequence of
> numbers.
>
> > For example it may
> > be very important to know what the signal represents (volts,
> > pascals..) and to know if the set of numbers we have represents a sub-
> > set of a supposed larger set - and if there may be rules of how the
> > numbers may behave.
>
> In the context of DSP this is irrelevant.
>
> > This is context. I think in this discussion it has
> > been referred to many times, sometimes rather dismissively, as 'the
> > model' or the 'assumptions'. What I am saying is that the model, the
> > assumptions, are criticial to doing signal processing because they
> > relate the results of processing back to the thing the signal
> > represents.
>
> This is why I think your thinking is mediocre: You mix the
> mathemathical domain and the problem domain. Yes, knowing
> what the data represent is crucial when you want to interpret
> the results.
>
> It is irrelevant when you crinch the numbers.
>
> > This is not suggesting 'intuition', and I do not think I said that. It
> > is saying that the model, the assumptions, are critical to signal
> > processing and not side-issues. The math is easy - the modelling,
> > implementation, and interpretation of results, is not.
>
> DSP is merely a collection of standard maths boxes that have
> no inherent meaning. No need to bring in any models or anything
> like that.
>
> > However, I disagree with you in dismissing the value of 'analogy'.
> > Analogy is a basic way to proceed in analysis, and may be fundamental
> > to communication.
>
> It is one of the worst obstacles to reaching insight.
>
> > Modern logic and philosophy of science tends to
> > suggest that metaphor and metonym are the two fundamental modes of
> > communicating meaning (cf Jakobson). To dismiss this seems to be going
> > back to the Royal Society view in the 17th century that we could
> > 'separate the knowledge of nature from the colours of rhetoric..'
>
> They were right. Using the correct terminology is a
> pre-requisite to obtaining meaningful, precise insight.
>
> > which, like Hilbert's aim of proving math from within, was doomed to
> > fail: in this case because analogy seems to be inevitable in any human
> > system of communication.
>
> Which is why the concept of 'science' is so recent and so
> narrow - it has only been around for 2 centuries and is
> more or less limited to the Western cultural sphere (which
> is *not* the same as Western geography!)
>
> > The danger in dismissing analogy is that all
> > systems of communication - including math - are based on analogy,
>
> Could you please provide refernces?
>
> > and
> > it is highly undesirable to ignore this limitation of those systems.
>
> Studying an analagy is totally ridiculous.
>
> > There is a great deal of work available in these areas, encompassed to
> > some extent in semiotics (the science of signs) and although its
> > interdisciplinary nature does make it less accessible to those of us
> > who are used to concise formal symbolic systems like math or formal
> > logic, it is very helpful to be reminded that systems of reasoning are
> > inherently limited, and of the dangers of failing to be aware of those
> > limitations and their effect.
>
> Parrot. There is nothing in your previous writings
> that carry any hint of you having the faintest clue
> of the meaning or implications of the paragraph above.
>
> Rune

> The danger in dismissing analogy is that all
> systems of communication - including math - are based on analogy,

Could you please provide references?

Jakobson, Roman, 'Language in relation to other communication
systems'. 'Selected writings' vol 2, Mouton, The Hague
Barthes, Roland, 'Elements of semiology', Jonathan Cape (also
avaialble in English translation)
Lakoff & Johnson, 'Metaphors we live by', Uni of Chicago Press

Also an extensive bibilography in 'semiotics' by Daniel Chandler,
Routledge

Chris
===============================
Chris Bore
BORES Signal Processing
www.bores.com

On Jan 24, 10:30&#4294967295;am, Chris Bore <chris.b...@gmail.com> wrote:
> On Jan 15, 9:10&#4294967295;am, Rune Allnor <all...@tele.ntnu.no> wrote:
>
>
>
>
>
> > On Jan 14, 10:11&#4294967295;am, Chris Bore <chris.b...@gmail.com> wrote:
>
> > > On Jan 13, 7:31&#4294967295;pm, Fred Marshall <fmarshall_xremove_the...@xacm.org>
> > > wrote:
>
> > > > On 1/12/2011 6:13 PM, Rune Allnor wrote:
> > > > ....snip.....
>
> > > > >> Dale repeats his point about the DFT being (in my terms) an abstract
> > > > >> thingy that is simply a mapping of N points - having nothing whatsoever
> > > > >> to do with any imagined or real samples which may exist outside the
> > > > >> sample regions.
>
> > > > > I garee with Dale on this.
>
> > > > ***And so did I Rune. &#4294967295;I just gave Dale credit for illuminating that
> > > > viewpoint.
>
> > > > >> &#4294967295; This is a surely a valid perspective of the FT as a
> > > > >> *mapping* but I've not reconciled how it fits in my own perspectives.
>
> > > > > It's the *only* perspective of the FT, in any of its
> > > > > shades, shapes or forms.
>
> > > > ***I'm disappointed to hear that there is only a single viewpoint or
> > > > framework possible. &#4294967295;That seems too restrictive in human thought.
>
> > > > >> If one takes an infinite continuous function and samples it then...
>
> > > > > Why do you bring sampling into this? We were discussing
> > > > > the FT up till this point, not sampling.
>
> > > > ***If I had not intended to discuss sampling then I guess I wouldn't
> > > > have brought it up. &#4294967295;But I did. &#4294967295;It seems obvious to me. &#4294967295;Surely if we
> > > > can discuss abstract mathematical relationships then we can discuss the
> > > > conversion from a particular continuous function to a discrete sequence, no?
>
> > > > >> OK. &#4294967295;So let's start out by sampling F'(w).
>
> > > > > Keeping in tune with your 'practical' approach: How do
> > > > > you 'sample' F(w)? What kinds of ADCs work in frequency
> > > > > domain?
>
> > > > ***Perhaps there is a flaw in the fabric.... &#4294967295;Well, let's see: &#4294967295;Dale
> > > > mentions that he worked for companies who made spectrum analyzers. &#4294967295;Many
> > > > of those devices generate the spectrum as a continuouss function. &#4294967295;And,
> > > > I'll bet, that some of them either started with sampled data to generate
> > > > that continuous function. &#4294967295;And, I will assert, that if I want to
> > > > notionally sample that continuous function then I may do it in my head
> > > > at least. &#4294967295;The *domain* really doesn't matter. &#4294967295;Let's not take the
> > > > notion of being practical all the way to "it must be demonstrated to
> > > > exist physically in order to discuss it".
>
> > > > ***What should one conclude from this comment? &#4294967295;One can compute the FT
> > > > of a continuous function/signal or of a discrete sequence. &#4294967295;The result
> > > > is a continous function. &#4294967295;Are we to conclude that it is somehow
> > > > unreasonable or improper to imagine sampling this continuous function?
> > > > Whey is that any more unreasonable than imagining sampling a time
> > > > function?
>
> > > > > All you have achieved is to swap a quagmire for quick sand.
>
> > > > ***I'll leave this to others to comment on.
>
> > > > ***What I attempted to do was:
>
> > > > 1) create a framework for *discussion* along the lines of something that
> > > > makes a lot of sense to me. &#4294967295;The intent was to unify related thoughts
> > > > and to point out possible differences on the way.
>
> > > > 2) seek constructive comments regarding what I may have left out, jumped
> > > > over, stated really incorrectly, etc.
> > > > I *tried* to say when things were fuzzy in my mind and did ask for help.
>
> > > > It appears that others have agreed by citing references of similar
> > > > discussions. &#4294967295;So far, I've not seen comments about how to improve the
> > > > discussion I presented. &#4294967295;It seems to me that this would be useful. &#4294967295;It's
> > > > presented in a step-by-step fashion so that any step might be dismissed
> > > > (with rationale I'd hope) or improved or embellished on.
>
> > > > For example, it seems like you have tried to dismiss sampling a
> > > > continuous function in frequency. &#4294967295;I welcome that. &#4294967295;But where's the
> > > > rationale?
>
> > > > Fred
> > > >> Dale repeats his point about the DFT being (in my terms) an abstract
> > > >> thingy that is simply a mapping of N points - having nothing whatsoever
> > > >> to do with any imagined or real samples which may exist outside the
> > > >> sample regions.
>
> > > Whilst I totally agree with this, I do think one can bear in mind that
> > > 'signal' processing in many cases does intend to process a 'signal' -
> > > which I interpret to be a real-w-rold thing.
>
> > You might interpret that as you which, but once you do, you
> > effectively limit yourself from exploiting efficient methods
> > to extract information from data. Even data that originate
> > in the Real World.
>
> > I have more than once told the story of how I developed a
> > passive sonar detector that worked orders of magnitude
> > better than the usual stuff - my initial simulations
> > indicated 10-12 dB better detection indexes - before
> > doing any of the fancy or elaborate stuff.
>
> > Of course, I had used *maths*, not *intuition* or *analogies*
> > to arrive at my algorithms, which meant that none of those
> > who ought to have had a huge interes in my results were
> > anywhere near capable of understanding what I had done.
>
> > But of ocurse, if you are content (proud, even...?) with
> > passing on your own mediocricy, then there is little I or
> > anyone else can do about it.
>
> > Rune
>
> I am not sure I referred to my own mediocrity or whether I was content
> or proud to pass it on. I don't think I am competent to comment on
> other people's mediocricy either.

...which is a hallmark of the mediocre...

> Let me try to clarify what I tried to say. Signals tend to represent
> things in the 'real' world. That means, for example, that they have
> properties in addition to being a set of numbers.

Nope, they don't. Not in the context of DSP. In the data
domain they do. There is a significant difference between
the sequence

x[n] ={ 37.1, 36.9, 37.3, 37.0 }

being interpreted as, say, body temperature readings in degree
Celsius (in which case they are perfectly normal), or if they
are lap times from a 10000 m speed skating race. In which case
they are 6-7 seconds behind what is presently considered world
class performance.

But for the purposes of any algorithm one might choose to
use to extract information, they are merely a sequence of
numbers.

> For example it may
> be very important to know what the signal represents (volts,
> pascals..) and to know if the set of numbers we have represents a sub-
> set of a supposed larger set - and if there may be rules of how the
> numbers may behave.

In the context of DSP this is irrelevant.

> This is context. I think in this discussion it has
> been referred to many times, sometimes rather dismissively, as 'the
> model' or the 'assumptions'. What I am saying is that the model, the
> assumptions, are criticial to doing signal processing because they
> relate the results of processing back to the thing the signal
> represents.

This is why I think your thinking is mediocre: You mix the
mathemathical domain and the problem domain. Yes, knowing
what the data represent is crucial when you want to interpret
the results.

It is irrelevant when you crinch the numbers.

> This is not suggesting 'intuition', and I do not think I said that. It
> is saying that the model, the assumptions, are critical to signal
> processing and not side-issues. The math is easy - the modelling,
> implementation, and interpretation of results, is not.

DSP is merely a collection of standard maths boxes that have
no inherent meaning. No need to bring in any models or anything
like that.

> However, I disagree with you in dismissing the value of 'analogy'.
> Analogy is a basic way to proceed in analysis, and may be fundamental
> to communication.

It is one of the worst obstacles to reaching insight.

> Modern logic and philosophy of science tends to
> suggest that metaphor and metonym are the two fundamental modes of
> communicating meaning (cf Jakobson). To dismiss this seems to be going
> back to the Royal Society view in the 17th century that we could
> 'separate the knowledge of nature from the colours of rhetoric..'

They were right. Using the correct terminology is a
pre-requisite to obtaining meaningful, precise insight.

> which, like Hilbert's aim of proving math from within, was doomed to
> fail: in this case because analogy seems to be inevitable in any human
> system of communication.

Which is why the concept of 'science' is so recent and so
narrow - it has only been around for 2 centuries and is
more or less limited to the Western cultural sphere (which
is *not* the same as Western geography!)

> The danger in dismissing analogy is that all
> systems of communication - including math - are based on analogy,

Could you please provide refernces?

> and
> it is highly undesirable to ignore this limitation of those systems.

Studying an analagy is totally ridiculous.

> There is a great deal of work available in these areas, encompassed to
> some extent in semiotics (the science of signs) and although its
> interdisciplinary nature does make it less accessible to those of us
> who are used to concise formal symbolic systems like math or formal
> logic, it is very helpful to be reminded that systems of reasoning are
> inherently limited, and of the dangers of failing to be aware of those
> limitations and their effect.

Parrot. There is nothing in your previous writings
that carry any hint of you having the faintest clue
of the meaning or implications of the paragraph above.

Rune