about maths: strictly speaking, off topic, but justified.
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From: jmfbahciv on 29 Mar 2010 08:22 Ste wrote: > On 28 Mar, 15:03, jmfbahciv <jmfbahciv(a)aol> wrote: >> Ste wrote: >> >>> But as I say, there >>> is no meaning relating to the physical world which is conveyed by >>> traditional language, that cannot be conveyed by maths. >> ARe you stating that all is known? The sciences will disagree with >> you. > > No, I wasn't stating that. I simply said that anything of meaning that > is known about the physical world can be conveyed mathematically, even > if cumbersomely. Where maths does fall down, and where traditional > language has a decided advantage, is in describing more abstract, > ethereal concepts. To put it another way, maths is not the language of > creativity and imagination. Which is a physical aspect. > > > >>> The real power >>> of traditional language is, I would imagine, it's ability to handle >>> more vague, analogue meanings and abstract concepts, which would >>> utterly confound a mathematical representation. >> IOW, your use of "traditional language" is referring to human >> language. Math isn't this kind of languge; it is a tool >> for descriptive purposes. > > I continue to insist that maths is a language, and I fail to see how > you demarcate the two by identifying maths as a "tool for descriptive > purposes" I guess we're done. A language has to have more than only adjectives. > > > >>>>>>> Are you looking for specific words, like "run"? If so, I think you're >>>>>>> presupposing the answers to your own questions, and making a spectacle >>>>>>> out of a rather trite observation that maths has no "verbs" in the >>>>>>> sense of "single words that qualitatively but loosely describe >>>>>>> everyday actions". >>>>>> You, yourself stated that maths only deal with everyday situations. >>>>> No I didn't say that at all. I said maths deals with the material >>>>> world. >>>> Not exclusively. >>> Yes exclusively, unless you want to elaborate on your views. >> and you are wrong. > > So I gather you don't want to elaborate. I don't think there's much > more I can say to someone who is really just making bald statements of > opinion and refuses to elaborate or discuss them. I give you the definition of the word but you won't accept that. > > > >>>>>> So, give an example of a math term which is a verb. >>>>> We've been over this already. >>>> OK. So you cannot give an example. >>> As I say, I've been over it already. You are being stubborn as a mule >>> in refusing to identify what you mean by "verb", bearing in mind the >>> questions of definition I've asked of you previously. >> Action. I have given what I mean. Since the definition cannot >> support your ideas about math, you begin to call me names and try >> change the topic. > > No, you haven't given what you mean, otherwise I wouldn't be asking > you to explain what you mean. Since you cannot give an example, you are claiming that you can't until I answer your question with an answer only you believe. > I'm calling you stubborn as a mule > because you've consistently failed to give more information as > requested, and indeed a number of other people besides me have > commented on this unwarranted failure to provide information that > would allow the discussion to progress. > Just because you have a majority of the stupid on your side doesn't imply that I didn't answer your question. I gave you my definition of verb. Action. > And I repeat, maths can convey action/change. If you are not willing > to accept the explanation that I've given, and not willing to explain > yourself further and progress the discussion, then I really don't see > what else you expect to get from this discussion. And just so we're > clear, this isn't me folding my arms and refusing to discuss it futher > - I'm interested in your point, even if I ostensibly disagree with it. > But there can be no further progress unless you try to answer some of > our questions about what you mean by "verb" and "action", since a > number of people including me have pointed out specific ways in which > maths conveys action and change. Your example just gave a story about counting. It had nothing to with math and didn't give an example of a verb in the math "language". > > > >>>>>>> As I said, my understanding of the function of verbs is to describe >>>>>>> action. Mathematics can also describe action, as stated. >>>>>> no. Math gives you the tools to analyze an action. That isn't >>>>>> a verb; if I stretch the definition of an adjective, the results >>>>>> of a calculation is an adjective. This doesn't make math a >>>>>> language. >>>>> Yes, but you haven't yet specified what you think a language is. I've >>>>> tried to narrow it down, but you haven't replied to specific >>>>> questions. >>>> Huh? All I've asked is, for those of you who declare that math >>>> is a language, to give an example of a verb. >>> But I'm *not sure what you mean* by these words, that's why I've asked >>> you to define them. The fact that you seem to think the definition of >>> words like "language" and "verb" is self-evident is a sure sign you >>> know nothing about this subject. Until you do define your words >>> further, all I can say is that (depending on your meanings) either >>> I've given you the answer already, or what you're asking is a non- >>> sequitur. >> IOW, you can't answer the question. > > Not unless you do more to explain what you are asking, no. A verb is a word which denotes an action. Now give me an example of a math verb. > > >>>>>>> Insofar as it >>>>>>> is a requirement of language that it can describe action, then >>>>>>> mathematics meets this test. >>>>>> Describes...that is an adjective, not a verb. >>>>> No it isn't. You have the most laughably naive understanding of >>>>> language. Do you know any foreign languages incidentally? >>>> No. None of that has to do with my question. >>> I think you'll find it does, because your lack of exposure to the >>> structures and grammar of other languages is almost certainly leading >>> you to naive assumptions about the essential components of language. >>> For example, word order is essential in English, it isn't in Greek >>> (for example, "the dog bit the man" means something quite different in >>> English to "the man bit the dog"). English also has a myriad of >>> prepositions, whereas Greek relies heavily on word endings - to put it >>> another way, discrete words found in English like "of" (used to >>> express the genitive case), are not found in Greek (for example, >>> "Theodore of Cyprus" would be "Theodoros Kyprou" in Greek). >>> It also seems (having just done a quick search) that there are a >>> number of Polynesian languages where, indeed, linguists struggle to >>> demarcate verbs. >>> I have pointed out how maths can express action and change in a >>> variety of ways, and other posters have pointed out that a number of >>> mathematical operators (for example, signs that represent addition, >>> summation, integration, etc) convey instructions about how >>> mathematical quantities interact. >> None of those are verbs; they are descriptors. > > How do verbs and "descriptors" differ then? You don't know the difference between an adjective and and a verb? <snip repetition> /BAH
From: J. Clarke on 29 Mar 2010 11:03 On 3/29/2010 8:09 AM, jmfbahciv wrote: > Richard Dobson wrote: >> On 28/03/2010 14:53, jmfbahciv wrote: >> .. >>>> As any programmer will tell you, >>> >>> No they won't. >> >> Here we go... "oh yes they will!". > > <grin> Nope. I are one and I don't make that statement. > >> >> I've been questioning the usage of the word "language" >>> w.r.t. HLL compilers and interpreters, too. >>> >> Question away. There does seem to be a great deal of enthusiasm on >> this list for redefining everything, one way or another. > > Sure. That happens to a computer term about every 4 years now. > > >> Take away established usage for established words and you need to >> supply an alternative that enables people to communicate at least as >> well as the original. And then persuade people to use it. What would >> be your preference - "Semiotic code"? > > I'm not advocating nor objecting to the usage. Somebody made a claim > and all I asked was to give an example of a verb. So far, their > replies are smoke and mirrors. > >> >> (http://www.aber.ac.uk/media/Documents/S4B/sem08.html) >> >> >> Maybe see also (if you can find a copy), Ch 8: "The Language Myth and >> Mathematical Notation as a Language of Nature", Daniel R. Davis, in: >> "the language Myth in Western Culture", Curzon Press, 2002." > > Thanks for the pointer. I'll try to find it. I'd like > to know where this attitude came from. > >> >> .. >>> All of the posters have been using the term as a human language, >>> not a machine language. >>> >> >> That much is very apparent, if unstated. > > But note that the same types of people consider a Fortran statement > and equation. Last month one guy thought that the angle brackets > used in HLLs were inequalities. > >> Anyway, the existing canon of thought with respect to language in >> general, and formal languages in particular, is "out there", ready to >> be drawn upon ad libitum, as is the work of Chomsky et al. Or ignore >> it; but whether that will reach any useful conclusion is as yet >> indeterminate. >> > All I wanted was an example of a verb. :-) I can't think of one so > the people who are declaring the concept should be able to give me > one. I don't consider counting an example of a verb. "Let X be an element of the set {whatever}" "For every X greater than 0 there exists Y such that . . ." Both mathematical statements, both have verbs. Remember, most of what mathematicians do is proofs, not calculations, calculations are the domain of mere engineers such as thee and me. So unless you want to take the language used in writing proofs out of the domain of mathematics you'll find plenty of verbiage.
From: Richard Dobson on 29 Mar 2010 12:00 On 29/03/2010 13:09, jmfbahciv wrote: ... >> Take away established usage for established words and you need to >> supply an alternative that enables people to communicate at least as >> well as the original. And then persuade people to use it. What would >> be your preference - "Semiotic code"? > > I'm not advocating nor objecting to the usage. Somebody made a claim > and all I asked was to give an example of a verb. So far, their > replies are smoke and mirrors. > Much of (classical) maths depends on elements not defined formally within the language itself. The basic idea of "true or false" is not represented by a symbol within the language. Thus "2 = 0" is a syntactically correct statement (in the form of "a = b"), but semantically false - because we "know it is" The truth or falsity of a statement cannot be represented directly as a symbol in the language (you need to add something like Boolean notation to do that). It may nevertheless appear as a statement in the language as the conclusion of a proof by contradiction. Most mathematicaly exposition involves a number of extra words used to connect or define statements, not least "let" as in "let a = 1". Perhaps that is a verb of sorts. Other words (tokens, symbols) include "where" and "therefore". "Equals" is probably the only principle in classical mathematics notation that is both represented as a symbol and plausibly a verb: "is equal to" (unless qualified by "let"). Everything else is either a name (symbolic or a literal value) or an "operator" - multiplication, integration, etc. Even inequalities require symbolic and semantic additions to the core language. This is actually common - an obvious example being additional symbols to handle matrices, vectors and other aspects of linear algebra. ... >> Maybe see also (if you can find a copy), Ch 8: "The Language Myth and >> Mathematical Notation as a Language of Nature", Daniel R. Davis, in: >> "the language Myth in Western Culture", Curzon Press, 2002." > > Thanks for the pointer. I'll try to find it. I'd like > to know where this attitude came from. > If you mean "The Language Myth", this is a concept developed since the 1980s by the UK linguist Roy Harris and colleagues, and presented most affordably in his recent paperback "Mindboggling". Well worth reading IMO. As a primitive example of the principle: it would assert that while one person uses a set of words, intending to communicate what is in their mind directly to that of another person, that intention is futile (and any analysis of communication based on that premise is flawed) - even if the receiver indicates they "understand", their internal meaning may still be (probably is) different. http://en.wikipedia.org/wiki/Roy_Harris_(linguist) One may rasonably argue that the "language" of mathematics, as with other examples of a formal language (including programming languages), is designed as far as is possible to take the human mind out of the loop, so to speak - to eliminate ambiguities and any consequences of associative thinking. Verbs (and other components of the vernacular) are intrisincally subject to both ambiguities and the effects of associative thinking (which in other contexts may be the whole point of them), so are "as far as is possible" excluded from the mathematical vocabulary. Richard Dobson
From: jmfbahciv on 30 Mar 2010 09:16 Richard Dobson wrote: > On 29/03/2010 13:09, jmfbahciv wrote: > .. >>> Take away established usage for established words and you need to >>> supply an alternative that enables people to communicate at least as >>> well as the original. And then persuade people to use it. What would >>> be your preference - "Semiotic code"? >> >> I'm not advocating nor objecting to the usage. Somebody made a claim >> and all I asked was to give an example of a verb. So far, their >> replies are smoke and mirrors. >> > > Much of (classical) maths depends on elements not defined formally > within the language itself. The basic idea of "true or false" is not > represented by a symbol within the language. Thus "2 = 0" is a > syntactically correct statement (in the form of "a = b"), but > semantically false - because we "know it is" The truth or falsity of a > statement cannot be represented directly as a symbol in the language > (you need to add something like Boolean notation to do that). It may > nevertheless appear as a statement in the language as the conclusion of > a proof by contradiction. > > Most mathematicaly exposition involves a number of extra words used to > connect or define statements, not least "let" as in "let a = 1". Perhaps > that is a verb of sorts. I've been thinking that it might be. This seems to imply that the verb is used in the set up of the math (axioms) and not part of the subsequent process. >Other words (tokens, symbols) include "where" > and "therefore". "Equals" is probably the only principle in classical > mathematics notation that is both represented as a symbol and plausibly > a verb: "is equal to" (unless qualified by "let"). This (equals) is used in the rare cases when there is one, and only one, solution. > Everything else is > either a name (symbolic or a literal value) or an "operator" - > multiplication, integration, etc. Even inequalities require symbolic and > semantic additions to the core language. This is actually common - an > obvious example being additional symbols to handle matrices, vectors and > other aspects of linear algebra. > However those are all symbols used as shorthand to indicate textbooks' worth of theory behind them. For instance, the symbol dx/dt conveys a meaning which involves all of the steps which led to the Fundamental Theorem of Calculus, plus a bunch more. So, is substituting a symbol for a plethora of work create a language? This causes my brain to get into a muddle. > .. >>> Maybe see also (if you can find a copy), Ch 8: "The Language Myth and >>> Mathematical Notation as a Language of Nature", Daniel R. Davis, in: >>> "the language Myth in Western Culture", Curzon Press, 2002." >> >> Thanks for the pointer. I'll try to find it. I'd like >> to know where this attitude came from. >> > > If you mean "The Language Myth", I mean the implied conclusion that math is a language of nature. It appears that Ste poster believes this and has added the word all to modify math. > this is a concept developed since the > 1980s by the UK linguist Roy Harris and colleagues, and presented most > affordably in his recent paperback "Mindboggling". Well worth reading > IMO. As a primitive example of the principle: it would assert that while > one person uses a set of words, intending to communicate what is in > their mind directly to that of another person, that intention is futile > (and any analysis of communication based on that premise is flawed) - Based on my experience, he's right ;-). > even if the receiver indicates they "understand", their internal meaning > may still be (probably is) different. > > http://en.wikipedia.org/wiki/Roy_Harris_(linguist) > > One may rasonably argue that the "language" of mathematics, as with > other examples of a formal language (including programming languages), > is designed as far as is possible to take the human mind out of the > loop, so to speak - to eliminate ambiguities and any consequences of > associative thinking. Verbs (and other components of the vernacular) are > intrisincally subject to both ambiguities and the effects of associative > thinking (which in other contexts may be the whole point of them), so > are "as far as is possible" excluded from the mathematical vocabulary. The computer manufacturer I worked for had damned good writers. They managed to find ways to document how to use what we shipped and how are our stuff worked so that all levels of computer users would understand what they read. None of that writing was trivial. /BAH
From: jmfbahciv on 30 Mar 2010 09:28
J. Clarke wrote: > On 3/29/2010 8:09 AM, jmfbahciv wrote: >> Richard Dobson wrote: >>> On 28/03/2010 14:53, jmfbahciv wrote: >>> .. >>>>> As any programmer will tell you, >>>> >>>> No they won't. >>> >>> Here we go... "oh yes they will!". >> >> <grin> Nope. I are one and I don't make that statement. >> >>> >>> I've been questioning the usage of the word "language" >>>> w.r.t. HLL compilers and interpreters, too. >>>> >>> Question away. There does seem to be a great deal of enthusiasm on >>> this list for redefining everything, one way or another. >> >> Sure. That happens to a computer term about every 4 years now. >> >> >>> Take away established usage for established words and you need to >>> supply an alternative that enables people to communicate at least as >>> well as the original. And then persuade people to use it. What would >>> be your preference - "Semiotic code"? >> >> I'm not advocating nor objecting to the usage. Somebody made a claim >> and all I asked was to give an example of a verb. So far, their >> replies are smoke and mirrors. >> >>> >>> (http://www.aber.ac.uk/media/Documents/S4B/sem08.html) >>> >>> >>> Maybe see also (if you can find a copy), Ch 8: "The Language Myth and >>> Mathematical Notation as a Language of Nature", Daniel R. Davis, in: >>> "the language Myth in Western Culture", Curzon Press, 2002." >> >> Thanks for the pointer. I'll try to find it. I'd like >> to know where this attitude came from. >> >>> >>> .. >>>> All of the posters have been using the term as a human language, >>>> not a machine language. >>>> >>> >>> That much is very apparent, if unstated. >> >> But note that the same types of people consider a Fortran statement >> and equation. Last month one guy thought that the angle brackets >> used in HLLs were inequalities. >> >>> Anyway, the existing canon of thought with respect to language in >>> general, and formal languages in particular, is "out there", ready to >>> be drawn upon ad libitum, as is the work of Chomsky et al. Or ignore >>> it; but whether that will reach any useful conclusion is as yet >>> indeterminate. >>> >> All I wanted was an example of a verb. :-) I can't think of one so >> the people who are declaring the concept should be able to give me >> one. I don't consider counting an example of a verb. > > "Let X be an element of the set {whatever}" > > "For every X greater than 0 there exists Y such that . . ." > > Both mathematical statements, both have verbs. I thought about those. I was not sure because it's using the English language to portray a concept. That would not make the word a verb in the "math language". and then I began to confuse myself but got distracted with the other nonsense posts. > Remember, most of what > mathematicians do is proofs, not calculations, calculations are the > domain of mere engineers such as thee and me. Right. Most of the math I see is a shorthand which assumes I've gone through all the textbooks' proofs which lie behind each notation. So, given this, the notation = isn't really a verb which should be a single entity; perhaps this (single and unique entity) is where I become muddled. > So unless you want to > take the language used in writing proofs out of the domain of > mathematics you'll find plenty of verbiage. > > There's plenty of verbiage in describing an IOWD (I/O word) data structure but none of those verbs are part of the machine language which uses the hardware concept. It's easy to identify a Spanish verb and its English equivalent. There isn't a similar method with math. Thus, math isn't a language for humans. If you assume that math is a language, then there should be the same kinds of "translations". I went through a matrix arithmetic book. I did the matrix work and checked my answers using both geometry and algebra. If math is a language, then there should be a set of rules to translate geometry to algebra to matrix arithmetic. So far, I haven't been able to think of a reproducible method. Part of this is blurred by my lack of math experience. /BAH /BAH |