about maths: strictly speaking, off topic, but justified.
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From: J. Clarke on 21 Mar 2010 12:23 On 3/21/2010 11:23 AM, Darwin123 wrote: > On Mar 21, 9:32 am, "J. Clarke"<jclarke.use...(a)cox.net> wrote: >> On 3/21/2010 9:01 AM, jmfbahciv wrote: >> >> >> >>> Ste wrote: >>>> On 20 Mar, 13:01, jmfbahciv<jmfbahciv(a)aol> wrote: >>>>> Ste wrote: >>>>>> On 19 Mar, 13:38, jmfbahciv<jmfbahciv(a)aol> wrote: >>>>>>> Ste wrote: >>>>>>>> On 18 Mar, 21:58, Urion<blackman_...(a)yahoo.com> wrote: >>>>>>>>> On Mar 18, 11:05 pm, Ste<ste_ro...(a)hotmail.com> wrote: > >> "Let" would be one of them. >> >> But most people who talk about "math" are really talking about algebra >> over the reals. > > When I talk about math, I am usually thinking about "word problems." > Word problems attempt to model the "reals" in terms of "algebra." > The use of words is very important in math. Math isn't really > about numbers. Math is about logic. > Math often involves abstractions. However, an abstraction is > usually just a model for "reals." Flag this post and when you have completed your first year of college-level study toward a math degree come back and take a look at it and see how far that year has taken you in your understanding. "Reals" in mathematics has a specific meaning that is unrelated to the meaning that you seem to be using. It refers to a set of numbers, and no more and no less. "Algebra over the reals" is a set of operations on that set, mapping pairs of reals onto a third real. There are many other kinds of algebra defined. Your "word problems" ask you to set up some kind of mathematical structure to allow the solution of the problem. They are not part of mathematics per se, they are more in the nature of physics or engineering.
From: Ste on 21 Mar 2010 20:03 On 21 Mar, 13:01, jmfbahciv <jmfbahciv(a)aol> wrote: > Ste wrote: > > >>> I think we'd need to be more specific about what we mean by "language" > >>> - I'm using it very generally, perhaps in the sense of "something that > >>> conveys meaning via abstract impressions on the senses". > >> What senses? Math doesn't have anything to do with senses. > > > It concerns the real world, > > No, it does not, thus... Then we disagree. I find it hard to identify any maths that does not ultimately have its basis and applicability in the real world. > >> I know > >> you are using the word language sloppily. So is the other guy. > >> Only the other guy is further confused by the use of the word > >> in the computer biz; I don't know if you're doing the same. > > > I'm not "confused" by the word. I've stated that I'm using it loosely, > > and I've asked you to clarify your questions. > > I don't know how to write the sentence more clearly than... > if you claim that math is a language, then what are the verbs? > I don't care how "loosely" you're defining the word language, > all have verbs. Yes, but action can be implied. For example, if I say Jack is at the house, and then next say Jack is at the market, then the verb (of "movement") is expressed at the level of a sentence or paragraph, rather than at the level of a word. Obviously mathematics as a language is not adapted to making detailed qualitative descriptions, but that is not to say that it is incapable of expressing actions. > >>>> So, answer the question: > >>>> what are the verbs in math? > >>> What do you mean by verbs? Clearly maths can be used to describe > >>> action/change. > >> Now answer the question. What are the verbs in math? Pick > >> any branch of mathematics and list the verbs. > > > I'm not refusing to answer the question! You've only asked me once, > > and I'm asking you to clarify what you mean by "verbs". > > Action. Look it up in the dictionary. I did, even before you told me to, in order to try and gather some further implicit detail about your question. > >Also if you > > asked me "what are the nouns" or "what are the adjectives", "which is > > the nominative case", etc, I'd still be asking you to clarify what you > > meant, because these terms don't tend to be used in maths - but you do > > have "variables", etc. > > [emoticon wafts the smoke away and breaks all the mirrors] > I didn't ask about nouns and other flavors of words. I asked about > verbs. Period. You know you're awfully abrasive towards someone who is merely asking for you to explain your question. As I pointed out above, "action" can be conveyed at a higher level than the word. But because you haven't clarified what you mean, I'm not sure whether you were specifically asking "where are the word- verbs in maths" as opposed to merely asking "how does maths describe action and change".
From: jmfbahciv on 22 Mar 2010 09:15 J. Clarke wrote: > On 3/21/2010 9:01 AM, jmfbahciv wrote: >> Ste wrote: >>> On 20 Mar, 13:01, jmfbahciv <jmfbahciv(a)aol> wrote: >>>> Ste wrote: >>>>> On 19 Mar, 13:38, jmfbahciv <jmfbahciv(a)aol> wrote: >>>>>> Ste wrote: >>>>>>> On 18 Mar, 21:58, Urion <blackman_...(a)yahoo.com> wrote: >>>>>>>> On Mar 18, 11:05 pm, Ste <ste_ro...(a)hotmail.com> wrote: >>>>>>>>> A point I would make however is that mathematics, like traditional >>>>>>>>> language, has no inherent meaning, and its meaning is learned in >>>>>>>>> exactly the same way as traditional language, of using our >>>>>>>>> senses to >>>>>>>>> make meaningful connections between language and concrete reality. >>>>>>>> Mathematics is a formal language and also an art. Currently it is >>>>>>>> the >>>>>>>> only way we have to describe the material universe using our >>>>>>>> cognitive >>>>>>>> faculties. This means that we cannot know anything about the >>>>>>>> universe >>>>>>>> beyond our biological senses. >>>>>>>> But I do agree with you that mathematics is not the real thing >>>>>>>> because >>>>>>>> it only uses a paper and a pencil. But currently it's all we have. >>>>>>> I think everyone agrees that language "is all we have" to describe >>>>>>> the >>>>>>> universe - not least because the verb "describe" strongly implies >>>>>>> the >>>>>>> use of language. >>>>>> I do not agree. Maps are not a language. >>>>> I think we'd need to be more specific about what we mean by "language" >>>>> - I'm using it very generally, perhaps in the sense of "something that >>>>> conveys meaning via abstract impressions on the senses". >>>> What senses? Math doesn't have anything to do with senses. >>> >>> It concerns the real world, >> >> No, it does not, thus... >> >>> and hence has everything to do with the >>> senses. >>> >> >> Nothing to do with the senses. >> >> >> >>> >>> >>>> I know >>>> you are using the word language sloppily. So is the other guy. >>>> Only the other guy is further confused by the use of the word >>>> in the computer biz; I don't know if you're doing the same. >>> >>> I'm not "confused" by the word. I've stated that I'm using it loosely, >>> and I've asked you to clarify your questions. >> >> I don't know how to write the sentence more clearly than... >> if you claim that math is a language, then what are the verbs? >> I don't care how "loosely" you're defining the word language, >> all have verbs. >> >>> >>> >>> >>>>>> So, answer the question: >>>>>> what are the verbs in math? >>>>> What do you mean by verbs? Clearly maths can be used to describe >>>>> action/change. >>>> Now answer the question. What are the verbs in math? Pick >>>> any branch of mathematics and list the verbs. >>> >>> I'm not refusing to answer the question! You've only asked me once, >>> and I'm asking you to clarify what you mean by "verbs". >> >> Action. Look it up in the dictionary. >> >>> Also if you >>> asked me "what are the nouns" or "what are the adjectives", "which is >>> the nominative case", etc, I'd still be asking you to clarify what you >>> meant, because these terms don't tend to be used in maths - but you do >>> have "variables", etc. >> >> [emoticon wafts the smoke away and breaks all the mirrors] >> I didn't ask about nouns and other flavors of words. I asked about >> verbs. Period. > > "Let" would be one of them. Finally! However, would you consider that to be part of the math? I'm assuming you are using the word let as geometry uses the word given. Part of the problem exhibited in this thread are people confusing the English words used to convey the hen scratches on the black board to other people. I was trying to sort this out in my head. > > But most people who talk about "math" are really talking about algebra > over the reals. And, more importantly, assuming that all math expressions have an equals sign which implies, one, and only one, solution. These are always the exceptions and never imply inequalities. /BAH
From: jmfbahciv on 22 Mar 2010 09:17 Darwin123 wrote: > On Mar 21, 9:32 am, "J. Clarke" <jclarke.use...(a)cox.net> wrote: >> On 3/21/2010 9:01 AM, jmfbahciv wrote: >> >> >> >>> Ste wrote: >>>> On 20 Mar, 13:01, jmfbahciv <jmfbahciv(a)aol> wrote: >>>>> Ste wrote: >>>>>> On 19 Mar, 13:38, jmfbahciv <jmfbahciv(a)aol> wrote: >>>>>>> Ste wrote: >>>>>>>> On 18 Mar, 21:58, Urion <blackman_...(a)yahoo.com> wrote: >>>>>>>>> On Mar 18, 11:05 pm, Ste <ste_ro...(a)hotmail.com> wrote: > >> "Let" would be one of them. >> >> But most people who talk about "math" are really talking about algebra >> over the reals. > > When I talk about math, I am usually thinking about "word problems." > Word problems attempt to model the "reals" in terms of "algebra." > The use of words is very important in math. Math isn't really > about numbers. Math is about logic. > Math often involves abstractions. However, an abstraction is > usually just a model for "reals." Only if you're doing high school algebra. Geometry and linear algebra are very different. So is calculus. /BAH
From: jmfbahciv on 22 Mar 2010 09:36
Matt wrote: > On Sun, 21 Mar 2010 11:25:55 -0500, Matt wrote: > >> On Sun, 21 Mar 2010 08:01:37 -0500, jmfbahciv wrote: >> >>> Ste wrote: >>>> On 20 Mar, 13:01, jmfbahciv <jmfbahciv(a)aol> wrote: >>>>> Ste wrote: >>>>>> On 19 Mar, 13:38, jmfbahciv <jmfbahciv(a)aol> wrote: >>>>>>> Ste wrote: >>>>>>> So, answer the question: >>>>>>> what are the verbs in math? >>>>>> What do you mean by verbs? Clearly maths can be used to describe >>>>>> action/change. >>>>> Now answer the question. What are the verbs in math? Pick >>>>> any branch of mathematics and list the verbs. >>>> I'm not refusing to answer the question! You've only asked me once, >>>> and I'm asking you to clarify what you mean by "verbs". >>> Action. Look it up in the dictionary. >>> >>>> Also if you >>>> asked me "what are the nouns" or "what are the adjectives", "which is >>>> the nominative case", etc, I'd still be asking you to clarify what you >>>> meant, because these terms don't tend to be used in maths - but you do >>>> have "variables", etc. >>> [emoticon wafts the smoke away and breaks all the mirrors] >>> I didn't ask about nouns and other flavors of words. I asked about >>> verbs. Period. >> Perhaps you are asking about verbs with insufficient latitude. >> >> Do you require that a language be composed of discrete elements >> communicated in a linear, sequential manner? If so, I submit that your >> definition of language is too narrow. Perhaps it is tainted by over >> exposure to computers, which require language to be of that form. >> >> The example of body language was given earlier. Where are the verbs in >> an exchange of glances through which one "gets lucky?" >> >> Is there no language in a painting that can evoke tears? Where are the >> verbs in a painting? >> >> Is there no language in "music that can tame the savage beast" and >> lift one from depression to dancing? Where are the verbs in a drum >> solo? >> >> Back to math as a language with verbs. Consider: >> 2 + 2 = 4. >> >> Is not "plus" a verb? > > "Plus" is the "action" you wanted. But it's not a movement. You are confusing how you would represent the reals on the number line with how you would show somebody what the plus does. > > Lest you point to an English dictionary and note that "plus" isn't > labeled as a verb: It isn't a _math_ dictionary. If math is a > language, it has its own dictionary. > > Plus, your requirement that a verb be related to action is also too > restrictive. > > http://en.wikipedia.org/wiki/Verb > a verb ... conveys ... a state of being I hate wiki. I'm not talking about states of beings; that will obfusicate (someday I'll unpack my dictionaries) this thread. > > Let's write a statement in math and its translation in English: > Math: 2 + 2 = 4 > English: Two plus two is equal to four. > > In the English translation, "is" is a verb. > > Every math statement with an equals symbol has a verb. > > That's how you verbalize the statement. It's not an action but an equivalence. The symbols + and = are used to portray the axioms of math used when writing the description of the number line. /BAH |