Math emojis
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Alright. I’ll bite. Why (or how) is “Let epsilon < 0” a joke? n Nicholas S. Thompson Emeritus Professor of Psychology and Biology Clark University http://home.earthlink.net/~nickthompson/naturaldesigns/ From: Friam [mailto:[hidden email]] On Behalf Of Carl Tollander ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives back to 2003: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove |
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"For every epsilon > 0, there exists a delta such that ..."
On Wednesday, January 30, 2019, 12:09:18 PM MST, Nick Thompson <[hidden email]> wrote:
Alright. I’ll bite. Why (or how) is “Let epsilon < 0” a joke?
n
Nicholas S. Thompson Emeritus Professor of Psychology and Biology Clark University http://home.earthlink.net/~nickthompson/naturaldesigns/
From: Friam [mailto:[hidden email]] On Behalf Of Carl Tollander
============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives back to 2003: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives back to 2003: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove |
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In reply to this post by Carl Tollander
Because the phrase let epsilon > 0 is extremely common in analysis texts. ----------------------------------- Frank Wimberly My memoir: https://www.amazon.com/author/frankwimberly My scientific publications: https://www.researchgate.net/profile/Frank_Wimberly2 Phone (505) 670-9918 On Wed, Jan 30, 2019, 11:18 AM Carl Tollander <[hidden email] wrote:
============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives back to 2003: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove |
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In reply to this post by Dean Gerber
The joke (such as it is) is a discourse joke, playing upon the fact
(incontestable to all fluent writers/speakers of MathEng, i.e., mathematicians' English) that the fragment of MathEng "For every \epsilon < 0" is perfectly well formed both syntactically and semantically, but violates the established pragmatics of MathEng. (Excuse the TeX, but when I try to paste the Greek letter epsilon into this window, hijinx ensue; imagine it's there, instead of \epsilon.) [Added before mailing: it occurs to me that you, as an expert on "pragmatism", may not be familiar with the linguists' term-of-art "pragmatics", which I learned long ago from my daughter Susanna, whom you met in Santa Fe. The first definition Google gives is what I mean: "the branch of linguistics dealing with language in use and the contexts in which it is used, including such matters as deixis, the taking of turns in conversation, text organization, presupposition, and implicature." In particular, the "joke" in question depends on presuppositions and implicatures.] Even as a hopeless non-fluent occasional witness of MathEng, Nick, you can easily acquire evidence in favor of my claim about syntax by browsing mathematical papers for fragments of the form "For every [glyph] < [glyph]" until you are convinced of the proposition that the MathEng discourse community accepts such a fragment as well-formed. With perhaps more work than you can be expected to do, you might also acquire evidence in favor of my claim about semantics by browsing for contexts that convince you of several propositions about MathEng: (1) very generally, the glyph (here expanded as) \epsilon is used in MathEng to denote a "real number"; (2) the glyph 0, in both MathEng and colloquial English, is used to denote the (real) number zero; (3) the glyph < is used in MathEng to denote a relationship that two real numbers may or may not bear to each other, namely, the string of glyphs p < q is used to denote that p is less than (and not equal to) q; (4) there *are* real numbers less than 0; ... and perhaps more; whence "For every \epsilon < 0" is a meaningful fragment of MathEng. *However*, without sufficient exposure to MathEng discourses (and certainly exposure more than you have had, or would tolerate having in the present or future) it would be unlikely that you could figure out on your own that IN PRESENT PRACTICE within the MathEng discourse community all the following propositions are true. (A) The glyph \epsilon is nearly always used to denote a "small" real number (or an "arbitrary" real number that "becomes" small), where in the context of "the real number system" (among others) "small" means "close to 0". (B) More specifically, in many (but not all) such contexts, "small" means "close to 0 BUT LARGER THAN 0". (C) The most common context of type (B)--at least for mathematics students and most, but probably not all, more fully-fledged Working Mathematicians)--are the MathEng discourse fragments "For every \epsilon > 0", "For every sufficiently small \epsilon > 0", and their variants with "every" replaced by "all". [This is an empirical claim. I have not done anything to test it (although if you have read those Book Fragments I sent you, you will see there several examples where I *have* accumulated strong empirical evidence, from exhaustive queries of extensive corpora of MathEng, for other claims about MathEng: which should convince you, I hope, that my MathEng intuitions are not invariably pulled out of my ass). I will bet you a shiny new dime that it's true.] THEREFORE, in the actually existing community of contemporary fluent users of MathEng, the syntactically and semantically impeccable fragment "For every \epsilon < 0" is pragmatically defective: nobody would say that! If that hasn't explained any slightest \epsilon of humor out of the joke, I don't know why not. Perhaps you could respond with a Peircean analysis of the semiotics of the joke, and *really* kill it dead. Lee ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives back to 2003: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove |
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Well, Ok. I can see that it's sort of like Carl Tollander's
"Let there be a spherical cow," which always makes me smile. Or Even the micro economists', "Let there be a fully informed consumer." But how do we tell the jokes from the foundational insights: Like: "Let there be a number which when multiplied by itself equals -1. Or that howler of mathematical howlers: "Think of a number greater than any number you can think of." Or Knewton's Knee-slapper: "Calculate the acceleration at an instant." Bridges built and airplanes flown on gales of laughter. Nick Nicholas S. Thompson Emeritus Professor of Psychology and Biology Clark University http://home.earthlink.net/~nickthompson/naturaldesigns/ -----Original Message----- From: Friam [mailto:[hidden email]] On Behalf Of [hidden email] Sent: Wednesday, January 30, 2019 3:10 PM To: The Friday Morning Applied Complexity Coffee Group <[hidden email]> Subject: Re: [FRIAM] FW: Math emojis The joke (such as it is) is a discourse joke, playing upon the fact (incontestable to all fluent writers/speakers of MathEng, i.e., mathematicians' English) that the fragment of MathEng "For every \epsilon < 0" is perfectly well formed both syntactically and semantically, but violates the established pragmatics of MathEng. (Excuse the TeX, but when I try to paste the Greek letter epsilon into this window, hijinx ensue; imagine it's there, instead of \epsilon.) [Added before mailing: it occurs to me that you, as an expert on "pragmatism", may not be familiar with the linguists' term-of-art "pragmatics", which I learned long ago from my daughter Susanna, whom you met in Santa Fe. The first definition Google gives is what I mean: "the branch of linguistics dealing with language in use and the contexts in which it is used, including such matters as deixis, the taking of turns in conversation, text organization, presupposition, and implicature." In particular, the "joke" in question depends on presuppositions and implicatures.] Even as a hopeless non-fluent occasional witness of MathEng, Nick, you can easily acquire evidence in favor of my claim about syntax by browsing mathematical papers for fragments of the form "For every [glyph] < [glyph]" until you are convinced of the proposition that the MathEng discourse community accepts such a fragment as well-formed. With perhaps more work than you can be expected to do, you might also acquire evidence in favor of my claim about semantics by browsing for contexts that convince you of several propositions about MathEng: (1) very generally, the glyph (here expanded as) \epsilon is used in MathEng to denote a "real number"; (2) the glyph 0, in both MathEng and colloquial English, is used to denote the (real) number zero; (3) the glyph < is used in MathEng to denote a relationship that two real numbers may or may not bear to each other, namely, the string of glyphs p < q is used to denote that p is less than (and not equal to) q; (4) there *are* real numbers less than 0; ... and perhaps more; whence "For every \epsilon < 0" is a meaningful fragment of MathEng. *However*, without sufficient exposure to MathEng discourses (and certainly exposure more than you have had, or would tolerate having in the present or future) it would be unlikely that you could figure out on your own that IN PRESENT PRACTICE within the MathEng discourse community all the following propositions are true. (A) The glyph \epsilon is nearly always used to denote a "small" real number (or an "arbitrary" real number that "becomes" small), where in the context of "the real number system" (among others) "small" means "close to 0". (B) More specifically, in many (but not all) such contexts, "small" means "close to 0 BUT LARGER THAN 0". (C) The most common context of type (B)--at least for mathematics students and most, but probably not all, more fully-fledged Working Mathematicians)--are the MathEng discourse fragments "For every \epsilon > 0", "For every sufficiently small \epsilon > 0", and their variants with "every" replaced by "all". [This is an empirical claim. I have not done anything to test it (although if you have read those Book Fragments I sent you, you will see there several examples where I *have* accumulated strong empirical evidence, from exhaustive queries of extensive corpora of MathEng, for other claims about MathEng: which should convince you, I hope, that my MathEng intuitions are not invariably pulled out of my ass). I will bet you a shiny new dime that it's true.] THEREFORE, in the actually existing community of contemporary fluent users of MathEng, the syntactically and semantically impeccable fragment "For every \epsilon < 0" is pragmatically defective: nobody would say that! If that hasn't explained any slightest \epsilon of humor out of the joke, I don't know why not. Perhaps you could respond with a Peircean analysis of the semiotics of the joke, and *really* kill it dead. Lee ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives back to 2003: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives back to 2003: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove |
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Well, the emoji post is from a blog of a math grad student trying to make sense of her existence as a math grad student and trying to explain concepts simply. I recommend noodling around her "other" posts...Baez recommended her blog. On Wed, Jan 30, 2019, 17:57 Nick Thompson <[hidden email] wrote: Well, Ok. I can see that it's sort of like Carl Tollander's ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives back to 2003: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove |
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In reply to this post by Nick Thompson
Nick:
> Well, Ok. I can see that it's sort of like Carl Tollander's > > "Let there be a spherical cow," which always makes me smile. > > Or > > Even the micro economists', > > "Let there be a fully informed consumer." I don't claim to be a native speaker of PhysicsEng, much less of EconoEng, but I've frequently hung out with some of the former, and I've always seen it stated "Assume a spherical cow". Further, if either of those one-liners were to be expanded to a longer joke-about-jargon-and/or-idealization, my strong intuition suggests that they would have to be expanded to something along the lines of "Let X be a spherical cow", "Let C be a fully informed consumer", followed by some fanciful bloviation (or bovination) about X and C, using fancy jargon (or pseudojargon; for instance, somewhere around here I have a very old photocopy of a parody astrophysics article, typeset in the style of--I believe--the Astrophysical Review, purporting to be "On the Imperturbability of Elevator Operators" by Chandrasekharan: the joke in the title rests on the facts that "operators" and "perturbation" are standard jargon in mathematical physics, and could quite reasonably appear near each other in MathPhysEng, but "elevator operators" is just a bit of slapstick). Just plain "Let there be", without providing a place-holding name for the assumed cow or consumer, rings very false. But (as before) this is empirical stuff, and if you've really heard them that way (and can prove it...), then they can occur that way and my skepticism is unwarranted. On the other hand, if you're *recreating* the material in quotation marks *as a representation of what you understood to be the joke*, then I think you're in the position of the (typically) British man who, in a meta-joke, tries to re-tell an American joke and gets it hilariously wrong. > But how do we tell the jokes from the foundational insights: > > Like: "Let there be a number which when multiplied by itself equals -1. > > Or that howler of mathematical howlers: "Think of a number greater than > any > number you can think of." > > Or Knewton's Knee-slapper: "Calculate the acceleration at an instant." Well, we do have the proverb "Many a true word is spoken in jest", and "kidding on the square" is an old and honorable idiom, whereas "kidding on the square of the hypotenuse" is just a quip, and "kidding on the hypothesis" might be a translation of "Hypothesis non fingo" but not a very good one. From your point of view as a pragmatist (Jamesian or Pierceian, take your pick), what should it *matter* whether we can or can't "tell the jokes from the foundational insights"? J: an insight that sees no inwardness is no insight. P: If something (a discourse fragment; a stone; a dream--well, not one of those, in your case) is a "foundational insight", that will (eventually) be found to be the case *because it became a foundation of something* in the long run. If something is a "joke", *that* will (eventually) be found to be the case because it made you laugh, most often--but not always--in the short run (and, yes, I have at least several times in my life suddenly "gotten" a joke decades after hearing or seeing or reading it, as I bet you have, too; conversely, I've more than several times realized that something an earlier "I" found to be a real side-splitter wasn't funny at all). ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives back to 2003: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove |
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Thanks, Lee. See larding below. Nick Nicholas S. Thompson Emeritus Professor of Psychology and Biology Clark University http://home.earthlink.net/~nickthompson/naturaldesigns/ -----Original Message----- Nick: > Well, Ok. I can see that it's sort of like Carl Tollander's > > "Let there be a spherical cow," which always makes me smile. > > Or > > Even the micro economists', > > "Let there be a fully informed consumer." I don't claim to be a native speaker of PhysicsEng, much less of EconoEng, but I've frequently hung out with some of the former, and I've always seen it stated "Assume a spherical cow". Further, if either of those one-liners were to be expanded to a longer joke-about-jargon-and/or-idealization, my strong intuition suggests that they would have to be expanded to something along the lines of "Let X be a spherical cow", "Let C be a fully informed consumer", followed by some fanciful bloviation (or bovination) about X and C, using fancy jargon (or pseudojargon; for instance, somewhere around here I have a very old photocopy of a parody astrophysics article, typeset in the style of--I believe--the Astrophysical Review, purporting to be "On the Imperturbability of Elevator Operators" by Chandrasekharan: the joke in the title rests on the facts that "operators" and "perturbation" are standard jargon in mathematical physics, and could quite reasonably appear near each other in MathPhysEng, but "elevator operators" is just a bit of slapstick). Just plain "Let there be", without providing a place-holding name for the assumed cow or consumer, rings very false. But (as before) this is empirical stuff, and if you've really heard them that way (and can prove it...), then they can occur that way and my skepticism is unwarranted. On the other hand, if you're *recreating* the material in quotation marks *as a representation of what you understood to be the joke*, then I think you're in the position of the (typically) British man who, in a meta-joke, tries to re-tell an American joke and gets it hilariously wrong. [NST==>Oh, well. I tried. In my defrocked English-Majory sort of way, I find it hard to see the difference between “Assume a…” and “Let there be…” I guess perhaps the latter has more of an order of Bible-speak, as we would say in Lee-Speak. <==nst] > But how do we tell the jokes from the foundational insights: > > Like: "Let there be a number which when multiplied by itself equals -1. > > Or that howler of mathematical howlers: "Think of a number greater > than any number you can think of." > > Or Knewton's Knee-slapper: "Calculate the acceleration at an instant." Well, we do have the proverb "Many a true word is spoken in jest", and "kidding on the square" is an old and honorable idiom, whereas "kidding on the square of the hypotenuse" is just a quip, and "kidding on the hypothesis" might be a translation of "Hypothesis non fingo" but not a very good one. From your point of view as a pragmatist (Jamesian or Pierceian, take your pick), what should it *matter* whether we can or can't "tell the jokes from the foundational insights"? J: an insight that sees no inwardness is no insight. P: If something (a discourse fragment; a stone; a dream--well, not one of those, in your case) is a "foundational insight", that will (eventually) be found to be the case *because it became a foundation of something* in the long run. If something is a "joke", *that* will (eventually) be found to be the case because it made you laugh, most often--but not always--in the short run (and, yes, I have at least several times in my life suddenly "gotten" a joke decades after hearing or seeing or reading it, as I bet you have, too; conversely, I've more than several times realized that something an earlier "I" found to be a real side-splitter wasn't funny at all). [NST==> Well, you absolutely correct about all of the above. In the Knewton Kneeslapper case, I have built my career on criticizing category errors in biology and psychology, and if “acceleration at an instant” isn’t a category error, I don’t know wtf a category error is. Seems like all of higher math is based on category errors. So we calculate the acceleration at a point, and then we do all sorts of operations with it, and then we build a bridge with those calculations and the damned bridge stands up, no matter what Nick Thompson says about its logical provenance. You are also correct that, as a pragmat[ci]st, I ought to be completely happy with that. So, whatever the joke is, it’s on me. <==nst] How’s the poetry going? Nick ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives back to 2003: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives back to 2003: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove |
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