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  • Joseph Nebus 6:00 pm on Thursday, 16 February, 2017 Permalink | Reply
    Tags: , , Crock, , , Mr Lowe, , , , unicorns   

    Reading the Comics, February 11, 2017: Trivia Edition 


    And now to wrap up last week’s mathematically-themed comic strips. It’s not a set that let me get into any really deep topics however hard I tried overthinking it. Maybe something will turn up for Sunday.

    Mason Mastroianni, Mick Mastroianni, and Perri Hart’s B.C. for the 7th tries setting arithmetic versus celebrity trivia. It’s for the old joke about what everyone should know versus what everyone does know. One might question whether Kardashian pet eating habits are actually things everyone knows. But the joke needs some hyperbole in it to have any vitality and that’s the only available spot for it. It’s easy also to rate stuff like arithmetic as trivia since, you know, calculators. But it is worth knowing that seven squared is pretty close to 50. It comes up when you do a lot of estimates of calculations in your head. The square root of 10 is pretty near 3. The square root of 50 is near 7. The cube root of 10 is a little more than 2. The cube root of 50 a little more than three and a half. The cube root of 100 is a little more than four and a half. When you see ways to rewrite a calculation in estimates like this, suddenly, a lot of amazing tricks become possible.

    Leigh Rubin’s Rubes for the 7th is a “mathematics in the real world” joke. It could be done with any mythological animals, although I suppose unicorns have the advantage of being relatively easy to draw recognizably. Mermaids would do well too. Dragons would also read well, but they’re more complicated to draw.

    Mark Pett’s Mr Lowe rerun for the 8th has the kid resisting the mathematics book. Quentin’s grounds are that how can he know a dated book is still relevant. There’s truth to Quentin’s excuse. A mathematical truth may be universal. Whether we find it interesting is a matter of culture and even fashion. There are many ways to present any fact, and the question of why we want to know this fact has as many potential answers as it has people pondering the question.

    Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 8th is a paean to one of the joys of numbers. There is something wonderful in counting, in measuring, in tracking. I suspect it’s nearly universal. We see it reflected in people passing around, say, the number of rivets used in the Chrysler Building or how long a person’s nervous system would reach if stretched out into a line or ever-more-fanciful measures of stuff. Is it properly mathematics? It’s delightful, isn’t that enough?

    Scott Hilburn’s The Argyle Sweater for the 10th is a Fibonacci Sequence joke. That’s a good one for taping to the walls of a mathematics teacher’s office.

    'Did you ever take a date to a drive-in movie in high school?' 'Once, but she went to the concession stand and never came back.' 'Did you wonder why?' 'Yeah, but I kept on doing my math homework.'

    Bill Rechin’s Crock rerun for the 11th of February, 2017. They actually opened a brand-new drive-in theater something like forty minutes away from us a couple years back. We haven’t had the chance to get there. But we did get to one a fair bit farther away where yes, we saw Turbo, that movie about the snail that races in the Indianapolis 500. The movie was everything we hoped for and it’s just a shame Roger Ebert died too young to review it for us.

    Bill Rechin’s Crock rerun for the 11th is a name-drop of mathematics. Really anybody’s homework would be sufficiently boring for the joke. But I suppose mathematics adds the connotation that whatever you’re working on hasn’t got a human story behind it, the way English or History might, and that it hasn’t got the potential to eat, explode, or knock a steel ball into you the way Biology, Chemistry, or Physics have. Fair enough.

     
  • Joseph Nebus 9:09 pm on Friday, 29 June, 2012 Permalink | Reply
    Tags: false, falsity, implication, , inference, introduction to logic, , libel, , logic class, logical implication, mathematical logic, null sets, , proposition, , true, , unicorns   

    Why You Failed Your Logic Test 


    An interesting parallel’s struck me between nonexistent things and the dead: you can say anything you want about them. At least in United States law it’s not possible to libel the dead, since they can’t be hurt by any loss of reputation. That parallel doesn’t lead me anywhere obviously interesting, but I’ll take it anyway. At least it lets me start this discussion without too closely recapitulating the previous essay. The important thing is that at least in a logic class, if I say, “all the coins in this purse are my property”, as Lewis Carroll suggested, I’m asserting something I say is true without claiming that there are any coins in there. Further, I could also just as easily said “all the coins in this purse are not my property” and made as true a statement, as long as there aren’t any coins there.

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    • Chip Uni 9:32 pm on Friday, 29 June, 2012 Permalink | Reply

      Aside from the standard logic, there are three ‘alternative’ definitions of logical implication possible:

      A=T, B=T A=T, B=F A=F, B=T A=F, B=F definition
      normal T F T T -A | B
      (1) T F T F B
      (2) T F F T A == B
      (3) T F F F A & B

      What happens to logic if we use any of these alternate definitions?

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      • Joseph Nebus 9:55 pm on Thursday, 5 July, 2012 Permalink | Reply

        I haven’t the chance to work it out this week since awfully high priority things are competing with the blog but I’ll try thinking it out when I can.

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  • Joseph Nebus 12:39 am on Tuesday, 26 June, 2012 Permalink | Reply
    Tags: alt.folklore.urban, Captain Kirk, , fiction, , , nonexistence, , , unicorns   

    What We Can Say About Nonexistent Things 


    The modern interpretation of what we mean by a statement like “all unicorns are one-horned animals” is that we aren’t making the assertion that any unicorns exist. If any did happen to exist, sure, they’d be one-horned animals, if our proposition is true, but we’re reserving judgement about whether they do exist. If we don’t like the way the natural-language interpretation of the proposition leads us, we might be satisfied by saying it’s equivalent to saying, “there are no non-one-horned animals which are unicorns”, and that doesn’t feel quite like it claims unicorns exist. You might not even come away feeling there ought to be non-one-horned animals from that sentence alone.

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    • Lucas Wilkins 3:33 pm on Monday, 2 July, 2012 Permalink | Reply

      Yeah, When people are doing this formally they usually define a ‘universe’ in which the statements, or parts of statements, are made. I guess an simple example would be if I said “it’s red”, you, the listener, would have to be working in a world where ‘it’ referred to the same object. Basically, every statement has underlying assumptions that affect how you interpret it formally. I recommend this book, it was in my bathroom for a while and explains things rather well.

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  • Joseph Nebus 12:08 am on Wednesday, 20 June, 2012 Permalink | Reply
    Tags: existential import, gold, , , , sovereigns, , unicorns   

    Getting This Existence Thing Straight 


    Midway through “What Lewis Carroll Says Exists That I Don’t” I put forth an example of claiming a property belongs to something which clearly doesn’t exist. The problem — and Carroll was writing this bit, in Symbolic Logic, at a time when it hadn’t reached the current conclusion — is about logical propositions. If you assert it to be true that, “All (something) have (a given property)”, are you making the assertion that the thing exists? Carroll gave the example of “All the sovereigns in that purse are made of gold” and “all the sovereigns in that purse are my property”, leading to the conclusion, “some of my property is made of gold”, and pointing out that if you put that syllogism up to anyone and asked if she thought you were asserting there were sovereigns in that purse, she’d say of course. Carroll has got the way normal people talk in normal conversations on his side here. Put that syllogism before anyone and point out that nowhere is it asserted that there are any coins in the purse and you’ll get a vaguely annoyed response, like when the last chapter of a murder cozy legalistically parses all the alibis until nothing makes sense.

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  • Joseph Nebus 1:55 am on Tuesday, 12 June, 2012 Permalink | Reply
    Tags: Bartley, elementary textbook, , grad student, , , , logic course, quotes, , unicorns, urban legend, , , william warren bartley, William Warren Bartley III   

    What Lewis Carroll Says Exists That I Don’t 


    I borrowed from the library Symbolic Logic, a collection of an elementary textbook — intended for children, and more fun than usual because of that — on logic by Lewis Carroll, combined with notes and manuscript pages which William Warren Bartley III found toward the second volume in the series. The first part is particularly nice since it’s text that not only was finished in Carroll’s life but went through several editions so he could improve the unclear parts. In case I do get to teaching a new logic course I’ll have to plunder it for examples as well as for this rather nice visual representation Carroll used for sorting out what was implied by a set of propositions regard “All (something) are (something else)” and “Some (something) are (this)” and “No (something) are (whatnot)”. It’s not quite Venn diagrams, although you can see them from there. Oddly, Carroll apparently couldn’t; there’s a rather amusing bit in the second volume where Carroll makes Venn diagrams out to be silly because you can make them terribly complicated.

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    • BunnyHugger 1:58 am on Tuesday, 12 June, 2012 Permalink | Reply

      You really have to deny existential import to those statements to make the rest of everything work sensibly. The fact that such statements are interpreted as a type of conditional in modern symbolic logic bears this out.

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      • Joseph Nebus 1:58 am on Wednesday, 13 June, 2012 Permalink | Reply

        Yes, and that’s the way it’s interpreted in mathematical logic. Bartley, the editor for this compilation, points out that it captures a moment in the history of mathematics where the question of existential import was not settled, or at least hadn’t been settled on a particular convention, and it’s interesting seeing a person who’s really quite good in logic arguing for the side that lost out. It’s a little moment showing mathematics — and philosophy — as an alive thing.

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    • BunnyHugger 2:04 am on Tuesday, 12 June, 2012 Permalink | Reply

      Of course, using the “all unicorns are one-horned animals” example sneakily sidesteps the real problem for ordinary intuition: that if existential import is not attributed to all/no statements, the straightforward result[1] is that any such statement about an empty class is (trivially) true.

      [1] The less straightforward way of dealing with this is to start positing imaginary objects or possible worlds.

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      • Joseph Nebus 2:00 am on Wednesday, 13 June, 2012 Permalink | Reply

        And though I mention it on Tuesday, and will in the follow-up to this article that I mean to write, I should point out to readers who stumble across this page alone that you’re absolutely right. I threw in an example that’s intuitively obvious and skipped that it leads also to some big, intuitively not obvious conclusions. In fact, it leads to conclusions that most people would intuitively say are wrong, but if we don’t accept those we have worse problems.

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