Comments for Maths for Mortals http://mathsformortals.wordpress.com Mathematics demystified Fri, 28 Dec 2007 17:34:26 +0000 http://wordpress.com/ hourly 1 Comment on Portia returns by vlorbik http://mathsformortals.wordpress.com/2007/12/13/portia-returns/#comment-14 vlorbik Fri, 28 Dec 2007 17:34:26 +0000 http://mathsformortals.wordpress.com/2007/12/13/portia-returns/#comment-14 oh, i get it. lead. somehow "Portia explains to her suitor that each inscription may be true or false, but that she has placed her portrait in one of the caskets in a manner that is consistent with this truth or falsity of the inscriptions." didn't get it for me (even after glancing at some of the comments). maybe something along the lines "*none* of the statements is paradoxical" might've been helpful ... oh, i get it. lead.

somehow
“Portia explains to her suitor that each inscription may be true or false, but that she has placed her portrait in one of the caskets in a manner that is consistent with this truth or falsity of the inscriptions.”
didn’t get it for me (even after glancing
at some of the comments). maybe
something along the lines
“*none* of the statements is paradoxical”
might’ve been helpful …

]]> Comment on A problem courtesy of Shakespeare by Denise http://mathsformortals.wordpress.com/2007/11/29/a-problem-courtesy-of-shakespeare/#comment-9 Denise Sat, 08 Dec 2007 00:36:20 +0000 http://mathsformortals.wordpress.com/2007/11/29/a-problem-courtesy-of-shakespeare/#comment-9 This is a good example of a problem where Guess-and-Check works more efficiently than the 4-page explanation at the link. The portrait either is or is not in the gold casket. If it is not, the inscription on the silver casket turns into one of those logical nonsense statements like "This statement is false," which can be true if and only if it is not true. So the question becomes, do you trust Portia, or don't you? This is a good example of a problem where Guess-and-Check works more efficiently than the 4-page explanation at the link. The portrait either is or is not in the gold casket. If it is not, the inscription on the silver casket turns into one of those logical nonsense statements like “This statement is false,” which can be true if and only if it is not true.

So the question becomes, do you trust Portia, or don’t you?

]]> Comment on A problem courtesy of Shakespeare by Jonathan Vos Post http://mathsformortals.wordpress.com/2007/11/29/a-problem-courtesy-of-shakespeare/#comment-7 Jonathan Vos Post Sun, 02 Dec 2007 18:23:14 +0000 http://mathsformortals.wordpress.com/2007/11/29/a-problem-courtesy-of-shakespeare/#comment-7 From Shakespeare's The Merchant of Venice. PORTIA: The quality of mercy is not strain'd, It droppeth as the gentle rain from heaven Upon the place beneath: it is twice blest [i.e. blessed x 2]; It blesseth him that gives and him that takes [i.e. + and -, or adjoint functors, or something like that] "The quality of mercy is not strained" through a sieve of Eratosthenes? Profit and loss analysis, with mathematical biotechnology focus: Fom Shakespeare's Merchant of Venice, 1596. The insistence by Shylock of the payment of Antonio's flesh is the central plot device of the play: SHYLOCK: The pound of flesh which I demand of him Is deerely bought, 'tis mine, and I will haue it. The figurative use of the phrase to refer to any lawful but nevertheless unreasonable recompense dates to the late 18th century. From Shakespeare’s The Merchant of Venice.

PORTIA: The quality of mercy is not strain’d,

It droppeth as the gentle rain from heaven
Upon the place beneath: it is twice blest
[i.e. blessed x 2];
It blesseth him that gives and him that takes
[i.e. + and -, or adjoint functors, or something like that]

“The quality of mercy is not strained” through a sieve of Eratosthenes?

Profit and loss analysis, with mathematical biotechnology focus:

Fom Shakespeare’s Merchant of Venice, 1596. The insistence by Shylock of the payment of Antonio’s flesh is the central plot device of the play:

SHYLOCK:
The pound of flesh which I demand of him Is deerely bought, ’tis mine, and I will haue it.

The figurative use of the phrase to refer to any lawful but nevertheless unreasonable recompense dates to the late 18th century.

]]> Comment on A problem courtesy of Shakespeare by Carnival of Mathematics #21: Bar-hopping at last « Secret Blogging Seminar http://mathsformortals.wordpress.com/2007/11/29/a-problem-courtesy-of-shakespeare/#comment-6 Carnival of Mathematics #21: Bar-hopping at last « Secret Blogging Seminar Sat, 01 Dec 2007 19:39:38 +0000 http://mathsformortals.wordpress.com/2007/11/29/a-problem-courtesy-of-shakespeare/#comment-6 [...] for Mortals uses A problem courtesy of Shakespeare (which doesn’t match too well with my recollection of the Merchant of Venice, but let’s [...] [...] for Mortals uses A problem courtesy of Shakespeare (which doesn’t match too well with my recollection of the Merchant of Venice, but let’s [...]

]]> Comment on A problem courtesy of Shakespeare by vlorbik http://mathsformortals.wordpress.com/2007/11/29/a-problem-courtesy-of-shakespeare/#comment-5 vlorbik Fri, 30 Nov 2007 19:23:22 +0000 http://mathsformortals.wordpress.com/2007/11/29/a-problem-courtesy-of-shakespeare/#comment-5 i've got this sneaky feeling that "exactly one of these propositions is true" isn't a proposition at all ... and a dead certainty that *i* can't make any sense at all of "... she has placed her portrait in one of the caskets in a manner that is consistent with this truth or falsity of the inscriptions." portia may be smarter than me ... but i think she's blowing smoke. i’ve got this sneaky feeling that
“exactly one of these propositions is true”
isn’t a proposition at all …
and a dead certainty that
*i* can’t make any sense at all of
“… she has placed her portrait in one of the caskets in a manner that is consistent with this truth or falsity of the inscriptions.”

portia may be smarter than me …
but i think she’s blowing smoke.

]]> Comment on The infimum by eeoam http://mathsformortals.wordpress.com/2007/10/18/the-infimum/#comment-4 eeoam Tue, 13 Nov 2007 09:39:30 +0000 http://mathsformortals.wordpress.com/2007/10/18/the-infimum/#comment-4 That's something I've been thinking myself. I think I've been going too far too fast. I'd like to reach people who are familiar with basic mathematics but want to move to the next level. My next post will take a gentler approach. That’s something I’ve been thinking myself. I think I’ve been going too far too fast. I’d like to reach people who are familiar with basic mathematics but want to move to the next level. My next post will take a gentler approach.

]]> Comment on The infimum by vlorbik http://mathsformortals.wordpress.com/2007/10/18/the-infimum/#comment-3 vlorbik Fri, 09 Nov 2007 15:45:39 +0000 http://mathsformortals.wordpress.com/2007/10/18/the-infimum/#comment-3 when i first saw this, i thought it was probably incoherent. in particular, the "golden rule" $latex X\sqcap Y\ \equiv\ X\ \equiv\ Y \equiv X\sqcup Y$ sure looks like it would benefit from some parentheses: $latex ((X\sqcap Y) \equiv\ X) :\equiv (Y \equiv (X\sqcup Y))$-- <I>i.e.</I>, we're <I>defining</I> $latex \sqcap$ in terms of $latex \sqcup$. but i looked a little more carefully and am now willing to admit that, for example, $latex (X\sqcap Y) \equiv\ ((X \equiv Y) \equiv X\sqcup Y)$ "equivales to Top" ("evaluates to True" in my preferred dialect) for any assignment of boolean values to X and Y --as you've observed, $latex \equiv$ is associative. now: why bother? "maths for mortals"? do you actually think this presentation will be *easier* for a beginner to follow than the more-or-less standard "truth tables and venn diagrams" approach? -- if so, don't get me wrong, you might very well be right. i was wrong about the golden rule and i might very well be wrong about thinking that nobody who isn't pretty doggone sure of themselves already would ever think of trying to jump in and wade through this depth of code without considerable amounts of coaching. i suppose my question for you is: who are you trying to reach here? when i first saw this, i thought
it was probably incoherent.
in particular, the “golden rule”
X\sqcap Y\ \equiv\ X\ \equiv\ Y \equiv X\sqcup Y
sure looks like it would benefit from some parentheses:
((X\sqcap Y) \equiv\ X) :\equiv (Y \equiv (X\sqcup Y))–
i.e., we’re defining \sqcap in terms of \sqcup.

but i looked a little more carefully and am now
willing to admit that, for example,
(X\sqcap Y) \equiv\ ((X \equiv Y) \equiv X\sqcup Y)
“equivales to Top” (“evaluates to True”
in my preferred dialect)
for any assignment of boolean values to X and Y
–as you’ve observed, \equiv is associative.
now: why bother? “maths for mortals”?
do you actually think this presentation
will be *easier* for a beginner
to follow than the more-or-less standard
“truth tables and venn diagrams” approach?
– if so, don’t get me wrong,
you might very well be right.
i was wrong about the golden rule
and i might very well be wrong about
thinking that nobody who isn’t
pretty doggone sure of themselves already
would ever think of trying to jump in
and wade through this depth of code
without considerable amounts of coaching.
i suppose my question for you
is: who are you trying to reach here?

]]> Comment on Equivalence by Science After Sunclipse http://mathsformortals.wordpress.com/2007/10/11/4/#comment-2 Science After Sunclipse Fri, 19 Oct 2007 20:56:11 +0000 http://mathsformortals.wordpress.com/2007/10/11/4/#comment-2 <strong>Carnival of Mathematics</strong> Mark Chu-Carroll hosts the latest Carnival of Mathematics with a theme dear to my heart, the way cholesterol is: spam! Among the notable posts are My Tiny Kingdom’s report on helping with long-division homework. This reminds me: can any of the ... Carnival of Mathematics

Mark Chu-Carroll hosts the latest Carnival of Mathematics with a theme dear to my heart, the way cholesterol is: spam!
Among the notable posts are My Tiny Kingdom’s report on helping with long-division homework. This reminds me: can any of the …

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