You receive a letter on a Friday that is either a rejection letter or an acceptance letter to medical
school. You have a wonderful weekend planned and don't want bad news interfering with it. Can you devise a way to learn the contents of the letter BUT ONLY if it is good news?
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. answer:

Have a friend open the letter.

Instruct them that IF it is good news they are to flip a coin and tell you the news ONLY if it comes up heads, otherwise tell you nothing.

AND, if it's bad news, tell you nothing.

This way you will either be told good news, OR STILL have 33% hope for good news, if they tell you nothing.

Not precisely mathematics, but this week's Sunday reflection by physicist Max Tegmark on why we need to be careful when it comes to programming artificial intelligence:

"If you're walking on the sidewalk and there's an ant there, would you actively go and stomp on it just for kicks? (Me: 'No.')
"Now, suppose you're in charge of this big hydroelectric plant that's
gonna bring green energy to a large region of the U.S. And just before
you turn the water on, you discover there's an anthill right in the
middle of the flood zone. What are you gonna do? It's too bad for the
ants, right? It's not that you hate ants. It's not that you're an evil
ant-killer. It's just that your goals weren't aligned with the goals of
the ants, and you were more powerful than the ants. Tough luck for the
ants. We want to design AI in the future so that we don't end up being
those ants."

Ben Orlin tapped my funny bone again this week... and brings out the toddler in all of us... with this offering on the role of rote repetition/practice in learning and mastery:

The format will be familiar to many of you.
I've given the answer farther below, but without explanation, so if you need that, you can go to the link, find the problem, and check the responses there.

***********************************

Two math grads run into each other at the shopping mall, having not seen each other in 20 years. Their conversation proceeds like this:

M1: How have you been?

M2: Great! I got married and now have 3 daughters.

M1: Wonderful... how old are they?

M2: Well, the product of their ages is 72, and the sum of their ages is the same as the number on that building over there.

M1: Sure, ok... er wait... Hmmm, I still don’t know their ages.

M2: Ohh sorry, the oldest one just started piano lessons.

A
beautiful, touching, scrumptious essay this week from Keith Devlin, on
the beauty of mathematics... a somewhat tiresome phrase that he breathes
life into here, focusing on calculus, or, as he quotes William Blake, "infinity in the palm of your hand":

It
deals with a student's recent response to a piece Keith had written almost 10
years earlier. I heartily commend it to all mathematicians, math
teachers, math majors, and students in general, and all those, who like
myself, simply love math from the sidelines. It almost has a fractal
quality, as a beautifully-crafted essay, about beautiful ideas, about
the beauty of beauty! ;-)
[p.s... Dr. Devlin suggests "if you are a math instructor at a college or university, maybe
print off this blog post and pin it somewhere on a corridor in the
department as a little seed waiting to germinate." I'll
second that suggestion, which derives, NOT from Keith's ego,
but from his infectious love of math teaching/learning.]

Actually,
half the post is simply a verbatim letter Dr. Devlin received from a
math student who had previously read another of Keith's essays, and now
was writing to say how much he finally appreciated that earlier
piece. Is there anything more rewarding to a teacher than to hear from a
student (and in this case not even Keith's own student) how much
something you said or did in the past has affected that student years
later!? Keith's earlier piece was about the deep, deep beauty of
calculus, or again from Blake,seeing "an infinite (and hence unending) process as a single, completed thing."
All
of us who've taken calculus will probably freely admit that, no matter
what our grade or ability in a first-year course, we lacked any deep
grasp of the subject at that point. To a lesser degree maybe that even
holds for algebra, geometry, trig… the student can't fully appreciate
these subjects 'til s/he has taken in much more mathematics for context,
depth, nuance. The "inner beauty" of math requires persistence and
commitment to fully access.

Dr. Devlin's post reminded
me slightly of the well-known Richard Feynman blurb that I've placed
below (and am sure most of you have already seen), wherein he speaks of
the "beauty of a flower," and how,
despite what an artist friend thinks, he as a physicist also has access
to seeing that beauty; perhaps even perceiving it at a deeper level than
does the artist.

I WISH I could see the
beauty of math the way Keith, and Ed Frenkel, and Steven Strogatz, and
others see it (seeing it, as Keith has previously written, from a
treetop overlooking the vast but inter-connected forest below). But
alas, as a rank-amateur, my vision is far more limited, far more myopic
than theirs. Yet even from my lowly vantage point mathematics resounds
in beauty, in "excitement, mystery, and awe" as Feynman refers to.

Some
of course call mathematics the language of science, or even the
language of God. But at base, I think its beauty lies in being a pure,
grand, and almost inexplicable creation (or discovery) of the human
mind... the pinnacle of that which our brains are capable. In a day
when our lives, politics, and society, seem inundated with violence,
intolerance, and irrationality, mathematical thinking stands out as a
beacon for the future, if we as a species are to have a future.

Growing
up, I watched my grandfather (and other seniors) become increasingly
cynical about the world as they aged, and swore to myself I would never
be like that. But I do now find myself saddened each day when I turn on
the news… cynicism is hard to repress. My hope today though, is that
every teacher out there, at least once in your lives, receives a letter
like the one Dr. Devlin has shared, or if you're not a teacher, that you
hear from some young person, when you're not expecting it, what a
difference you made in their lives.

The oddball Count
(and father of General Semantics), Alfred Korzybski wrote that we humans
are a "time-binding" species (different from all other species that
only "space-bind") because of the way we routinely transfer our
increasing knowledge across generations. That, in part, is what I see
going on in Dr. Devlin's piece, "time-binding" with a younger
generation... and, as always, the younger generation is our real hope
for the future... and, our shield against cynicism!

Finally, as I was completing this post a new blogpost from Megan Schmidt
crossed my webfeed. If you need a reminder that teachers impact young
lives (or even if you don't) I hope you will read it as well, (be
sure to click on and read the student exposition she provides): http://mathybeagle.com/2015/10/03/where-do-we-go-from-here/

Woodbridge Hall/Yale U. via Nick Allen/WikimediaCommons

Well, Ben Orlin leaves me ROFLOL once again as he explains
why... if you can believe it... he purposefully avoids things that 'feel like spiders
crawling out of his eyeballs':**

h/t to Julie Rehmeyer for pointing to some short (~4-5 min.) video clips relating the issue of gender in mathematics, as touched upon by the play entitled, "One Girl's Romp Through M.I.T.'s Male Math Maze":

"Mathematics and contemporary art may seem to make an odd pair. Many people think of mathematics as something akin to pure logic, cold reckoning, soulless computation. But as the mathematician and educator Paul Lockhart has put it, 'There is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics.' The chilly analogies win out, Lockhart argues, because mathematics is misrepresented in our schools, with curricula that often favor dry, technical and repetitive tasks over any emphasis on the 'private, personal experience of being a struggling artist'…

"…During his four minutes, Alain Connes, a professor at the Institut des Hautes Etudes Scientifiques, described reality as being far more 'subtle' than materialism would suggest. To understand our world we require analogy -- the quintessentially human ability to make connections ('reflections' he called them, or 'correspondences') between disparate things. The mathematician takes into another hoping that they will take, and not be rejected by the recipient domain. The creator of 'noncommutative geometry', Connes himself has applied geometrical ideas to quantum mechanics. Metaphors, he argued, are the essence of mathematical thought. "Sir Michael Atiyah, a former director of the Isaac Newton Institute for Mathematical Sciences in Cambridge, used his four minutes to speak about mathematical ideas 'like visions, pictures before the eyes.' As if painting a picture or dreaming up a scene in a novel, the mathematician creates and explores these visions using intuition and imagination. Atiyah's voice, soft and earnest, made attentive listeners of everyone in the room. Not a single cough or whisper intervened. Truth, he continued, is a goal of mathematics, though it can only ever be grasped partially, whereas beauty is immediate and personal and certain. 'Beauty puts us on the right path.'"

I'll remind folks that Presh Talwalkar also does a weekly wrap up of math picks later on Fridays at his "Mind Your Decisions" blog (usually quite different from my MathTango selections): http://mindyourdecisions.com/blog/

...and Crystal Kirch has been doing Sunday linkfests for teachers at her "Flipping With Kirch" blog: http://flippingwithkirch.blogspot.com/ (check 'em out on Sun.)

If
there are other regular weekly math linkfests you think worth knowing
about, feel free to send them along (via comments or email). I'm happy
to publicize other sites that are spreading the math wealth!

"I don't want to belong to any club that would accept me as a member."

Hmmm, after using this quote for decades, I just suddenly realized what a deep-thinking set-theorist
Groucho Marx was (...and, a whole LOT funnier than Bertrand Russell too!).
;-)

Recommended to everyone is the freely downloadable book (pdf) on RH by Barry Mazur and William
Stein. Get it! ==> UGHH, looks like link for download no longer works, so consider yourself lucky if you already got it; otherwise look forward to the book when eventually published. I understand the publisher not wishing free downloads to be available; on-the-other-hand I suspect most of those downloading will eventually want a hard copy of the final version anyway.

A super post from biologist Lior Pachter addressing Common Core from a different angle, employing unsolved problems (LOT of potential food for thought here):

As Pachter puts it, he believes there is a major "shortcoming in the almost universal perspective on education that the common core embodies: The emphasis on what K–12 students ought to learn about what
is known has sidelined an important discussion about what they should
learn about what is not known."

Pachter proposes several unsolved problems that can be introduced to young people at different levels. While admitting that K-12 students aren't likely to find solutions to such problems he argues that the problems "provide many teachable moments and context for the
mathematics that does constitute the common core, and (at least
in my opinion) are fun to explore (for kids and adults alike). Perhaps
most importantly, the unsolved problems and conjectures reveal that the
mathematics taught in K–12 is right at the edge of our knowledge: we are
always walking right along the precipice of mystery. This is true for
other subjects taught in K–12 as well, and in my view this reality
is one of the important lessons children can and should learn in school."

Just a remarkable post I commend to all educators! (some of the perspective Pachter is proposing I think may already be inherent to the goals of Common Core, but not in the precise way he outlines).

I'm a number-luvin' primate; hope you are too! ... "Shecky Riemann" is the fanciful pseudonym of a former psychology major/lab-tech (genetics), now cheerleading for mathematics! A product of the 60's he remains proud of his first Presidential vote for George McGovern ;-) ...Cats, parrots, and shelties revere him.
Li'l more bio here.

............................... --In partial remembrance of Martin Gardner (1914-2010) who, in the words of mathematician Ronald Graham, “...turned 1000s of children into mathematicians, and 1000s of mathematicians into children.” :-) ............................... Rob Gluck