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Friday, December 2, 2016

Prescience... [+Addendum]

Just a recent tweet passing my way this morning:

A bit more HERE, and Richard Rorty in Wikipedia.

[Will just add that some of us have been making essentially these same predictions ever since the election of Ronald Reagan to a 2nd term in 1984.]

ADDENDUM: talk about prescient, how did I not think to include this classic 1976 movie clip here:

Tuesday, November 29, 2016

A Quantum Primer

As a “bonus” link on last Friday’s potpourri I gave Sean Carroll’s recent Gifford Lectures In Natural Theology. They generally last about an hour with a Q-and-A period following. Just to further entice you, I’ll post the 2nd talk ("The Stuff of Which We Are Made") below:

Sunday, November 27, 2016

Mathematics Is Surprising

Sunday reflection:
"Perhaps the most surprising thing about mathematics is that it is so surprising. The rules which we make up at the beginning seem ordinary and inevitable, but it is impossible to foresee their consequences. These have only been found out by long study, extending over many centuries. Much of our knowledge is due to a comparatively few great mathematicians such as Newton, Euler, Gauss, or Riemann; few careers can have been more satisfying than theirs. They have contributed something to human thought even more lasting than great literature, since it is independent of language."
-- Edward Charles Titchmarsh, quoted in Mathematical Maxims and Minims by N. Rose

[between all the Holiday and political hoopla, blogposts here might be a little scarce the next few weeks, but I do have a new year-end book wrap over at MathTango today.]

Sunday, November 20, 2016

Elusive Truth...

Sunday reflection:
“Gödel didn’t believe that truth would elude us. He proved that it would. He didn’t invent a myth to conform to his prejudice of the world — at least not when it came to mathematics. He discovered his theorem as surely as if it was a rock he had dug up from the ground. He could pass it around the table and it would be as real as that rock. If anyone cared to, they could dig it up where he buried it and find it just the same. Look for it and you’ll find it where he said it is, just off center from where you’re staring. There are faint stars in the night sky that you can see, but only if you look to the side of where they shine. They burn too weakly or are too far away to be seen directly, even if you stare. But you can see them out of the corner of your eye because the cells on the periphery of your retina are more sensitive to light. Maybe truth is just like that. You can see it, but only out of the corner of your eye.” 
— Janna Levin (from “A Madman Dreams of Turing Machines”)

Friday, November 18, 2016

Gödel's Loophole

I don't have a lot of potpourri picks for you this week (over at MathTango), so I'll add this long, older pdf that seems timely, on the well-known story of Kurt Gödel and a possible loophole in Article V (perhaps) of the U.S. Constitution (a surprisingly interesting read, coming from a law review journal!):

Thursday, November 17, 2016

Either Jim Propp is Santa Claus or Just a Great Blogger

I wrote shortly ago that I expected Jim Propp to have an interesting take on self-referential sentences sometime this month, and that exceedingly-rich post is now up, full of fascinating ideas (...I’ll admit ‘self-reference’ isn’t everyone’s cup-of-tea of a topic, but for those it is, Jim’s thoughts and many great links and endnotes are must-reading, including Jim’s own self-referential ‘test,’ if you’re in the mood for a real mind-twister):

[One, of many, small interesting sidelights for me was discovering that Janna Levin, better known for her physics writing, had written a 2007 novel intertwining the lives of Kurt Gödel and Alan Turing. 
-- p.s. here's a link to Dr. Levin's appearance at "The Moth," which Brainpickings' Maria Popova once called "the greatest story ever told on The Moth").]

Wednesday, November 16, 2016

Making Secondary Math Education Great Again!

Hopefully, by now I don’t even need to link to Ben Orlin’s posts, because you’re already reading him anyway. If you’re not reading Ben you should be locked up! He has a bigly (almost yuuuge) post today on the secondary math curriculum with plenty of neat ideas for consideration and discussion. They are very good, BELIEVE ME.** 
This has already been, for awhile, a topic among math educators, who ought not miss Ben’s take on how to drain the math swamp and re-build it anew:

** I’m trying to get comfortable with the current vernacular

Sunday, November 13, 2016

Carl Sagan Agreed...

Sunday reflection:

We are stardust
Billion year old carbon
We are golden
Caught in the devil's bargain
And we've got to get ourselves
Back to the garden”

— Joni Mitchell (from song, "Woodstock")

Friday, November 11, 2016

Leonard Cohen (1934 - 2016)

"I did my best, it wasn’t much
I couldn’t feel, so I tried to touch
I’ve told the truth, I didn’t come to fool you
And even though
It all went wrong
I’ll stand before the Lord of Song
With nothing on my tongue but Hallelujah"
— Leonard Cohen

Something appropriate I s’pose that a free-spirit like Leonard Cohen should die in a year, and indeed a week, when freedom itself seems to be expiring....

[plenty more links here: http://tinyurl.com/j73cmgc ]

Wednesday, November 9, 2016

Pesky Language

Here's another one of those simple problems (I’ve cited before) where language gets in the way!….

Walter Hickey posted a dozen old classic math problems in nice big graphic form:
[these dozen examples offer some good ones for primary/secondary students, and youngsters are especially susceptible to the following 'broken water heater' fallacy.]

#6 he calls “The Broken Water Heater Problem”… I’ve seen it in many forms, and there are a zillion ways to set it up. Hickey posts it as follows (quoting verbatim):
Last week, the heat in my apartment crapped out because my water heater broke.
I went to a person, showed him the water heater, he used a bunch of spare parts and then fixed it. I paid him for the repairs.
Is this person more likely:
An accountant?
An accountant and a plumber?
Even if you’re not familiar with these type-questions, hopefully upon a moment of logical thought the reader recognizes the answer should be that the person is “an accountant.”
The problem is, often people DON'T really give a moment of ‘logical thought,’ instead jumping to the conclusion that it's more likely (more probable) that the individual must have plumbing skills, and thus must be “an accountant and a plumber.” But of course ANYone who is ‘an accountant and a plumber’ is automatically ‘an accountant’ — in Venn diagram terms, the circle of accountants includes wholly within it the circle of ‘accountants and plumbers.’
Again, I just like this because it once more demonstrates how easily words and language often short-circuit, rather than aid, our logic. [In fact, I dare say our latest election is clearly another example of mere visceral words/language overriding reason.]

Sunday, November 6, 2016

A Little Backstory… the Erdos/Tao photo

A substitute ‘Sunday reflection’ today, because of my experience with a tweet last evening….

I’ve always loved the above photo (brings me a smile everytime) of a 10-yr.-old Terry Tao with Paul Erdös, which I dropped into a tweet last night — the look on the faces, the synchronous postures, the concentration, the shared passion…  It originally showed up on the ’Net in 2013 courtesy of Terry himself, and went somewhat viral at the time within math circles:
(...and a h/t to Patrick Honner who was the first to bring it to my own awareness, back then)

Is that not great! I thought it was iconic by now and viewed by everyone multiple times. But a few folks (responding to the tweet) apparently were not familiar with it, and while usually recognizing Erdös, were unsure of the youngster involved. So just to clear any confusion, am posting the little bit of history that I know (thanks again to Dr. Tao for sharing it originally -- apparently the pic comes from the University of Adelaide in Australia at an awards ceremony of the Australian Mathematics Competition,1985).
As some responders have noted, two people, bridging a large generation gap, one originally Hungarian, one originally Australian, who both came to America, and in different manners contributed so much to our joy of mathematics, and continue to delight us, in both death and life.

p.s... among Erdös' many noted linguistic idiosyncracies, he referred to young children as "epsilons," and as one of the commenters to Terry's original post says, he had finally found an interesting "epsilon." ;-)

Wednesday, November 2, 2016

Peter Wason and His Famous Test

from Wikipedia

Some interesting overview and history of the 'deceptively easy' Wason Selection Task  in today's Nautilus:

Perhaps this test and its implications, by a man who treated "reasoning as an enigma" is even extra pertinent in a week that people are engaged in especially important political decision-making! From his 2003 obituary: His aim was to reveal a surprising phenomenon—to show that thinking was not what psychologists including himself had taken it to be.”

[If by any chance you're not familiar with the task, the article contains an interactive video you can play with.  And it's a fun test to run by students and adults at various levels.]

Also, as with many puzzles I enjoy, language or words, in addition to strict abstract reasoning, potentially come into play here, as the article indicates.

[ADDENDUM:  just realized, this article is a RE-run of a piece Nautilus ran in May 2015]

Monday, October 31, 2016

Vote Like the Future... and That of Science, Depends On It

"The only thing necessary for the triumph of evil is for good men to do nothing."  -- Edmund Burke

No math today, just blather about this craziest election of my lifetime….

Months ago, I surmised that if by some deranged alignment of planetary forces Donald Trump actually won the Republican nomination I expected a response from STEM people as never before seen in a presidential campaign: 100s or 1000s of scientists signing open letters from various organizations/societies and independent groups to denounce a Trump candidacy.  There have been a trickle of such efforts and certainly individual STEM folks have voiced their concern via Twitter, Facebook, Google, etc… but the large-scale outpouring I envisioned hasn’t materialized.

Many feel uncomfortable or even constrained (sometimes contractually) from involving themselves publicly in politics; it is not a customary activity for the science crowd, and perhaps many conclude they’d only be preaching to the choir anyway (…and, as unfathomable as it seems, some scientists even support the absurdity that is Donald Trump). 

But something is seriously wrong when folks who call themselves patriotic, or religious, or God-fearing, or simply concerned about the future, say they are voting for Donald Trump, as if wearing blinders. Gullibility and timidity of citizenry during the rise of German Fascism led of course to unprecedented human tragedy. I’m a bit ashamed by the lack of concerted, organized response from the STEM community to a narcissistic authoritarian in our midst — with demagogic speeches and political rallies reminiscent of Jim Jones’ assemblies. And please spare me your objections to the German Fascist analogies (they ARE apt, and I don't doubt for a second that if Hitler rose from the dead to campaign across America today, 30%+ of current voters would back him).

Those who fail to learn the lessons of history are doomed to repeat it’… Trump will most likely lose this election… but there are more like him coming down the pike. That his antics and laughably-shallow “policies” appeal to so many doesn’t bode well for the future. And science is in their crosshairs. Those who dare ‘preach’ evolution or vaccination or climate mitigation or brain science or particle physics or space travel or… or… are all vulnerable (no doubt Jews, gypsies, and trade-unionists, are as well). 
Perhaps America’s 200+ year-old experiment in democracy and slow liberal progressivism is simply running out of steam to continue against the regressive, anti-science, anti-rational sentiment and thuggery that is creeping across the globe. Make no mistake about it though, silence is not golden; it is complicit. Admittedly, whatever the outcome of this election the Trump cult will remain, potentially sabotaging the next four years, even worse than Republicans sabotaged the last eight.

"We will not walk in fear, one of another. We will not be driven by fear into an age of unreason, if we dig deep in our history and our doctrine, and remember that we are not descended from fearful men — not from men who feared to write, to speak, to associate and to defend causes that were, for the moment, unpopular. This is no time for men who oppose Senator McCarthy's methods to keep silent, or for those who approve. We can deny our heritage and our history, but we cannot escape responsibility for the result. There is no way for a citizen of a republic to abdicate his responsibilities. As a nation we have come into our full inheritance at a tender age. We proclaim ourselves, as indeed we are, the defenders of freedom, wherever it continues to exist in the world, but we cannot defend freedom abroad by deserting it at home. The actions of the junior Senator from Wisconsin have caused alarm and dismay amongst our allies abroad, and given considerable comfort to our enemies. And whose fault is that? Not really his. He didn't create this situation of fear; he merely exploited it — and rather successfully. Cassius was right. 'The fault, dear Brutus, is not in our stars, but in ourselves.' Good night, and good luck."
-- Edward R. Murrow (1954)
Good luck... Indeed! 

(...and if you have the option, vote EARLY!)


ADDENDUM (11/11/16):  When you turn voters against their government, as Reagan did, and against the press as Trump did, and against science, as the GOP has done, don't be surprised if democracy withers and dies.

Sunday, October 30, 2016

Science Is Provisional... And Mathematics a Luxury

Sunday reflection:
That’s how real science advances… Three steps forward, two steps back. Mathematicians have the luxury of living in a logical bubble, where once something is proved true, it remains true. Interpretations and proofs may change, but the theorems don’t get unproved by later discoveries. Though they may become obsolete or irrelevant to current concerns. Science is always provisional, only as good as the current evidence. In response to such evidence, scientists reserve the right to change their minds.

— Ian Stewart in Epilogue to “Calculating the Cosmos

Saturday, October 29, 2016

Games With Facebook (...and Ramsey Theory)

As Seinfeld fans know, one of the things that made that show so enjoyable was a style they developed of weaving two (or more) disparate plots together, in a single 30-min. episode, that somehow resolved or came together at the end.

I suddenly realized that, to some degree, this is also what makes many of Evelyn Lamb’s posts for her “Roots of Unity” blog so wonderful. She’s developed a knack for bringing up multi-subjects or ideas and showing how a mathematical thread draws them together.  In her newest post she weaves Ramsey Theory and birthdays into Facebook with her own little fun daily game (also, includes several excellent links):

Of course math is EVERYwhere, and so too 'interesting configurations.' Always fun to be reminded of it. Lamb writes that she wants to "share a little way in which a little bit of math enhances my life a little" ...and in so doing she enhances her readers.

Sunday, October 23, 2016

Real vs. Imaginary...

Sunday reflection:
…the terminology is misleading, for it suggests that there is some greater ‘reality’ to these so-called real numbers than there is to the so-called imaginary numbers. This impression comes about, I suppose, because there is the feeling that distance measures are, in some sense ‘really’ such real-number quantities. But we do not know this. We know that these real numbers are indeed very good for describing distances and times, but we do not know that this description holds good at absolutely all scales of distance or time."We have no actual understanding of the nature of a physical continuum at a scale of, say, one googolith of a metre or of a second, for example. The so-called real numbers are mathematical constructions, which are, nevertheless immensely valuable for the formulation of the physical laws of classical physics.
— Sir Roger Penrose in Fashion, Faith, and Fantasy