Friday, May 31, 2019

Chi-i-i-i-i-i-ll Friday *

[ *  "Chill Friday" is Math-Frolic's meditative musical diversion, heading into each weekend]

Wednesday, May 29, 2019

A Li'l Arithmetic Magic

This re-run puzzle comes verbatim from Alfred Posamentier's "Mathematical Amazements and Surprises":


"You are seated at a table in a dark room. On the table there are twelve pennies, five of which are heads up and seven of which are  tails up. (You know where the coins are, so you can move or flip any coin, but because it is dark you will not know if the coin you are touching was originally heads up or tails up.) You are to separate the coins into two piles (possibly flipping some of them) so that when the lights are turned on there will be an equal number of heads in each pile."

"Your first reaction is 'you must be kidding!' How can anyone do this task without seeing which coins are heads or tails up? This is where a most clever (yet incredibly simple) use of algebra will be the key to the solution."

Posamentier Continues:

"Let's 'cut to the chase' (You might actually want to try it with 12 coins.) Separate the coins into two piles, of 5 and 7 coins each. Then flip over the coins in the smaller pile. Now both piles will have the same number of heads! That's all! You will think this is magic. How did this happen. Well, this is where algebra helps us understand what was actually done."

Explanation: ...At the start, there are 5 heads showing among 12 coins. After separating into piles, let's say the 7-pile now has "h" heads. The 5-pile then has "5 - h" heads, and "5 - (5 - h)" tails (or, just "h" tails). Once you flip the entire smaller pile, all the tails ("h" of them) become heads, and all the heads become tails. Thus you are left with "h" heads in the "5-pile," the same as the number in the "7-pile." Whaaa-laaahhhh! 

Sunday, May 26, 2019

Imposter Syndrome... for real

Another blast-from-the-past today. Futility Closet has long served up wonderfully quirky offerings sometimes almost hard-to-believe. One-such, via their podcast, I linked to well over a year ago was the bizarre story of bookish Mark Hewitta 20th century American imposter who taught physics, math, and engineering at various academic institutions, despite being a high school dropout. If you missed it, or just to enjoy it again, give a listen:

Friday, May 24, 2019

A Little Self-reference Via Taylor Swift (...and others)

A substitute today for the usual "Chill Friday" offering...
I keep on-hand a folder of odd miscellany to occasionally pull posts from… including, for example, this today:

Long time readers here know I’m interested in self-reference and recursion, so for today's entertainment (if you’re a Taylor Swift fan), a favorite tidbit harking back to 2012 when Taylor Swift’s song “Mean” won the Grammy Award for “Best Country Song” of the year. For any who were vacationing on the pseudo-planet Pluto for all of 2012 and don’t know the backstory, “Mean” was a li’l ditty off Taylor’s award winning “Speak Now” album that wasn’t originally intended as a single release, but grew popular as an anthem for young people battling bullying at the time, and was released to great demand.
Swift wrote the song as a rebuke to a particular critic who bashed her singing time and time again, predicting she'd rapidly fade from stardom. Swift admitted such criticisms hurt, and as she often does, wrote a song striking back… little realizing the song would take on a life of its own, in a sense, proving the critic wrong, by its very overwhelming popularity and reception.

So, in short, Taylor writes a simple song to vent about a specific critic, the song gets released as a single, shoots up the charts, is nominated as a Grammy “Song-of-the-Year,” and then actually wins the award… sort of like sticking a knife in the back of a personal nemesis and twisting it again and again… and, yeah, again. 
But as if that’s not enough, at the Grammy ceremonies singers (and their bands) perform their nominated songs. Two lines from the chorus of "Mean" repeat several times through the lyrics as follows:
Someday I'll be living in a big old city
And all you're ever gonna be is mean

Near the end of their Grammy performance, with those two lines approaching yet one more time, without missing a beat, Taylor made a small one-time alteration to them:

Someday, I’ll be singing this at the Grammys
And all you’re ever gonna be is mean

It was a simple, delicious self-reflexive moment in pop culture I’ve always relished (everyone else has probably forgotten), and well-appreciated by the audience of performers at the time (who weren’t too fond of critics themselves)... Normal song version at top of post, tweaked Grammy version here:

...and a couple of recursive add-ons:

1)  First, from George Carlin this quote I just read a couple of days ago for the first time:
 "For years and years and years, I thought my brain was the most important organ of my body, until one day I thought, hmmm, look who's telling me that!"

2)  ...and just yesterday I spied this bumper sticker on the car in front of me:

Sunday, May 19, 2019

Al Jean…. D'OH!!

I’ve done 5 Sunday ‘profiles’ here of fairly well-known Web folks and wanted to go with something different for the next profile. So I found a mathematician who’s name might not be that familiar to many of you, even though his work likely is familiar.  If the name “Al Jean” doesn't ring a bell then how about the name “Homer Simpson”? Read on….

Al Jean was born in Michigan on January 9, 1961 (before the water there could mess with his brain... uhh, too much), making him over 8 in shaggy dog years. He shares a birthday with Richard Nixon and was born exactly 20 years after Joan Baez (you do all remember Joan Baez, don’t you?… the folk-singing daughter of the uncle of mathematician John Carlos Baez, who writes the blog Azimuth, and who, just to complete the circle, was also born in 1961, as was Barack Obama and Heather Locklear... so much for astrology).
Al’s full name is Alfred Ernest Jean III (not even a hint of comedic ring to THAT), and he has two children, Bart and Lisa… no, no, I have no idea what his children’s names are… but according to the last survey I could find (2018) the greatest probability, believe it or not, would be Liam and Emma (Bob and Mary having faded completely out-of-style, along with Beanie Babies).

In 1977 (while I was probably bussing tables somewhere), Jean tied for 3rd place in the Michigan Mathlete competition. He was a nerd from early on; indeed nerdy enough to go to Harvard at the age of 16 and graduate in 1981 with his BS in mathematics, at which point he apparently asked himself the question, “When will I ever use this stuff?” And his answer was, well, a little different from most…

It was also at Harvard that, with Mike Reiss, Jean honed his comedy chops working at the Harvard Lampoon. Then through the 80’s, instead of math jobs, he wrote comedy for a number of TV shows (including for Johnny Carson and Gary Shandling) before landing a job with an animated sitcom called “The Simpsons” in 1989 — a show not expected to last long that was merely destined to become America’s longest-running weekly TV series ever, D'OH!; yes, even longer than "Married With Children" (who knew!) — in the time since our nation has watched the Republican Party go from George H. W. Bush as President to deranged Donald Trump, the Simpsons have been gracing American living rooms (on the Faux Channel, er, I mean, Fox Channel) — now I’m not sayin’ the Simpsons had anything to do with that evolution (or degeneration) of the GOP, but still, there just might be a PhD. thesis for someone willing to investigate it further.
Anyway, The Simpsons are celebrating their 30th anniversary this year (way more than any current married couples will ever experience, although some car owners with Volvos may be able to relate), and Jean still works there. He says that what he loves about it is that, though it is a comedy show, it has “depth and warmth.” And heaven knows, mathematicians need as much depth and warmth as they can muster (as perhaps Doron Zeilberger would attest to?).

In the third season of The Simpsons Jean and buddy Mike Reiss were promoted to Executive Producers of the show and as Simon Singh put it they would “parachute their own mathematical jokes into episodes," as exemplified here:

And also on YouTube, "Mathologer" has done several videos on math bits in the Simpsons:

In fairness I should note that several of the Simpsons’ writers have strong math backgrounds, and I only picked out Jean because he had been with the Simpsons off-and-on since the beginning and has an actual mathematics degree. Some of the other writers possess mere physics degrees, and for all I know may even believe in the multiverse, LOL (may Karl Popper have mercy on their souls). With all that said, Sean Carroll has yet to write even a single episode of The Simpsons, apparently preferring to put his material on physics ArXiv. Go figure! (By the way, Stephen Hawking, having made multiple appearances on it, once called The Simpsons "the best thing on American television" -- of course, I s'pose some might say that restricting it to 'American television' is setting a low bar).

Jean has received eight Emmy Awards and one Peabody Award for his work on The Simpsons (several of them well-deserved), more, I'm pretty certain, than Pee Wee Herman ever got for Pee Wee’s Playhouse.

Jean says that the Simpsons’ character he most relates to is Lisa, no doubt due to her rational, insightful, scientific mind… or, perhaps it’s just a simple case of gender dysphoria.
Anyway, I think Al’s career is itself a good response for whenever that pesky, sugar-infused 8th grader, with head cocked and eyes rolling, indeed asks, in Bart Simpson overtones, “But hey, WHEN will I ever use this stuff?” and you can then reply to the li’l ungrateful, hormone-awash twerp that he/she/they just might use it when they’re a head writer for the longest running, gosh-darn TV sitcom in the history of the Milky Way galaxy (or even the second longest)… or, you might alternatively use it when you’re figuring out how to fly a drone over the Principal’s house and capture some compromising photographs of he and Secretary Sweeney on their lunch hour… or, when you’re trying to scam the elderly, like your grandparents, over your smartphone, out of their entire life savings… there are just SO MANY lovely, practical day-to-day creative uses of mathematics (and we haven't even gotten yet to suppressing the vote in key electoral states/districts -- Republicans will pay you a pretty penny up front for that).

In any event, if you’ve never read Simon Singh’s book about math in the Simpsons it’s one of the most entertaining popular math reads of the last several years. It’s a little slice of nerd heaven, so check it out... at least it should hold you over while you're waiting for someone to explain, in English, Mochizuki's proof of the ABC conjecture.

Al has a Twitter account at @AlJean where you can join his other almost 40,000 6th-grade-level followers. I think Taylor Swift’s cat may have more followers than that, but it is waaaaay more than Donald Trump has if you eliminate all the phony Russian bots following him, and the real PGA members ("Pussy-Grabbers Anonymous") that revere him.

Almost a dozen years ago, when the Simpsons had only been around a mere 18 years, Jean was a guest on NPR's "Fresh Air" here:

...and here's another fine interview with him from a different site around the same time period:

So hey kiddies just keep in mind that demand for mathematicians in the future is expected to soar; it's one of the very best fields to enter these days, with so many areas requiring your talents: actuary, economist, cryptographer, financial planner, operations research analyst, statistician, investment analyst, insurance adjuster, programmer, data analyst/scientist, market researcher, engineer, teacher... AND, of course, comedy writer!!
So when you're sending out those applications to MIT, Harvard, Berkeley, and Pomona College, you may want to also be dropping notes to Seth Myers, Jimmy Fallon, Saturday Night Live, and Phyllis Diller's heirs (because eventually you're gonna have to pay all those student loans back!). Just saying....

Anyway, here's hoping The Simpsons are on for another 30 years, because my conjecture is that so long as Bart Simpson doesn't grow up, well then, neither shall I. D'OH!!

Prior Sunday profiles have been of: 


Friday, May 17, 2019

Chi-i-i-i-i-i-ll Friday *

[ *  "Chill Friday" is Math-Frolic's meditative musical diversion, heading into each weekend]

(...will there be another Sunday "profile" this weekend?... why yes, there will be, though I feel safe defying anyone to guess of who)

Sunday, May 12, 2019

Cathy O’Neil… Big Data Meets Its Match

For all the mathematician-profile fans, time for another Math-Frolic-generated portrait!
After 3 male and one female Sunday “profiles,” perhaps time to focus on another female. Thus, today's drum-r-r-r-r-r-roll for…. Cathy O’Neil.
Cathy’s not just a mathematician though, she’s an observer/commentator/ranter of first order on all worldly things. Hopefully, she needs little introduction for most of you, but still we’ll start at the beginning.

Cathy was born on July 13th sometime in the 20th century (I couldn’t find the actual year… females are so good at hiding such details). That makes her a Cancer, or in her case really more of a Can-do person!  She told a few more details of her early math life back when I interviewed her in 2014 (like how she decided in the summer of her 15th year to become a math professor instead of a pianist):
Now she is 5 years richer, famous-er, and well-travelled (her ultimate pro-guide to travel, by the way, is HERE)!

Her adult-like life began with attendance at Berkeley perhaps in the early 90s… and perhaps accounting for her leftward leanings (…or maybe she attended Maoist summer boot camps, the records for which have been expunged). She followed Berkeley up with a PhD. from Harvard in 1999, where her advisor was Barry Mazur, no slouch of a mathematician himself. She taught for awhile but left academia in 2007 to go work as a quant in the private finance industry (raising the question of why do kids growing up wanna be policemen, and firemen, and doctors, but never "quants"?). Anyway, she was there just in time to witness George Bush & Friends nearly bring down the entire world economy in 2008/9 without even trying (before the Government figured out creative ways to milk the middle-class for more funds with which to pay off all the failed bankers, industries, and their poor broke CEOs… and, plant the seeds for it to happen all over again… hey, maybe even this year!).  That experience lessened Cathy's affections for private finance and she abandoned it before necessitating the quintuple-hernia-bypass operation, that most quants accept as part of the job. Incidentally, she was interviewed for “Frontline” about the financial crisis and all its dysfunctionalities way back here:

Cathy lives in New York city (which is apparently do-able though I’ve never quite understood how?). There, her son Aise sometimes performs standup comedy at the Gotham Comedy Club. Below is one of his earlier club performances (…which, by the way, I take as proof-positive of at least a one-time rendezvous between Cathy and Steven Wright some decades ago… not that that’s any of our business... all of which kinda reminds me of that time when I had a skylight installed at my apartment, making my upstairs neighbors furious!):

She has another son who's name I couldn't find (though I feel safe in guessing it isn't "Archie"), and a third son named “Wolfie” — now THAT is a great name! (…but then I think the whole world would be better off if all kids were named after plants or animals — in fact, if you wish, you have permission, like my first girlfriend, to henceforth, simply call me “Stallion”).
Uhhhh, moving on….

Cathy doesn’t seem to like to do anything for too long a time (a clear case of A.D.H.B... Attention Darting Hither and Beyond), and following quant-hood she started a blog on the Web under the moniker “Mathbabe;” a place for, in her words, “exploring and venting about quantitative issues” — with, dare-I-say, emphasis on the present-participle “venting.” Cathy is one of the best ranters around. And she can rant on all manner of things; doesn’t have to be something mathematical, like the quadratic formula or credit default swaps. She could probably rant about baseball or apple pie or even Matt Damon if the need arose. She’s as good and lively a writer as there is in the expository-quantitative-in-your-face-opinionated-digitized-and-emojied world of bloggerland.

At a certain point on the blog, Cathy introduced an alter-ego “Aunt Pythia” as an advice columnist, covering all manner of human foibles. If you’ve ever had an issue, question, or sorrow regarding the human heart or state of affairs, I suggest you read all her past columns, because somewhere buried therein you will likely find an answer to your woes (and besides, Ann Landers is long deceased… and was a tad stodgy in her day — one thing that Cathy and Aunt Pythia are NOT, is stodgy).

Like so many bipedal primates, Dr. O’Neil has had a bit of a love/hate relationship with Twitter over the years (or perhaps more of a tolerate/hate relationship), so she has periods of extended non-presence on the platform (and, like most sane and decent carbon-based lifeforms, she has dropped Facebook altogether). I assume Nassim Taleb has her blocked, but YOU can follow her on Twitter at @mathbabedotorg.

Her husband is also a mathematician (at Columbia)… funny how often mathematicians marry other mathematicians; I mean for the sake of the gene pool shouldn’t mathematicians be marrying sociologists or English lit majors or maybe New York city sanitation workers, just to, you know, kinda mix up all that DNA and mitochondria, and keep the species going?Just something to ponder... before we all expire from climate change anyway. Que sera sera.

In 2016, Cathy came out with her first book, “Weapons of Math Destruction,” all about societal dangers inherent to the algorithms that now run our lives and turn us into numbers, if not zombies (as she puts it, "algorithms are opinions embedded in code"). It was easily the best book title since Steven Strogatz’s “The Joy of X,” which was easily the best title since Erica Jong’s “Fear Of Flying” (which just barely beats out THIS item). I cited Cathy’s book as my own “math-book-of-the-year” for 2016 (…and yet never received a single ruble under the table from Cathy in return; still, I shan’t retract).
She covers many of the book’s main ideas in this TED talk:

Cathy was active in the Occupy Wall Street movement that began in 2011 (apparently thinking, in adorable fashion, that masses of passionate young people with body rings could stop the upper 1% from siphoning off everyone else’s life savings to off-shore bank accounts). Since she got involved, I think the Dow Jones average has risen about 931%, not that she, nor I, nor any other vassal will ever see any of that, with income-inequality now fully invoked as the Sharia law of the land.

I always especially enjoyed her take on the weekly Slate Money Podcast which, like other projects, she departed, despite there never having been even a hint of financial harassment from male host Felix Salmon.
She now writes short opinion pieces for Bloomberg, but honestly, they don’t have the punch and pizazz of her blog writing (though they may help pay for pet treats — I was not able to find out if Cathy owns a Pit Bull, a Rottweiler, or a Doberman, and will stand in utter disbelief if informed she owns a Labradoodle):

Her next project, started in 2017, was her own consulting company, “O’Neil Risk Consulting & Algorithm Auditing,” a bit of a mouthful, but shortened to ORCAA for seafaring clients. Yo Google, I think you should put her on retainer! And Goldman Sachs, you too (...and don't forget her Christmas bonus!).
Her company runs third-party audits on tech algorithms that are employed by businesses, for their fairness and legitimacy. Of course finding companies that are interested in fairness or legitimacy markedly limits your potential clientele (...but perhaps Equifax or Wells Fargo can help her find some). Anyway, a couple of previous articles on her work here:

She’s also now actively writing her second book, this time on “shame,” very timely for the 83% of Twitter users who have been publicly shamed at one point or another.  And then there are the 52% of white adult women who voted for Trump in 2016 and probably deserve a whole chapter all to themselves (…it will be entitled, “What the %#@!*(&%!!! Hell Were You Numbskulls Thinking or Were You in a Botox-induced Coma At the Time, Just Askin'?”).

Cathy’s been known to dye her hair teal, strongly indicating a genealogical link at some point to Evelyn Lamb who did the same and who I profiled before. I’m guessing the common ancestor in both of their lineages may be Susan B. Anthony; though it's possible they both came up through the Pocahontas-Elizabeth Warren line?

You sort of never know what Cathy will do next (but you know it will be good)… In fact I’m a little surprised she isn’t running for President right now; heck, I’m pretty certain she’d draw more support than Kirsten Gillibrand.

What ya gotta love about Dr. O’Neil is that she’s just out there — if something’s on her mind, she just says it… out loud… no beating around the bush or weasel words. WYSIWYG. And her heart seems to always be in the right place… left of center, right above her liver.
We need more people like Cathy out there fighting the good fight and being vocal about it (like Jeff Tiedrich)… so that if Donald somehow manages to get mindlessly re-elected (because 52% of white women are apparently certifiably nuts), many of us will at least have good company on that eventual cattle-car ride we're given to a camp in Idaho (and if for some reason I can’t travel with Cathy then I want Andy Borowitz by my side).

To conclude, Cathy names 97-year-old Betty White as one of her idols, saying she wants to be just like Betty when she’s older, so what better way to end than with a couple of episodes of “Betty’s Happy Hour”:

[and there’s plenty more where these come from]


[p.s… Previous Sunday profiles have been of: Matt, Evelyn, David, and Sean.]

Friday, May 10, 2019

Chi-i-i-i-i-i-ll Friday *

[ *  "Chill Friday" is Math-Frolic's meditative musical diversion, heading into each weekend]

(...and for Sunday another mathematician profile is in store)

Wednesday, May 8, 2019

Courtesy of Stanislas Dehaene

Another verbatim re-run of an earlier posting from this blog, for those who missed it on the first go-around:
Try this exercise, I've copied directly from another book:

"Answer the following questions as fast as you can:

-2 + 2 = ?

-4 + 4 = ?

-8 + 8 = ?

-16 + 16 = ?

Now quick! Pick a number between 12 and 5. Got it?
The number you picked is 7, isn't it?"

...I succumbed to this piece of 'mindreading' when I read it in Stanislas Dehaene's 1997 "The Number Sense: How the Mind Creates Mathematics." Did you?
He calls this a "demonstration of the automaticity of arithmetic memory" and explains it thusly:
"How did I read your mind? The mere presentation of the numbers 12 and 5 seems enough to trigger an unconscious subtraction 12 - 5 = 7. This effect is probably amplified by the initial addition drill, the reversed order of the numbers 12 and 5, and the ambiguous phrase 'between 12 and 5' that may incite you to compute the distance between the two numbers. All these factors conspire to enhance the automatic activation of 12 - 5 up to a point where the result enters consciousness. And you believed that you were exercising your 'free will' when selecting a digit!"
I'm not sure I find Dehaene's explanation completely satisfactory... but, I can't argue with the effect, which I did fall for.


Sunday, May 5, 2019

3 Varied Books... for thy reading pleasure

Just a filler post today to pass along 3 non-math books I’ve perused/enjoyed lately:

1)  (Physicist) Paul Steinhardt’s “The Second Kind of Impossible” is one of the more interesting (to me) popular physics volumes I’ve seen for awhile. Partly because it entails a bit of adventure along with the science/physics, but also because its main focus, quasicrystals, isn’t covered that much in other works. Since quasicrystals leads into a lot of discussion of symmetry there IS some mathy feel to parts of the text as well. The book gets away from some of the cosmology debates that frequent a lot of popular physics writing these days (though with that said, I did also enjoy Sabine Hossenfelder's "Lost In Math" volume). Steinhardt is an award-winning Princeton theoretical physicist well-known for offering alternative notions to the popular 'multiverse' view of cosmology.

2)  No doubt many of you will agree with me that the greatest living writer of English literature is Dave Barry ;) and his latest work, “Lessons From Lucy” is a must read for all dog lovers, probably all pet lovers, and generally lovers of fine literature everywhere, or simply those in need of a little self-help philosophy-of-life.  Dave, now past 70, recounts lessons he’s learned about life from his mutt Lucy. Hysterically funny, in patented Barryesque-style, though with a final section (about a family matter) that completely veers off in an unexpectedly different, but poignant and touching, direction and tone. Just perhaps more 'self-help' available in this little volume than in many books approaching the topic more seriously.

3)  William Poundstone is among my favorite popular writers, in part because he often deals with topics related to human cognition that interest me. Somehow I missed his 2016 volume, “Head In the Cloud” which basically reviews the ‘shocking ignorance’ of citizens in today’s world, with a lot of focus on the much-cited “Dunning-Kruger” effect. He has recommendations to improve the situation, but, given that the book came out in 2016, I have to wonder if he still sees hope after watching Trump get elected in November of that year! There are lots of examples and surveys (some of which I was a bit skeptical of), and I very much enjoyed the book overall (it's my favorite of the 3 mentioned here), though it bogged down a bit toward the end. It was timely, if not prescient in 2016, and just as timely now. I mean we humans need to be reminded repeatedly what doofuses we are.
[On Wednesday, by the way, I posted about one question posed in the volume.]

Anyway, I recommend all 3 of these books, varied as they are.

[For next Sunday another mathematician 'profile' is in the works...]

Friday, May 3, 2019

Chi-i-i-i-i-i-ll Friday *

[ *  "Chill Friday" is Math-Frolic's meditative musical diversion, heading into each weekend]

Wednesday, May 1, 2019

Pushing A Button?… (ethics)

After some jest on Sunday, a bit more serious entry today....
Recently I mentioned on Twitter a simple survey question that William Poundstone reports at the very end of his 2016 volume “Head In the Cloud,” which runs as follows:
Would you push a button that made you a billionaire but killed a random stranger? No one else would know you were responsible for the death, and you could not be charged with a crime.
Poundstone says that close to 20% of survey responders answered yes to this query, which I honestly thought was surprisingly low. I haven't seen the origin or actual survey this question was a part of, but would like to know more details about it, like the sample size, and any breakdowns by gender, age, economic class, geographic region, etc. It’s hard for me to believe there wouldn’t be significant differences between some possible categories. (If anyone happens to know more about the specific survey Poundstone was referencing, and there’s a link to it somewhere with more details, let us know.)

On a side-note, when I tweeted this out Jim Propp let me know that the question is very similar to one posed in a wonderfully entertaining Twilight Zone episode written decades ago based on a Richard Matheson story. In fact the Poundstone version seems like just an updated, modified take on it. (If you've never seen it, and especially if you're a Twilight Zone fan, give the episode a view!)

The question is similar in nature to the various “trolley car” problems posed in psychology/philosophy to test ethical conundrums (I think there’s even a term for thought experiments of this genre, but it currently escapes me?). The trolley car varieties can trudge into difficult, debatable ethical quandaries. I think on the surface, Poundstone’s inquiry strikes people as less ethically ambiguous, because it seems as if greed is simply motivating one to kill someone. But I don’t think it’s that easy.  One can argue that with a billion dollars one could do a lot of good in the world, that might go undone save but for this one random death, completely apart from any joy the dollars may bring the recipient… and of course everyone is going to die anyway, you are simply altering the timing (and perhaps even giving a humane death to someone who would otherwise suffer). Possibly the random person will be a truly horrid individual who brings great harm to others; or a sickly or elderly person very near death anyway (of course, possibly not). If you think along certain lines (trying to justify pushing the button) than does the whole equation change if for the same billion dollars, 10 random people, or 100, will die? 1000? Or what if instead of a billion dollars, you receive only 1 million, or (as in the Twilight Zone episode), $500,000? Obviously LOTS of possible tweaks.
What if you know that half the adults in the world are all being simultaneously given this same option... does that change your decision? Or, all adults?
So many ways to modify the question slightly that might alter any given individual’s response (HERE'S one pretty comical version I found on the Web). I suspect some folks think they would never push the button, that their ethical standards are too high to do so. But what if instead of a random person being killed, it’s say a random monkey, cow, dog, horse, etc. — I suspect that may change the decision for many people… but should it, really? 

A lot depends of course on how one views death and the preciousness of (human?) life (which in Western culture especially, tends to be an automatic assumption, but again, should it be?); and of course religious thought/indoctrination enters into it. Still, in reality we exist in a crass world where pragmatics take precedence over strict ethics throughout daily routines (probably far more than we realize or dare admit). Strictly speaking, I’d contend that very few of our decisions during waking hours are ethical ones, but instead selfish ones (not that 'selfish' and 'ethical' can't coincide sometimes). "Red in tooth and claw" is a phrase commonly applied to nature (animals), but, at least in a metaphorical sense, perhaps applies equally to human activity as well. "Altruistic" behaviors do of course occur, but principally, humans act in their own personal (or loved-ones') best interests, often to the detriment of others.

Anyway, for whatever reason, I find 'the button' an interesting abstract thought experiment.  Worth noting too, that increasingly 'trolley car' type problems, have 'real life' consequences, with driverless cars being produced right now that must include software incorporating 'ethical' decisions.  And humans will write that software. 'Ethics' will become a product of corporate focus groups (not that it hasn't been the 'product' of religious and legal groups in the past). Theoretically, ethics should be reducible to algorithms... or... should it? 

I've long thought that in another century "privacy" simply won't exist any longer except as a quaint forgotten (almost laughable) concept in student history books. Am beginning to wonder the same thing about "ethics." :(  Will 'ethics' be so built into the zeroes and ones of AI that it no longer exists as a subject of contemplation or debate? Luckily, I won't be here to find out ;)
(...but hey, maybe once again, the current Administration and its ethical-void is simply weighing too much on my mind.)