The World According to Bret

The world is really complicated. I can't figure it out anymore. That's one reason I haven't been blogging much. I find myself unable to put together any coherent arguments with sufficient context to make sense to anyone including myself.

Consider the following image:

You've probably seen this illusion before or at least one like it. The two circles are the same color (yellow). Yet they look completely different because of the context. And the context is kinda similar: a bunch of greenish and purplish stripes.

I subscribe to only one newspaper: The New York Times. It's somewhat left of center in the political spectrum of the United States. I read a number of blogs, most of them to the right of center.

What is striking to me is the difference in context between the left of center New York Times and the right of center media that I read. They can take the exact same yellow circle and make it look completely different.

A trivial example is "mostly peaceful protests." If you have 100 protestors and 95 of them are perfectly peaceful and 5 are not peaceful, it is, by definition, a mostly peaceful protest. Indeed, it's 20 times more peaceful than a protest in which all 100 people were not peaceful.

Now we can build a context around the "mostly peaceful protest." We can focus on the 95 peaceful protestors and their message and their treatment by their ideological opposition and by police and authorities. Perhaps they were tear gassed. Perhaps the were forced to stop protesting. Perhaps they have a very important message that's being stifled. And so forth.

Or our context can be what the 5 not peaceful protestors are doing. Perhaps they're attacking police. Perhaps they're burning dumpsters or even buildings. Perhaps there's other violence: arson, rape, even murder. Our context can be full of the lawlessness and chaos of the non peaceful protestors and can be quite frightening. And so forth.

Same story either way, but radically different contexts which causes radically different optics and impressions.

When I was 15 I was a communist. At 30 I was a libertarian. At 45 I was sort of a conservative. Now? I'm the devil's advocate. Whatever you tell me, I have a strong inclination to argue the opposite. Fortunately, I've also learned to mostly keep my mouth shut because, let me tell you, always taking the other side doesn't tend to make a lot of friends!!

When advocating for the other side, I often am told, "I can't fathom why you believe X, I've just provided evidence that contradicts it!!!!" But that evidence is like the circle above. I said the circle is yellow and they showed me a circle that looks orange within their context, within their perspective, the context on the left. To me the circle looks (or at least can look) yellow, because I can see the circle within the context on the right.

I often try to estimate how many (English) words it would take to fully describe an issue. For example, I estimate that to fully describe race relations in the United States with complete context would be more than a trillion words. I've perhaps read a million words on the subject and based on that extremely incomplete yet still significant knowledge I have developed a certain feel/intuition about the subject.

If you now show me a one-thousand word article that doesn't match that intuition, it's not gonna affect me all that much. Why? First, like every human I suffer from confirmation bias and I tend to discount things that don't fit within my worldview. Second, even if I get over my confirmation bias, you've shown me one-thousandth the information I've already processed, a lot of it already in conflict, so it wouldn't make sense for me to suddenly ignore everything I "know" and adopt a completely new perspective based on this small new bit of evidence you've shown me. Third, while your new information looks like an orange circle within the context you've provided, I probably don't share that context so the circle looks yellow to me.

To put it another way, I know a millionth of what there is to know about race relations, you then showed me a billionth of what there is to know, and either way we'll both continue to swim in a vast sea of ignorance regarding that particular subject with alarmingly incomplete and distorted contexts. Oh sure, I may be off by a couple of orders of magnitude with my estimates but the gist remains the same.

That's one subject. There are millions of subjects with similar complexity so that sea of ignorance becomes a universe (multiverse?) of ignorance.

Given that ignorance is bliss, I'm apparently so blissed out that I'm unaware of it!

Have a blissful day!

In The Latest Critter News ...

... Rats taught to drive tiny cars to lower their stress levels.




The most important part of this bizarre story: "The rats were not required to take a driving test at the end of the study."

However, I'm wondering, did any of the rats suffer from road rage?

In the Wilds of San Diego

I ran into my friend Tom while mountain biking today ...

... My friend Tom T. Tarantula.

(It be more accurate to say I almost ran over Mr. Tarantula).

Text Me Merry Christmas

It's the least that you could do!

More Computing Efficiency

Not only have computers gotten exponentially faster per dollar, they've also gotten amazingly more energy efficient:

Over the past 60 years, the energy efficiency of ever-less expensive logic engines has improved by over one billion fold. No other machine of any kind has come remotely close to matching that throughout history.

Consider the implications even from 1980, the Apple II era. A single iPhone at 1980 energy-efficiency would require as much power as a Manhattan office building. Similarly, a single data center at circa 1980 efficiency would require as much power as the entire U.S. grid. But because of efficiency gains, the world today has billions of smartphones and thousands of datacenters.

Of course an iPhone would have been impossible to build at any price in 1980 and even if possible would have required the space of an entire Manhattan office building!

The Worst Is Yet to Come

That's the subtitle of an article in The Atlantic. That may well be - we'll see. The surprising part is that my mother sent me the link to the article. I think my response to her is somewhat entertaining so here it is:

Hi Mom,

I didn't know you were such a political animal! I'm not much of a political animal anymore and probably wouldn't've even read this article if it wasn't you who sent it.

You'll probably find it kinda funny, but the sentence that caught my eye most in the entire article was this one:

"These kinds of views [all political] make it difficult for me and some of my New Year’s [from decades past] guests to speak about anything at all [anymore]."

Really? Political views make it impossible to talk about the weather? About your favorite restaurant? About a cool new jazz song you heard? About your family? About going for a bicycle ride? And a million other things?

One thing I really, really like about barbershop singing is that, via the Barbershop Harmony Society rules, discussing politics (and religion) is forbidden at all official society meetings (which includes rehearsals). Yet somehow, hard as it is to believe, we still find things to talk about! Even stuff other than barbershop music, though that topic does feature prominently. It really is possible to have friendships and positive collegial interactions without ever even knowing each others' preferred ideologies! Who'd have thunk it!

Outside of official rehearsals, political discussions are allowed. One singer was complaining about Trump and racists and fascists and nazis to which I mostly just politely listened. At one point he asked if I would "sing with a Nazi." I said, "Of course. I'll sing with anybody, anytime - any race, any religion, any gender, any ideology. Singing is separate and above all that. Besides, it's not like not singing with this hypothetical nazi would somehow change him (or her) into a non-nazi. Indeed, the opposite is plausible - that he'd see me as a human being even though I'm of jewish ancestry and soften his nazi beliefs because of the singing together. Isolating said hypothetical nazi will do nothing good and probably just make him more extreme."

This singer quit shortly after that and at least partly because any organization that accepted folks like me who would even contemplate hypothetically singing with a nazi was evil (even though he'd readily admit that I wasn't a nazi) and he wanted no part of that. Too bad, because he was a really good singer and his leaving the chorus has noticeably damaged it. If that's my fault, then oops!

To me, the fundamental problem underlying every problem discussed in the article is the inability or unwillingness of people to even talk (or sing) with others if they don't have the same professed ideology.

Yet politics is really not that important. Vote for who you think is best and speak out if you must, but beyond that it's so much less important than almost everything else in life. Ten or twenty years ago I was complaining about some politician or other and a friend asked, "So has this politician really had a major direct impact on your life? I mean other than the mere fact of his existence pisses you off?" It was a good question and the answer was no, it really didn't much affect me. Indeed, my being annoyed about whatever it was negatively impacted me far more than any of the actions or policies of the politician. In fact, none of the presidents or congresses of my lifetime have made any provable substantial difference to me. Have they made a difference to anybody? Of course, they're always winners and losers. But to me, not really much of a difference and far less difference than more immediate events. At that point I decided it was really silly to take political stuff so seriously. I'll do my homework and vote and that's it.

And I'll sing with whoever wants to sing with me!

Photobombed by a Seagull

Here I was, just trying to take a nice sunset picture for your enjoyment and I see I was photobombed!

Ah well, consider it an action shot sunset:

Damn, I must be transforming into a Leftist! Now I agree with something Noam Chomsky said regarding Russia interfering in the 2016 (and other) elections!

It’s a pretty remarkable fact that—first of all, it is a joke. Half the world is cracking up in laughter. The United States doesn’t just interfere in elections. It overthrows governments it doesn’t like, institutes military dictatorships. Simply in the case of Russia alone—it’s the least of it—the U.S. government, under Clinton, intervened quite blatantly and openly, then tried to conceal it, to get their man Yeltsin in, in all sorts of ways. So, this, as I say, it’s considered—it’s turning the United States, again, into a laughingstock in the world.

Of course Russia interferes in our elections! Of course many other countries do as well. And, of course, Chomsky is quite right that we interfere in other countries all the time.

I still personally dislike Chomsky since I think he personally set natural language processing and semantic analysis back decades, but in this case I think he's right.

My New Favorite Word

dithyramb

[dith-uh-ram, -ramb]

noun

1. a Greek choral song or chant of vehement or wild character and of usually irregular form, originally in honor of Dionysus or Bacchus.
2. any poem or other composition having similar characteristics, as an impassioned or exalted theme or irregular form.
3. any wildly enthusiastic speech or writing.

-----

I saw it in the following paragraph:

Having produced not one iota of discovery in this criminal case the unlawfully appointed Special Counsel requests a special and unprecedented blanket protective order covering tens of millions of pages of unclassified discovery. Having made this special request based on a secret submission to the Court and a hysterical dithyramb about the future of the American elections, one would think that the Special Counsel would cite to case holdings that support this remarkable request. But no, instead, the Special Counsel seeks to equate this make-believe electioneering case to others involving international terrorism and major drug trafficking, and relies only on irrelevant dicta from inappropriate, primarily out-of-circuit cases. In short, fake law, which is much more dangerous than fake news.

When you've lost Ann Coulter...

She wrote a book called "In Trump We Trust", yet she nowadays is only one tweet away from asking for his impeachment:

It was four nights after Coulter had aimed a bitter Twitter blast at the 45th president of the United States—who had complained last Friday, after signing the $1.3 trillion omnibus spending bill that contained generous funding for liberal social and cultural programs favored by Democrats, including the Corporation for Public Broadcasting, but zero dollars for his vaunted wall, that he would never do such a thing again.

“Yeah, because you’ll be impeached,” Coulter had tweeted to her 1.94 million followers, one of whom is Trump. (Later during the debate, she repeated a report that the president was seriously considering vetoing the spending legislation, but after White House chief of staff John Kelly explained that such a veto would mean missing his planned weekend at Mar-a-Lago, Trump said “f--- it!” and signed the bill instead.)

Of course, it is not easy to defend Trump and yet be coherent with any system of thought, if we can be kind enough to call her Nativism as such, given Trump is so erratic a thinker (again, I am very kind). It is then no surprise she nowadays hedges like this:

“I knew he was a shallow, lazy ignoramus, and I didn’t care,”

Well, I can't quite agree the man is lazy - he could be spending all of his time in Mar-a-Lago,  like any other good Floridian retiree, yet he is out there making the biggest reality show we've ever seen. No, lazy he is not.

At least Mrs. Coulter, sad as she is because that Wall keeps not coming, can still keep her sense of humor:

So you are in favor of giving the president a spanking?” Long quipped—the night’s only reference, and a veiled one at that, to the Stormy Daniels situation.
At which Coulter laughed and said, “I do not remind him of his daughter!”

The Precarious Future of Jobs

When someone quotes a dubious statistic in conversation, I often reply by interjecting the somewhat humorous, "Did you know that 47% of all statistics are made up on the spot?" I always use 47% as the made up number - it's a nice prime number and has a good ring to it in my opinion.

So I almost always chuckle when someone puts forth 47 percent as an actual statistic. In this case:

...a now-famous Oxford University analysis forecasted that 47 percent of all jobs are threatened in the United States [by robots and automation].

Yup, that definitely elicited a chuckle. Yet while the exact percentage of jobs that are threatened is of course completely unknown and the statistic is meaningless in any case without a timeframe associated with it (threatened by next week? Next year? A million years?), the concept is serious and perhaps deadly serious.

As a roboticist, I do see automation based on AI and increasingly intelligent and flexible computing accelerating. For example, autonomous vehicles alone could replace several million workers within ten years (maybe more, maybe less, who knows?).

I predict my company of 4 people will eliminate thousands or maybe even tens of thousands of jobs in agriculture over the next 5 years. And the problem is that as workers move to new jobs, we'll end up automating those too, making it difficult for them to ever get back to a stable job situation. That's potentially different than in the past. Sure, buggy whip workers lost their jobs once upon a time but then went on to work in the automobile industry which was stable for the rest of their careers. Maybe new industries and opportunities will develop as old jobs are automated away, but it looks to me like the destruction of jobs in Schumpeter's Creative Destruction process will far outpace the creation, especially the creation of lower to middle skilled occupations.

While automation could promise ever more plentiful availability of goods, it's possible that we'll face widespread poverty as more and more workers find it impossible to land stable and reasonably well-paying jobs. One straightforward way of mitigating that is the Universal Basic Income where all citizens get a fixed monthly stipend, no strings attached. That would at least keep people from starving in the streets. And if so much is automated and there's so much wealth being produced, the UBI would be easily affordable.

But what about work itself? Can humans live without working? Or is work part of what humans need to be fulfilled? Are idle hands the devil's workshop? Will opioid and other drug addiction become even more widespread? Will all these things lead to the collapse of civilization?

Or will we all become barbershop quartet singers (I'm the guy on the right) and live happily ever after?

Impeachment

Consider the following excerpt from a recent article.

Imagine America had as its president a man manifestly unfit by character and temperament to hold such an important public trust and exercise the important constitutional powers of the office. The president’s conduct in office had demonstrated him to be racist, mercurial, intransigent, personally crude, obsessed with his own public image and perceptions of his authority and success, and prone to intemperate public tirades, heaping abuse upon political enemies, the press, and all who opposed him. 

As president, he expressed sympathy for – at times even seemed to side with – the nation’s avowed enemies: persons and forces that until very recently had been the nation’s overt military adversaries and who still sought to undermine America’s political system. He collaborated openly with such persons. He offered excuses for vicious racists – and uttered some distressingly racist remarks himself – as he failed to protect a large swath of the American population from racial violence, intimidation and oppression at the hands of private parties. He blamed the victims, as much as the perpetrators – for supposedly having pressed too far and thereby provoked the retaliation that fell on their heads.

... He arguably abused the power to fire subordinates, removing or seeking to remove from office those who would not pliantly carry out his wishes to defy or disregard the law. He valued personal loyalty to him above all else and seemed indifferent to competent service to the nation. As shocking as it might sound, many judged the president unfit to issue direct commands to the military – impulsive, capricious, erratic and thus potentially dangerous.

He was an intemperate bully. He was politically artless and witless. But he was a snazzy dresser, or so he fashioned himself.

A couple of days ago was the 150th anniversary of the impeachment of Andrew Johnson and the above excerpt was describing him (just in case you thought it might have been describing a different president).

The most interesting thing about the article to me is that, according to constitutional scholars, the phrase "high crimes and misdemeanors" need not be linked to a specific crime but can instead include the president's overall character and conduct. That was the first I had heard that.

The article also served to remind me that bad presidents (and other politicians and bureaucrats) have not been vanishingly rare, but simply do come to power from time-to-time. Yet another reason that checks and balances are so important.

Anagram of the Month

Did you know than an anagram for "The New York Times" is "The Monkeys Write"?

A remarkable coincidence!

US Culture Becomes More Absurd By The Day

This one is from the "you couldn't make this stuff up" category and is so absurd that I've been diligently waiting for Snopes to say it's a hoax but as of right now, it seem to be legitimate.

The first part of the story is straightforward - nothing unusual here:

Apple’s first-ever vice president of diversity and inclusion, Denise Young Smith, is leaving Apple at the end of this year, TechCrunch has learned. Young Smith, who has only been in the position since May of this year, previously served as Apple’s head of worldwide human resources for three years.

So why did she leave? Perhaps because Ms. Young Smith, a black woman, made an interesting comment at the One Young World Summit earlier this year:

... there can be 12 white blue-eyed blonde men in a room and they are going to be diverse too because they’re going to bring a different life experience and life perspective to the conversation.

I'm neither blue-eyed, nor blonde, but I can't say that I disagree with that, at least not strongly.

Nonetheless, Apple and Ms. Young Smith have parted ways, perhaps because a diversity and inclusion expert really ought not say such things in this day and age. Here's the funny take on it (by a black columnist, in case that matters):

I am not saying that God, the universe, Rihannayoncé or whoever you worship as a higher power is petty, but in one of the most hilarious twists of fate ever, Apple’s vice president of inclusion and diversity, Denise Young Smith, who once whitesplained how hiring 12 white, blond, blue-eyed men could actually be seen as promoting diversity, has been replaced.

By a blond, blue-eyed white woman.

:-)

Ho-hum San Diego Sunset

Now that Irma (and Harvey before her) have dissipated, we're back to what I lovingly and jokingly call "ho-hum sun in a clear blue sky sinking into the ocean sort of sunsets."

They're beautiful, for sure, but not the knock-your-socks-off jaw-dropping sunsets that we had during the hurricanes.

Don't worry, soon I'll stop spending so much time watching sunsets and I'll write a real post for this blog.

Homophobia

"Homophobia" is an interesting word and in my opinion has evolved in a way that muddies the relationship in society between gays and non-gays. Let's start with phobia:

phobia

noun

1.a persistent, irrational fear of a specific object, activity, or situation that leads to a compelling desire to avoid it.

"Phobia" is derived from Phobos, the Greek god of fear, and virtually every phobia definition defines some fear. For example, acrophobia is "a pathological fear of heights," nothing more, nothing less.

But homophobia is doesn't fit the pattern:

homophobia

noun

1.unreasoning fear of or antipathy toward homosexuals and homosexuality.

Suddenly "antipathy" is added to "fear" and the British definition from the same page pushes it further: "intense hatred or fear of homosexuals or homosexuality" with "intense hatred" coming before "fear." It's probably not uncommon to hate that which one has a "pathological fear" of, but it's far from inherent and that brings me to today's story.

Once upon a time, long ago (summer of 1980) and far away (in Boston, Massachusetts), when I was still in college, I was invited to a party with free beer, and being a young college party animal, free beer was a huge draw. The party was thrown by the friend of a girl friend of one of my friends. That's pretty indirect, but there was free beer. The party thrower was one of five housemates. Two of the housemates were gay males, the other three were not and it was planned as a party mixing gays and non-gays with free beer. So, enticed by free beer, a group of seven of us decided to attend.

At the last minute, the three non-gay housemates pulled out of the party, making it a gay party. Or more accurately, a party with 80 gay guys and the seven of us non-gay, intrepid, free-beer seekers. Since we had absolutely nothing against gay guys, we decided to go anyway. Did I mention free beer?

We went to the party and we talked to various gay party goers for a while and we eventually retreated to hanging about the keg. The keg was at the edge of a dance area. As the party progressed, the gay guys started dancing and it was no big deal. Then they started slow dancing. Then, while slow dancing, they started kissing and grinding and fondling. And two guys at a time would head into a bathroom at the edge of the dance floor for a minute or two before emerging with smiles on their faces.

Suddenly, I had a overwhelming panic attack and found myself literally running out of that house. I couldn't stop to tell any of my friends I was leaving nor could I stop to say goodbye to the hosts and thank them for the free beer. There was no hate involved. There was simply overwhelming fear - in other words, a phobia.

I found what happened next quite interesting. There I was, quite surprised at my reaction. After all, I had intentionally gone to gay party because as far as I knew, I had no problem with any aspect of homosexuality. "All sex is good sex" had been one of my frequent (and apparently naive) sayings up until that point.

So there I was, miles from home, in the days before cell phones so I couldn't let anybody know that I left, my ride was still at the party and as a poor student I couldn't afford a taxi, so I was readying myself for a long walk home.

I looked up as I was getting ready to walk, and there were two of my friends on the sidewalk who had left the party before me. The same thing had happened to them - they had also completely freaked out and exited the party at a rapid pace without telling anyone else. We were trying to decide what to do when out of the door came two more of our friends with panicked expressions on their faces (it was comical) and fortunately one of them was our ride. We exchanged our embarrassing stories with lots of nervous laughter (ok, I'll admit it, we were giggling like junior high girls) and decided to do "rock, paper, scissors" to determine which two of us would somehow find our courage to go back inside to the "scary gay party" (yes, we knew how unbelievably ridiculous that sounds) to let the last two of our friends know that we were leaving and if they wanted a ride, now was the time to say goodbye to the free beer and the rest of the party. Fortunately, before we even finished "rock, paper, scissors" the last two friends exited the party. They weren't particularly panicked but admitted to "significant discomfort."

Seven out of seven.

Seven out of seven guys who intentionally went to a gay party because they were completely confident that homosexuality didn't bother them at all had negative reactions ranging from "significant discomfort" to complete panic. Maybe the two with merely "discomfort" wouldn't qualify as homophobic, but at least five of us were clearly homophobic. And this was a self-selected group that was willing to go to a gay party. Seven out of seven in this self-selected group indicates to me that our reaction isn't terribly unusual or abnormal. I believe that the majority of homophobia is simply like that which happened here.

There was no hate. None of us hated gays. I don't hate gays now. I just panic or feel fear when seeing gay physical intimacy. At this point, I've been sensitized, so I feel mild panic when I see a couple of guys with arms around each other or even holding hands. I realize that's totally my problem just like my fear of heights (which isn't quite a phobia - I go rock climbing for example) is my problem.

It's moderately popular among some groups to hate homophobics. They think that they're hating haters, an attitude which I think has some problems anyway because it legitimizes hate. But I'm not a hater and I have no more control over my reaction to homosexual physical intimacy than gays have control over being gay. Yet I'm supposed to support them, but they and their supporters are supposed to revile me. And when I tell this story to those that revile me and those like me, they simply call me a liar and continue their hate.

Ah well, nobody said life was fair.

Trump Accidentally Coins a New Word

Covfefe: ('Co-VEH-Feh') adj. The state one finds oneself as the Ambien you took 20 minutes ago when you got into bed interacts with the two glasses of wine you had for dinner, resulting in late night half-finished or nonsensical social media postings.

Example: "he was completely covfefe when he wrote that tweet"

========================

Also, an excellent name for a dog.

Adversaries

It's no secret that Trump hates the press (and the press hates him right back). Continuing his adversarial relationship with the press, tonight at his Florida rally, Trump said:

"Nothing can be believed which is seen in a newspaper. Truth itself becomes suspicious by being put into that polluted vehicle."

Fake news and all that.

Wait! What?

He was quoting Thomas Jefferson written in a correspondence on June 14, 1807!

Huh.

I guess Presidents and the press have had an adversarial relationship for a really, really long time!

Fun With Infinity

Infinity and infinite series and sets are concepts that stretch human intuition to the breaking point and as a result, are kinda fun - for masochists. The particular infinite series I'm gonna look at today is:

S = 1 + 2 + 3 + 4 + ...

What is the value of S?

The NY Times recently had an article demonstrating that a possible answer is -1/12 (there's a more rigorous proof that shows the answer is indeed -1/12 but is beyond what I can show on a blog). I know that some of you studiously avoid the NY Times and therefore might not have seen it, so I'll duplicate it here with a little more explanation.

There's only one somewhat non-intuitive bit to the proof, so let me address that before I get started. The best illustration of this bit of non-intuition is called Hilbert's Paradox of the Grand Hotel:

Consider a hypothetical hotel with a countably infinite number of rooms, all of which are occupied. One might be tempted to think that the hotel would not be able to accommodate any newly arriving guests, as would be the case with a finite number of rooms... 

Suppose a new guest arrives and wishes to be accommodated in the hotel. We can (simultaneously) move the guest currently in room 1 to room 2, the guest currently in room 2 to room 3, and so on, moving every guest from his current room n to room n+1. After this, room 1 is empty and the new guest can be moved into that room.

What this demonstrates is that if I have two infinite sets (such as rooms and guests) with a one-to-one correspondence between each pair of elements in the sets, I can shift over all of the elements of one of the infinite sets, leaving one element without a corresponding element in the other set (room 1 in the example above), yet have all of the other elements of both sets still have a one-to-one correspondence.

Okay, we need to find the values of some infinite series. The first one is:

S1 = 1 - 1 + 1 - 1 + 1 - 1 + ...

What is the value of S1? To find an answer, we add it to itself and do the hotel room operation above (in other words, shift over one copy of the series).

2 * S1 = S1 + S1 =  1 - 1 + 1 - 1 + 1 - 1 + ...
                  +     1 - 1 + 1 - 1 + 1 - ...
                    ---------------------------
                  = 1 - 0 + 0 - 0 + 0 - 0 + ...

or, 2 * S1 = 1
therefore, S1 = 1/2

The second series we need is:

S2 = 1 - 2 + 3 - 4 + 5 - 6 ...

And we start with the same infinite shift operation that we used on the previous series:

2 * S2 = S2 + S2 =  1 - 2 + 3 - 4 + 5 - 6 + ...
                  +     1 - 2 + 3 - 4 + 5 - ...
                    ---------------------------
                  = 1 - 1 + 1 - 1 + 1 - 1 + ...

But that's the same as the 1st series that we already know an answer to:

2 * S2 = S1 = 1/2
therefore, S2 = 1/4

So now let's work on our original series. We'll subtract S2 to help us find an answer:

S - S2 =  1 + 2 + 3 + 4 + 5 + 6 + ...
        -[1 - 2 + 3 - 4 + 5 - 6 + ... ]
          ---------------------------
        = 0 + 4 + 0 + 8 + 0 +12 ..
        = 4 * [ 1 + 2 + 3 + ... ]

The right hand side is now 4 * S so rewriting we have:

S - S2 = 4 * S

or (subtracting S from both sides)

- S2 = 3 * S

Since we know S2 = 1/4, we have

- 1/4 = 3 * S

or

S = -1/12

or

1 + 2 + 3 + 4 + ... = -1/12

This sort of proof, where the sum of an ever increasing series is a negative fraction, makes some people's heads explode. I hope you're not one of them. It's just a little fun with infinity!

Bug or Feature?

Congrats to Betsy DeVos, confirmed as the Secretary of Education by literally the narrowest margin possible (Vice-President Pence had to cast the tie-breaking vote in the Senate).

One of the charges leveled against her was that she's completely unqualified to be the Secretary of Education and utterly clueless about what it takes to keep the education bureaucracy afloat.

I can't say I disagree. But is that a bug or a feature?

To me it seems like the entire education edifice is in catastrophically poor condition with kids not being very well educated and/or prepared for life as an adult even though funding has hugely increased over the last few decades. Perhaps a truly incompetent secretary of education will damage the system enough that it simply collapses and then it can be rebuilt from scratch. Especially with online and other tools improving at a rapid rate, catastrophic destruction of the whole thing may be the best way to ultimately improve it.

So, as I say, congrats, but I'm not sure if I wish her good luck or bad luck. A little incompetence coupled with some bad luck may be just what we need right now!