INTHITS 2: Franzen Need

There are two types of climate denialism. The first type, practised by Liberals and Republicans and Murdoch hacks, is to deny the science, to deny that humans have been and are continuing to heat the planet in an unsustainable manner. The second type, practised by pretty much everyone else, is to deny the politics and the psychology, to deny that human society appears incapable of altering its behaviour sufficiently to deal with scientific reality.

The New Yorker has just published an essay by Jonathan Franzen on this second type of denialism, on the refusal to confront our current and impending death. Franzen’s essay is gentle, heartfelt, pleading and depressing. The essay, along with its author, has also been condemned far and wide.

Franzen’s essay has not convinced me that we are doomed. Much more convincing has been the vicious and fundamentally empty response, which does nothing so much as to prove Franzen’s point.

VCAA’s Mathematical Reasoning

OK, Dear Readers, turn off the footy and/or the cricket. You have work to do.

We have written before of VCAA‘s manipulative “review” of Victoria’s senior mathematics curriculum, complete with scale-thumbing, push-polling and hidden, hand-picked “experts”. Now, according to their latest Bulletin,

[t]he VCAA will undertake a second phase of Stage 1 consultation …

Good. With any luck, the VCAA will subsequently get stuck on the nth phase of Stage 1, and Victoria can be spared their Potemkin Mathematics for another decade or so.

Still, it is strange. The VCAA has indicated nothing of substance about the results of the first phase of consultation. Why not? And, what is the supposed purpose of this second phase? What is the true purpose? According to the VCAA, one of two reasons for Phase Two is

to further investigate [t]he role of aspects of mathematical reasoning and working mathematically in each of the types of mathematics studies.

(The second reason concerns “Foundation Mathematics” which, try as we might, we just cannot pretend any interest.)

As part of this new consultation, VCAA has posted a new paper, and set up a new questionnaire (and PDF here), until 16 September.

And now, Dear Readers, your work begins:

  • Please fill in the questionnaire.
  • Please (attempt to) read VCAA’s new paper and, if you can make any sense of it whatsoever, please comment to this effect below.

We suspect, however, that this is all a game, disguising the true purpose of Phase Two. It’d be easier to be sure if the VCAA had reported anything of substance about the results of Phase One, but we can still hazard a pretty good guess. As one of our colleagues conjectured,

“There was probably sufficient lack of support [in Phase One] for some radical departure from the norm, and so they will take longer to figure out how to make that happen.”

That is, although the VCAA’s nonsense received significant pushback, the VCAA haven’t remotely given up on it and are simply trying to wait out and wear down the opposition. And, since the VCAA controls the money and the process and the “experts” and the “key stakeholders” and the reporting and everything else except public sentiment, they will probably win.

But they should be made to earn it.

WitCH 21: Just Following Orders

This WitCH come courtesy of a smart VCE student. It concerns the newly instituted VCE subject of Algorithmics, and comes from the 2017 exam:

The Examiners’ Report indicates that half of students gave the intended answer of A, and notes

It is important for students to understand that Big-O notation describes an upper bound, and so is only used for analysis of worst-case running times.

Have fun.

WitCH 20: Tattletail

This one is like complaining about the deck chairs on the Titanic, but what the Hell. The WitCH is courtesy of John the Merciless. It is from the 2018 Specialist Mathematics Exam 2:

The Examiners’ Report notes the intended answer:

H0: μ = 150,   H1: μ < 150

The Report indicates that 70% of students gave the intended answer, and the Report comments on students’ answers:

The question was answered well. Common errors included: poor notation such as  H0 = 150 or similar, and not understanding the nature of a one-tailed test, evidenced by answers such as H1: μ ≠ 150.

Have fun.

Which WitCH is a WitCH?

It seems it might be worthwhile itemising the outstanding WitCHes, and inviting a general discussion about the WitCHES, and perhaps the blog in general. So, first to the outstanding WitCHes:

  • WitCH 8 is a jungle, that will presumably not be further unjungled. It’s still open for discussion, but I’ll update soon.
  • WitCH 10 has turned out to be very interesting. It is done, except for one (in the opinion of at least some mathematicians) major issue. There is now included near the end of the comments an (admittedly cryptic) clue.
  • WitCH 12 is not a deep one, though there are aspects that really annoy me. The absence of comments suggests others are less bothered (or more resigned). I’ll update soon.
  • WitCH 18 is a semi-WitCH, and commenters have pretty much highlighted the absurdity of it all. I’d suggest the analysis could be a bit more mathsy, but it’s no big deal, and I’ll update soon.
  • WitCH 19 has just been posted. It’s not deep, but we’ll see what commenters make of it.

Now, as to the WitCHes in general, what do people think of them? Are they interesting? Are they just nitpicking? Is there any value in them? Which WitCHes are Column A and which are Column B?

Of course I have my own reasons for posting the WitCHes, and for writing this blog generally in the manner I do. But I’m genuinely curious what people think. What is (arguably) interesting here is an (ex)-mathematician’s blunt criticism crashing into teachers’ and students’ reality, notably and unexpectedly highlighted by WitCH 10. But do commenters, and teachers and students in particular, regard this as interesting and/or entertaining and/or helpful, or merely demoralising and/or confusing and/or irritating?

To be clear, I am inviting criticism. It doesn’t mean I’ll agree (or pretend to agree) with such criticism. It doesn’t mean I’ll switch gears. But to the extent that people think this blog gets it wrong, I am willing and keen to hear, and will treat all such criticism with due respect.  (I presume and know that this blog actively irritates many people. It seems, however, that these people do not wish to lower themselves to comment here. Fair enough.)

WitCH 19: A Powerful Solvent

The following WitCH is from VCE Mathematical Methods Exam 2, 2009. (Yeah, it’s a bit old, but the question was raised recently in a tutorial, so it’s obviously not too old.) It is a multiple choice question: The Examiners’ Report indicates that just over half of the students gave the correct answer of B. The Report also gives a brief indication of how the problem was to be approached:

    \[\mbox{\bf Solve } \boldsymbol{\frac{1}{k-0} \int\limits_0^k \left(\frac1{2x+1}\right)dx = \frac16\log_e(7) \mbox{ \bf for $\boldsymbol k$}.\ k = 3.}\]

Have fun.

Update (02/09/19)

Though undeniably weird and clunky, this question clearly annoys commenters less than me. And, it’s true that I am probably more annoyed by what the question symbolises than the question itself. In any case, the discussion below, and John’s final comment/question in particular, clarified things for me somewhat. So, as a rounding off of the post, here is an extended answer to John’s question.

Underlying my concern with the exam question is the use of “solve” to describe guessing/buttoning the solution to the (transcendental) equation \mathbf {\frac1{2k}{\boldsymbol \log} (2k+1) = \frac16{\boldsymbol \log} 7}.  John then questions whether I would similarly object to the “solving” of a quintic equation that happens to have nice roots. It is a very good question.

First of all, to strengthen John’s point, the same argument can also be made for the school “solving” of cubic and quartic equations. Yes, there are formulae for these (as the Evil Mathologer covered in his latest video), but school students never use these formulae and typically don’t know they exist. So, the existence of these formulae is irrelevant for the issue at hand.

I’m not a fan of polynomial guessing games, but I accept that such games are standard and that  “solve” is used to describe such games. Underlying these games, however, are the integer/rational root theorems (which the EM has also covered), which promise that an integer/rational coefficient polynomial has only finitely many candidate roots, and that these roots are easily enumerated. (Yes, these theorems may be a less or more explicit part of the game, but they are there and they affect the game, if only semi-consciously.) By contrast, there is typically no expectation that a transcendental equation will have somehow simple solutions, nor is there typically any method of determining candidate solutions.

I find something generally unnerving about the exam question and, in particular, the Report. It exemplifies a dilution of language which is at least confusing, and I’d suggest is actively destructive. At its weakest, “solve” means “find the solutions to”, and anything is fair game. This usage, however, loses any connotation of “solve” meaning to somehow figure out the way the equation works, to determine why the solutions are what they are. This is a huge loss.

True, the investigation of equations can continue independent of the cheapening of a particular word, but the reality is that it does not. Of course, in this manner the Solve button on CAS is the nuclear bomb that wipes out all intelligent life. The end result is a double-barrelled destruction of the way students are taught to approach an equation. First, students are taught that all that matters about an equation are the solutions.  They are trained to give the barest lip service to analysing an equation, to investigating if the equation can be attacked in a meaningful mathematical manner. Secondly, the students are taught that that there is no distinction between a precise solution and an approximation, a bunch of meaningless decimals spat out by a machine.

So, yes, the exam question above can be considered just another poorly constructed question. But the weird and “What the Hell” incorporation of a transcendental equation with an exact solution that students were supposedly meant to “solve” is emblematic of a an impoverishment of language and of mathematics that the CAS-infatuated VCAA has turned into an art form.

The Moon Landing Hoax Hoax

July 20th was the 50th anniversary of Neil Armstrong’s walking on the moon. Well, maybe.

I still have vivid-grainy memories of watching Armstrong’s first steps. A random few students from each class in Macleod State School were selected to go to the library to watch the event on the school’s one TV. I was not one of the lucky few. But Mr. Macrae, our wonderful Grade 4 teacher, just declared “Bugger it!”, determined which student in our class lived closest to the school, and sent out a posse to haul back the kid’s 2-ton TV. We then all watched the moon landing, enthralled and eternally grateful to Mr. Macrae.

But did it really happen?

There have been plenty of questions and questioners, suggesting that the moon landings were faked. How, for example, is the flag in the above photo flapping, given there is no atmosphere to flap it? Then, there is the fake photo of astronauts playing golf on the moon. And the lack of stars in moon photos. And the killer radiation that didn’t kill. And the strange links to Stanley Kubrick. And on and on.

Can all this evidence of doctoring be discounted? Did Man really walk on the moon?

The answers, of course, are Yes and Yes.

The idea that the moon landing was faked is completely ridiculous, and it takes a wilful stupidity to believe it. Which includes about 5% of Americans, and 10% of millenials. (The funniest take is that Kubrick did indeed stage the moon landings, but he was such a perfectionist that he went to the moon to do it.)

There is more to this story, however, than a bunch of conspiracy clowns and gullible slobs. As the brilliant Matt Taibbi writes, there is, indeed, plenty of sleight of hand going on.

The important question is why so many people are willing to believe something so patently false? The answer must be some combination of an inability to discern truth with a lack of concern for truth. And why might that be? Well, just perhaps one factor is an extended history of media and government authorities willing to misdirect and to obfuscate and to flat out lie about everything else. Just perhaps people don’t trust authorities because authorities have abused people’s trust for too long. As Taibbi writes:

“… the flowering of conspiracy theories has an obvious correlation, to a collapse of trust in institutions like the news media and the presidency. … It’s simple math. You can only ask the public to swallow so many fictions before they start to invent their own. The moon story is a great illustration.”

Which is a huge problem. It doesn’t matter a damn if people believe moon landing conspiracy crap. But if they believe that crap then they’ll also believe, more easily, climate change conspiracy crap. And then, an authority that has lost authority is powerless to convince them otherwise. And then, we’re doomed.

But at least we can laugh at the dumb slobs while the Earth goes down in flames.

And It’s One, Two, Three …

A new country, and the same old psychopathic war mongers, the same old compliant Christian soldiers, and the same old moronic media cheerleaders.

UPDATE (25/08/19)

And so it begins. Gung-ho Morrison and his moronic Foreign Minister, supported by Labor thugs, and sycophantically reported by stenographic stooges, sends Australians off to the Gulf of Tonkin, or wherever, for yet another episode of Middle Eastern idiocy.