Tuesday, June 30, 2020

Maths learning: go figure, by Paddington

In over 40 years of teaching and tutoring Mathematics, and reading lots of studies in Mathematics Education, I have become convinced of the following:

1. Almost (*) everyone can learn more Mathematics than they currently know.
2. There is a fairly clear hierarchy of difficulty in the subject: Arithmetic, Algebra, Basic Functions, Calculus, Advanced Calculus, Real Analysis and the higher level material. Almost (*) everyone has a maximum level that they can achieve, long before the top.
3. The top level for 80% of the population appears to be Basic Algebra or lower, with only about 5% able to pass a standard Engineering Calculus I course.

Understandably, these observations have met with a great deal of resistance, especially from politicians and administrators who have read the studies that performance in college-level Mathematics classes is a good predictor of overall academic success (undeniably true). This leads to the insistence that we pass more students without lowering standards.

The people who insist that this is possible tend to fall into two categories: Those who themselves do not perform well in the subject, but blame all of their experiences on a single bad teacher, and those who found the subject relatively easy.

Large scale experiments, such as the mess in the O- and A-level syllabi in England from 1980 to 2000 show that increased pass rates mean lower achievement. In the US, cases such as the impressive improvement at Georgia State a few years ago were a result of lowered standards, but the people in charge blinded themselves to the fact.

Nonetheless, a higher percentage of jobs are now tied to higher education (including many trades), and most of the degrees in demand require levels of Mathematics far higher than Basic Algebra. We have also built an Education system which treats students as consumers, and the failure rates in Mathematics are unacceptably high to the administrators and political overseers. Never mind that those rates are close to the same across countries and decades, if not centuries.

What to do?

Form the perspective of a politician or administrator, especially one trained outside of the STEM areas, the obvious answer is to increase pass rates, and pretend to be maintaining standards.

This has been happening for decades, but it is getting worse. Be prepared for the majority of college graduates to have the paper qualifications, but not the actual abilities.

They will, however, be full of confidence in those missing abilities, thanks to the Dunning-Kruger
(**) effect, which is all that really matters.


To follow on, I would point out that one of the loudest and all-knowing groups to criticize what we did were the Engineering and Science professors.

Some decided that they could do much better, and tried to create courses which took students with the base competence to start Precalculus, and tried to get them do do Differential Equations in a semester. That did not go well.

Another group decided that our placement process was too restrictive, and insisted that they could tutor and nurture the students with weak backgrounds. Those students simply couldn't get through.

Yet another group thought that we were just too harsh, and were not getting students through to their courses. They believed the famous 'Calculus is a weeder course' meme. They encouraged students to take their Math courses at online places, or local institutions who were known to have higher pass rates (i.e. lax standards). Those students got great grades in those courses, and then couldn't pass the higher-level Engineering courses.

In short, we Mathematicians generally know what we are doing.

(*) Excluding mathematical greats such as the late Paul Erdos, Terence Tao and the like.

(**) 'The Dunning-Kruger effect is a type of cognitive bias in which people believe that they are smarter and more capable than they really are. Essentially, low ability people do not possess the skills needed to recognize their own incompetence.'

Sunday, June 28, 2020

Energy and Liberty

As the statue-rollers do their bit to help capitalism collapse under its self-contradictions, one should have thought the PC response to energy issues is 'renewable/small is beautiful'; but it seems Greenery has its own conundrums. Even Greta Thunberg is not immune from Left criticism, as witness Cory Morningstar's series on how 'Joan of Aargh!' is part of a plan to cash in on eco-investment and the charity/quango gravy train; this is a revolution that, like the French one and pace vegetarianism, threatens to eat its own children.

Nick Drew, writer at Capitalists@Work, here discusses another campaigner's idea that renewables may be a Bad Thing because of a 'power struggle' in two senses...

An important line of thought in energy matters is how coal transformed the entire world by being a very dense (and fairly convenient) form of energy.  Oil is even better.  (Google ERoEI for quantified approaches to these thoughts.)  Cheap coal and oil were the basis of industrial civilisation, and cheap electricity the basis of the modern way of life.  Oooh-errr, missus: isn't "green energy" going to be of much poorer ERoEI, and much more expensive? ... and hence, the end of civilisation as we know it?

When allied to the obvious observation that activist "greens" are generally ignorant to the point of causing despair; and those that aren't daft romantics are often outright malcontents (sometimes anarchists and sometimes malevolent & motivated anti-capitalists) - oh, and add China to the mix, because they ain't falling for this crap but we are!  -  there's scope for some fairly apocalytic visions.    Oooh-errr, missus ...

For a well-written example of this thesis my attention was drawn by our good host to a piece by one John Constable, a name that will be familiar to those who get their kicks from the very peculiar output of the Global Warming Policy Foundation.  His article is here.

Now I understand this "intellectual" line of thinking, and it's always nice to have something theoretical to worry about: but I'm deeply skeptical of it, on three immediate grounds
  • ad hominem: Constable is a deep fellow but always leaves the indelible impression he's pursuing an unacknowledged agenda
  • "Attempting to reverse this process by returning much or all of the energy system to low density flows means handing over to those who control the renewable energy sector the majority of the potential for change available to our society.  The political implications of this are terrifying, and not even public ownership of those resources could avoid the concentration of power and constriction of human freedom that would result.
  • he's dramatically (and, given his considerable knowledge, wilfully) wrong when he talks about "low density flows" as if that's anything remotely new**
Well, it's true Rebecca Long-Bailey (when shadow energy minister before GE2019) planned to hand the whole thing over to local authorities (the irony! when you see what a cock-up they make of their energy endeavours), right down to the level of parish councils and even "local communities ... of around 200 homes"; and of course all workers in the sector to be unionised.   But that ain't going to happen - anywhere.

So whom does Constable imagine has been controlling the energy system** up until now (in the open-market era, i.e. post 1990)?  The nearest UK candidates are, in broad coalition, (a) National Grid (b) Ofgem (c) HMG.  The CCC helps a bit and snipes a bit, from the sidelines: other related quangos are either more helpful (being more closely directed by government and industry) or more snipey (being "greener").  Similar in most countries.  With most aspects of detailed development / delivery / execution outsourced to private companies (and/or municipal utilities in some countries), small and large (EDF is an egregious counter-example, but doomed in its present form).  Any serious signs it's about to be handed over to Greta?  What does she know about constructing anything more weighty than a tweet?

No: as I keep saying (C@W passim): net zero carbon has gone completely mainstream now (since 2019, specifically, in my assessment).  So - it's in the hands of the engineering companies, the traditional energy companies (who ain't volunteering to go the way of the dinosaurs) as well as a rash of really creative newer engineering / technology companies, and the banks.++  Right now I'm working on a project for a gigantic "traditional polluter" whose products are vital for our way of life, whose efforts to go green up until last year were next to nil, and who now are throwing all their excellent people into really bold schemes to go zero carbon!  And when you see real, competent people working these Big (very big) Problems, it makes the idea of "handing things over to parish councils" look utterly, utterly absurd.  And despite RLB's talk of the unions taking a controlling stake in all this, whose side do you think a practical GMB man is on?   (Or Kier Starmer?)  For reasons both of jobs, and keeping the lights on, nobody in the real world will do anything other than let the big corporates do what they're doing.

Now: will our 2050 energy end up being more expensive?  Not sure.  Yes, there are huge upfront capital costs - but right now, that's surely going to be spent on Something Big, on Keynsian grounds at least, so it might as well be building clean & useful stuff.  (Plus adaptation / mitigation, of course - a key part of the 2019 breakthrough-to-mainstream.)  And the beauty of wind and solar is that once the (substantial, but fast declining) capital expenditure has been taken care of, the operating costs are wholly unburdened by the fuel costs that dominate "conventional" energy.  (Don't fret about the details like grid balancing, over which Mr Constable frequently hyper-ventilates - and I used once to worry myself, see this blog a few years ago.  It's just an engineering problem: the Grid is very good at it; lots of clever people are beavering away at it - and the costs of all that will fall, too.)

But let's suppose, as seems possible, that Chinese coal+wind+solar beats western hydrogen+wind+solar+batteries on cost.  So what?  Globalism is over!  We ain't gonna be buying our stuff from them on the same scale anymore, anyway.  Are we ..?

Nick Drew

** the whole point about the gas industry is that methane is INCREDIBLY low in energy density, (even when you freeze it to put it in ships, it's still quite poor) - but an exceptionally useful form of energy.  And so, highly specialised infrastructures (physical, financial and commercial) have long since been established to cater for this.  In many respects (although the technical analogies aren't easily mapped for non-scientists), the electricity situation is even more extreme.  Neither of these massive industries are in the hands of the Green Blob.  Anywhere.  Whatever daftness sometimes surfaces in the legislation under which they conduct their resolutely practical business.

++ OK, yes, and a bunch of chancers, con artists and would-be 'war profiteers' at the margin    

Saturday, June 20, 2020

SATURDAY ESSAY: Faked images and the arrival of Photoshop, by Wiggia

Faked or staged images have been around since the beginning of photography. Politicians were quick to seize on the possibility of promoting themselves in a more favourable light from the start of film and photographers soon got the hang of creating a ‘better’ image.

In those early days photography being in its infancy had an almost magical appeal. The use of images as in today's world was not something the man or woman of the period could have comprehended; as with the magic lantern a forerunner to cinema it was indeed magic and image makers were soon quick to take advantage of that belief.

Even today it is easy to get sucked in. The reason for this post was I emailed on a volcanic explosion viewed it was said from a CCTV camera only for me to be ‘corrected by JD who pointed out the fake was in fact a simulation video. What gave it away if I had bothered to delve a bit deeper was the fact that the volcano, Sinabung in Idonesia, was in fact a land-based volcano, and of course claiming to be from CCTV footage explains the rather surreal ending.

Some of the first fake or staged photos came from events like the American Civil War. The one of General Ulysses S. Grant is a classic:

It came from three separate negatives:

These early’fakes’ were much more enduring than those of today as general knowledge to what was going on in photo manipulation was simply not out there, seeing was believing.

The Cottingley Fairies is when you look at the images almost laughable to us today, kid's work, and it was kids who created the picture using paper fairies straight from a children's fairy tale book, yet adults believed it !


William Mumler's ghost photo using two images was another early attempt - and a successful one - to deceive.

These early deception pictures fall into the same category as bearded ladies at the fairground and eight legged dogs: most were fakes, but the public fell for it.

The one photo that is not faked but is staged, that of the workmen having lunch on a girder 840 ft above the Rockefeller Plaza in 1932, has survived as an icon of the age. The bigger mystery is who actually took the picture: two different photographers claimed or are cited as having taken it, but there is no evidence they ever did; as to the real photographer, no one knows !

Robert Capa is renowned as being one of the best war photographers of all time (and for many the best), yet one of his best known images from the Spanish civil war has always been surrounded by controversy. It depicts a man falling backwards after being shot, but again many have doubted its authenticity saying it was staged. No one has ever really proved it was fake though a local historian has years later given the background landscape to a different area to that claimed for the photo, yet again he doesn't show the alternative.

Capa  answered later to charges it had been staged by saying “In Spain you don’t need tricks to shoot photos.The pictures are there, and you just make them.Truth is the best picture.” It was his first great picture.

A similar iconic picture was the raising of the US flag on Iwo Jima in WW 11 by Joe Rosenthal. It was actually the second flag to be raised, the first was considered too small to be seen from another US strongpoint and a larger flag was then put up; this is the photo that resulted from that moment:

But even this caused a lot of controversy. Was it staged? Many said it had to be, 'too perfect in so many ways' was the most heard comment. Again the photographer denied any staging, and in war with so many hundreds of thousands of photographs taken occasionally someone gets lucky and it all falls into place. Staged or not, it has endured the test of time.

A more light-hearted picture was the Loch Ness monster of 1934. This was accepted as probably genuine for 50 years, until the truth that came out that it was a toy submarine with a hand-made and grafted-on neck, which destroyed the public's belief that a monster had ever existed. People did then, now less so.

It was known as the surgeon's photo as the owner (he did not take the photo) was a London gynaecologist, Robert Kenneth Wilson; the rest can be found here:


The use during war for propaganda purposes of fake or doctored images was fairly common. The likes of Stalin and Hitler would regularly issue pictures with individuals removed and in many cases those removed were removed permanently; but few are memorable other than for the unfortunates.

In more modern times the use of photoshopped pictures has become quite common. With modern image editing software anything is possible and it becomes increasingly difficult to tell if something is genuine or not. A combination of staging and photoshopping has been used in the recent ‘refugee’ arrivals from the middle east to the near shores of Europe.

In cases such as those the pictures are altered to an agenda, one to promote sympathy for an aggrieved people. They are shamelessly political, something any journalist photo or otherwise should not be part of, yet photo journalism is no longer the realm of the professional - and even they are swayed these days - but of also the opportunist. Digital imaging has reached the masses and alteration and photoshopping are all too easy when an agenda is to pushed.

This one is typical of a whole swathe of the type - this one, for a change, is from Georgia:

Already during the BLM protests images that are not telling the whole truth have been published, many show injured police from riots or protests from previous years and a video depicting alleged EDL thugs shouting 'f*** the police' was added on from a Chelsea football supporters' video from a couple of years back.

Even I with limited skills have faked holiday snaps. Unlike professional photographers I do not have the time to wait for the right moment or the right light or conditions; often the hour or so I have in a particular place will be the only time in my life I will be there so that moment has to do, and who would know when I show a sunny scene from far away that I have changed the sky, turned up the colours, given more sunlight to an area of gloom?

As the illusionist said ’now you see me...’ and should add 'and as never before.'

Friday, June 19, 2020

FRIDAY MUSIC: Anne Harris, by JD

The musical river never runs dry and this week's 'star' is violinist Anne Harris, another lesser known gem of a musician. I don't know much about her except to say that she is very good and seems to be at ease in so many different styles of music.


Saturday, June 13, 2020

Smashing the heathen’s idols

It is not enough to believe; you must eliminate the unbeliever. Nigel Farage’s defenestration from LBC shows how the tide of totalitarianism is flooding in ‘through creeks and inlets.’ His sin was to obey the Catchphrase maxim ‘say what you see.’

See this from the Wail, for example...

… but please don’t notice the ethnicity of the five hands-on destructors (and almost everyone else there), even though it’s much the same as the suspiciously well-prepared Umbrella Man’s. Otherwise you might think there’s a deeper agenda at work.

In the photo above, a 125-year-old statue of a man dead 300 years is rolling on its way to Bristol harbour. It was made and erected not because of his connection with slavery, but to commemorate his benefactions to the city, worth c. £15 million in today’s terms.  How embarrassing it must be to find that even villains may have their good points.

That leads us to the next stage in the process: destroying records and symbols. Our mother remembered going into her East Prussian school’s library one day after the National Socialists had taken over, and seeing gaps in the shelves where all the Jewish and socialist writers had been.

It’s an ancient strategy. At the back of every believer’s mind is the awareness that there may be an alternative belief, or none at all; this is so threatening that all such evidence must be erased. Look in Deuteronomy12: 2-3, after the conquest of Canaan:

 2 Destroy completely all the places on the high mountains, on the hills and under every spreading tree, where the nations you are dispossessing worship their gods. 3 Break down their altars, smash their sacred stones and burn their Asherah poles in the fire; cut down the idols of their gods and wipe out their names from those places.

Much later, but before the founder of Islam had even been born, two giant statues of Buddha were being constructed in Afghanistan; the Taliban (Islam’s equivalent of our seventeenth-century Puritans) blew them up in 2001. All that’s left of them is the holograms set up five years ago; perhaps something like that is the coming fate of Western liberal civilisation.

Now there is a distinction to be drawn between the statue-smashing in the UK and the USA. Many set up in the States were, so my American brother tells me, deliberate provocations by segregationists who hated the advancement of black civil rights. He refers me to James Loewen’s 1999 book ‘Lies Across America.’ I’m not surprised, then, that so many call for such monuments to be pulled down.

Here, though, it’s different: we offshored our slavery and only the profits came home. In my naivety, I long thought that Britain outlawed the trade in 1833 because of the moral force of the abolitionists’ arguments; I didn’t know about the massive financial compensation paid to estate-owners who had until then struggled to waste on architecture, art, drink, whores and gambling the annual fortunes it had brought them. It took the Treasury until 2015 to extinguish the debt for that payoff

Having said that, what’s taught in schools about the slave trade is myopic. I remember the horror of a nice black girl in a class I was teaching when I explained to her that the slavers didn’t simply hunt down their prey, they bought them from West African chiefs. Even now, not all West African nations have apologized unreservedly for their part in this atrocious business. Also, schoolchildren need to be aware of Thomas Sowell’s startling statistic that

‘More whites were brought as slaves to North Africa than blacks brought as slaves to the United States or to the 13 colonies from which it was formed. White slaves were still being bought and sold in the Ottoman Empire, decades after blacks were freed in the United States.’

… and that slavery still goes on around the world, on a big scale. 

Yet, how fast have the current protests spread! It is almost as though some people have been preparing for revolution for a long time.

They have. I recall from the Seventies a graduate student at Oxford, living from one Social Sciences Research Council grant to another, telling me obvious things about society’s power structures. Another college acquaintance went to work at the Cowley car plant after graduating, to spread the Marxist message to fellow workers on the production line – they beat him up several times, but he persisted and they started to listen, he told me. Some Communists held that political action betrayed a lack of faith in the inevitability of the classless society, so I remember one who contented himself with local good works like a mediaeval limitour, such as fixing plumbing for a poor householder. Later, a trainer on my teaching course in Birmingham made some comment about social change and my not wanting to get my hands ‘dirty’, which even then I interpreted as ‘bloody.’

When it is over, when the Republican Calendar begins and the Cult of Reason is celebrated, the world will be made anew and all the evidence of the old will be annihilated to save us from the danger of relapse. As Orwell’s O’Brien says, ‘It is intolerable to us that an erroneous thought should exist anywhere in the world, however secret and powerless it may be.’ Roll that statue, smash that altar, pull down that sacred pole.

Friday, June 12, 2020

FRIDAY MUSIC: Caravan Palace, by JD

By way of an introduction; what is electro swing music?

According to Wiki; "Electro swing, or swing house music, is a music genre that combines the influence of vintage or modern swing and jazz mixed with house, hip hop, and EDM. Successful examples of the genre create a modern and dance-floor focused sound that is more readily accessible to the modern ear, but that also retains the energetic excitement of live brass and early swing recordings. Electro swing groups typically include singers, musicians playing traditional jazz instruments (e.g. trumpet, trombone, clarinet, saxophone) and at least one DJ."

And, as mentioned at the end of the above video, one of the most popular exponents are Caravan Palace.

Zoé Colotis seems to have unlimited energy to be able to sing and dance the way she does and in the final video the dance choreography and microphone handover is brilliantly executed (you may need to watch it more than once to see it!)

Wednesday, June 10, 2020

Pic of the week

Black Lives Matter protesters rolling a statue of British slave trader Edward Colston.
Photo by Giulia Spadafora/NurPhoto via Getty Images.

A mob of black people, their faces contorted with rage at the killing of George Floyd 3,900 miles away, spontaneously pull down a 125-year-old statue and roll it into Bristol harbour.

Monday, June 08, 2020

Is the real problem - plenty?

"a researcher named John B Calhoun made a world for mice in which everything they could ever want was provided and they did not have to work for any of it. ... male mice, without a reason to defend their territory or food source (since both were plentiful) became dejected, forming cliques that randomly attacked one another for seemingly no reason. In the lead up to this, certain of the male mice began continually mating with whatever mouse happened to be around, be it male or female. Many of the mice also began to simply kill and eat one another, despite the abundance of other food sources; mothers abandoned babies, mice would crowd together in groups of 50 or more in pens designed to hold 15 individuals, while pens with plentiful bedding sat empty inches away."



Friday, June 05, 2020

FRIDAY MUSIC: Michael Maier and unity through song, by JD

Dr Iain McGilchrist in his book 'The Master and his Emissary' explains that music predates language. Human communication began with music which developed into language, first as sung poetry and then as the spoken word. [1]

"What is music?" Dr Jason Martineau in his book 'The Elements of Music' answers that question- "Music is a mother's lullaby. It gives sound to our feelings when we have no voice, words when we are silent. In it we praise, love, hope and remember. The breath of the soul....music shapes and shivers into endless colours, nuanced and diverse, and eternally creative. It is spirit taking form" [2]

"Before there were any stars or galaxies, 13.8 billion years ago, our universe was just a ball of hot plasma -- a mixture of electrons, protons, and light. Sound waves shook this infant universe, triggered by minute, or "quantum," fluctuations happening just moments after the big bang that created our universe." [3]

Pythagoras introduced the notion of the 'Music of the Spheres' incorporating the metaphysical principle that mathematical relationships express qualities or "tones" of energy which manifest in numbers, visual angles, shapes and sounds – all connected within a pattern of proportion. [4] And it was Pythagoras who invented/discovered 'music' [5]

McGilchrist and Martineau have both written of the spiritual and metaphysical 'core' of music and one man in history incorporated such idea in his writings and that was Michael Maier (1568 - 1622) who was a physician and a councellor to the Hapsburg Emperor Rudolf ll [6]

Maier wrote a small book called Atalanta Fugiens based on the Greek myth of Hippomenes and his courtship of Atalanta [7] The book is subtitled 'New Emblems concerning the alchemical secrets of mature' and on the title page Maier writes 'the book is designed in part for the eyes, the intellect...and for the ears' - The eyes can see and study the arcane emblems; the intellect can read and follow the Latin maxims and mottos; the ears can hear and follow the music.

The music is set out in the form of 50 fugues and there is an obvious linguistic link to the book's title in that 'fugiens', fleeing, is from the same root as 'fugue', to put to flight. Fugue also means a loss of awareness of one's identity, often coupled with flight from one's usual environment, associated with certain forms of hysteria and epilepsy.(OED definition)

And so after that long winded introduction, to the music!

Adam McClean of Alchemywebsite.com [8] has set his hand-colored renditions of the Atalanta Fugiens emblems to midi renditions of the music and assembled all 50 fugues in the following video. (29m 30s)

According to Maier in the book the fugues are intended to be sung and so here they are in sequence sung by Rachel Platt, Emily Van Evera, Richard Wistreich and Rufus Müller.

In summary and extracted from McGilchrist's book [1] -

"....that we should use non verbal means such as music to communicate is hardly surprising.... we in the west have lost the sense of the central position music once occupied in communal life, and still does in most parts of the world today. Despite the fact that there is no culture anywhere in the world that does not have music and in which people do not join together to sing or dance we have relegated music to the sidelines of life. We might think of music as an individualistic, even solitary experience, but that is rare in the history of the world. In more traditional societies, performance of music plays both an integral and an integrative role not only in celebration, religious festivals, and other rituals but also in daily work and recreation; and it is above all a shared performance not just something we listen to passively.It has a vital way of binding people together, helping them to be aware of shared humanity, shared feelings and experiences, and actively drawing them together. In our world, competition and specialisation have made music something compartmentalised, somewhere away from life's core: Oliver Sacks writes - The primal role of music is to some extent lost today, when we have a special class of composers and performers, and the rest of us are often reduced to passive listening. One has to go to a concert, or a church, or a music festival, to recapture the collective excitement and bonding of music. In such a situation there seems to be an actual binding of nervous systems."