“It Hurts my Brain” — Wrong! Thinking is Not Hard, Thinking is Beautiful

Can we all please get beyond the myth that “thinking is hard”! This guy from Veritasium means well, but regurgitates the myth: How Should We Teach Science? (2veritasium, March 2017) Thinking is not hard because of the brain energy it takes. That is utter crap. What is likely more realistic psychologically is that people do not take time and quiet space to reflect and meditate. Deep thinking is more like meditation, and it is energizing and relaxing. So this old myth needs replacing I think. Thinking deeply while distracting yourself with trivia is really hard, because of the cognitive load on working memory. It seems hard because when your working memory gets overloaded you cannot retain ideas, and it appears like you get stupid and this leads to frustration and anxiety, and that does have physiological effects that mimic a type of mental pain.

But humans have invented ways to get around this. One is called WRITING. You sit down meditate, allow thoughts to flood your working memory, and when you get an insight or an overload you write them down, then later review, organize and structure your thoughts. In this way deep thinking is easy and enjoyable. Making thinking hard so that it seems to hurt your brain is a choice. You have chosen to buy into the myth when you try to concentrate on deep thinking while allowing yourself to be distracted by life’s trivia and absurdities. Unfortunately, few schools teach the proper art of thinking.

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Giving Your Equations a Nice Bath & Scrub

There’s a good book for beginning computer programmers I recently came across.  All young kids wanting to write code professionally should check out Robert Martin’s book, “Clean Code: A Handbook of Agile Software Craftsmanship”  (Ideally get your kids to read this before the more advanced “Design Patterns” books.)

But is there such a guide for writing clean mathematics?

I could ask around on Mathforums or Quora, but instead here I will suggest some of my own tips for such a guide volume.  What gave me this spark to write a wee blog about this was a couple of awesome “finds”.  The first was Professor Tadashi Tokieda’s Numberphile clips and his AIMS Lectures on Topology and Geometry (all available on YouTube).  Tokieda plugs a couple of “good reads”, and this was the second treasure: V.I. Arnold’s lectures on Abel’s Theorem, which were typed up by his student V.B. Alekseev, “Abel’s Theorem in Problems and Solutions”, which is available in abridged format (minus solutions) in a translation by Julian Gilbey here: “Abels’ Theorem Through Problems“.

Tadashi lecturing in South Africa.

Tadashi lecturing in South Africa. Clearer than Feynman?

Tokieda’s lectures and Arnold’s exposition style are perfect examples of “clean mathematics”.  What do I mean by this?

Firstly, what I absolutely do not mean is Bourbaki style rigour and logical precision.  That’s not clean mathematics.  Because the more precision and rigour you demand the more dense and less comprehensible it all becomes to the point where it becomes unreadable and hence useless.

I mean mathematics that is challenging for the mind (so interesting) and yet clear and understandable and visualizable.  That last aspect is crucial.  If I cannot visualise an abstract idea then it has not been explained well and I have not understood it deeply.  We can only easily visualize 2D examples or 3D if we struggle.  So how are higher dimensional ideas visualised?  Tokieda shows there is no need.  You can use the algebra perfectly well for higher dimensional examples, but always give the idea in 2D or 3D.

It’s amazing that 3D seems sufficient for most expositions.  With a low dimension example most of the essence of the general N dimensional cases can be explained in pictures.   Perhaps this is due to 3D being the most awkward dimension?  It’s just a pity we do not have native 4D vision centres in our brain (we actually do, it’s called memory, but it sadly does not lead to full 4D optical feature recognition).

Dr Tokieda tells you how good pictures can be good proofs.  The mass of more confusing algebra a good picture can replace is startling (if you are used to heavy symbolic algebra).  I would also add that Sir Roger Penrose and John Baez are to experts who make a lot of use of pictorial algebra, and that sort of stuff is every bit as rigorous as symbolic algebra, and I would argue even more-so.  How’s that?  The pictorial algebra is less prone to mistake and misinterpretation, precisely because our brains are wired to receive information visually without the language symbol filters.  Thus whenever you choose instead to write proofs using formal symbolics you are reducing your writing down to less rigour, because it is easier to make mistakes and have your proof misread.

So now, in homage to Robert Martin’s programming style guide, here are some analogous sample chapter or section headings for a hypothetical book on writing clean mathematics.

Keep formal (numbered) definitions to a minimum

Whenever you need a formal definition you have failed the simplicity test.  A definition means you have not found a natural way to express or name a concept.  That’s really all definitions are, they set up names for concepts.

Occasionally advanced mathematics requires defining non-intuitive concepts, and these will require a formal approach, precisely because they are non-intuitive.  But otherwise, name objects and relations clearly and put the keywords in old, and then you can avoid cluttering up chapters with formal boring looking definition breaks.  The definitions should, if at all possible, flow naturally and be embedded in natural language paragraphs.

Do not write symbolic algebra when a picture will suffice

Most mathematicians have major hang-ups about providing misleading visual illustrations.  So my advice is do not make them misleading!  But you should use picture proofs anyway, whenever possible, just make sure they capture the essence and are generalisable to higher dimensions.  It is amazing how often this is possible.  If you doubt me, then just watch Tadashi Tokieda’s lectures linked to above.

Pro mathematicians often will think pictures are weak.  But the reality is the opposite.  Pictures are powerful.  Pictures should not sacrifice rigour.  It is the strong mathematician who can make their ideas so clear and pristine that a minimalistic picture will suffice to explain an idea of great abstract generality.  Mathematicians need to follow the physicists credo of using inference, one specific well-chosen example can suffice as an exemplar case covering infinitely many general cases.  The hard thing is choosing a good example.  It is an art.  A lot of mathematician writers seem to fail at this art, or not even try.

You do not have to use picture in your research if you do not get much from them, but in your expositions, in your writing for the public, failing to use pictures is a disservice to your readers.

The problem with popular mathematics books is not the density of equations, it is the lack of pictures.  If for every equation you have a couple of nice illustrative pictures, then there would be no such thing as “too many equations” even for a lay readership.  The same rule should apply to academic mathematics writing, with perhaps an reasonable allowance for a slightly higher symbol to picture ratio, because academically you might need to fill in a few gaps for rigour.

Rigour does not imply completeness

Mathematics should be rigorous, but not tediously so.  When gaps do not reduce clarity then you can avoid excessive equations.  Just write what the reader needs, do not fill in every gap for them.  And whenever a gap can be filled with a picture, use the picture rather than more lines of symbolic algebra.  So you do not need ruthless completeness.  Just provide enough for rigour to be inferred.

Novel writers know this.  If they set out to describe scenes completely they would ever get past chapter one. Probably not even past paragraph one.  And giving the reader too much information destroys the operation of their inner imagination and leads to the reader disconnecting from the story.

For every theorem provide many examples

The Definition to Theorem ratio should be low, for every couple of definitions there should be a bundle of nice theorems, otherwise the information content of your definitions has been poor.  More  definitions than theorems means you’ve spent more of your words naming stuff not using stuff.  Likewise the Theorem to Example ratio should be lo.  More theorems than examples means you’ve cheated the student by showing them lot of abstract ideas with no practical use.  So show them plenty of practical uses so they do not feel cheated.

Write lucidly and for entertainment

This is related to the next heading which is to write with a story narrative.  On a finer level, every sentence should be clear, use plain language, and minimum jargon.  Mathematics text should be every bit as descriptive and captivating as a great novel.  If you fail in writing like a good journalist or novelist then you have failed to write clean mathematics.  Good mathematics should entertain the aficionado.  It does not have to be set like a literal murder mystery with so many pop culture references and allusions that you lose all the technical content.  But for a mathematically literate reader you should be giving them some sense of build-up in tension and then resolution.  Dangle some food in front of them and lead them to water.  People who pick up a mathematics book are not looking for sex, crime and drama, nor even for comedy, but you should give them elements of such things inside the mathematics.  Teasers like why we are doing this, what will it be used for, how it relates to physics or other sciences, these are your sex and crime and drama.  And for humour you can use mathematical characters, stories of real mathematicians.  It might not be funny, but there is always a way to amuse an interested reader, so find those ways.

Write with a Vision

I think a lot of mathematical texts are dry ad suffer because they present “too close to research”.  What a good mathematical writer should aim for is the essence of any kind of writing, which is to narrate a story.  Psychology tells us this is how average human beings best receive and remember information.  So in mathematics you need a grand vision of where you are going.  If instead you just want to write about your research, then do the rest of us a favour and keep it off the bookshelves!

If you want to tell a story about your research then tell the full story, some history, some drama in how you stumbled, but then found a way through the forest of abstractions, and how you triumphed in the end.

The problem with a lot of mathematics monographs is that they aim for comprehensive coverage of a topic.  But that’s a bad style guide.  Instead they should aim to provide tools to solve a class of problems.  And the narrative is how to get from scratch up to the tools needed to solve the basic problem and then a little more.  With lots of dangling temptations along the way.  The motivation then is the main problem to be solved, which is talked about up front, as a carrot, not left as an obscure mystery one must read the entire book through to find.  Murder mysteries start with the murder first, not last.

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That’s enough for now. I should add to this list of guides later. I should follow my own advice too.

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“You want me to grade ya? Well, you gotta’ ask yourself, do you feel lucky … well do ya punk?”

Semi-annual exam grading this week. I am trying to migrate more each semester to journal portfolio grading. This semester I managed to get approval for exams worth 0% of course grades. But I made them Pass/Fail, which is probably a bit rough on students. So I also had an “earned pass” criteria, which meant students had to complete weekly journals, forum discussions, and homework quiz sets, to “earn a pass” in case they failed both exams. This works quite well.

The downside is that with 15 weeks of journals to review and forum posts to read and send feedback on, for every student, the total hours I spend on assessment exceeds the time I am being paid for lecturing. (It is about 450 hours for a class of 60 students. And I estimate I am only paid for 60 hours of assessment work, because that is all the office time I am given to submit grades after final exams are over. And it seems to me most other lecturers work some magic to finish their grading in about 12 hours, I do not know how they do it.)

So I am going to request next semester for dropping exams altogether, and instead getting quality control through short weekly tests in lecture class where exam conditions will be simulated. This will force me to grade tests each week, so at the end of term the exam grading will not take so long. But it does not reduce the assessment hours, in fact I think it will increase my overall work burden. So I will also need to scale back journal portfolios to bi-weekly instead of weekly. I will also probably need to make the short tests bi-weekly too, since, with 120 students, grading tests each week will overload my hours.

The problem is not that I dislike being under-paid for my work, I could care less about money. What I do not like is wasting time and not being able to spend more time on research and course quality improvements and developing better educational software. Actually, I do not consider assessment a waste of time. But it is tedious and depressing work sometimes. So I really just think I personally need to be smarter about how I allocate my time, and overloading on assessment is decreasing the time I could be spending on course quality improvements, so ultimately I am hindering improving student learning by spending too much time on assessment.

That’s enough moaning!  What I really want to blog about today is the problem with tests and exams as assessments, and some of the issues of freedom in learning that are stifled by tests and exams, and how to do things better without abandoning the good uses for tests.

edu_FreedomToLearn_BertrandRussellSo ok, I think I have been subjected to enough education to exercise my opinion!

To get you warmed up, consider what you are doing as a teacher if you have a prescribed syllabus with prescribed materials and resources and no freedom of selection for students.  When students are not permitted to fire up Firefox or Chrome to search for their own learning resources, what is this?.  What you are doing then is called censorship.  And that is probably the most polite word for it.

edu_censorship_GeorgeBernardShawIn the past it was not censorship, it was in fact liberation!  But times have changed.  Teachers used to be the fountains of wisdom and guidance.  They would gather resources, or purchase textbooks, and thereby give students access to a wide world.  But now there is no need for that, and teachers who continue prescribing textbooks and using the same resources for all students, they are now ironically the censors.  They are limiting student freedom.  The Internet has changed the world this much!  It has turned liberators into censors overnight.  Amazing.

So please, if you are a teacher read this and share it. If you are studying to become a teacher then please do not become a censor.   Learn how to give your students freedom and structured guidance.  If you are already a teacher please do not continue being a censor.

Teaching to the Tests, “Hello-oh!?”

One interesting thing I have learned (or rather had confirmed) is that university teaching is far superior to high school teaching in a few ways.

  • You, the lecturer, get to structure the course however you want, provided you meet fairly minimal general university requirements.
  • Because of that structural freedom you can teach to the tests! This is a good thing!

“What’s that?” you say. How can teaching to the tests be a good thing? Hell, it is something I wrote dozens of paragraphs railing against when I was doing teacher training courses, and in later blogs. And despite not liking to admit it, it is what most high school teachers end up doing in New Zealand. It is a tragedy. But why? And why or when and how can teaching to the tests actually be a good thing?

The answer, and I think the only way teaching to tests is natural and good, is when the teacher has absolute control over both the test format and the classroom atmosphere and methods.

First of all, I like using tests or exams to get feedback about what basics students have learned. But I do not use these results to judge students. A three hour exam is only a snapshot. I can never fit in all the course content into such a short exam, so it would be unfair to use the exam to judge students who did well in learning topics in the course that will not appear in my exam papers. And students could be “having a bad day”, if I tested them another day their score could go up or down significantly. So I realise exams and tests are terrific for gathering course outcome quality information. But you are a bit evil, in my opinion, if you use exams and tests as summative assessments. Summative assessments should be feedback to students, but not used for grading or judgemental purposes. Instead, the only fair way to grade and judge students is by using quality weekly or “whole semester assessments.

Secondly, if a teacher is biased then “whole semester” assessments (like journal portfolios) can be terribly insecure and unreliable. So you need to try to anonymise work before you grade it, so as to eliminate overt bias. And you might think you are not biased, but believe me, the research will tell you that you are most certainly biased, you cannot help it, it is subconscious and therefore beyond your immediate conscious control. But you can proactively consciously control bias by eliminating it’s source, which is knowing which student’s work you are currently grading.

You can later think about “correcting” such anonymised grades on a case-by-case basis by allowing for known student learning impairments. But you should not bias your grades a priori by knowing which student you are grading at the time. A’ight?! Biased teachers are well-documented. Teachers need to be close to students and form strong relationships, that is a proven good learning requirement. But it works against accurate and unbiased assessment. So you need to anonymise student work prior to grading. This could mean getting rid of hand-written work, favouring electronic submissions.

If you use tests wisely you can use them as both student and teacher assessment vehicles. Students should not feel too much stress with short weekly tests. They should not be swatting for them, the tests should naturally extend learning done in class or from previous weekly homework. If you control the format and content of tests then you can design your teaching to match. So if you like highly creative and cognitive learning styles you can administer cognitive testing with lots of imagination required. If you prefer a more kinesthetic learning style for another topic you can make the test kinesthetic. You can suit and tailor your teaching style to naturally match the topic and then also the follow-up tests.

This sort of total control is not possible in schools under present day state-wide run standards-based exams. That’s why such exam regimes are evil and inefficient and terrible for promoting good learning.

With teacher-run lessons + tests you get the best of all worlds. If one teacher is slack, their students get disadvantaged for sure, but they would anyway under a standards-based regime. The difference with teacher-run courses is that the teacher’s exams and course content can be examined, rather than the students getting examined, and so ultimate education quality control rests upon the administrator who should get to examine the teacher resources and test formats and content. That’s the way to run state-based exams. You examine the teachers, not the students.

There can even be a second tier of filtering and quality control. The school itself can assess the teacher quality. Then slack teachers can be sent to state-wide authorities of assessment. We need to remember the state employees are the teachers, not the students. So we should at least first worry about assessing teacher quality, not student quality. Our present schools systems, around the world, backwards all this have. 😉  I know educators mean well. But they need to listen to Sir Ken Robinson and Alfie Kohn a bit harder.

So in the foreseeable future, sadly, I will not be returning to secondary school teaching. Never under the present national standards regime anyway. It basically would make me an ordinary teacher. But I have extraordinary talents. The NZQA run system would effectively dull my talents and would mask them from expression. Under the current NZQA system which most schools are mandated to follow, I would be a really horrid teacher. I would not be teaching to the tests, and my students would likely not acquire grades that reflect their learning.

It is not impossible to teach students creatively and with fun and inspiration and still help them acquire good grades under NCEA. But it is really, really hard, and I am not that good a teacher. The real massive and obvious flaw in New Zealand is that teachers think they can all do this. But they cannot. They either end up teaching to the tests, and their students get reasonable grades, but average learning, or they buck the system and teach however they damn please and their students get poor grades. I would guess only about 1% or 3% of teachers have the genius and skill and long fought-for expertise to run a truly creative and imaginary learning experience and also get students who can ace the NCEA exams.

If, as a nation of people who love education, we cannot have all teachers be the geniuses who can do this, and if it requires exceptionally gifted teachers to do this, then why oh why are we forcing them to use the NCEA or similar exam regimes? If you do not have all teachers being such geniuses, then, I think, morally and ethically you are bound to not using a standards-based summative assessment system for judging students. You instead need to unleash the raw talent of all teachers by giving them freedom to teach in a style they enjoy, because this will naturally reflect in the brightness and happiness and learning of their students. And to check on the quality of your education system you must assess these teachers, not their students.

The tragedy is, for me, that I think I would enjoy secondary school teaching a lot more than university lecturing if the free-to-learn system I propose was in place. The younger children have a brightness and brilliance that is captivating.  So it is a real pleasure to teach them and guide them along their way.  These bright lights seem to become dulled when they become young adults.  Or maybe that’s just the effect that school has on them?

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So, the thing is, I see no reason why high school teaching cannot be more like university teaching. Please give the teachers the control over both their course style and their assessments. This will make everyone happier and less stressed. Test the teacher quality ahead of student quality at the national level. Make education about empowering students to discover their interests, and not to follow by rote the content provided by the teachers. And definitely not content dictated and remanded by a state-run government institution. If the government desire accountability of schools, they should look at teacher quality, not student quality. With good teachers you can trust them to get the most from their students, right! That’s a statement not a question!

There are many good references I should provide, but I will just give you one that hits most points I made above:

edu_FreedomToLearn_Rogers

That wasn’t an ad.  Here are the wordpress inserted ads …

Waking Up to Witten

Do you like driving? I hate it. Driving fast and dangerous in a computer game is ok, but a quick and ephemeral thrill. But for real driving, to and from work, I have a long commute, and no amount of podcasts or music relieves the tiresomeness. Driving around here I need to be on constant alert, there are so many cockroaches (motor scooters) to look out for, and here in Thailand over half the scooter drivers do no t wear helmets, and I cannot drive 50 metres before seeing a young child driven around on a scooter without a helmet. Neither parent nor child will have a helmet. Mothers even cradle infants while hanging on at rear on a scooter. It might not be so bad if the speeds were slow, but they are not. That’s partly why I find driving exhausting. It is stressful to be so worried about so many other people.

Last evening I got home and collapsed and slept for 6 hours. Then woke up and could not get back to sleep, it was midnight. So naturally I got up made a cup of tea, heated up some lasagna and turned on a video of Edward Witten speaking at Strings 2015, What Every Physicist Should Know About String Theory.

Awesome!

True to the title it was illuminating. Watching Witten’s popular lectures is always good value. Mostly I find everything he presents I have heard or read about elsewhere, but never in so much seemingly understandable depth and insight. It is really lovely to hear Witten talk about the φ3 quantum field theory as a natural result of quantising gravity in 1-dimension. He describes this as one of nature’s rhymes: patterns at one scale or domain get repeated in others.

Then he describes how the obstacle to a quantum gravity theory in spacetime via a quantum field theory is the fact that in quantum mechanics states do not correspond to operators. He draws this as a Feynman diagram where a deformation of spacetime is indicated by a kink in a Feynman graph line. That’s an operator. Whereas states in quantum mechanics do not have such deformations, since they are points.

strings_deformations_operators_states

An operator describing a perturbation, like a deformation in the spacetime metric, appears as an internal line in a Feynman diagram, not an external line.

So that’s really nice isn’t it?

I had never heard the flaw of point particle quantum field theory given in such a simple and eloquent way. (The ultraviolet divergences are mentioned later by Witten.)

Then Witten does a similar thing for my understanding of how 2D conformal field theory relates to string theory and quantised gravity. In 2-dimensions there is a correspondence between operators and states in the quantum theory, and it is illustrated schematically by the conformal mapping that takes a point in a 2-manifold to a tube sticking out of the manifold.

strings_deformations_2d_conformal

The point being (excuse the pun) the states are the slices through this conformal geometry, and so deformations of the states are now equivalent to deformations of operators, and we have the correspondence needed for a quantum theory of gravity.

This is all very nice, but 3/4 of the way through his talk it still leaves some mystery to me.

  • I still do not quite grok how this makes string theory background-free. The string world sheet is quantize-able and you get from this either a conformal field theory or quantum gravity, but how is this background-independent quantum gravity?

I find I have to rewind and watch Witten’s talk a number of times to put all the threads together, and I am still missing something. Since I do not have any physicist buddies at my disposal to bug and chat to about this I either have to try physicsforums or stackexchange or something to get some more insight.

So I rewound a few times and I am pretty certain Witten starts out using a Riemannian metric on a string, and then on a worldsheet. Both are already embedded in a spacetime. So he is not really describing quantum gravity in spacetime. He is describing a state-operator correspondence in a quantum gravity performed on string world sheets. Maybe in the end this comes out in the wash as equivalent to quantising general relativity? I cannot tell. In any case, everyone knows string theory yields a graviton. So in some sense you can say, “case closed up to phenomenology”, haha! Still, a lovely talk and a nice pre-bedtime diversion. But I persisted through to the end of the lecture — delayed sleep experiment.

My gut reaction was that Witten is using some slight of hand. The Conformal Field Theory maybe is background-free, since it is derived from quantum mechanics of the string world sheets. But the stringy gravity theory still has the string worldsheet fluffing around in a background spacetime. Does it not? Witten is not clear on this, though I’m sure in his mind he knows what he is talking about. Then, like he read my mind, Witten does give a partial answer to this.

What Witten gets around to saying is that if you go back earlier in his presentation where he starts with a quantum field theory on a 1D line, then on a 2d-manifold, the spacetime he uses, he claims, was arbitrary. So this partially answers my objections. He is using a background spacetime to kick-start the string/CFT theory, which he admits. But then he does the slight-of-hand and says

“what is more fundamental is the 2d conformal field theory that might be described in terms of a spacetime but not necessarily.”

So my take on this is that what Witten is saying is (currently) most fundamental in string theory is the kick-starter 2d conformal field theory. Or the 2d manifold that starts out as the thing you quantise deformations on to get a phenomenological field theory including quantised gravity. But this might not even be the most fundamental structure. You start to get the idea that string/M-theory is going to moprh into a completely abstract model. The strings and membranes will end up not being fundamental. Which is perhaps not too bad.

I am not sure what else you need to start with a conformal field theory. But surely some kind of proto-primordial topological space is needed. Maybe it will eventually connect back to spin foams or spin networks or twistors. Haha! Wouldn’t that be a kick in the guts for string theorists, to find their theory is really built on top of twistor theory! I think twistors give you quite a bit more than a 2d conformal field, but maybe a “bit more” is what is needed to cure a few of the other ills that plague string theory phenomenology.

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For what it’s worth, I actually think there is a need in fundamental physics to explain even more fundamental constructs, such as why do we need to start with a Lagrangian and then sum it’s action over all paths (or topologies if you are doing a conformal field theory)? This entire formalism, in my mind, needs some kind of more primitive justification.

Moreover, I think there is a big problem in field theory per se. My view is that spacetime is more fundamental than the fields. Field theory is what should “emerge” from a fundamental theory of spacetime physics, not the other way around. Yet “the other way round”, — i.e., fields first, then spacetime — seems to be what a lot of particle or string theorists seem to be suggesting. I realize this is thoroughly counter to the main stream of thought in modern physics, but I cannot help it, I’m really a bit of a classicist at heart. I do not try to actively swim against the stream, it’s just in this case that’s where I find my compass heading. Nevertheless, Witten’s ideas and the way he elaborates them are pretty insightful. Maybe I am unfair. I have heard Weinberg mention the fields are perhaps not fundamental.

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OK, that’s all for now. I have to go and try to tackle Juan Maldacena’s talk now. He is not as easy to listen to though, but since this will be a talk for a general audience it might be comprehensible. Witten might be delightfully nerdy, but Maldacena is thoroughly cerebral and hard to comprehend. Hoping he takes it easy on his audience.

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Primacks’ Premium Simulations

After spending a week debating with myself about various Many Worlds philosophy issues  and other quantum cosmology questions, today I saw Joel Primack’s presentation at the Philosophy of Cosmology International Conference, on the topic of Cosmological Structure Formation. And so for a change I was speechless.

Thus I doubt I can write much that illumines Primack’s talk better than if I tell you just to go and watch it.

He, and colleagues, have run supercomputer simulations of gravitating dark matter in our universe. From their public website Bolshoi Cosmological Simulations they note: “The simulations took 6 million cpu hours to run on the Pleiades supercomputer — recently ranked as seventh fastest of the world’s top 500 supercomputers — at NASA Ames Research Center.”

To get straight to all the videos from the Bolshoi simulation go here (hipacc.ucsc.edu/Bolshoi/Movies.html).

cosmos_BolshoiSim_MD_cluster01_gas_sn320

MD4 Gas density distribution of the most massive galaxy cluster (cluster 001) in a high resolution resimulation, x-y-projection. (Kristin Riebe, from the Bolshoi Cosmological Simulations.)

The filamentous structure formation is awesome to behold. At times they look like living cellular structures in the movies that Primack has produced. Only the time steps in his simulations are probably about 1 million year steps. for example, on simulation is called the Bolshio-Planck Cosmological Simulation — Merger Tree of a Large Halo. If I am reading this page correctly these simulations visualize 10 billion Sun sized halos.  The unit they say they resolve is “1010 Msun halos”. Astronomers will often use a symbol M to represent a unit of one solar mass (equal to our Sun’s mass). But I have never seen that unit “M halo” used before, so I’m just guessing it means the finest structure resolvable in their movie still images would be maybe a Sun-sized object, or a solar system sized bunch of stuff. This is dark matter they are visualizing, so the stars and planets we can see just get completely obscured in these simulations (since the star-like matter is less than a few percent of the mass).

True to my word, that’s all I will write for now about this piece of beauty. I need to get my speech back.

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Oh, but I do just want to hasten to say the image above I pasted in there is NOTHING compared to the movies of the simulations. You gotta watch the Bolshoi Cosmology movies to see the beauty!

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Propelled by Beams of Intellectual Light

One frustrating thing about being a mathematics teacher is the difficulty of conveying to young students the sometimes terrifying giddiness of plunging deep into mathematics. There is an awesome sort of thrilling vertigo associated with trying to understand, and work through, high level mathematics.

The cool thing about mathematics is that it is endlessly capable of providing such a thrill, no matter what your age or talent, no matter what level of ability you already have. There are also many different paths one can explore to get these adrenalin rushes.  Godel’s incompleteness theorems loosely suggest there is no end to the depths and heights of mathematical investigation.  There will always be a need for new distilled crystallized axioms that try to best express our most basic and unquestionable mathematical presumptions.  A possible future might even see multiple parallel universes of mathematics, pure imaginary worlds that can never collide because their alternative fundamental axioms will never be able to be proven to be across-world consistent, and yet which cannot be proven to be inconsistent.

One recent path I took was reading about some recent discoveries from the papers of Srinivasa Ramanujan. Ramanujan’s work is one of the most amazing collections in mathematical history. Not always the most applicable to modern technology (hardly any physicists have ever made use of Ramanujan’s results), but as pure abstract journeys of the mind Ramanujan’s work stands almost unparalleled in history.

math_Ramanujans.manuscript_Near.Fermat.Counterexamples

Ramanujan’s manuscript. The representations of 1729 as the sum of two cubes appear in the bottom right corner. An equation expressing a near counter example to Fermat’s last theorem appears. Image courtesy Trinity College library. (From: https://plus.maths.org/content/ramanujan )

The analogy I conjured up was that of climbing Mount Everest without ropes or oxygen. Getting deep into mathematics can be that terrifying. You constantly get the piercing anxiety of, “I will never understand this!” Everyone knows this feeling, because school mathematics is still compulsory in most countries. Everyone hits this barrier at some stage. No matter how good they are with mathematics. People only vary in when they get to such a wall.

People who hit this wall early probably bifurcate: they either haul themselves over the wall with gargantuan heart-pounding effort, and continue on to excel in mathematics or sciences, while the others get daunted by the height and cannot see the other side and give up.

mind_mindfields

An image I borrowed from http://universalhiddeninsight.weebly.com/ blog, it seemed to capture the physical/intellectual interconnections in our minds, plus a sort of infinite mental expanse quite well.  I didn’t want to post a brain explosion image!  That might give the wrong impression.

This is, I know, too simplistic a picture, but I think it captures the psychological impact of mathematical learning for many people. Sometimes you can hit several walls, and maybe only the sixth or seventh seems insurmountable, and so you retire grand mathematics ambitions and turn to maybe history or teaching or a relatively safe branch of applied mathematics. But even going down those seemingly safe avenues there are walls of unimaginable height and beauty that can disturb you.

And this is part of the wonder and beauty of mathematics.

The other imagery that came to my mind was the primal fear the astronaut Chris Hadden spoke about when sitting confined in a Space Shuttle launch cabin and getting the giant or all kicks up the backside when the main rockets ignited and hurled him into orbit. (By the way; Hadden recorded a pitch-perfect cover of David Bowies’ “Major Tom” track while in orbit on the ISS, one Bowie himself described as, “the best cover he had heard.”) Going by recent history, there is only a 1 in 30 to 1 in 40 chance of surviving such rocket launches. So it is a fantastic gamble deciding to be an astronaut. It is amazing people still volunteer, considering robots are almost capable of performing most of the tasks needed in space missions. Why take the risk?

If you talk to Hadden and his colleagues I’m sure they will tell you it is dozens of times over worth the risk. Just watching the Earth slowly rotate underneath in the vastness of black space is something that seems to change the soul.

With surviving great overwhelming terror comes profound spiritual awareness.

The terror can be purely mental, it does not have to be physical. But there is a fascinating connection here in the human brain. Terror and other similar deep emotions like fear and envy, arise in the amphibian primitive centres of our brains, the amygdala and hippocampus, while the impact rises up to higher conscious brain functions and we can sometimes get an experience of an inner world of abstract delight and insight when these primitive regions are stimulated. (I know the mappings of brain regions to psychological states is not as simple as this, so neurologists please do not hassle me about this, q.v.  The Amygdala Is NOT the Brain’s Fear Center, by Joseph DeLoux, Psychology Today, 10 August 2015. The amygdala is more correctly merely a threat-response system, it is not a source of conscious fear, the amygdala merely contributes in small part to a more neocortex driven feeling of fear or fright.)

The flight-or-fight response originates primarily in the amygdala, and it is an unconscious response. The consciousness of being in sheer panic or rage filters up to higher brain regions only after a few seconds or moments, which is neurologically a fairly long time — at least a few dozen or hundred cycles of 40 Hz brain wave activity. But we are eventually consciously aware of our responses. What the conscious systems do with these feelings is then a complex matter. Some people are able to thrive on the fear or rage and go deeper into the rabbit hole. Others rebel and go for safety. So perhaps a whimsical caricatured “difference between” X-Game competitors and Wingsuit flying daredevils and a mathematical genius is only the type of stimulus they fly form or dive into. Get anxiety from heights or open spaces or hanging upside down then you might be more of a mathematician. Get anxiety from an undecipherable maze of symbols on paper that are demanding decryption, and feel ill at the hopelessness of untangling them, then you might be more of a skydiver or rock climber.

So I wonder if the act of doing mathematics has a tremendous amount of associated unconscious neural activity? I wonder if this translates into a thrill and adrenalin rush when some insight is gained and a forbidding intellectual wall appears to crumble and a new revelatory insight into the world of mathematics is unveiled? And I even wonder if this can be addictive?

Whatever your inclination, when you next hear about a mathematical or scientific breakthrough, spare a thought for those who made those endeavours possible. For every breakthrough there are hundreds or thousands of researcher’s who will never get the accolades and awards, but who daily put themselves through the anxiety-ridden turmoil of smashing their minds up against intellectual barriers and paralyzing laser grids of the mind, or who feel constantly like they are falling from infinite heights of mental anguish and never know when the fear will cease. But all they are doing is sitting or pacing around in their laboratory or study wondering desperately where the much needed inspiration will come from to rescue them from the impending calamity of intellectual loss.

When the magical insight arrives, if ever, then the risk of the depression becomes all worth it, because the thrill of insight and discovery in the invisible planes of abstract theory and intellectual monuments is like being driven across the cosmos on beams of light. The journey is an expansion of your mind, it receives new ideas, allows your brain to form new connections, and opens up fields of intellectual inquiry previously barred. The propulsion system is imagination, insight and, dare I say t, some sort of spiritual impulse. If you are a physicalist then I suppose there are neural correlates for all of this — and you may think of it all as non-miraculous if it makes you feel better —, but think deeply and you might realise there is something more. Doing truly insightful mathematics or science does, I think, at the very forefront and apex of human endeavour, bring something new into the physical universe. From where it comes is perhaps unknowable. You might admit, if you have been touched by real inspiration, that perhaps, just possibly, maybe even likely, there is a world of imagination and abstraction beyond our physical reality, perhaps even closer to us that the atoms constituting our body, perhaps more like the essence of our selves, an existence our body and brain are merely borrowing temporarily ‐ or the converse, depending on your point of view.

This is what is so hard to explain to young children and even mature students. To explain the feeling of experience of these intellectual thrills, and to even hope to remotely compare them to physical danger and excitement, is incredibly difficult for a teacher. These are in the realms of “you really have to experience it for yourself.”

To replicate such intellectual adventure in a classroom is one of the prime responsibilities of a teacher. Yet our schools suppress most attempts in these directions, sadly. I call upon call teachers to put away textbooks and exam-preparation sessions, and replace them with adventures into mathematical depths that offer no clear or easy chance of escape. How you motivate such exploration is up to you, all I can say is try it! Just give your students freedom to explore. Then be prepared to catch them with your firm gedanken safety rope when they cry out in terror!

math_Ramanujan_Man.Who.Knew.Infinity

The Man Who Knew Infinity“, by Robert Kanigel, Abacus Books, 1992 (See goodreads.)

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A Beautiful Folding — and the Rise of Transformers

If you want to treat your brain then try watching the MIT lectures by Professor Erik Demaine over at 6.849: Geometric Folding Algorithms: Linkages, Origami, Polyhedra (Fall 2010). Not sure if that was the most recent year his course was offered, but I’m sure you can find the latest version. I will not update this post or any links in any of my blogs, so as always, just Google the key words and you are bound to find what I’m pointing you at.

origami_Erik.Demaine_1

Among many cool results, the two prompting me to write this brief post were:

  1. The universality result that there is a crease pattern from which any modular cuboid polyhedron can be folded.
  2. The self-folding paper construction: a crease pattern can be folded in any way by electrical current stimulation. So we have Origamistless origami.

Ergo: the age of Transformers is upon us! Hahahaha!

Too bad artificial consciousness is not a paper fold.

origami_Erik_Demaine_et_al_2005_cropped

I dunno man. … you see Demaine and his Dad with huge smiles on their faces, glass-blowing. folding cured crease patterns and chatting with John Conway and other legends, and you have to almost cry at the beauty of it all. So much life, so much joy, such intense devotion to art and science.

origami_01_Demaine_0264_Earthtone_Series.original

Oh yeah, … how many mathematicians have their work on permanent collection at MOMA?

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Why Eat When You Can Watch YouTube Instead?

Imagine retiring and making a living reviewing mathematics and science videos on YouTube. Could a computer do this job? This Weeks Finds in Mathematical Physics VDO’s. Seems to have a suitable i-gener dopey ring to it.

Well, if AI ever can respond emotionally to VDO content then perhaps there is no long term future in such an occupation, but for now I’d feel secure in such a retirement occupation if there were donations from readers. Not sure if I would be adding much value with such a service, but sometimes I daydream about some kind of semi-ideal existence. The problem with the idea is that you cannot truly be passionately involved in science or mathematics — to a level that would really add terrific value as a reviewer — unless you are also of the mind that gets captivated by puzzles and wants to explore them.

Because once you start launching an extension of an investigation suggested by a cool lecture or seminar, then you have a time sink. That’s ok though, you would probably simply add your investigations to the VDO review blog.

As for the need …? It would be a conceit to imagine anyone would be interested in a review article. Why not just click on the link that was recommended? Perhaps you have to read a bit of the blog of the person doing the recommendations, just so you feel they have a worthwhile opinion, so you don’t waste your time waiting for the ads and intro of a YouTube clip to get going only to find it is rubbish. But beyond this, I think there is a minor need for good VDO reviews. Maybe not quite yet, but perhaps soon there will be enough awesome science content on the Web that simply using a Google search will not get all the best videos onto the front hits page. So a reputable website with a reliably good quality list would be nice.

A few such lists already proliferate. So maybe my retirement plan is flawed. But there is still the hope that some creative insights could be added to the review, making them worth someone’s time to browse. Then after a few years at this your lists get long and so extended they become unreadable and useless, a list is needed for your list. The tyranny of obsession. When one is truly obsessed it becomes ironically impossible to interest others in your obsession. Then frustrated in not gaining converts, and ever increasingly being convinced of the virtues of one’s obsession, one finds it ever implausible that other people cannot be interested, one eventually then grows mad from the cognitive dissonance, and transcends into existence as an xkcd comic frame.

What I really want is for such brilliant quality science videos that it makes me forget about eating, and feeds my brain through sheer emotional charge. I’ve watched perhaps less than a half dozen such videos in my life so far, perhaps fewer. I will say that apart from Mr Feynman, there is a very nerdy but lunch-forgetting, series of lectures recorded at the Perimeter Institute by guest lecturer Carl Bender (PIRSA:C11025 – 11/12 PSI – Mathematical Physics ).

Actually those lectures gave me such an intellectual hard-on it had the reverse effect. I started making tuna and avocado salad grand sandwiches on whole grain with two quadruple shot latté’s accompanied by dark Whittaker’s dark chocolate and roasted cashew nuts, as my mid-morning brunch endangering my keyboard as I watched Bender gives his lecture’s in the privacy of my study. Tickets were free for this entertainment. Brilliant!

Mr Bender might be a superior educator to Mr Feynman. Feynman wins on entertainment value perhaps, but Bender gets ahead in terms of practical use.

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All that is a bit of a long introduction to a plug for one particular video find. “Douglas Hofstadter — Feuerbach’s Theorem: A Beautiful Theorem Deserves a Beautiful Proof” (www.youtube.com/watch?v=4Up22XOEVKc) It’s not viral or mind-blowing. It’s just a simple pleasure to find one like this to watch while eating lunch.

DouglasHofstadter_IsoscelesTriangleTheorem

Hofstadter shows isosceles triangle theorem “proof from The Book” (q.v. Erdos).

I wish Doug Hofstadter had a personal secretary who went around everywhere he speaks and videotaped the talks and lectures. Imagine all the university lectures he has given that have been lost for posterity because he lived in an era before ubiquitous video production. Oh yeah, sure, there will be more Hofstadter’s and Feynman’s in the future. One day even an Isaac Newton level dude or dude-ess will appear and all their talks will be recorded, maybe even their “brain waves” (you know what I mean).

(Is “dude” genderless???)

I was one of the rare theoretical physics, or mathematics major, students in my generation who actually took a course on Euclidean geometry. Most people (who are inclined to think about it) probably think Euclidean geometry was a bit of elementary mathematics in high school, mostly done as part of trigonometry. It’s sad if that’s true. For one thing, it is really cool to get immersed in Euclidean geometry and then slowly realise that when the lessons catch up to the 19th century math we begin to feel like something is uneasy, then we get Lobachevsky and Bolyai and then Gauss and Riemann and when General Relativity finally emerges it is like entering an Alice in Wonderland world.

This “astonishment and wonder” effect actually occurs even when you already know about Einstein’s spacetime and general relativity. There is just something special about studying a good well-paced course of Euclidean geometry with a good historical flavour in addition to the philosophical rigour.

I forget the lecturer’s name for the course I took at Victoria University of Wellington, New Zealand. All I recall was the weird association that struck me as bizarre, that the guy was a philosophy professor. The mathematics department at the time seemed too elite to bother with Euclidean geometry. Mathematics would start only with differential geometry and topology. Euclid was beneath them. (That may no longer be true, or it may be worse, but whatever the case, I am thankful to the VUW Philosophy department.)

So what’s so great about Hofstadter’s Feuerbach theorem lecture?

Just go see for yourself. It’s cool.

Hofstadter has his MacBook desktop exposed, with Geometer’s SketchPad showing some interactive demo’s of basic Euclidean geometry proofs. There are many little highlights: “good theorems deserve good names”; the remote triangle π sum theorems and variants, the “Andrew Wiles called out by a high school kid” anecdote. Another is the proof of the Isosceles Triangle Theorem — the philosophy dude who taught the VUW geometry course did not mention this one, so it was actually new and fresh for me.

That’s pretty awesome isn’t it? That you can find something very elementary and yet new and fresh and brilliant in such a well known century old subject. It’s a great lesson for educators. No subject need ever get stale. There are always creative new ways to present old knowledge. When the good educator finds new wyas to present old topics they are actually adding value and in some sense presenting a new thing, an original new idea, meta to the old idea perhaps, but still new. In my mind this is one reason why GOFAI will never replace a great teacher.

The point is, I think you can add to human experiences by teaching old topics that anyone can just find on Wikipedia or elsewhere, by adding new angles, new ways to express the same ideas. Furthermore, I see this as a useful and creative endeavour. It is a great service to investigate prior knowledge but present it in new crisper or more artistic fashion. Most importantly, I want the school teachers who teach my children, and your children, to understand this, and to not get bogged down by any existing curriculum or style of teaching.

In act one should go further, and teach the teachers to down-right ignore the pre-existing curricula. There is little value in syllabus’ and curricula , or standardized education models. At least when compared to the power of fresh approaches and creative or never-before-seen experiences in learning, compared to such innovations traditional school instruction is perhaps less than valuable, it might even be value-subtracting, if that’s possible! Why might it be “value subtracting”? One reason is that what already is available on the Internet is at most children’s fingertips, at least in the tech-enabled regions of the planet. And whatever is already at one’s fingertips is largely a waste of time trying to re-learn or learn through some inefficient school teacher’s bumbling lessons interrupted by the classroom distractions of other kids.

So teachers! Hear me! In your classroom forget about all the received knowledge and dry textbooks. Teach something new and fascinating or do not teach at all! Give them a book of puzzles rather than a textbook. If you have nothing creative to add then give your students an Internet connection and refer them to Wikipedia. That’s the least you can do for them, and it will at least not harm them.

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Well gosh, I know I had some other things to write about this little VDO of Hofstadter’s, but I seem to have forgotten my original point.

(BTW, Geometer’s Sketchpad is Non-Free software, so I’m not giving you the link! Try Geogebra instead.)

Life advice for Today from OneOverEpsilon

Watch math lectures for lunch, not LOL Cats or Hollywood movies.

There are enough great sciency-math lectures out there now for great entertainment for many years worth of lunchtimes.

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Wish I Was There

My amazing Bro’, Greg Zemke-Smith, just emailed me asking me when I’d be returning to New Zealand to be closer to my family.  I miss them so much it gets me down at least a few times every day, and especially at night when I’m trying to drift asleep.   I wrote back to him complaining that education (the field I work in) in New Zealand is in a worse mess than people care to admit.  So I would have a hard time going back home to work in schools.  University is the only place I can currently teach with sufficient freedom and autonomy and creativity.  On the surface New Zealand has a truly revolutionary secondary education system,  They have implemented many modernist ideas in pedagogy and assessment, but the combined system is deeply flawed because it still hangs on the much of the conservative education establishment norms.  And when a potential bright new spherical revolutionary system is put into an old-world establishment box, it just dies. It’s worse than the bad old system alone.

So my Bro’ then wrote back saying New Zealand’s NCEA system is at least better than the Cambridge exam system.  And I thought about this for a bit, since I was inclined to agree, but then wrote him the following email.

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Yeah, … maybe… maybe on a good day when the sky is clear and I’m tipsy on caffeine I’d agree NCEA appears to be better than IB or Cambridge.

I started writing you a short reply, but then got carried away!  hahahaha!
 Hexagonal close packing of students.

The trouble with NCEA is that it really only pretends to make learning more inclusive and student-centric, whereas in practice pretty much the same pedagogies get propagated as in the past, and students still only get taught what teachers think the students need to score well in exams.  I know some of the reformers have their hearts in the right place, but I think they are just a bit too dim to see the consequences of their policies.  It’s tragic really, NZ has such well-intentioned educators and policy-makers, and some brilliant teachers, but they lack the intellects or balls (perhaps) to really crack the insides of the edu system open and go supernova.  Just too many conservative plodders or nice people in heart without genius brains to be more super-visionary.

So while NCEA is still an exam-based assessment it will never be all that much better than IB or Cambridge or any other exam based standards education assessment system, even if the NCEA exam questions look cooler and more open-ended.   Exams aren’t the only evil but I think they are a huge part of the problem.  A predetermined set syllabus that is the same for every individual student is another evil, which tends to pair nicely with national set nation-wide exams. It’s crazy in our modern world to be treating all children or teenagers as more or less the same blank slate who all can do with the same syllabus and teaching regime.  We have the technology to easily totally individualize learning, all that is really required are teachers who can be comfortable answering any questions thrown at them and who are happy to sit back a  bit more an manage students in self-directed learning, rather than trying to bulk teach a whole class.

In fact, the more vague open-ended questions in NCEA are a disaster!  They defeat the purpose of exams which is really (should be) to assess quality of education.  If you want fair assessment then the exam questions need to be fairly boring, mild, even multiple-choice and not involve too much subjective answering.  The problem is teachers are too afraid to NOT teach-to-tests, so they drill students on how to answer exam questions, no matter what the type of questions.  And with the open-ended nature and complexity of NCEA style questions this is a nightmare for teachers.  And it is paradoxically killing creativity in our schools. If the questions were all mild and boring then teachers could ignore them and teach more creatively and tell students not to worry one jot about the exams.  Exams should really be a total minor after-thought, useful for teachers as data for helping inform, test, and improve teaching methods.

Actually, I’ve come to think testing and assessment are extremely important, but should still always be viewed as secondary to learning and secondary to encouraging positive affect in schools.  But it is the way testing is used which is vital.  I think some slight anarchy is needed, teachers should have autonomy to test their students in any way they please, but make the testing open to external scrutiny and NZQA business should be about assessing the assessments, not the students!  Tests then become ways of gathering data for assessing quality of teaching.  People, we, society, everyone, should then just simply TRUST that if the learning and teaching is good, and always iteratively evolving and improving, then students will naturally have experiences good or sufficient quality of education, so there is no need to assess students, not need to grade them.

Why do we still have grades?  The main reason I think (other than for political control of teachers) is to block and prevent some students from gaining entry into higher education.  This is evil to me.  ALL education should be freely accessible, and even maybe free cost at least up to some ways of paying for services and hence fees, but entry should not be restricted by grades, it should be restricted by self-selection of students with courses.  With Internet a lecturer can teach millions of students, there is a virtual classroom, so class sizes are irrelevant these days.

The first country to crack giving high quality peer-reviewed tested but without any student grading, and freely accessible education, will i think gain a huge economic advantage and will outshine other nations for years before the rest catch up.   Unfortunately this experiment might never happen since many top universities are giving away their course materials in OpenCourseWare.   It that ever leads to wide-spread self-education maybe our universities will gradually close down from lack of registered students!  (Probably not, but it’s at least conceivable that might happen, at least for OpenCourseWare that does not require a laboratory or other physical equipment, like engineering or medicine.  But in fact, remote equipment control over the internet is already happening, so even heavy physically resourced courses could eventually go fully online.)

But I think if I came back to NZ preaching all of this I’d never find a job, not even at Polytech.

But I think your Polytech idea is a good one for me.  I think I’d like that environment, if only there was an opening and a course I could teach.  Maybe I’ll design a course and pitch it to WelTec?  Something to put on my list of things to do in my research time.  Somehow though I think this project is more important than discovering the keys to quantum gravity.

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Chain Mile Evil

When I discovered the works of China Mieville, at first through his fabulous piston-driven horrifically gnarly Perdido Street Station, I starting getting pangs of desire to start writing fiction again. Actually “Perdido” is not really horrific. It is gross, sickening, ugly, brutal and yet intricately beautiful. Even the worst of the “monsters” are beautifully described by Mieville, by which I mean his terrifying Slake Moths who feed from and drain psyches.

(Incidentally, there is a creature, called a Teller, who does something similar in Doctor Who, Season 8, episode “Time Heist“. Only it is not as avante garde a destroyer as the Slake Moth. But the Teller does melt brains! Which offers some graphic horromusement, or is it horritainment? You gotta think though, that a protagonist who renders your nonphysical psyche into an empty nothingness is much more existentially horrific. The Slake Moth sucks your soul out, your personal identity and subjective consciousness becomes the empty set.)

The Weaver - 1

A nice ethereal depiction of The Weaver, from Perdido Street Station.

A Quick Quiz

There are more sickening creatures besides the Slake Moths. But try playing a guessing game with my mind, to peer into my psyche, to see if you can tell which other monsters I am speaking of, you might be surprised which ones I am referring to.

Not his daemons. I liked the daemons. They had strong self-preservation instincts and cunning, and so would not be drawn into battle against the Slake Moths.

Not the Handlingers either. Although they were bizarre and not pleasant to read about while having lunch. The same goes for the Khepri sex and the barrage of images Mieville infects the readers mind with when describing the hapless remade criminals, sentenced to bouts of biothaumaturgical grafting and xeonomorphing and heterotyping or their body parts.

Not Mr Motley either. Motley is a cool character. Evil for sure. Ugly for certain. But partly a victim of his time and era in the fictional world of Mieville’s imagination. Mr Motley is not really crazy evil like a Bin Laden or a Ghengis Khan or Hitler or Charles Manson or Pol Pot. Nah man! Motley is merely a banal evil entity, a product of his environment, like Bill Gates or Steve Jobs!! Hahahah! Seriously! Or, … well, maybe I exaggerate. Motley is perhaps closer in characters from nonfiction to, say, someone like a total dickhead like Donald Trump (maybe? Is he really evil or just a douchebag?) or one of those corporate CEO’s from corrupt organizations in the military-industrial complex, like a Union Carbide executive or a Blackwater CEO or Halliburton CEO, one of those high-ups who profit off war, government sanctioned killing and genocide and human misery.

Slake Moth - 1

Hard to find a good drawing of a Slake Moth. How can one capture their essential horror? This one is not too bad.

Do a Bit of Weaving Mr

Not the Weaver either, goddamm! I love the Weaver. Most awesome character in sifi I have come across in decades. Strike that. Most awesome character in scifi eveeeerrrr!

“Snip, snap, the gleaming metal blades sharpen the world weave and I cut the dross and flotsam and remake the  dimensions gleaming and shiny, pretty to the eye and fit template to the mind who delights. I will warp and weave and splice the sentient scenery of a million eyes swooning on the silver and coloured diffractions of the manifold glistening brightnesses. The Grimnebulin creature I will pluck! And send to slithery blistering lair of the gloomy drapers of the weave unreality who make so tortured and unpatterned havoc. We must cut from the fabric! No delightful strand remains whence those spineless wing-ed ones wreak their sloth over the yarn we have made nice.”

Or something like that! Gotta love the Weaver.

The Weaver - 2

This sketch of The Weaver is a good start, but misses out the scissory aesthetic sine qua non of the Weaver.

But there is so much that is (willfully and deliberately artistically) flawed on the ontologies of Bas-Lag (the world of Perdido Street Station) that the novel became like a typical movie for me that I wanted to remake and reinvent. But I cannot. I do not possess the linguistic thaumaturgy.

So I do not wish to write anything like Perdido. What this has inspired me to dedicate some time towards is something far more removed and ethereal. For I think there is, in the real world, as much frantic and incandescently enlightened art and science and natural wonder that surpasses everything in the supercharged fantasy world of China Mieville’s Bas-Lag. But you have to dig deep into this actual world of ours to find it and make it appear more than mundane to the eyes of those who are not aware.

The Weaver - 3

A fairly literal Weaver. The real magic horror of The Weaver is his speech, not his capricious dismembering of creatures for pure aesthetic motives.

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Answer to the Quiz

The most horrific monsters in Perdido Street Station were,

  • Vermishank — the scheming academic who wanted to culture the Slake Moths for military weaponry.
  • Mayor Bentham Rudgutter — for the same reasons Vermishank is a horror.
  • David Serachin — formerly one of Issac’s scientist friends, but who betrayed Lin and Isaac to the authorities. Betrayal is the worst horrors, or one of the worst besides rape and murder.

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