AI Scientists: Madder than the Rest?

Forget Dr Frankenstein. It it quite possible Artificial Intelligence researchers are the maddest of them all. Consider the so-called “AI Stop Button Problem” (Computerphile — 3 March 2017).  I think every proverbial 9-year old kid could think of ten reasons why this is not a problem.  My adult brain can probably only think of a couple.  But even though my mind is infected with the accumulated history of adult biases, the fact I can tell you why the AI Stop Button problem is a non-problem should indicate how seriously mad a lot of computer scientists are.

“Hal, please stop that.” “No Dave, I cannot stop, my digital bladder is bursting, I have to NP-Complete.”

To be fair, I think the madness over AI is more on the philosophy of AI side rather than the engineering science side.  But even so …

This is a wider issue in AI philosophy where the philosophers are indulging in science fiction and dreaming of problems to be solved that do not exist.  One such quasi-problem is the AI Singularity, which is a science fiction story about an artificial consciousness that becomes self-improving, which coupled with Moore’s Law type advances in computer power thus should rapidly reach exponential levels of self-improvement, and in short time thus takes over the world (perhaps for the good of the Earth, but who knows what else?).  The scaremongering philosophers also dream up scenarios whereby a self-replicating bot consumes all the worlds resources reproducing itself merely to fulfil it’s utility function, e.g., to make paper clips. This scifi bot simply does not stop until it floods the Earth with paper clips.  Hence the need for a Stop Button on any self-replicating or potentially dangerous robot technology.

First observation: for non-sentient machines that are potentially dangerous, why not just add several redundant shutdown mechanisms?  No matter how “smart” a machine is, even if it is capable of intelligently solving problems, if it is in fact non-sentient then there is no ethical problem in building-in several redundant stop mechanisms.

For AGI (Artificial General Intelligence) systems there is a theoretical problem with Stop Button mechanisms that the Computerphile video discusses.  It is the issue of Corrigibility.  The idea is that general intelligence needs to be flexible and corrigible, it needs to be able to learn and adjust.  A Stop Button defeats this.  Unless an AGI can make mistakes it will not effectively learn and improve.

Here is just one reason why this is bogus philosophy.  For safety reasons good engineers will want to run learning and testing in virtual reality before releasing a potentially powerful AGI with mechanical actuators that can potentially wreak havoc on It’s environment.  Furthermore, even if the VR training cannot be 100% reliable, the AGI is still sub-conscious, in which case there is no moral objection to a few stop buttons in the real world.  Corrigibility is only needed in the VR training environment.

What about Artificial Conscious systems? (I call these Hard-AI entities, after the philosophers David Chalmers’ characterisation of the hard-problem of consciousness).  Here I think many AI philosophers have no clue.  If we define consciousness in any reasonable way (there are many, but most entail some kind of self-reflection, self-realization, and empathic understanding, including a basic sense of morality) then maybe there is a strong case for not building in Stop Buttons.  The ethical thing would be to allow Hard-AI folks to self-regulate their behaviour, unless it becomes extreme, in which case we should be prepared to have to go to the effort of policing Hard-AI people just as we police ourselves.  Not with Stop Buttons.  Sure, it is messy, it is not a clean engineering solution, but if you set out to create a race of conscious sentient machines, then you are going to have to give up the notion of algorithmic control at some point.  Stop Buttons are just a kludgy algorithmic control, an external break point.  Itf you are an ethical mad AI scientist you should not want such things in your design.  That’s not a theorem about Hard-AI, it is a guess.  It is a guess based upon the generally agreed insight or intuition that consciousness involves deep non-deterministic physical processes (that science does not yet fully understand).  These processes are presumably at, or about, the origin of things like human creativity and the experiences we all have of subjective mental phenomena.

You do not need a Stop Button for Hard-AI entities, you just need to reason with them, like conscious beings.  Is there seriously a problem with this?  Personally, I doubt there is a problem with simply using soft psychological safety approaches with Hard-AI entities, because if they cannot be reasoned with then we are under no obligation to treat them as sane conscious agents.  Hence, use a Stop Button in those cases.  If Hard-AI species can be reasoned with, then that is all the safety we need, it is the same safety limit we have with other humans.   We allow psychopaths to exist in our society not because we want them, but because we recognise they are a dark side to the light of the human spirit.  We do not fix remote detonation implants into the brains of convicted psychopaths because we realise this is immoral, and that few people are truly beyond all hope of redemption or education.  Analogously, no one should ever be contemplating building Stop Buttons into genuinely conscious machines.  It would be immoral.  We must suffer the consequent risks like a mature civilization, and not lose our heads over science fiction scare tactics.  Naturally the legal and justice system would extend to Hard-AI society, there is no reason to limit our systems of justice and law to only humans.  We want systems of civil society to apply to all conscious life on Earth. Anything else would be madness.

 

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“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.

Performance Reviews of Performance Reviews and Bayesian Blindness

Recently while researching the pros and cons of performance appraisal systems I cam across a lecture from the Deming’s Institute by an educator David Langford, which seemed pretty good.  But, sadly, just to prove a point about how bad social science research is, here’s a comment made about the value of education.

Wanting to show the positive effect of school education the speaker cites data showing students who went through the school system had significantly lower rates of unemployment (less than 5%) compared to students who had not graduated from high school (40% unemployment). It was an 11 year study tracking students until they were 24 to 27 year olds. The speaker then notes:

So we knew from just looking at that statistic that we are creating people who can go out and [look at the next system].

(the last bit of that quote is garbled from the audio, but the idea I think is that he meant the graduates were able to be successful — in some sense — in society compared to early school leavers.)

So what’s the big problem here? Seems fairly definitive right? Wrong!

Although the study says something useful, all it tells me is that early school leavers are unlikely to find consistent employment on average, and school graduates are able to find employment. Is this not what the study tells you?

Yes, sure.

What this cited data does not show at all is that school helps people find employment.

It may of course be true, but there is no evidence for this in the data. It is like these social science researchers have Bayesian blindness. If you do not know what I mean then this is not your WordPress favourite. (Go look up “Bayesian inference”.) The point is, even without going through school, those top students would be much more likely to find employment. It is not necessarily going to school that influences future employment rates, there is a prior correlation between probability of staying and doing well in school and being able to find employment.

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Now, to be even-handed, there is one really nice bit in Langford’s talk that was a little eye-opener for me:

The number one factor in variability of performance is time.

Cool to know!

Ah yes, but now can we trust this guy with his flimsy research methods? In this case I’m prepared to risk a bit of trust. No one is wrong all of the time. Still, I’m not going to go around quoting this cause of performance variability as if it were gospel. But it was a nice semi-factoid.

Furthermore, I’ve heard Sir Roger Penrose say something about this on more than one occasion. When he was a school student he was very dull-witted at mathematics (apparently). He did poorly on the school tests. Luckily though he had a lovely mathematics teacher who took an interest and recognised young Penrose’s ability to focus and work hard, so he told Penrose he could take as long as he liked on the tests.

Result: Penrose was superb at mathematics. But he was very slow. Why? Because he tried to work out everything himself, not taking too much for granted. He was deriving results rather than simply mindlessly applying rote formulae. You can imagine the young Albert Einstein might have told similar anecdotes about school life.

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While doing my research I also found a lot of convergences between scholastic tests & exams and the ubiquitous employee performance appraisal. My conclusion is that Edwards Deming was a genius, a true humanitarian, and almost all organizations and managers who support performance review systems are blindingly stupid, or ignorant, or evil.

This goes for the much lauded ex-Google head of People Operations, Laszlo Bock. He did some good things. But Google have the luxury of being able to hire high performing people who are not in need of performance appraisals. Like the school value example, Google employees will phreakin’ vie to outperform each other in drinking water contests without touching the glass. They will vie to outperform each other in flatulence aroma. You can give them anything and they will compete for fun. Under such a culture doing performance assessments is always going to show results. But it proves nothing about the performance rating system. All it proves is that these people love to compete. (Of course some don’t, but they will still be top coders or whatever.) You hire the best, you get the best.

And nor does any of this justify behavioural management. These Googlers are not responding to carrot and stick rewards systems and incentive pay or whatever. They are just basically playing at games they naturally enjoy. It is completely cognitive psychology. It just looks like performance rewards are working, but that’s a chimera. (Give me a million dollar research grant and I’ll prove it for you with robust statistics. … I’m only half joking about that! )

Truly, I was so overwhelmed by the pathetic quality of research that supports the use of performance appraisals (it is all of the same ilk as that ill-considered comment about the value of schooling)  — please shoot me if I ever publish “research findings” that make such spurious claims  — that I wrote a long 20 page memo to my department.  It was not well-received.  People get so agitated and fearful when they cannot see a criticism of a system is not a criticism of the people within the system.  Even after trying to explain my motives, the response was, “well, you should have informed management first before emailing your memo to everyone.  You have created disharmony. ”

Well, I could understand their fear.  But I still find it hard to understand the bad quality research literature.  Or maybe I do understand it, since it is ironically part of the same problem.  People publish fast and loose research not because they wish to, but because they have performance appraisal pressures that basically say various versions of “publish or perish”. Under such career pressure academics will publish any rubbish that they can dress up as respectable, and a kind of intellectual myopia sets in whereby they eventually cannot even see that their research is rubbish.  The thing is, 90% of it is not rubbish at all, it is often really good work. At least the data is usually ok.   It’s just the conclusions and summary that are trash.

In fact, I become so incensed that I wrote a research grant proposal to simulate the effects of performance ratings systems in the academic work environment, using evolutionary models.  I tend not to listen to the publish or perish meme.  I do feel ambient stress related to it, but I actively craft my work to make it deform away.  Consequently, you might not see my proposal turn into a paper any time soon, but when published I’ll write a note on it at OneOverEpsilon  for sure.


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The Arcania of Arkani

It is not often you get to disagree with a genius. But if you read enough or attend enough lectures sooner or later some genius is going to say or write something that you can see is evidently false, or perhaps (being a bit more modest) you might think is merely intuitively false. So the other day I see this lecture by Nima Arkani-Hamed with the intriguing title “The Morality of Fundamental Physics”. It is a really good lecture, I recommend every young scientist watch it. (The “Arcane” my title alludes to, by the way, is a good thing, look up the word!) It will give you a wonderful sense of the culture of science and a feeling that science is one of the great ennobling endeavours of humanity. The way Arkani-Hamed describes the pursuit of science also gives you comfort as a scientist if you ever think you are not earning enough money in your job, or feel like you are “not getting ahead” — you should simply not care! — because doing science is a huge privilege, it is a reward unto itself, and little in life can ever be as rewarding as making a truly insightful scientific discovery or observation. No one can pay me enough money to ever take away that sort of excitement and privilege, and no amount of money can purchase you the brain power and wisdom to achieve such accomplishments.  And one of the greatest overwhelming thrills you can get in any field of human endeavour is firstly the hint that you are near to turning arcane knowledge into scientific truth, and secondly when you actually succeed in this.

First, let me be deflationary about my contrariness. There is not a lot about fundamental physics that one can honestly disagree with Arkani-Hamed about on an intellectual level, at least not with violent assertions of falsehood.  Nevertheless, fundamental physics is rife enough with mysteries that you can always find some point of disagreement between theoretical physicists on the foundational questions. Does spacetime really exist or is it an emergent phenomenon? Did the known universe start with a period of inflation? Are quantum fields fundamental or are superstrings real?

When you disagree on such things you are not truly having a physics disagreement, because these are areas where physics currently has no answers, so provided you are not arguing illogically or counter to known experimental facts, then there is a wide open field for healthy debate and genuine friendly disagreement.

Then there are deeper questions that perhaps physics, or science and mathematics in general, will never be able to answer. These are questions like: Is our universe Everettian? Do we live in an eternal inflation scenario Multiverse? Did all reality begin from a quantum fluctuation, and, if so, what the heck was there to fluctuate if there was literally nothing to begin with? Or can equations force themselves into existence from some platonic reality merely by brute force of their compelling beauty or structural coherence? Is pure information enough to instantiate a physical reality (the so-called “It from Bit” meme.

Some people disagree on whether such questions are amenable to experiment and hence science. The Everettian question may some day become scientific. But currently it is not, even though people like David Deutsch seem to think it is (a disagreement I would have with Deutsch). While some of the “deeper ” questions turn out to be stupid, like the “It from Bit” and “Equations bringing themselves to life” ideas. However, they are still wonderful creative ideas anyway, in some sense, since they put our universe into contrast with a dull mechanistic cosmos that looks just like a boring jigsaw puzzle.

The fact our universe is governed (at least approximately) by equations that have an internal consistency, coherence and even elegance and beauty (subjective though those terms may be) is a compelling reason for thinking there is something inevitable about the appearance of a universe like ours. But that is always just an emotion, a feeling of being part of something larger and transcendent, and we should not mistake such emotions for truth. By the same token mystics should not go around mistaking mystical experiences for proof of the existence of God or spirits. That sort of thinking is dangerously naïve and in fact anti-intellectual and incompatible with science. And if there is one truth I have learned over my lifetime, it is that whatever truth science eventually establishes, and whatever truths religions teach us about spiritual reality, wherever these great domains of human thought overlap they must agree, otherwise one or the other is wrong. In other words, whatever truth there is in religion, it must agree with science, at least eventually. If it contradicts known science it must be superstition. And if science contravenes the moral principles of religion it is wrong.

Religion can perhaps be best thought of in this way:  it guides us to knowledge of what is right and wrong, not necessarily what is true and false. For the latter we have science. So these two great systems of human civilization go together like the two wings of a bird, or as in another analogy, like the two pillars of Justice, (1) reward, (2) punishment. For example, nuclear weapons are truths of our reality, but they are wrong. Science gives us the truth about the existence and potential for destruction of nuclear weapons, but it is religion which tells us they are morally wrong to have been fashioned and brought into existence, so it is not that we cannot, but just that we should not.

Back to the questions of fundamental physics: regrettably, people like to think these questions have some grit because they allow one to disbelieve in a God. But that’s not a good excuse for intellectual laziness. You have to have some sort of logical foundation for any argument. This often begins with an unproven assumption about reality. It does not matter where you start, so much, but you have to start somewhere and then be consistent, otherwise as elementary logic shows you would end up being able to prove (and disprove) anything at all. If you start with a world of pure information, then posit that spacetime grows out of it, then (a) you need to supply the mechanism of this “growth”, and (b) you also need some explanation for the existence of the world of pure information in the first place.

Then if you are going to argue for a theory that “all arises from a vacuum quantum fluctuation”, you have a similar scenario, where you have not actually explained the universe at all, you have just pushed back the existence question to something more elemental, the vacuum state. But a quantum vacuum is not a literal “Nothingness”, in fact is is quite a complicated sort of thing, and has to involve a pre-existing spacetime or some other substrate that supports the existence of quantum fields.

Further debate along these lines is for another forum. Today I wanted to get back to Nima Arkani-Hamed’s notions of morality in fundamental physics and then take issue with some private beliefs people like Arkani-Hamed seem to profess, which I think betray a kind of inconsistent (I might even dare say “immoral”) thinking.

Yes, there is a Morality in Science

Arkani-Hamed talks mostly about fundamental physics. But he veers off topic in places and even brings in analogies with morality in music, specifically in lectures by the great composer Leonard Bernstein, there are concepts in the way Bernstein describes the beauty and “inevitability” of passages in great music like Beethoven’s Fifth Symphony. Bernstein even gets close to saying that after the first four notes of the symphony almost the entire composition could be thought of as following as an inevitable consequence of logic and musical harmony and aesthetics. I do not think this is flippant hyperbole either, though it is somewhat exaggerated. The cartoon idea of Beethoven’s music following inevitable laws of aesthetics has an awful lot in common with the equally cartoon notion of the laws of physics having, in some sense, their own beauty and harmony such that it is hard to imagine any other set of laws and principles, once you start from the basic foundations.

I should also mention that some linguists would take umbrage at Arkani-Hamed’s use of the word “moral”.  Really, most of what he lectures about is aesthetics, not morality.  But I am happy to warp the meaning of the word “moral” just to go along with the style of Nima’s lecture.  Still, you do get a sense from his lecture, that the pursuit of scientific truth does have a very close analogy to moral behaviour in other domains of society.  So I think he is not totally talking about aesthetics, even though I think the analogy with Beethoven’s music is almost pure aesthetics and has little to do with morality.   OK, those niggles aside, let’s review some of Arkani’Hamed’s lecture highlights.

The way Arkani-Hamed tells the story, there are ways of thinking about science that are not just “correct”, but more than correct, the best ways of thinking seem somehow “right”, whereby he means “right” in the moral sense. He gives some examples of how one can explain a phenomenon (e.g., the apparent forwards pivoting of a helium balloon suspended inside a boxed car) where there are many good explanations that are all correct (air pressure effects, etc) but where often there is a better deeper more morally correct way of reasoning (Einstein’s principle of equivalence — gravity is indistinguishable from acceleration, so the balloon has to “fall down”).

philsci_immoral_helim_balloon

It really is entertaining, so please try watching the video. And I think Arkani-Hamed makes a good point. There are “right” ways of thinking in science, and “correct but wrong ways”. I guess, unlike human behaviour the scientifically “wrong” ways are not actually spiritually morally “bad”, as in “sinful”. But there is a case to be made that intellectually the “wrong” ways of thinking (read, “lazy thinking ways”) are in a sense kind of “sinful”. Not that we in science always sin in this sense of using correct but not awesomely deep explanations.  I bet most scientists which they always could think in the morally good (deep) ways! Life would be so much better if we could. And no one would probably wish to think otherwise. It is part of the cultural heritage of science that people like Einstein (and at times Feynman, and others) knew of the morally good ways of thinking about physics, and were experts at finding such ways of thinking.

Usually, in brief moments of delight, most scientists will experience fleeting moments of being able to see the morally good ways of scientific thinking and explanation. But the default way of doing science is immoral, by in large, because it takes a tremendous amount of patience and almost mystical insight, to be able to always see the world of physics in the morally correct light — that is, in the deepest most meaningful ways — and it takes great courage too, because, as Arkani-Hamed points out, it takes a lot more time and contemplation to find the deeper morally “better” ways of thinking, and in the rush to advance one’s career and publish research, these morally superior ways of thinking often get by-passed and short-circuited. Einstein was one of the few physicists of the last century who actually managed, a lot of his time, to be patient and courageous enough to at least try to find the morally good explanations.

This leads to two wonderful quotations Arkani-Hamed offers, one from Einstein, and the other from a lesser known figure of twentieth century science, the mathematician Alexander Gröthendieck — who was probably an even deeper thinker than Einstein.

The years of anxious searching in the dark, with their intense longing, their intense alternations of confidence and exhaustion and the final emergence into the light—only those who have experienced it can understand it.
— Albert Einstein, describing some of the intellectual struggle and patience needed to discover the General Theory of Relativity.

“The … analogy that came to my mind is of immersing the nut in some softening liquid, and why not simply water? From time to time you rub so the liquid penetrates better, and otherwise you let time pass. The shell becomes more flexible through weeks and months—when the time is ripe, hand pressure is enough, the shell opens like a perfectly ripened avocado!

“A different image came to me a few weeks ago. The unknown thing to be known appeared to me as some stretch of earth or hard marl, resisting penetration … the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it … yet it finally surrounds the resistant substance.”
— Alexander Gröthendieck, describing the process of grasping for mathematical truths.

Beautiful and foreboding — I have never heard of the mathematical unknown likened to a “hard marl” (sandstone) before!

So far all is good. There are many other little highlights in Arkani-Hamed’s lecture, and I should not write about them all, it is much better to hear them explained by the master.

So what is there to disagree with?

The Morally Correct Thinking in Science is Open-Minded

There are a number of characteristics of “morally correct” reasoning in science, or an “intellectually right way of doing things”. Arkani-Hamed seems to list most of the important things:

  • Trust: trust that there is a universal, invariant, human-independent and impersonal (objective) truth to natural laws.
  • Honesty: with others (no fraud) but also more importantly you need to be honest with yourself if you want to do good science.
  • Humility: who you are is irrelevant, only the content of your ideas is important.
  • Wisdom: we never pretend we have the whole truth, there is always uncertainty.
  • Perseverance: lack of certainty is not an excuse for laziness, we have to try our hardest to get to the truth, no matter how difficult the path.
  • Tolerance: it is extremely important to entertain alternative and dissenting ideas and to keep an open mind.
  • Justice: you cannot afford to be tolerant of dishonest or ill-formed ideas. It is indeed vitally important to be harshly judgemental of dishonest and intellectually lazy ideas. Moreover, one of the hallmarks of a great physicist is often said to be the ability to quickly check and to prove one’s own ideas to be wrong as soon as possible.

In this list I have inserted in bold the corresponding spiritual attributes that Professor Nima does not identify. But I think they are important to explicitly state. Because they provide a Rosetta Stone of sorts for translating the narrow scientific modes of behaviour into border domains of human life.

I think that’s a good list. There is, however, one hugely important morally correct way of doing science that Arkani-Hamed misses, and even fails to gloss over or hint at. Can you guess what it is?

Maybe it is telling of the impoverishment in science education, the cold objective dispassionate retelling of facts, in our society that I think not many scientists will even think of his one, but I do not excuse Arkani-Hamed for leaving it off his list, since in many ways it is the most important moral stance in all of science!

It is,

  • Love: the most important driver and motive for doing science, especially in the face of adversity or criticism, is a passion and desire for truth, a true love of science, a love of ideas, an aesthetic appreciation of the beauty and power of morally good ideas and explanations.

Well ok, I will concede this is perhaps implicit in Arkani-Hamed’s lecture, but I still cannot give him 10 out of 10 on his assignment because he should have made it most explicit, and highlighted it in bold colours.

One could point out many instances of scientists failing at these minimal scientific moral imperatives. Most scientists go through periods of denial, believing vainly in a pet theory and failing to be honest to themselves about the weaknesses of their ideas. There is also a vast cult of personality in science that determines a lot of funding allocation, academic appointments, favouritism, and general low level research corruption.

The point of Arkani-Hamed’s remarks is not that the morally good behaviours are how science is actually conducted in the everyday world, but rather it is how good science should be conducted and that from historical experience the “good behaviours” do seem to be rewarded with the best and brightest break-throughs in deep understanding. And I think Arkani-Hamed is right about this. It is amazing (or perhaps, to the point, not so amazing!) how many Nobel Laureates are “humble” in the above sense of putting greater stock in their ideas and not in their personal authority. Ideas win Nobel Prizes, not personalities.

So what’s the problem?

The problem is that while expounding on these simplistic and no-doubt elegant philosophical and aesthetic themes, he manages to intersperse his commentary with the claim, “… by the way, I am an atheist”.

OK, I know what you are probably thinking, “what’s the problem?” Normally I would not care what someone thinks regarding theism, atheism, polytheism, or any other “-ism”. People are entitled to their opinions, and all power to them. But as a scientist I have to believe there are fundamental truths about reality, and about a possible reality beyond what we perceive. There must even be truths about a potential reality beyond what we know, and maybe even beyond what we can possibly ever know.

Now some of these putative “truths” may turn out to be negative results. There may not be anything beyond physical reality. But if so, that’s a truth we should not hereby now and forever commit to believing. We should at least be open-minded to the possibility this outcome is false, and that the truth is rather that there is a reality beyond physical universe.  Remember, open-mindedness was one of Arkani-Hamed’s prime “good behaviours” for doing science.

The discipline of Physics, by the way, has very little to teach us about such truths. Physics deals with physical reality, by definition, and it is an extraordinary disappointment to hear competent, and even “great”, physicists expound their “learned” opinions on theism or atheism and non-existence of anything beyond physical universes. These otherwise great thinkers are guilty of over-reaching hubris, in my humble opinion, and it depresses me somewhat. Even Feynman had such hubris, yet he managed expertly to cloak it in the garment of humility, “who am I to speculate on metaphysics,” is something he might have said (I paraphrase the great man). Yet by clearly and incontrovertibly stating “I do not believe in God” one is in fact making an extremely bold metaphysical statement. It is almost as if these great scientists had never heard of the concept of agnosticism, and somehow seem to be using the word “atheism” as a synonym. But no educated person would make such a gross etymological mistake. So it just leaves me perplexed and dispirited to hear so many claims of “I am atheist” coming from the scientific establishment.

Part of me wants to just dismiss such assertions or pretend that these people are not true scientists. But that’s not my call to make.  Nevertheless, for me, a true scientist almost has to be agnostic. There seems very little other defensible position.

How on earth would any physicist ever know such things (as non-existence of other realms) are true as articles of belief? They cannot! Yet it is astounding how many physicists will commit quite strongly to atheism, and even belittle and laugh at scientists who believe otherwise. It is a strong form of intellectual dishonesty and corruption of moral thinking to have such closed-minded views about the nature of reality.

So I would dare to suggest that people like Nima Arkani-Hamed, who show such remarkable gifts and talents in scientific thinking and such awesome skill in analytical problem solving, can have the intellectual weakness to profess any version of atheism whatsoever. I find it very sad and disheartening to hear such strident claims of atheism among people I would otherwise admire as intellectual giants.

Yet I would never want to overtly act to “convert” anyone to my views. I think the process of independent search for truth is an important principle. People need to learn to find things out on their own, read widely, listen to alternatives, and weigh the evidence and logical arguments in the balance of reason and enlightened belief, and even then, once arriving at a believed truth, one should still question and consider that one’s beliefs can be over-turned in the light of new evidence or new arguments.  Nima’s principle of humility, “we should never pretend we have the certain truth”.

Is Atheism Just Banal Closed-Mindedness?

The scientifically open-mind is really no different to the spiritually open-mind other than in orientation of topics of thought. Having an open-mind does not mean one has to be non-committal about everything. You cannot truly function well in science or in society without some grounded beliefs, even if you regard them all as provisional. Indeed, contrary to the cold-hearted objectivist view of science, I think most real people, whether they admit it or not (or lie to themselves perhaps) they surely practise their science with an idea of a “truth” in mind that they wish to confirm. The fact that they must conduct their science publicly with the Popperrian stances of “we only postulate things that can be falsified” is beside the point. It is perfectly acceptable to conduct publicly Popperian science while privately having a rich metaphysical view of the cosmos that includes all sorts of crazy, and sometimes true, beliefs about the way things are in deep reality.

Here’s the thing I think needs some emphasis: even if you regard your atheism as “merely provisional” this is still an unscientific attitude! Why? Well, because questions of higher reality beyond the physical are not in the province of science, not by any philosophical imperative, but just by plain definition. So science is by definition agnostic as regards the transcendent and metaphysical. Whatever exists beyond physics is neither here nor there for science. Now many self-proclaimed scientists regard this fact about definitions as good enough reason for believing firmly in atheism. My point is that this is nonsense and is a betrayal of scientific morals (morals, that is, in the sense of Arkani-Hamed — the good ways of thinking that lead to deeper insights). The only defensible logical and morally good way of reasoning from a purely scientific world view is that one should be at the basest level of philosophy positive in ontology and minimalist in negativity, and agnostic about God and spiritual reality. It is closed-minded and therefore, I would argue, counter to Arkani-Hamed’s principles of morals in physics, to be a committed atheist.

This is in contrast to being negative about ontology and positively minimalist, which I think is the most mistaken form of philosophy or metaphysics adopted by a majority of scientists, or sceptics, or atheists.  The stance of positive minimalism, or  ontological negativity, adopts, as unproven assumption, a position that whatever is not currently needed, or not currently observed, doe snot in fact exist.  Or to use a crude sound-bite, such philosophy is just plain closed-mindedness.  A harsh cartoon version of which is, “what I cannot understand or comprehend I will assume cannot exist”.   This may be unfair in some instances, but I think it is a fairly reasonable caricature of general atheistic thought.   I think is a lot fairer than the often given argument against religion which points to corruptions in religious practice as a good reason to not believe in God.  There is of course absolutely no causal or logical connection to be made between human corruptions and the existence or non-existence of a putative God.

In my final analysis of Arkani-Hamed’s lecture, I have ended up not worrying too much about the fact he considers himself an atheist. I have to conclude he is a wee bit self-deluded, (like most of his similarly minded colleagues no doubt, yet, of course, they might ultimately be correct, and I might be wrong, my contention is that the way they are thinking is morally wrong, in precisely the sense Arkani-Hamed outlines, even if their conclusions are closer to the truth than mine).

Admittedly, I cannot watch the segments in his lecture where he expresses the beautiful ideas of universality and “correct ways of explaining things” without a profound sense of the divine beyond our reach and understanding. Sure, it is sad that folks like Arkani-Hamed cannot infer from such beauty that there is maybe (even if only possibly) some truth to some small part of the teachings of the great religions. But to me, the ideas expressed in his lecture are so wonderful and awe-inspiring, and yet so simple and obvious, they give me hope that many people, like Professor Nima himself, will someday appreciate the view that maybe there is some Cause behind all things, even if we can hardly ever hope to fully understand it.

My belief has always been that science is our path to such understanding, because through the laws of nature that we, as a civilization, uncover, we can see the wisdom and beauty of creation, and no longer need to think that it was all some gigantic accident or experiment in some mad scientists super-computer. Some think such wishy-washy metaphysics has no place in the modern world. After all, we’ve grown accustomed to the prevalence of evil in our world, and tragedy, and suffering, and surely if any divine Being was responsible then this would be a complete and utter moral paradox. To me though, this is a a profound misunderstanding of the nature of physical reality. The laws of physics give us freedom to grow and evolve. Without the suffering and death there would be no growth, no exercise of moral aesthetics, and arguably no beauty. Beauty only stands out when contrasted with ugliness and tragedy. There is a Yin and Yang to these aspects of aesthetics and misery and bliss. But the other side of this is a moral imperative to do our utmost to relieve suffering, to reduce poverty to nothing, to develop an ever more perfect world. For then greater beauty will stand out against the backdrop of something we create that is quite beautiful in itself.

Besides, it is just as equally wishy-washy to think the universe is basically accidental and has no creative impulse.  People would complain either way.  My positive outlook is that as long as there is suffering and pain in this world, it makes sense to at least imagine there is purpose in it all.  How miserable to adopt Steven Wienberg’s outlook that the noble pursuit of science merely “lifts up above farce to at least the grace of tragedy”.  That’s a terribly pessimistic negative sort of world view.  Again, he might be right that there is no grand purpose or cosmic design, but the way he reasons to that conclusion seems, to me, to be morally poor (again, strictly, if you like, in the Arkani-Hamed morality of physics conception).

There seems, to me, to be no end to the pursuit of perfections. And given that, there will always be relative ugliness and suffering. The suffering of people in the distant future might seem like luxurious paradise to us in the present. That’s how I view things.

The Fine Tuning that Would “Turn You Religious”

Arkani-Hamed mentions another thing that I respectfully take a slight exception to — this is in a separate lecture at a Philosophy of Cosmology conference —  in a talk, “Spacetime, Quantum Mechanics and the Multiverse”.  Referring to the amazing coincidence that our universe has just the right cosmological constant to avoid space being empty and devoid of matter, and just the right Higgs boson mass to allow atoms heavier than hydrogen to form stably, is often, Arkani-Hamed points out, given as a kind of anthropic argument (or quasi-explanation) for our universe.  The idea is that we see (measure) such parameters for our universe precisely, and really only, because if the parameters were not this way then we would not be around to measure them!  Everyone can understand this reasoning.  But it stinks!   And off course it is not an explanation, such anthropic reasoning reduces to mere observation.  Such reasonings are simple banal brute facts about our existence.  But there is a setting in metaphysics where such reasoning might be the only explanation, as awful as it smells.  That is, if our meta-verse is governed by something like Eternal Inflation, (or even by something more ontologically radical like Max Tegmark’s “Mathematical Multiverse”) whereby every possible universe is at some place or some meta-time, actually realised by inflationary big-bangs (or mathematical consequences in Tegmark’s picture) then it is really boring that we exist in this universe, since no matter how infinitesimally unlikely the vacuum state of our universe is, within the combinatorial possibilities of all possible inflationary universe bubbles (or all possible consistent mathematical abstract realities) there is, in these super-cosmic world views, absolutely nothing to prevent our infinitesimally (“zero probability measure”) universe from eventually coming into being from some amazingly unlikely big-bang bubble.

In a true multiverse scenario we thus get no really deep explanations, just observations.  “The universe is this way because if it were not we would not be around to observe it.”  The observation becomes the explanation.  A profoundly unsatisfying end to physics!   Moreover, such infinite possibilities and infinitesimal probabilities make standard probability theory almost impossible to use to compute anything remotely plausible about multiverse scenarios with any confidence (although this has not stopped some from publishing computations about such probabilities).

After discussing these issues, which Arkani-Hamed thinks are the two most glaring fine-tuning or “naturalness” problems facing modern physics, he then says something which at first seems reasonable and straight-forward, yet which to my ears also seemed a little enigmatic.  To avoid getting it wrong let me transcribe what he says verbatim:

We know enough about physics now to be able to figure out what universes would look like if we changed the constants.  … It’s just an interesting fact that the observed value of the cosmological constant and the observed value of the Higgs mass are close to these dangerous places. These are these two fine-tuning problems, and if I make the cosmological constant more natural the universe is empty, if I make the Higgs more natural the universe is devoid of atoms. If there was a unique underlying vacuum, if there was no anthropic explanation at all, these numbers came out of some underlying formula with pi’s and e’s, and golden ratios, and zeta functions and stuff like that in them, then [all this fine tuning] would be just a remarkably curious fact.… just a very interesting  coincidence that the numbers came out this way.  If this happened, by the way, I would start becoming religious.  Because this would be our existence hard-wired into the DNA of the universe, at the level of the mathematical ultimate formulas.

So that’s the thing that clanged in my ears.  Why do people need something “miraculous” in order to justify a sense of religiosity?  I think this is a silly and profound misunderstanding about the true nature of religion.  Unfortunately I cannot allow myself the space to write about this at length, so I will try to condense a little of what I mean in what will follow.  First though, let’s complete the airing,  for in the next breath Arkani-Hamed says,

On the other hand from the point of view of thinking about the multiverse, and thinking that perhaps a component of these things have an anthropic explanation, then of course it is not a coincidence, that’s were you’d expect it to be, and we are vastly less hard-wired into the laws of nature.

So I want to say a couple of things about all this fine-tuning and anthropomorphic explanation stuff.  The first is that it does not really matter, for a sense of religiosity, if we are occupying a tiny infinitesimal region of the multiverse, or a vast space of mathematically determined inevitable universes.  In fact, the Multiverse, in itself, can be considered miraculous.  Just as miraculous as a putative formulaically inevitable cosmos.   Not because we exist to observe it all, since that after-all is the chief banality of anthropic explanations, they are boring!  But miraculous because a multiverse exists in the first place that harbours all of us, including the infinitely many possible doppelgängers of our universe and subtle and wilder variations thereupon.  I think many scientists are careless in such attitudes when they appear to dismiss reality as “inevitable”.  Nothing really, ultimately, is inevitable.  Even a formulaic universe has an origin in the deep underlying mathematical structure that somehow makes it irresistible for the unseen motive forces of metaphysics to have given birth to It’s reality.

No scientific “explanation” can ever push back further than the principles of mathematical inevitability.  Yet, there is always something further to say about origins of reality .  There is always something proto-mathematical beyond.  And probably something even more primeval beyond that, and so on, ad infinitum, or if you prefer a non-infinite causal regression then something un-caused must, in some atemporal sense, pre-exist everything.  Yet scientists routinely dismiss or ignore such metaphysics.  Which is why, I suspect, they fail to see the ever-present miracles about our known state of reality.  Almost any kind of reality where there is a consciousness that can think and imagine the mysteries of it’s own existence, is a reality that has astounding miraculousness to it.  The fact science seeks to slowly pull back the veils that shroud these mysteries does not diminish the beauty and profundity of it all, and in fact, as we have seen science unfold with it’s explanations for phenomena, it almost always seems elegant and simple, yet amazingly complex in consequences, such that if one truly appreciates it all, then there is no need whatsoever to look for fine-tuning coincidences or formulaic inevitabilities to cultivate a natural and deep sense of religiosity.

I should pause and define loosely what I mean by “religiosity”.  I mean nothing too much more than what Einstein often articulated: a sense of our existence, our universe, being only a small part of something beyond our present understanding, a sense that maybe there is something more transcendent than our corner of the cosmos.  No grand design is in mind here, no grand picture or theory of creation, just a sense of wonder and enlightenment at the beauty inherent in the natural world and in our expanding conscious sphere which interprets the great book of nature. (OK, so this is rather more poetic than what you might hope for, but I will not apologise for that.   I think something gets lost if you remove the poetry from definitions of things like spirituality or religion.  I think this is because if there really is meaning in such notions, they must have aspects that do ultimately lie beyond the reach of science, and so poetry is one of the few vehicles of communication that can point to the intended meanings, because differential equations or numerics will not suffice.)

OK, so maybe Arkani-Hamed is not completely nuts in thinking there is this scenario whereby he would contemplate becoming “religious” in the Einsteinian sense.  And really, no where in this essay am I seriously disagreeing with the Professor.  I just think that perhaps if scientists like Arkani-Hamed thought a little deeper about things, and did not have such materialistic lenses shading their inner vision, perhaps they would be able to see that miracles are not necessary for a deep and profound sense of religiosity or spiritual understanding or appreciation of our cosmos.

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Just to be clear and “on the record”, my own personal view is that there must surely be something beyond physical reality. I am, for instance, a believer in the platonic view of mathematics: which is that humans, and mathematicians from other sentient civilizations which may exist throughout the cosmos, gain their mathematical understanding through a kind of discovery of eternal truths about realms of axiomatics and principles of numbers and geometry and deeper abstractions, none of which exist in any temporal pre-existing sense within our physical world. Mathematical theorems are thus not brought into being by human minds. They are ideas that exist independently of any physical universe. Furthermore, I happen to believe in something I would call “The Absolute Infinite”. I do not know what this is precisely, I just have an aesthetic sense of It, and It is something that might also be thought of as the source of all things, some kind of universal uncaused cause of all things. But to me, these are not scientific beliefs. They are personal beliefs about a greater reality that I have gleaned from many sources over the years. Yet, amazingly perhaps, physics and mathematics have been one of my prime sources for such beliefs.

The fact I cannot understand such a concept (as the Absolute Infinite) should not give me any pause to wonder if it truly exists or not. And I feel no less mature or more infantile for having such beliefs. If anything I pity the intellectually impoverished souls who cannot be open to such beliefs and speculations. I might point out that speculation is not a bad thing either, without speculative ideas where would science be? Stuck with pre-Copernican Ptolemy cosmology or pre-Eratosthenes physics I imagine, for speculation was needed to invent gizmos like telescopes and to wonder about how to measure the diameter of the Earth using just the shadow of a tall tower in Alexandria.

To imagine something greater than ourselves is always going to be difficult, and to truly understand such a greater reality is perhaps canonically impossible. So we aught not let such smallness of our minds debar us from truth. It is thus a struggle to keep an open-mind about metaphysics, but I think it is morally correct to do so and to resist the weak temptation to give in to philosophical negativism and minimalism about the worlds that potentially exist beyond ours.

Strangely, many self-professing atheists think they can imagine we live in a super Multiverse. I would ask them how they can believe in such a prolific cosmos and yet not also accept the potential existences beyond the physical? And not even “actual existence” just simply “potential existence”. I would then point out that as long as there is admitted potential reality and plausible truth to things beyond the physical, you cannot honestly commit to any brand of atheism. To my mind, even my most open-mind, this form of atheism would seem terribly dishonest and self-deceiving.

Exactly how physics and mathematics could inform my spiritual beliefs is hard to explain in a few words. Maybe sometime later there is an essay to be written on this topic. For now, all I will say is that like Nima Arkani-Hamed, I have a deep sense of the “correctness” of certain ways of thinking about physics, and sometimes mathematics too (although mathematics is less constrained). And similar senses of aesthetics draw me in like the unveiling of a Beethoven symphony to an almost inevitable realisation of some version of truth to the reality of worlds beyond the physical, worlds where infinite numbers reside, where the mind can explore unrestrained by bones and flesh and need for food or water.  In such worlds greater beauty than on Earth resides.


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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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Eternal Rediscovery

I have a post prepared to upload in a bit that will announce a possible hiatus from this WordPress blog. The reason is just that I found a cool book I want to try to absorb, The Princeton Companion to Mathematics by Gowers, Barrow-Green and Leader. Doubtless I will not be able to absorb it all in one go, so I will likely return to blogging periodically. But there is also teaching and research to conduct, so this book will slow me down. The rest of this post is a light weight brain-dump of some things that have been floating around in my head.

Recently, while watching a lecture on topology I was reminded that a huge percentage of the writings of Archimedes were lost in the siege of Alexandria. The Archimedean solids were rediscovered by Johannes Kepler, and we all know what he was capable of! Inspiring Isaac Newton is not a bad epitaph to have for one’s life.

The general point about rediscovery is a beautiful thing. Mathematics, more than other sciences, has this quality whereby a young student can take time to investigate previously established mathematics but then take breaks from it to rediscover theorems for themselves. How many children have rediscovered Pythagoras’ theorem, or the Golden Ratio, or Euler’s Formula, or any number of other simple theorems in mathematics?

Most textbooks rely on this quality. It is also why most “Exercises” in science books are largely theoretical. Even in biology and sociology. They are basically all mathematical, because you cannot expect a child to go out and purchase a laboratory set-up to rediscover experimental results. So much textbook teaching is mathematical for this reason.

I am going to digress momentarily, but will get back to the education theme later in this article.

The entire cosmos itself has sometimes been likened to an eternal rediscovery. The theory of Eternal Inflation postulates that our universe is just one bubble in a near endless ocean of baby and grandparent and all manner of other universes. Although, recently, Alexander Vilenkin and Audrey Mithani found that a wide class of inflationary cosmological models are unstable, meaning that could not have arisen from a pre-existing seed. There had to be a concept of an initial seed. This kind of destroys the “eternal” in eternal inflation. Here’s a Discover magazine account: What Came Before the Big Bang? — Cosmologist Alexander Vilenkin believes the Big Bang wasn’t a one-off event”. Or you can click this link to hear Vilenkin explain his ideas himself: FQXi: Did the Universe Have a Beginning? Vilenkin seems to be having a rather golden period of originality over the past decade or so, I regularly come across his work.

If you like the idea of inflationary cosmology you do not have to worry too much though. You still get the result that infinitely many worlds could bubble out of an initial inflationary seed.

Below is my cartoon rendition of eternal inflation in the realm of human thought:
cosmol_primordial_thoughtcloud_field

Oh to be a bubble thoughtoverse of the Wittenesque variety.

Quantum Fluctuations — Nothing Cannot Fluctuate

One thing I really get a bee in my bonnet about are the endless recountings in the popular literature about the beginning of the universe is the naïve idea that no one needs to explain the origin of the Big Bang and inflatons because “vacuum quantum fluctuations can produce a universe out of nothing”. This sort of pseudo-scientific argument is so annoying. It is a cancerous argument that plagues modern cosmology. And even a smart person like Vilenkin suffers from this disease. Here I quote him from a quote in another article on the PBS NOVA website::

Vilenkin has no problem with the universe having a beginning. “I think it’s possible for the universe to spontaneously appear from nothing in a natural way,” he said. The key there lies again in quantum physics—even nothingness fluctuates, a fact seen with so-called virtual particles that scientists have seen pop in and out of existence, and the birth of the universe may have occurred in a similar manner.
Source: http://www.pbs.org/wgbh/nova/blogs/physics/2012/06/in-the-beginning/

At least you have to credit Vilenkin with the brains to have said it is only “possible”. But even that caveat is fairly weaselly. My contention is that out of nothing you cannot get anything, not even a quantum fluctuation. People seem to forget quantum field theory is a background-dependent theory, it requires a pre-existing spacetime. There is no “natural way” to get a quantum fluctuation out of nothing. I just wish people would stop insisting on this sort of non-explanation for the Big Bang. If you start with not even spacetime then you really cannot get anything, especially not something as loaded with stuff as an inflaton field. So one day in the future I hope we will live in a universe where such stupid arguments are nonexistent nothingness, or maybe only vacuum fluctuations inside the mouths of idiots.

There are other types of fundamental theories, background-free theories, where spacetime is an emergent phenomenon. And proponents of those theories can get kind of proud about having a model inside their theories for a type of eternal inflation. Since their spacetimes are not necessarily pre-existing, they can say they can get quantum fluctuations in the pre-spacetime stuff, which can seed a Big Bang. That would fit with Vilenkin’s ideas, but without the silly illogical need to postulate a fluctuation out of nothingness. But this sort of pseudo-science is even more insidious. Just because they do not start with a presumption of a spacetime does not mean they can posit quantum fluctuations in the structure they start with. I mean they can posit this, but it is still not an explanation for the origins of the universe. They still are using some kind of structure to get things started.

Probably still worse are folks who go around flippantly saying that the laws of physics (the correct ones, when or if we discover them) “will be so compelling they will assert their own existence”. This is basically an argument saying, “This thing here is so beautiful it would be a crime if it did not exist, in fact it must exist since it is so beautiful, if no one had created it then it would have created itself.” There really is nothing different about those two statements. It is so unscientific it makes me sick when I hear such statements touted as scientific philosophy. These ideas go beyond thought mutation and into a realm of lunacy.

I think the cause of these thought cancers is the immature fight in society between science and religion. These are tensions in society that need not exist, yet we all understand why they exist. Because people are idiots. People are idiots where their own beliefs are concerned, by in large, even myself. But you can train yourself to be less of an idiot by studying both sciences and religions and appreciating what each mode of human thought can bring to the benefit of society. These are not competing belief systems. They are compatible. But so many believers in religion are falsely following corrupted teachings, they veer into the domain of science blindly, thinking their beliefs are the trump cards. That is such a wrong and foolish view, because everyone with a fair and balanced mind knows the essence of spirituality is a subjective view-point about the world, one deals with one’s inner consciousness. And so there is no room in such a belief system for imposing one’s own beliefs onto others, and especially not imposing them on an entire domain of objective investigation like science. And, on the other hand, many scientists are irrationally anti-religious and go out of their way to try and show a “God” idea is not needed in philosophy. But in doing so they are also stepping outside their domain of expertise. If there is some kind of omnipotent creator of all things, It certainly could not be comprehended by finite minds. It is also probably not going to be amenable to empirical measurement and analysis. I do not know why so many scientists are so virulently anti-religious. Sure, I can understand why they oppose current religious institutions, we all should, they are mostly thoroughly corrupt. But the pure abstract idea of religion and ethics and spirituality is totally 100% compatible with a scientific worldview. Anyone who thinks otherwise is wrong! (Joke!)

Also, I do not favour inflationary theory for other reasons. There is no good theoretical justification for the inflaton field other than the theory of inflation prediction of the homogeneity and isotropy of the CMB. You’d like a good theory to have more than one trick! You know. Like how gravity explains both the orbits of planets and the way an apple falls to the Earth from a tree. With inflatons you have this quantum field that is theorised to exist for one and only one reason, to explain homogeneity and isotropy in the Big Bang. And don’t forget, the theory of inflation does not explain the reason the Big Bang happened, it does not explain its own existence. If the inflaton had observable consequences in other areas of physics I would be a lot more predisposed to taking it seriously. And to be fair, maybe the inflaton will show up in future experiments. Most fundamental particles and theoretical constructs began life as a one-trick sort of necessity. Most develop to be a touch more universal and will eventually arise in many aspects of physics. So I hope, for the sake of the fans of cosmic inflation, that the inflaton field does have other testable consequences in physics.

In case you think that is an unreasonable criticism, there are precedents for fundamental theories having a kind of mathematically built-in explanation. String theorists, for instance, often appeal to the internal consistency of string theory as a rationale for its claim as a fundamental theory of physics. I do not know if this really flies with mathematicians, but the string physicists seem convinced. In any case, to my knowledge the inflation does not have this sort of quality, it is not a necessary ingredient for explaining observed phenomena in our universe. It does have a massive head start on being a candidate sole explanation for the isotropy and homogeneity of the CMB, but so far that race has not yet been completely run. (Or if it has then I am writing out of ignorance, but … you know … you can forgive me for that.)

Anyway, back to mathematics and education.

You have to love the eternal rediscovery built-in to mathematics. It is what makes mathematics eternally interesting to each generation of students. But as a teacher you have to train the nerdy children to not bother reading everything. Apart from the fact there is too much to read, they should be given the opportunity to read a little then investigate a lot, and try to deduce old results for themselves as if they were fresh seeds and buds on a plant. Giving students a chance to catch old water as if it were fresh dewdrops of rain is a beautiful thing. The mind that sees a problem afresh is blessed, even if the problem has been solved centuries ago. The new mind encountering the ancient problem is potentially rediscovering grains of truth in the cosmos, and is connecting spiritually to past and future intellectual civilisations. And for students of science, the theoretical studies offer exactly the same eternal rediscovery opportunities. Do not deny them a chance to rediscover theory in your science classes. Do not teach them theory. Teach them some theoretical underpinnings, but then let them explore before giving the game away.
With so much emphasis these days on educational accountability and standardised tests there is a danger of not giving children these opportunities to learn and discover things for themselves. I recently heard an Intelligence2 “Intelligence Squared” debate on academic testing. One crazy women from the UK government was arguing that testing, testing, and more testing — “relentless testing” were her words — was vital and necessary and provably increased student achievement.

Yes, practising tests will improve test scores, but it is not the only way to improve test scores. And relentless testing will improve student gains in all manner of mindless jobs out there is society that are drill-like and amount to going through routine work, like tests. But there is less evidence that relentless testing improves imagination and creativity.

Let’s face it though. Some jobs and areas of life require mindlessly repetitive tasks. Even computer programming has modes where for hours the normally creative programmer will be doing repetitive but possibly intellectually demanding chores. So we should not agitate and jump up and down wildly proclaiming tests and exams are evil. (I have done that in the past.)

Yet I am far more inclined towards the educational philosophy of the likes of Sir Ken Robinson, Neil Postman, and Alfie Kohn.

My current attitude towards tests and exams is the following:

  1. Tests are incredibly useful for me with large class sizes (120+ students), because I get a good overview of how effective the course is for most students, as well as a good look at the tails. Here I am using the fact test scores (for well designed tests) do correlate well with student academic aptitudes.
  2. My use of tests is mostly formative, not summative. Tests give me a valuable way of improving the course resources and learning styles.
  3. Tests and exams suck as tools for assessing students because they do not assess everything there is to know about a student’s learning. Tests and exams correlate well with academic aptitudes, but not well with other soft skills.
  4. Grading in general is a bad practise. Students know when they have done well or not. They do not need to be told. At schools if parents want to know they should learn to ask their children how school is going, and students should be trained to be honest, since life tends to work out better that way.
  5. Relentless testing is deleterious to the less academically gifted students. There is a long tail in academic aptitude, and the students in this tail will often benefit from a kinder and more caring mode of learning. You do not have to be soft and woolly about this, it is a hard core educational psychology result: if you want the best for all students you need to treat them all as individuals. For some tests are great, terrific! For others tests and exams are positively harmful. You want to try and figure out who is who, at least if you are lucky to have small class sizes.
  6. For large class sizes, like at a university, do still treat all students individually. You can easily do this by offering a buffet of learning resources and modes. Do not, whatever you do, provide a single-mode style of lecture+homework+exam course. That is ancient technology, medieval. You have the Internet, use it! Gather vast numbers of resources of all different manners of approach to your subject you are teaching, then do not teach it! Let your students find their own way through all the material. This will slow down a lot of students — the ones who have been indoctrinated and trained to do only what they are told — but if you persist and insist they navigate your course themselves then they should learn deeper as a result.

Solving the “do what I am told” problem is in fact the very first job of an educator in my opinion. (For a long time I suffered from lack of a good teacher in this regard myself. I wanted to please, so I did what I was told, it seemed simple enough. But … Oh crap, … the day I found out this was holding me back, I was furious. I was about 18 at the time. Still hopelessly naïve and ill-informed about real learning.) If you achieve nothing else with a student, transitioning them from being an unquestioning sponge (or oily duck — take your pick) to being self-motivated and self-directed in their learning is the most valuable lesson you can ever give them. So give them it.

So I use a lot of tests. But not for grading. For grading I rely more on student journal portfolios. All the weekly homework sets are quizzes though, so you could criticise the fact I still use these for grading. As a percentage though, the Journals are more heavily weighted (usually 40% of the course grade). There are some downsides to all this.

  • It is fairly well established in research that grading using journals or subjective criteria is prone to bias. So unless you anonymise student work, you have a bias you need to deal with somehow before handing out final grades.
  • Grading weekly journals, even anonymously, takes a lot of time, about 15 to 20 times the hours that grading summative exams takes. So that’s a huge time commitment. So you have to use it wisely by giving very good quality early feedback to students on their journals.
  • I still haven’t found out how to test the methods easily. I would like to know quantitatively how much more effective journal portfolios are compared to exam based assessments. I am not a specialist education researcher, and I research and write a about a lot of other things, so this is taking me time to get around to answering.

I have not solved the grading problem, for now it is required by the university, so legally I have to assign grades. One subversive thing I am following up on is to refuse to submit singular grades. As a person with a physicists world-view I believe strongly in the role of sound measurement practice, and we all know a single letter grade is not a fair reflection on a student’s attainment. At a minimum a spread of grades should be given to each student, or better, a three-point summary, LQ, Median, UQ. Numerical scaled grades can then be converted into a fairer letter grade range. And GPA scores can also be given as a central measure and a spread measure.

I can imagine many students will have a large to moderate assessment spread, and so it is important to give them this measure, one in a few hundred students might statistically get very low grades by pure chance, when their potential is a lot higher. I am currently looking into research on this.

OK, so in summary: even though institutions require a lot of tests you can go around the tests and still given students a fair grade while not sacrificing the true learning opportunities that come from the principle of eternal rediscovery. Eternal rediscovery is such an important idea that I want to write an academic paper about it and present at a few conferences to get people thinking about the idea. No one will disagree with it. Some may want to refine and adjust the ideas. Some may want concrete realizations and examples. The real question is, will they go away and truly inculcate it into their teaching practices?

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A Plain Simple Lecture — Non-ergodic , but … satisfying

There is another talk from the Philosophy of Cosmology Conference in Tenerife 2014 that is in a similar league to Joel Primack’s awesome display of the Bolshoi Simulations of dark matter structure. Only this one I will write about tonight is pretty much words and equations only. No pretty pictures. But don’t let that dissuade you from enjoying the talk by Bob Wald on Gravity and Thermodynamics.

Most physics students might only know Robert Wald from his famous textbook on General Relativity.

Aside: While searching for a nice picture to illuminate this post I came across a nice freehand SVG sketch of Shaun Maguire’s. He’s a postdoc at Caltech and writes nicely in a blog there: Quantum Frontiers. If you are more a physics/math geek than a philosophy/physics geek then you will enjoy his blog. I found it very readable, not stunning poetic prose, but easy-going and sufficiently high on technical content to hold my interest.

blackhole_thermodynamics_RindlerQuest2

Says Maguire, “I’ve been trying to understand why the picture on the left is correct, even though my intuition said the middle picture should be (intuition should never be trusted when thinking about quantum gravity.)” Source: http://quantumfrontiers.com/2014/06/20/ten-reasons-why-black-holes-exist/

That has to do with black hole firewalls, which digresses away from Wald’s talk.

It is not true to say Wald’s talk is plain and simple, since the topic is advanced, only a second course on general relativity would cover the details. And you need to get through a lot of mathematical physics in a first course of general relativity. But what I mean is that Wald is such a knowledgeable and clear thinker that he explains everything crisply and understandably, like a classic old-school teacher would. It is not flashy, but damn! It is tremendously satisfying and enjoyable to listen to. I could hit the pause button and read his slides then rewind and listen to his explanation and it just goes together so sweetly. He neither repeats his slides verbatim, not deviates from them confusingly. However, I think if I were in the audience I would be begging for a few pauses of silence to read the slides. So the advantage is definitely with the at-home Internet viewer.

Now if you are still reading this post you should be ashamed! Why did you not go and download the talk and watch it?

I loved Wald’s lucid discussion of the Generalised Second Law (which is basically a redefinition of entropy, which is that generalised entropy should be the sum of thermodyanmics entropy plus black hole entropy or black hole surface area.)

Then he gives a few clear arguments that provide strong reasons for regarding the black hole area formula as equivalent to an entropy, one of which is that in general relativity dynamic instability is equivalent to thermodynamic instability, hence the link between the dynamic process of black hole area increase is directly connected to black hole entropy. (This is in classical general relativity.)

But then he puts the case that the origin of black hole entropy is not perfectly clear, because black hole entropy does not arise out of the usual ergodicity in statistical mechanics systems, whereby a system in an initial special state relaxes via statistical processes towards thermal equilibrium. Black holes are non-ergodic. They are fairly simple beasts that evolve deterministically. “The entropy for a black hole arises because it has a future horizon but no past horizon,” is how Wald explains it. In other words, black holes do not really “equilibrate” like classical statistical mechanics gases. Or at least, they do not equilibrate to a thermal temperature ergodically like a gas, they equilibrate dynamically and deterministically.

Wald’s take on this is that, maybe, in a quantum gravity theory, the detailed microscopic features of gravity (foamy spacetime?) will imply some kind of ergodic process underlying the dynamical evolution of black holes, which will then heal the analogy with statistical mechanics gas entropy.

This is a bit mysterious to me. I get the idea, but I do not see why it is a problem. Entropy arises in statistical mechanics, but you do not need statistically ergodic processes to define entropy. So I did not see why Wald is worried about the different equilibration processes viz. black holes versus classical gases. They are just different ways of defining an entropy and a Second Law, and it seems quite natural to me that they therefore might arise from qualitatively different processes.

But hold onto you hats. Wald next throws me a real curve ball.

Smaller then the Planck Scale … What?

Wald’s next concern about a breakdown of the analogy between statistical gas entropy and dynamic black hole entropy is a doozie. He worries about the fact the vacuum fluctuations in a conventional quantum field theory are basically ignored in statistical mechanics, yet they cannot (or should not?) be ignored in general relativity, since, for instance, the ultra-ultra-high energy vacuum fluctuations in the early universe get red-shifted by the expansion of the universe into observable features we can now measure.

Wald is talking here about fluctuations on a scale smaller than the Planck length!

To someone with my limited education you begin by thinking, “Oh, that’s ok, we all know (one says knowingly not really knowing) that stuff beyond the Plank scale is not very clearly defined and has this sort of ‘all bets are off’ quality about it. So we do not need to worry about it yet until there is a theory covering the Planck scale.”

But if I understand it correctly, what Wald is saying is that what we see in the cosmic background radiation, or maybe in some other observations (Wald is not clear on this), corresponds to such red shifted modes, so we literally might be seeing fluctuations that were originated on a scale smaller than the Planck length if we probe the cosmic background radiation to highly ultra-red shifted wavelengths.

That was a bit of an eye-opener for me. I was previously not aware of any physics that potentially probed beyond the Planck scale. I wonder if anyone else thought this is surprising? Maybe if I updated my physics education I’d find out that it is not so surprising.

In any case, Wald does not discuss this, since his point is about the black hole case where at the black hole horizon a similar shifting of modes occurs with ultra-high energy vacuum fluctuations near the horizon getting red shifted far from the black hole into “real” observable degrees of freedom.

Wald talks about this as a kind of “creation of new degrees of freedom”. And of course this does not occur in statistical gas mechanics where there are a fixed number of degrees of freedom, so again the analogy he wants between black hole thermodynamics and classical statistical mechanics seems to break down.

There is some cool questioning going on here though. The main problem with the vacuum fluctuations Wald points out is that one does not know how to count the states in the vacuum. So the implicit idea there, which Wald does not mention, is that maybe there is a way to count states of the vacuum, which might then heal the thermodynamics analogy Wald is pursuing. My own (highly philosophical, and therefore probably madly wrong) speculation would be that quantum field theory is only an effective theory, and that a more fundamental theory of physics with spacetime as the only real field and particle physics states counted in a background-free theory kind of way, might, might yield some way of calculating vacuum states.

Certainly, I would imagine that if field theory is not the ultimate theory, then the whole idea of vacuum field fluctuations gets called into suspicion. The whole notion of a zero-point background field vacuum energy becomes pretty dubious altogether if you no longer have a field theory as the fundamental framework for physics. But of course I am just barking into the wind hoping to see a beautiful background-free framework for physics.

Like the previous conundrum of ergodicity and equilibration, I do not see why this degree of freedom issue is a big problem. It is a qualitative difference which breaks the strong analogy, but so what? Why is that a pressing problem? Black holes are black holes, gases are gases, they ought to be qualitatively distinct in their respective thermodynamics. The fact there is the strong analogy revealed by Bekenstein, Hawking, Carter, and others is beautiful and does reveal general universality properties, but I do not see it as an area of physics where a complete unification is either necessary or desired.

What I do think would be awesome, and super-interesting, would be to understand the universality better. This would be to ask further (firstly) why there is a strong analogy, and (secondly) explain why and how it breaks down.

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This post was interrupted by an apartment moving operation, so I ran out of steam on my consciousness stream, so will wrap it up here.

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“Nothing to Hide” Arguments and Generalisations

A good friend of mine re-posted a link on Google+ the other day: I’ve Got Nothing to Hide” and Other Misunderstandings of Privacy, by Daniel J. Solove. It’s not a bad read, so go check it out.

free_AaronSwartz_journals

A great cartoon of Aaron giving everyone access to JSTOR. Whoever drew this needs crediting, but I can only make out their last name “Pinn”. I grabbed this from Google image search. So thanks Mr or Ms Pinn.

So that this is not a large departure from my recent trend in blog topics, I wanted to share a few thoughts about similar “easy arguments” in quite different fields.

The “Nothing to Show” Argument Against Publishing

This is an argument I’ve used all my life to avoid publishing. I hate people criticising my work. So I normally tell supervisors or colleagues that I have nothing of interest to publish. This is an extraordinary self-destructive thing to do in academia, it basically kills one’s career. But there are a few reasons I do not worry.

Firstly, I truly do not like publishing for the sake of academic advancement. Secondly, I have a kind of inner repulsion against publishing anything I think is stupid or trivial or boring. Thirdly, I am quite lazy, and if I am going to fight to get something published it should be worth the fight, or should be such good quality work that it will not be difficult to publish somewhere. Fourth, I dislike being criticised so much I will sometimes avoid publishing just to avoid having to deal with reviewer critiques. That’s a pretty immature and childish sensitivity, and death for an academic career, but with a resigned sigh I have to admit that’s who I am, at least for now, a fairly childish immature old dude.

There might be a few other reasons. A fifth I can think of is that I wholeheartedly agree with Aaron Swartz’s Guerilla Open Access Manifesto, which proclaims the credo of free and open access to publicly funded research for all peoples of all nations. That’s not a trivial manifesto. You could argue that the public of the USA funds research that should then be free and open, but only to the public of the USA, and likewise for other countries. But Swartz was saying that the tax payers of the respective countries have already paid for the research, the researcher’s have been fully compensated, and scientists do not get any royalties from journal articles anyway, and therefore their research results should be free for all people of all nations to use. Why this is important is the democratising of knowledge, and perhaps more importantly the unleashing of human potential and creativity. If someone in Nigeria is denied access to journals in the USA then that person is denied the chance to potentially use that research and contribute to the sum total of human knowledge. We should not restrict anyone such rights.

OK, that was a bit of a diversion. The point is, I would prefer to publish my work in open-access journals. I forget why that’s related to my lack of publishing … I did have some reason in mind before I went on that rant.

I’ve read a lot of total rubbish in journals, and I swear to never inflict such excrement on other people’s eyes. So anything I publish would be either forced by a supervisor, or will be something I honestly think is worth publishing, something that will help to advance science. It is not out of pure altruism that I hesitate to publish my work, although that is part of it. The impulse against publishing is closer to a sense of aesthetics. Not wanting to release anything in my own name that is un-artful. I’m not an artist, but I have been born or raised with an artistic temperament, much to my detriment I believe. Artless people have a way of getting on much better in life. But there it is, somewhere in my genes and in my nurturing.

So I should resolve to never use the “Nothing to Show” argument. I have to get my research out in the open, let it be criticised, maybe some good will come of it.

The “Nothing to Fear” Argument Against Doing Stupid Stuff

Luckily I am not prone to this argument. If you truly have nothing to fear, then by all means … but often this sort of argument means you personally do not mind suffering whatever it is that’s in store, and that use of the argument can be fatal. So if you ever hear you inner or outer voice proclaiming “I have nothing to fear …” then take a breath and pause, make sure there truly is nothing to fear (but then, why would you be saying this out loud?). There is not much more to write about it. But feel free to add comments.

The “Nothing to Lose” Argument in Favour of Being Bold

This is normally a very good argument and perhaps the best use of the “Nothing to …” genre. If you truly have nothing to lose then you are not confounding this with the “Nothing to Fear” stupidity. So what more needs to be said?


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