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Teaching and learning by aphorism

Hi, guys and gals (and others in between),

This page is dedicated to a few of the things I keep close by me (in my head) as I try to navigate the mean streets of life, education, and love. I now believe it is possible to teach computer science by these (and other) aphorisms. [See remainder of my introductory remarks after the contents list, next.]

Contents

Introductory remarks

... You may think differently, and you may be surprised that I seem to start with topics that are not (apparently) computer science. I assure you that CS is a broad discipline, and the education of students needs to be broader still; they come to class at different points in their development, of course, but with a yearning (one must assume) to learn important things; useful nuggets about how to work, and how to stay well, are of great value to their study of CS, and their future lives - that's my considered view.

I hope these aphorisms, then, are of use to you, whatever your current dreams and hopes, and past, painful experiences. Nourish your hopes!

If you are an AI robot, and not a guy or gal (or in-betweener), and can understand any of the aphorisms, below, and apply them in the world, do please write me. I'd love to ask you some questions!

Bot or human, if you have a comment you want made public, I will do my best to add it here with attribution. Just email me, please.

PLEASE NOTE: Most of the aphorisms below are written from memory, not checking, so wording may not be perfect. I apologise, and you may email me to correct me. Some of the aphorisms are by me, Joshua Knowles, indicated as "JK". I attach short notes as to how I think they should best be interpreted. Now, while the total number of bits on this page is not so great (particularly when you look only at the fundamental CS aphorisms), and so could be communicated over a noisy channel quickly, the amount of learning required to understand them properly is great. This is why Buddhist monks in training are given a koan to contemplate for several days or weeks, and then are tested on it by arguing (in speech) for their interpretation, against other monks in training, or a Master. Are we doing the same at the academy, or are we giving students a load of rubbish they do not need, and NO time to contemplate and practise their understanding?

The Aphorisms (a selection)

Aphorisms for life and learning

The purpose of the warrior is always peace (von Clausewitz; On War)
JK comments: Notice that this is no paradox; it says warrior and not warmonger, and not terrorist. The warrior is at the opposite pole to those. So, do karate, or box, or Feng Shui (I'm kiddin'), or Tai Chi, as these will inure you to pain, and the bouts always end with a deep bow and mutual respect and love. And send your students and kids along too!

There is nothing noble in being superior to your fellow man; true nobility is being superior to your former self. (Ernest Hemingway)
JK comments: Do I really need to say anything? It's so true, it should be engraved on our forearms at birth, and taken as medicine every day!

The most difficult subjects can be explained to the most slow-witted man if he has not formed any idea of them already; but the simplest thing cannot be made clear to the most intelligent man if he is firmly persuaded that he knows already, without a shadow of doubt, what is laid before him. (Leo Tolstoy)

The pen is mightier than the sword. (Edward Bulwer-Lytton in 1839)
JK comments: No, it really is - way mightier. Compare President Obama with the fencing olympic gold medalist, whose name we don't even know. President Obama has a Nobel Peace prize, and while some dislike this fact, it is the case that he was awarded it, and accepted it, and the title of his memoir was, "The Audacity of Hope".

The Pythagorean rule, as any mathematical theorem, is not diminished with more use - it is a renewable resource, rather like "The Magic Pudding" (N. Lindsay). So, spread the word of all your mathematical theorems far and wide, and the world will be a richer place.
JK, January, 2017
JK comments: I have heard something similar to the first part somewhere but don't know the source. If you know or find out, let me know, please.

You will die; why not live a little first?
JK, December 2016
JK notes: I'm sure someone must have said this before, but I will let you tell me as I don't have time to look it up right now...

Games are a compromise between intimacy and keeping intimacy away. (Eric Berne; psychotherapist)
JK comments: this is beautiful simplicity but speaks volumes. Contemplate, and contemplate again. Consider all your relationships at work, at home, and with yourself and ask fearlessly whether you are yearning too much (why?), or running away.

Q. Who are the biggest contributors to education of the public (say, in the UK), who are alive today?
A. I would say my top five are: (1) Tim Berners-Lee; (2) Jimmy Wales; (3) Melvyn Bragg ("In Our Time"; BBC Radio 4); (4) Kirsty Wark (broadcaster, journalist, "critic"); and, (5) Sean Rafferty (music broadcaster on BBC Radio 3).
JK, December 2016
JK comments: notice that a computer scientist/physicist is No 1. He has to be, right? You wouldn't be able to read this if Berners-Lee hadn't come up with the WWW, albeit someone else would have, but that's by the bye.

I'm thinkin' about the fireworks that go off when you smile (Chrissie Hynde; Don't get me wrong (song lyric))

The purpose of life is not the avoidance of pain. Yet, this is how many people live their lives (whether or not they see it), and try to help others avoid it too, with their little counsels to take care, by which they mean fawn and comply and be repressed. Don't do it: take pain, and give pain, in equal and generous measure. And love too. You will be remember'ed.
JK, December 2016

Thereupon he turned pale and cried "Ah!" as if he were pierced to the heart....Then Palamon knit his brows angrily.
(Chaucer; The Knights' Tale)
JK personal note: Someone texted me that I knit my brow sometimes, and this pierced my heart as surely as the poor knight's of the tale. (This is why I know this little passage from Chaucer as I had to see where such a lovely phrase originated.) Pain is good though; I am alive!

Blood, sweat and tears (Winston Churchill; speech: "blood, toil, tears, and sweat")
JK comments: this is all Churchill said he could promise, and his plain statement of that hard truth was a hope to a nation torn. Students, I can offer you know more than blood, toil, tears, and sweat... But the ecstasy will be yours alone.

The agony and the ecstasy (Irving Stone; book of the same name)

I feel sorry for guys on Tour today because they don't know tough things. I had tough things every day of my life. (Ben Hogan; professional golfer)
JK comments: Hogan won 5 US Opens, and The Open championship on his only attempt, beating Peter Thomson into second place, who then subsequently won it 5 times!

Freedom's just another word for nothing left to lose, nothin' don't mean nothin' 'less it's free. (Kris Kristofferson; Me and Bobby McGee)
JK comments: Best sung by Janis Joplin in my humble opinion. Try having loved and lost, and listen to that song! Immensely hard.

In theory, theory and practice are the same; in practice they are not. (GEP Box; statistician)

Prediction is difficult, especially about the future. (Yogi Berra; baseball player)

What feats he did that day (Shakespeare; Henry V)
JK comments: Like Churchill, he is rousing an army before a bloody battle, and telling them of their future glory "if he come safe home".

Walk across the damned grass if you like. You will feel the damp, cool blades beneath your feet, and the conversation you have with the park keeper will brighten his day.
JK, December 2016

Matrices don't f***ing commute!* Remember this, as it will save you a lot of s***! Especially if you try to control robot arms, or render 3D graphics.
JK, December 2016
*The matrix product is not commutative in general (Wikipedia)
JK comments: I use colourful language here to add to the likelihood that the student would understand the importance of this, and remember it, and appreciate that others have felt pain at matrices that don't commute (give the same answer whichever way around they are multiplied). This leads to fewer bad mistakes in exams or real life, and less heartache and self-hate for the student. Doesn't it?

It is only shallow people who do not judge by appearances. The true mystery of the world is the visible, not the invisible... (Oscar Wilde)

Remember that great things are not just possible, they are inevitable, and intrinsic to the very fabric of time and space. Remember Nelson Mandela, alone in his banishment, and remember his return, and the peace he brought to his nation, and the beacon of light that reached every corner of the globe, and the outpouring of love that will be for time eternal.
JK, December 2016
JK comments: To me, as quite an abstract thinker, it is very obvious that Nelson Mandela is a product of physics or the universe, of gravity, or the weak and strong force, etc., and is the magic of the universe, and its mystery. We may never be able to do the quantum physics of Mandela, and have to use some other ways of getting to explain him, but that's my point: he needs explaining, and if we are to create bots like Mandela, we must use every tool at our disposal! Aphorism, for example.

Don't worry; pray instead. Even if you don't believe in God, pray every day. By using the word "pray", you will be forced to connect to the greatest truths, and hopes, and the eternal; and all your days will be filled with joy and hope and yes, pain.
JK, December 2016

Learn to schedule your pain, and meet it first. Delay gratification. It is the only decent way to live. (M. Scott Peck; The Road Less Travelled) Modest paraphrasing by JK, December 2016

Listen to the most tragic and heartrending music, and appreciate all great art. Appreciate the human sacrifice involved. Do not believe for one moment that it took only 10,000 hours, or that it is the result of talent alone. It is the inevitable result of profound love practised patiently every day. Everything yields to patience and love.
JK, December 2016

The Ugly Duckling (Hans Christian Andersen; title of the fable on growth and rebirth)

The Sun Also Rises (Ernest Hemingway; title of the book about post-WW1 decadence and the lost generation)

Still I Rise (Maya Angelou; poem / song)

Who dares wins (motto of the SAS).

The most difficult subjects can be explained to the most slow-witted man if he has not formed any idea of them already; but the simplest thing cannot be made clear to the most intelligent man if he is firmly persuaded that he knows already, without a shadow of doubt, what is laid before him. (Leo Tostoy)
JK comments: bears repeating! Many of these bear repeating, to be honest. And contemplating for a while. Just come back another day. Hit bookmark.

Always deliver your talks naked; else, what's the point?
JK, December 2016
Obviously, with your clothes on, unless you want to be before the Dean.

Always digress.
JK, December 2016, but with significant influence from JD Salinger's Catcher in the Rye.
JK comments: I have not said enough on this page about narrative form, so far. But the classic narrative is to introduce a character, put him/her/it in strife, and then resolve the strife. Salinger follows the form (of course). It is both an important part of Holden's character, introduced in the first pages, that he likes to hear teachers and students digress from the main topic (maybe because he is a deep thinker and likes to see what things really concern them, not what they are forced to say). So, I digress on purpose (or with awareness) too. Do you? I also digress because of distractedness because I am far from perfect, but students need to see that too (go naked; see above). I digress ;-)

An expert is someone who demonstrates elite skill at something.
JK, December 2016.
JK notes: Always trust experts; hardly ever trust people who claim to be experts. Jimmy Carr is an expert on comedy; he recently hosted a Horizon documentary on laughter, and was polite to academics who claimed expertise, yet it was patently clear who the expert in the room was to anyone with their eyes and ears open. (Although, to be fair, it can be difficult to keep your eyes open when you are bent over double, guffawing!) Armando Iannucci is another expert comedian, and of course there are many more; academics no s*** about why people laugh, or how to make it happen in large droves.

What computer science is

I think the following could be a short course on computer science for people new to the subject, whether they are five years old (my younger son is six and he already knows some of this stuff), or seventy-five (Dad). I transmit few bits (that is, binary digits, or raw information) here, yet with digression and time for contemplation on the students' and my part, it could still fill a semester. It could also be given in one hour if needs be. You would need to adapt, and add illustrations and digressions, as all good teachers do. But I hope to have captured some of the essentials, and some brief comments that cut through common misconceptions that could immediately arise, and that are unhelpful misconceptions. Let me know if you agree, or disagree. (Please forget my job title, and write to me as an equal. We are all equals, really).

Computer science is a modern subject with ancient foundations (of course!)
JK, December 2016.

Computer science comprises several foundational theories:
- computability theory
- information theory
- complexity theory, and the theory of NP-completeness
- logic, methods of inference, and learning theory
- decision theory
- game theory
- (network or) graph theory
- set theory
- discrete mathematics, including combinatorics and basic number theory...

...and their applications.
JK, December 2016

Computability theory is mostly about what a certain type of (Universal) machine can (and can't) figure out by step-by-step shifting of bits around.
JK, December 2016

Information theory deals with compression of information, and the reverse, adding redundancy to it, so that we can send it efficiently over noisy communication wires, or store it, without error.
JK, December 2016

Complexity theory is illustrated by the question of how to add up all the numbers from 1 to 100 without adding up all the numbers from 1 to 100. Euler showed us that it can be done by oberving that if we write the numbers out twice (on two lines), with the numbers in reverse order on the second line, and sum all those columns, we end up with 100 lots of 101 = 100 times 101. We then need to halve the result, to give finally, 5050. This is efficient if we can multiply efficiently.
JK, December 2016
JK comments: If anyone is out there who doesn't feel sure what an algorithm is (and I know there are such people), then the Euler method of summing an "arithmetic series" (that's just a bunch of numbers that get bigger, usually by adding a constant to the previous number, such as the numbers 1-100), given above, is as good an example of an (efficient) algorithm as any. Notice that an algorithm is just a step-by-step procedure or recipe for transforming some input into some output (both must be clearly defined), reliably and effectively (meaning that the procedure reaches a stop point, at some point of time and gives a result). Note also that my description of this Euler method in words does not make it not an algorithm. Careful expression in words is often how algorithms are communicated; using computer code just gets a load of rubbish in the way, and leaves things more open to bugs in the computer, or to the human (mis)conception.

The theory of NP-completeness posits the idea that it is harder to compose a (new) Mozart opera, than to appreciate (or check) an existing one. It does so rather more formally, but that is the gist. We don't know if this is true, but we suspect it is!
JK, December 2016
Note how profound the theory is. It IS this profound. And it IS an open question!!!!!

Learning theory says several things, but arguably the most important thing about learning is the retention of the essential, and the throwing out of everything else, so that a short, indexable, useful nugget of knowledge can be stored, and used efficiently for perception, recognition, cognition, etc.
JK, December 2016

Decision theory can be summarised as how to choose a car at the lot.
JK, December 2016
JK comments: this really does capture the essence, but consider how hard it would be for a robot to choose you a good car at the lot; it would require understanding preferences, and the psychology of the salesman, and your own weaknesses for impractical red Ferraris, and innumerable other things!

Game theory is just about how to get the maximum payoff in interactions with an other (or others) when formal rules of engagement apply.
JK, December 2016
Yup, that is all it is. We teach children through games, and we should learn to play them better through all our lives, and learn new ones. And we test AI programs with games. And games speak to strategy in war, in politics, in arbitration, and in love.

"Games people play" (Eric Berne)
JK comments: A classic text on "transactional analysis" (part of psychotherapy) about payoffs in human interactions when conversation, and body language, and gestures, and tone of voice, are the (quite unstructured and open-ended) modes of interaction. Yet, this has many links with Game Theory proper.
JK, December 2016

Graph theory talks about objects made up of nodes connected by links (like a web or network), and asks questions about the existence of particular graphs, how many there are of a certain type, how to move from one specific node to another specific one through a graph (by hops along the links) efficiently, and so on. It's important to know that the nodes don't usually have locations - it is an abstraction of networks in the real world; the only thing we need to know to define a graph is how many nodes there are, and which are connected to which others .
JK, December 2016

Set theory is just about collections (or groups - but "group" is a reserved work in maths with a different meaning, not entirely unrelated to sets, but different) of things, and how we can reason about adding those sets together, or differencing them, etc. In a typical set, each element is unique. E.g. you can't have a normal set with two 2s in it, (because 2 is just 2). In set theory, you will draw lots of Venn diagrams!
JK, December 2016

Combinatorics is about how many combinations (or permutations) of the elements of a set there can be; it is closely related to complexity theory and is really a sub-discipline of set theory.
JK, December 2016

[Note: to write about Steve Eisman (from The Big Short fame)].


Leave now and come back to this page often, and contemplate a different aphorism each time!

More soon..., peops / bots!