Socrates and Shoelaces

I have quite some time to think these days. Thinking is a process that is frequently non-linear, arbitrary and sometimes causeless. I rely on tools, mostly mathematical and sometimes probabilistic which shape the next part of the thread. Thinking is exhausting, especially when a degree of conscientiousness is required. It has been suggested, erroneously in my view, that ten thousand hours of practice can turn a novice into an expert, irrespective of innate ability.  Building neural pathways to solve specific problems is not enough. Until we learn and appreciate the value of lateral observation, thinking becomes no more than a mechanistic, hence unrewarding activity, which, dopamine-addicted as we all are, is counter-productive. Great teachers are not those who can manage gigantic classes and convey some information. Great teachers ask individuals, who then deduce partial solutions from which greater understanding comes. It comes as no surprise to learn that tutored students do better by a measurably significant amount than those who sit in large classrooms and are lectured along with a large number of others. It takes intense concentration for individuals to engage appropriately with the material in such a setting with little or no feedback. ‘How am I doing?’ is the perennial question, the answer to which is what every student really wants to know.

For these questions, you need to ask someone else the how-am-I-doing part. There aren’t any right answers, just interesting lines of enquiry. For each of them, you have to ask subsidiary questions, the accuracy of which will determine the quality of your final answer.

First, Fermi estimation. This is the process of coming up with estimates of the correct order of magnitude for various real-world quantities often with little or no hard data. Here are a few examples.

1. How much does a cloud weigh?

2. How many people could fit into the Island of Manhattan?

3. How many piano tuners are there in Chicago? [a classic example- I’ll post the standard solution in a comment – you might like to try to compute the uncertainties in the calculation]

4. If the average temperature of the sea were to rise by a degree, then by how much would thermal expansion cause sea levels to rise?

5. How many molecules from Socrates’s last breath are in the room?

Now for some more difficult ones.

6. How do speed cameras work? How accurate are they likely to be? (The basic technique I’m talking about is taking two photos in quick succession.)

7. Why does a mouse survive a big fall when a human doesn’t? (There are many questions similar to this, such as why elephants have thick legs, ants can carry several times their body weight, etc.)

8. Somebody pours you a cup of coffee but you aren’t yet in a position to drink it. You take milk, and the milk provided is cold. You want your coffee as warm as possible. When should you put in the milk: now, or just before you drink it, or some time in between?

9. You are walking from one end of an airport terminal to the other. The airport has several moving walkways, and you need to stop to tie your shoelace. Assuming you want to get to the other end as quickly as possible, is it better to tie your shoelace while you are on a moving walkway or while you are between walkways?

This question comes from a blog post ofTerence Tao

10. You have a collection of suitcases, boxes and bags of various sizes, shapes and degrees of squashiness. You want to pack them all into the boot of a car and it’s not obvious whether you can. What is the best method to use? If you don’t like the idea of suitcases, try thinking about plastic containers of varying sizes and robustness, some with lids and some without. How can they be fitted into the least and most accessible space?

If these kinds of exercises bewilder you, that's fine. A significant part of our time is spent wondering what to do next. Wondering is what we do best. I sometimes wonder in common with the comedian Mark Russell whether  the rings of Saturn are entirely composed of lost airline luggage.

Blood and Magic

I haven't written very much in recent times, having recently returned from America and additionally I've been rather preoccupied by an impending move, possibly to a war zone. More of this later, perhaps. By way of divertissement, what if we all sat down with a nice cup of tea and gave thought to the problems in Israel, from a totally different standpoint. So, here's a novel perspective. Forget two states. It hasn't gained any traction up till now and it won't work because, bottom line, the militants want to reclaim the whole lot as part of ummah and the Israelis are having none of it.

A rather radical solution was recently presented as an op-ed in theNew York Times which you'll have to read otherwise none of the rest makes much sense.

How about just one centrally governed state?

Here's my modest take on it.

From one who holds a chair in political science, Professor Lustick's rhetoric relies on weak argument and logical fallacy. From the start it would seem that he has abandoned any pretence of academic rigour since he's trying to convince us that he might be right through nothing more tangible than a 'good idea' and a few half-baked and irrelevant analogies.

Just for the record, any elementary student of philosophy will have picked up on at least one or two of the following.



1. Appeal to fear + Slippery slope - "The stage will be set for ruthless oppression, mass mobilization, riots, brutality, terror, Jewish and Arab emigration and rising tides of international condemnation of Israel. And faced with growing outrage, America will no longer be able to offer unconditional support for Israel".  Unconditional support? It's like Obamacare, everyone has to have it but nobody can really afford it.

2. Relying on irrelevant authority - "secular Palestinians in Israel and the West Bank could ally with Tel Aviv’s post-Zionists, non-Jewish Russian-speaking immigrants, foreign workers and global-village Israeli entrepreneurs. Anti-nationalist ultra-Orthodox Jews might find common cause with Muslim traditionalists."
Well, of course they could. How shortsighted of us not to notice.

3. False dilemma - he's trying to say that it's either one state, or the abyss (the appeal to fear). In fact, just as in the NYT, there's a multitude of opinions and options, not the "do what I say or die" approach Ian Lustick took.



4. Appeal to ignorance – he doesn't bother to prove he's right, he just hopes you can't see past flaky logic. Why can people who comment not quite grasp the idea that this is a religious conflict and any political solution is basically doomed to long-term failure?

It's unfortunate that a new, homegrown kind of terrorism has also begun to surface. The murder of an IDF officer outside his home, bludgeoned to death by people not, it would seem, bankrolled by Hamas or other organised group; instead perpetrated by self-proclaimed activists who act with no authority but their own - a behaviour which can only have been learned in the classroom or in the mosque. How Professor Lustick expects reason to prevail under such circumstances defies comprehension. I did agree with one short phrase which will make quite a passable sound-bite when Ian Lustick is fawned upon by a sycophantic and largely ignorant media. He said “peacemaking and democratic state building require blood and magic”. Quite so. But, in what proportion?

Afflicting the Comfortable

Rembrandt's Rich Man

I’m going to bang on a bit about religion, if that’s OK. If it’s not, go watch ‘Top Gear’ or something. Now, I don’t normally write blog posts about sermons since most of the time they pass me by like Brutus’ idle wind, which all too often I regard not. I was late for church yesterday, which is not unusual and arrived halfway through the sermon, which meant that I was really, really late and the man in the front was well into his stride.

The great thing about using lectionaries is that you know where you’re supposed to be going and this week the preacher was talking about that curious, impenetrable parable about the 'unjust steward', a canny little tale from Luke 16. It took me a while to figure out where we were, having found just about the last seat in the house right at the back of the gallery. A few minutes in, I was almost regretting coming, because I've never really got the point of the story before and it looked as if all we were going to get was the usual ‘box clever, wily as serpents’ routine. This little story begins with the fact that the steward had wasted resources which didn't belong to him. It then goes on to condone dishonesty, sharp business practice worthy of Alan Sugar, a measure of duplicitousness and a seasoning of forgiveness. Who gave the man authority to forgive debts? Er, nobody. Great public relations - he looked good, the master looked good. But the steward still got fired - a kind of reverse performance related bonus.

But, what outrageous behaviour, but how joyously characteristic. Jesus turns the whole notion of good order and sound practice on its head by even telling the story in the first place. It’s almost as if he really quite enjoyed afflicting the comfortable, taking a poke at the Pharisees, instead of as was more usual, comforting the afflicted.

God's arithmetic isn't like mine. Many religious have a kind of 'weighed-in-the-balance' view about debt - or sin, if you prefer - if we do more good stuff than bad stuff, we'll tip the scales in our favour as if  God is no more than a cosmic bean-counter, with due deference to some of my friends who earn a fat crust from accountancy.

Reading stories like this would suggest that God is more likely to throw the scales across the room and come dancing forward to embrace us. Grace is unfair, profligate, and ridiculous which is why the scribes and Pharisees were almost permanently ticked off. It's lavished on us, whether we deserve it or not. Mostly, we don't.

Fairy Tales

This week marked the opening of a film about Stephen Hawking, premiered at the Cambridge Film Festival. It's a journey through his remarkable life and a testament to what can be achieved in the face of handicaps so profound that most would have collapsed under the weight of them.

I did rather wonder where the swearing-in-church questions were, which were conspicuously absent, according to one reviewer. Hawking's status as a scientist is often spoken of in oracular terms, like Einstein's and Isaac Newton's but one rather wonders if his scientific achievements have been somewhat inflated because of his disability. Others do cosmology equally well - not very many, it has to be said, since the mathematics are impenetrably dense and I have to confess is as far away to me as the edge of the Universe. The idea of n-dimensional spaces with fancifully named abstractions such as M-Theory - the M stands for 'membrane', 'mystery', 'magic'- even 'mother' since it attempts to unite five different string theory proposals, is known to few and understood by even fewer.

A Calabi-Yau membrane. Is this what the Universe looks like?

Some suggest that if completed, the Holy Grail of physics, a theory of everything might emerge with a formula small enough to fit on a T-shirt. Hawking's astonishing achievements lie in the fact that he has the ability to hold phenomenally complex ideas in his short term memory for extended periods since it takes him anything up to half an hour to 'write down' a couple of sentences.

Eight million people bought "A Brief History Of Time". Probably a couple of hundred got further than page twenty-six and almost everybody read the last sentence...

"However, if we discover a complete theory, it should in time be understandable by everyone, not just by a few scientists. Then we shall all, philosophers, scientists and just ordinary people, be able to take part in the discussion of the question of why it is that we and the universe exist. If we find the answer to that, it would be the ultimate triumph of human reason - for then we should know the mind of God."

Which, of course, is the saving grace of the whole book. We all want to know the mind of God. This from Isaiah 40, 12-15:

12 

Who has measured the waters in the hollow of his hand, or with the breadth of his hand marked off the heavens?
 Who has held the dust of the earth in a basket, or weighed the mountains on the scales and the hills in a balance?

13 

Who can fathom the Spirit of the Lord, or instruct the Lord as his counsellor?

14 

Whom did the Lord consult to enlighten him, and who taught him the right way?
 Who was it that taught him knowledge, or showed him the path of understanding?

The "who" is rabbinical rhetoric, almost ironic, since the answer is enshrouded in the unknown, the "mind of God".

"I'll be back."

What else, therefore, do we, like the citizens of Nineveh, not know as we do not know our right hand from our left? We do not know about the afterlife, the Hereafter, the journey across the Styx, the tunnels of light, the shouts of welcome on Jordan's further bank as the processor shuts down like the winking, blinking red light of the Terminator's eye as it fades and darkens, and without power, fails to reboot.

A land far away

Most cultures have developed a mythology of continuance after bodily functions cease. Some suggest that it is a fear of oblivion, the darkness and the cold that causes mankind to construct elaborate fantasies, delusional states, predisposed and woven into the fabric of consciousness and reinforced by religious adherence and indoctrination. Others have a sense of transience. It is here that one waits, perhaps. Here is C S Lewis' bus station in a forgotten, rainy, 'grey town', the train terminus or the airport lounge. Later, the arrival of 'here' is somewhere or somewhen else. Perhaps Vladimir Nabokov's  suggestion that 'our existence is but a brief crack of light between two eternities of darkness' should be stood on its head. Here is the dark, the light was before it and will be after it. I am therefore guilty of the heresy of not believing that my brain deludes itself into believing instead in the eternality of its owner.

Professor Hawking concluded his biopic with a Q and A, making remark about the afterlife which misses the point, rather:

"It's theoretically possible to copy a brain on to a computer to provide a form of life after death. However, this is way beyond our present capabilities. I think the afterlife is a fairytale for people who are afraid of the dark."

Perhaps he might consider that life in the here and now is a fairytale for those afraid of the light.