{"id":1306,"date":"2010-07-07T05:55:27","date_gmt":"2010-07-06T19:55:27","guid":{"rendered":"http:\/\/www.somethinkodd.com\/oddthinking\/?p=1306"},"modified":"2010-07-11T14:39:08","modified_gmt":"2010-07-11T04:39:08","slug":"lamport-on-buridans-principle","status":"publish","type":"post","link":"https:\/\/www.somethinkodd.com\/oddthinking\/2010\/07\/07\/lamport-on-buridans-principle\/","title":{"rendered":"Lamport on Buridan’s Principle"},"content":{"rendered":"
My “Blog Articles To Do” pile is full of these blog ideas that started simple, but then grew to add another item, and then another item, until they became too long to write in one or two sessions, I got bored of the topic, and they died on the vine. Here I present a number of connected ideas, deliberately stilted, so I can get to the real point faster.<\/div>\n

When Chaos Theory was making the news in the late 80’s, I was left confused. <\/p>\n

Poor science reporting was part of the problem. I remember TV special leaving me bewildered about the connections between the different aspects, until I watched it a second time and noticed the segue along the lines of “Talking about non-linear systems…” The two topics it introduced in one section were completely unrelated; trying to link them in my mind was giving me headaches.<\/p>\n

Once you got past the “really good patterns that you could put on a t-shirt” (to quote Terry Pratchett), and the desperate attempts to make them at all relevant, what was really there? <\/p>\n

Some surprising result about periodic doubling? Nice, but what predictions can you make with this? How is it going to change the world as much as they claimed.<\/p>\n

The realisation that in some systems tiny changes in input could lead to big changes in output? Whoopee. That’s news? No, it is pretty bloody obvious, as anyone who has tried putting a ping-pong ball in the clown’s mouth at a fairground should know.<\/p>\n

\n

Leslie Lamport<\/a> is a living legend of Computer Science. I’ve read Distributed Computing papers by him. I’ve used his software<\/a>. I’ve quoted his aphorism: “A distributed system is one in which the failure of a computer you didn’t even know existed can render your own computer unusable.”<\/p>\n

He’s a man who has had a great impact on Computer Science<\/a>.<\/p>\n

\n

One way to make a successful fad is to take an old idea that people should already know (but perhaps is too boring for them to learn about,) add an irrelevant piece of (preferably proprietary) junk, bundle it with a ribbon (and perhaps some terminology and the claim that it is revolutionary), and Bob’s your aunt’s de facto.<\/p>\n

Weight-loss supplements (to be consumed with a balanced diet and regular exercise) are one example.<\/p>\n

Agile development (to be consumed with high-quality unit-testing, peer-review, iterative development, good communication with an interested customer and small teams sitting near each other) is another.<\/p>\n

\n

One day, an Economy student explained to me the different theories about what drove stockmarket fluctuations. If I recall correctly, he explained that people thought that either (a) there was a hugely complicated function taking lots of inputs that no-one could completely fathom, or (b) there was randomness or (c) some combination of the two.<\/p>\n

When I suggested that there was, of course, another option: a relatively simple repeated function which was sensitive to small fluctuations in a large number of inputs, he looked at me strangely, and patiently explained that that could not be the case, because of the complexity of the output.<\/p>\n

Suddenly, I wondered if Chaos Theory was like these other fads. The ideas may seem old and obvious if you have the background, but to many people they may seem new. Maybe the excitement about Chaos Theory was a whole lot of people understanding the “old and obvious” at the same time?<\/p>\n

\n

I remember seeing a cartoon of a donkey in an early book for children about computers. The donkey was stuck between two stacks of hay, and couldn’t choose between them. I didn’t get it at the time.<\/p>\n

Today, I learnt the donkey was Buridan’s Ass<\/a>, which is an illustration of a paradox in philosophy. Apparently, the idea goes back a few thousand years – the idea being if the donkey was placed exactly halfway between two identical haystacks, it would be unable to choose between them, and remain where it was, starving to death.<\/p>\n

Apparently, this “paradox” is useful in discussing free will, but also in discussing electronics – particularly when trying to make analog circuits act digital, and finding that they are “meta-stable” and don’t damp down into one state quickly enough.<\/p>\n

\n

Leslie Lamport wrote an article about Buridan’s Principle<\/a>.<\/p>\n

In it, he discusses some of the real implications of the rule to software development, but I don’t want to discuss that.<\/p>\n

In the first section, he formalises the principle, and shows that the assumptions that lead to the unexpected result that there is always some position between the haystacks where the ass cannot choose (within a given period of time) which stack to head towards.<\/p>\n

He defines At<\/sub>(x) as the position of the ass at time, t, given it was initially placed at position, x, between the two stacks. He then explains:<\/p>\n

The ass is a physical mechanism subject to the laws of physics. Any such mechanism is continuous, so At<\/sub>(x) is a continuous function of x.<\/p><\/blockquote>\n

Unsurprisingly, given Lamport’s background, his paper’s typography handles such mathematical expressions far more beautifully than WordPress.<\/div>\n

Lamport explains:<\/p>\n

When first told of Buridan\u00e2\u20ac\u2122s Principle, people usually find it unbelievable and propose mechanisms to circumvent it.<\/p><\/blockquote>\n

He examines some of these mechanisms, such as adding noise or quantum effects to try to break these physical implications, and make the function discontinuous. <\/p>\n

However, I guess I am one of the people who find this paradox unbelievable, and I, too, am immodest enough to propose a mechanism. But I am happy to continue to work in the physics of a classical universe.<\/p>\n

[Update<\/strong>: Andrew, in the comments, gives me some insight into why my following argument is bogus, and that Lamport was right all along. You’ll find my apology to Lamport in the comments too.]<\/p>\n

I do so by rejecting the claim that physical mechanisms must exhibit continuity in all directions. I submit that physics requires At<\/sub>(x) to be a continuous function of time (t)<\/em> – that is, after being placed, the ass may not be seen to teleport between any two positions. However, I do not believe that physics requires At<\/sub>(x) to be continuous in x.<\/p>\n

If you move the animal slightly to the right before revealing the haystacks, and replay the scenario, its position at time t may be completely different (and discontinuous) from where it would have been in the animal had been left in the original starting position.<\/p>\n

In effect, I am claiming “fractals” are a legitimate answer here to the paradox. More accurately, I am denying that physics requires the location of an object to be continuous when comparing different timelines branching at slightly different starting conditions.<\/p>\n

\n

A small part of me is thinking I sound like a crackpot to be taking on a well-known computer scientist (and PhD in Mathematics) talking about a subject he has written a paper about, while I just heard about it today, and I am doing so by waving my hands and saying “Chaos Theory”, “Butterflies flapping their wings can cause storms” and “Watch what happens when I move my ass discontinuously!”<\/p>\n

Especially because last week, I smirked at a Fields Medalist for wild inaccuracies in his maths. He was dabbling with a mathematical model of the likelihoods of some sports results. It is an area I have been studying for a while<\/a>, and his model contained the logical equivalent of assuming that “race-horse are perfect spheres running inside a vacuum”.<\/div>\n

Furthermore, I have made no effort to see if Lamport has changed his views in the intervening two decades (apart from noting that I am referring to an updated version of the paper) or seeing whether other people have weighed in in the meantime. I feel a little guilty about that laziness. Sorry.<\/p>\n

Nonetheless, I stand by my crackpottery: I think that Lamport is wrong in justifying the use of an uncomfortable assumption with a physical claim.<\/p>\n

(Nothing here invalidates the use of Buridan’s Ass as an analogy for challenging explanations of free will or for real-live effects in electrical circuits.)<\/p>\n","protected":false},"excerpt":{"rendered":"

In which Julian attacks weight-loss supplements, Agile development, TV show segues, Chaos Theory and Economics, just so build up enough momentum to attack a much-beloved (by him!) computer science legend about something he wrote over 20 years ago.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_s2mail":"","footnotes":""},"categories":[24,31,29,21,34],"tags":[],"class_list":["post-1306","post","type-post","status-publish","format-standard","hentry","category-cathartic-rant","category-geek","category-influencing-others","category-observation","category-software-development"],"_links":{"self":[{"href":"https:\/\/www.somethinkodd.com\/oddthinking\/wp-json\/wp\/v2\/posts\/1306","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.somethinkodd.com\/oddthinking\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.somethinkodd.com\/oddthinking\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.somethinkodd.com\/oddthinking\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.somethinkodd.com\/oddthinking\/wp-json\/wp\/v2\/comments?post=1306"}],"version-history":[{"count":13,"href":"https:\/\/www.somethinkodd.com\/oddthinking\/wp-json\/wp\/v2\/posts\/1306\/revisions"}],"predecessor-version":[{"id":1318,"href":"https:\/\/www.somethinkodd.com\/oddthinking\/wp-json\/wp\/v2\/posts\/1306\/revisions\/1318"}],"wp:attachment":[{"href":"https:\/\/www.somethinkodd.com\/oddthinking\/wp-json\/wp\/v2\/media?parent=1306"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.somethinkodd.com\/oddthinking\/wp-json\/wp\/v2\/categories?post=1306"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.somethinkodd.com\/oddthinking\/wp-json\/wp\/v2\/tags?post=1306"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}