Sunday, July 18, 2010

On the mathematics of juggling: teaching an old dog new tricks

Mathematicians have developed notations for juggling, including something called Site-Swap Notation. It turns out that a formal language has helped discover tricks that had eluded jugglers for thousands of years.

In his book Alex's Adventures in Numberland, Alex Bellos quotes Colin Wright.

"Once you have a language to talk about a problem, it aids your thought process. Maths is not sums, calculations and formulae. It is pulling things apart to understand how things work."




Casual readers of Alex's piece might get the impression that Colin Wright was the chief creator of sideswap theory, but Colin himself disavowed this on a juggling newsgroup in December 2008, and provided a brief sketch of sideswap history.

Monday, July 5, 2010

Why Wise

When does the plural of WHY become WISE?

@ntaleb "People are so prone to overcausation that you can make the reticent turn loquacious by dropping an occasional "why" in the conversation."

Which reminded me of a recent conversation with Kristof Dierckxsens on Twitter.

@kdierc "on asking questions ... I have used the 5 why principle successfully on several occasions"

@richardveryard "In English, "why" questions are unclear, can be interpreted as request for (i) intention/purpose (ii) cause/trigger or (iii) excuse."

@kdierc "I'm not a linguist, but I find it very handy sometimes to keep on asking why to get the real answers to some problem."

@richardveryard "I know it ought to work, but for me it often goes off in unintended directions. I'd be really interested to see a real example."

@kdierc "Maybe it's me not understanding it the 1st time I ask :-) thing is need to keep on asking, not always why, is my experience."


Kristof sees the choice of questioning as linguistics. I prefer to see it as a combination of philosophy and psychology.

Philosophy tells us that there are different categories of cause - Aristotle identified four. A WHY question can be interpreted as a request for any of these.

Psychology tells us that a WHY question can trigger a variety of rational and irrational responses, especially if the setting involves some anxiety. "Why are you doing this?" "Okay then I'll stop." "No I didn't mean you to stop, I just wanted to understand exactly how what you are doing fits into the production process." "So why didn't you ask that?"

Questions of all kinds carry a second level of meaning - what is the agenda behind this question, what are the power and status and trust relations that enable or inhibit a full and honest answer? This second level of meaning is known as metacommunication. WHY questions seem to be particularly prone to the bad effects of metacommunication. (Compare with Clean Language or X-Ray Listening.)

Repeated WHY questions can be even more annoying, especially if they are asked by a consultant who adopts the Elephant's Child style of investigation. See my post on Satiable Curtiosity. So I welcome Taleb's use of the word "occasional".

Kettle Logic

In the muddled thinking of inconsistent excuses, Freud's example of the borrowed kettle provides a perfect example. Hence the name "kettle logic".

  1. I never borrowed a kettle from you
  2. And anyway I returned it to you unbroken
  3. And anyway the kettle was already broken when I got it from you.

This kind of logic is one of the characteristic features of defensive denial, which I identify as one of the symptoms of organizational stupidity. I should welcome some more specific examples of this kind of argument, especially in a business organization setting.

Further examples


Here is Fake Steve Jobs defending the iPhone: "I want to go on record saying this: There is no “antenna problem” on the iPhone 4, and we’re not going to fix anything, because nothing needs to be fixed".(And although FSJ must of course be regarded as satire and not a fair account of Apple's true position on design flaws, the reason this kind of satire touches a raw nerve is that a corporate self-image (identity) based around design perfection can easily result in this kind of denial - "it couldn't happen to us" and "because we are so brilliant, critics will always latch onto the most trivial issue" and "of course we aren't perfect (yes we are)". See Apple Is "Not Perfect," Says Steve Jobs, New York Times via Slate, 16 July 2010. It would be interesting to explore in more detail the links between denial and identity. )

In a recent case of public lewdness and adultery, the accused woman denied she and her lover were having sex, and said anyway they had chosen a picnic table out of the view of others in the park [Daily Mail 9 June 2010].


In politics, Slavoj Žižek uses this schema to understand WMD in Iraq as well as Islamic holocaust denial (via Alain), while Phil Edwards writes about Tony Blair and our relation to his unconscious.

Debaters often accuse their opponents of using kettle logic. For example, in evangelist debating circles, Robert Price attacks Josh McDowell while Jon attacks William Lane Craig. See also Pagan Origins of the Christian Myth.

Thursday, July 1, 2010

Understanding Complexity

@zennie62 claims that McChrystal is not a systems thinker. What is the evidence for this claim?

Zennie's main argument is based on the fact that U.S. General Stanley McChrystal, whom President Obama recently sacked as Afghan war commander for making disparaging remarks about various people (see Mark Urban's blog), is on record making a disparaging remark about a certain systems dynamics diagram.

In my post Visualizing Complexity, I discussed this very diagram, which is an attempt to visualize the complexity of the situation in Afghanistan using system dynamics, rendered as a PowerPoint slide. (Many people have chosen to blame PowerPoint for the complexity of this diagram.)

General McChrystal's remark was that "When we understand that slide, we’ll have won the war." But that's the kind of remark that can be made either by someone who doesn't get systems thinking, or at the other extreme by someone who really gets systems thinking. Surely only a novice systems thinker would claim to fully understand a system as complex as this, especially while events are still unfolding.

Furthermore, there is an important distinction between systems thinking as a theoretical exercise and systems practice as a way of engaging with complex reality. From the latter perspective, it makes a lot of sense to see "understanding the slide" and "winning the war" as inextricably linked. For a practical systems thinker, the only authentic way to learn more about highly complex systems is to engage with them. (This is a critical element of what we call "next practice".)

And maybe General McChrystal just doesn't like this particular diagram. Zennie illustrates this point inadvertently by including an alternative systems dynamics diagram in his blog, using a completely different notation, which some systems thinker might prefer.

Zennie Abraham closes his article with a further double whammy to "prove" that McChrystal is not a systems thinker

"If Gen. McChrystal knew systems thinking, and were honest, he'd realize the best course of action is not to be in Afghanistan."

"If Gen. McChrystal were a systems thinker, he would not have got himself into the trouble that cost him his job."

But these two points contradict one another. Surely if McChrystal didn't want to be in Afghanistan, the obvious course of action would be to give an interview to Rolling Stone that would get him fired. And although Ahmed Rashid calls this a "hurtful rumour" (Petraeus's Baby, New York Blog, 14 July 2010), this is exactly what some commentators are suggesting.

"McChrystal gave the interview in order that he be fired. And why did he want to be fired? He wanted to be fired because he knew that the policies he was pursuing and championing in the war in Afghanistan were not working, could not work. And he didn't want to be the one tarnished with the public blame." (Immanuel Wallerstein, Why McChrystal Did It, Middle East Online, 1st July 2010)

So maybe McChrystal is a systems thinker after all. POSIWID.

The Power of Preconceptions

Post partly based on Chapter 2 of Organizational Intelligence by Harold Wilensky, published in 1967.


In his book, Wilensky presents a detailed account of the history of Allied strategic bombing during the Second World War, which demonstrates the longevity of preconceptions in the face of evidence.

British and American leaders strongly believed that strategic bombing would win the war, and that large-scale use of ground forces would be unnecessary. Their faith in the efficacy of bombing was reinforced by selectively listening to those advisers who were most strongly committed to the doctrine of bombing (for example, Churchill relied upon Lord Cherwell and "Bomber" Harris), and ignoring those scientists who articulated disparate views. Although there was growing evidence during the war that bombing was failing to achieve its strategic goals, and was diverting resources from more effective tactics, it was not until after the war had ended that there was a general willingness to examine the evidence more open-mindedly.

As it happens, the British and Americans held slightly different versions of this doctrine. The British preferred area bombing, which they wrongly expected to damage the German economy as well as undermining German morale. They did not regard as relevant evidence the fact that German bombing had not significantly affected the British economy or morale: perhaps they couldn't imagine that the German population might be equal to the British in initiative and resilience and resolve.

Meanwhile, the Americans preferred precision bombing, which they wrongly expected to disrupt the German production of armaments. As it happens, the Germans also had this expectation, for example in fearing the effects of American attacks on German ball bearing production, and had underestimated their own ability to find spare capacity as well as relocating production away from the factories that had been bombed.

Although there was some early systems thinking within the intelligence communities, and some intelligence analysts might have been able to think about the urban area or the armaments supply chain as a system, this kind of thinking did not significantly influence the dominant narrative.

In any case, the so-called precision bombing wasn't at all precise, so it wasn't that different in practice from area bombing; thus the apparent difference of doctrine between the British and the Americans was more imaginary than real. Difference of opinion at one level hides a fundamental agreement at a deeper level.

Writing during the Vietnam War, Wilensky notes how these beliefs, which had been discredited by military analysts after the Second World War, had mysteriously reemerged a generation later. Even if the decision-makers were aware of the evidence that strategic bombing had been an expensive failure during the Second World War, they may have thought that this evidence was no longer relevant, because they now had much more sophisticated technology - the B52.

And of course the same beliefs have continued to reemerge at regular intervals since, such as the conflicts in the Balkans and Iraq/Afghanistan. Faith in strategic bombing seems to be based on a combination of blind trust in expensive technology ("We've spent billions of dollars on this hardware, so it's gotta be good.") and wishful thinking ("We sure don't want to use ground troops here.").

More generally, we can identify any number of powerful preconceptions, across the public and private sector. There is typically a great deal invested in this kind of false doctrine - a combination of ego, political credibility and hard cash - as well as powerful vested interests who will profit financially or politically from the continuation of the doctrine. Surely one of the primary responsibilities of a critical intelligence is to challenge preconceptions of all kinds.


If your organization or industry is driven by preconceptions and false doctrines, I'd love to hear from you.