Euclidean ideals

Brian Hayes offers the following delightful quote from John Aubrey’s Brief Lives, concerning the 17th century philosopher Thomas Hobbes:

He was 40 yeares old before he looked on geometry; which happened accidentally. Being in a gentleman’s library in…, Euclid’s Elements lay open, and ’twas the 47 El. libri I. He read the proposition. “By G—,” sayd he (he would now and then sweare, by way of emphasis), “this is impossible!” So he reads the demonstration of it, which referred him back to such a proposition; which proposition he read. That referred him back to another, which he also read. Et sic deinceps, that at last he was demonstratively convinced of that trueth. This made him in love with geometry.

Hobbes is of course most famous, and of continuing relevance, for his thoughts on what life is like in the absence of strong central government, i.e., “solitary, nasty, poor, brutish and short”, which seems an increasingly accurate picture of Iraq. But Hobbes made interesting observations on many other matters, including the nature of thought.

Hayes claims that

What’s most remarkable about this tale—whether or not there’s any trueth in it—is the way Hobbes is persuaded against his own will. He starts out incredulous, but he can’t resist the force of deductive logic. From proposition 47 (which happens to be the Pythagorean theorem), he is swept backward through the book, from conclusions to their premises and eventually to axioms. Though he searches for a flaw, each step of the argument compels assent. This is the power of pure reason.

“Remarkable” is to some extent in the mind of the marker. Hobbes’ inability to resist the force of deductive logic seems to me commonplace; every one of us, every day, is forced to accept unpalatable conclusions when presented with deductive, or even just strong, arguments.

Rather, the most remarkable feature of this situation may be the fact that Euclid’s propositions were presented in such a systematic and transparent way that Hobbes was able to follow, without confusion or misdirection, a long chain of inferences. In other words, the special feature of Euclid’s Elements – the feature of the greatest intellectual significance – is that a very complex set of arguments had been laid out in such a way that the inferential connections among propositions were unambiguously detectable.

In other words, Euclid’s arguments had been properly mapped.

This is quite remarkable because most of the time, in Euclid’s era and today, arguments of the greatest significance are not properly mapped out. They are not articulated to the point where even the authors are fully clear about the inferential relationships among their propositions; and their readers are presented with the hopeless task, at which they generally fail miserably, of attempting to figure out what those propositions and relationships are.

Euclid sets a standard to which we ought to be continually aspiring, even in non-mathematical domains. These days we have even less excuse for falling short, because we have better tools for rapidly mapping complex arguments and presenting the results.

Year in Ideas tidbits

Last week the New York Times published its “6th Annual Year in Ideas” in its Magazine.  81 bite-sized presentations of new ideas or trends; worth a read.  Trouble is, not much of what we read is remembered for very long.  Below I’ve listed the ones I’d like to be able to recall in a week or even a year’s time. 

• Empty-Stomach Intelligence.  Mice think better when they’re hungry.  Maybe we do too.  “Ghrelin” is the hormone at work.
• Eyes of Honesty. People are more virtuous when they’re being watched.  Even by obviously-fake eyes, such as on a poster.
• Hidden-Fee Economy.  People can be sorted into “sophisticates” who seek low up-front prices and avoid hidden fees (such as exorbitant mini-bar prices in hotels), and “myopes” (or “suckers”) who are constantly shelling out.  
• Homophily. Social websites are exploring ways to overcome “our inexorable tendency to link up with one another in ways that confirm rather than test our core beliefs.”
• Hyperopia - an excess of far-sightedness.  In the long term, ants tend to have more regrets than grasshoppers about how they spent their time.  This quirk of human psychology doesn’t mean you should just relax and indulge now though.   
• Low Starting Prices.  On Ebay, lower starting prices result in higher final prices – a kind of reverse anchoring effect.  This is because the anchoring effect is overcome by other effects.  A low start price results in many more bidders, enhancing the apparent value of the item, and exploiting people’s sense of commitment to create greater competition.
• Publication Probity.  The Journal of Spurious Correlations is devoted to publishing only negative results, aiming to counteract pervasive “publication bias” whereby positive results are published much more readily than negative, distorting our understanding of the world.
• Voting Booth Feng Shui.  How we vote is affected by where we vote.  People voting in schools are more likely to vote for state support for education.

Argument Mapping in Introduction to Philosophy

For many years the only university subject I’ve been teaching has been Critical Thinking: The Art of Reasoning, at the University of Melbourne. This is one-semester subject devoted almost entirely to improving reasoning, argument and critical thinking skills – a kind of “boot camp” for rational thinkers. This subject has been the environment in which our argument mapping techniques and software have been developed and field tested.

It’s been a fascinating time, and I’m not bored with it yet. Still, on occasion I also wonder what it would be like to teach some other subject, a subject where logical thinking is a tool rather than the focus, and where argument mapping can be evaluated not for its impact on critical thinking skill gains, but rather for its benefits in supporting learning and inquiry.

In particular, given my background in philosophy, what would it be like to teach – say – Introduction to Philosophy, incorporating argument mapping?

A prior question is – how would argument mapping actually be used in such a subject?

Some early adopters have already been leading the way in terms of introducing argument mapping into general philosophy. For example there’s David Spurrett in Durban, South Africa, who for a number of years has been using Reason!Able, Rationale’s predecessor, in various subjects.

Looking at what people like Dave have been doing, and trying to imagine what I would probably do, here are some ideas:

1. Use Rationale during preparation of lectures to create graphics of the main arguments under consideration to include in Powerpoint overheads.
2. Or better still, display “live” argument maps during lectures from within an argument mapping application such as Rationale. That way, you can easily modify the maps to bring out points during the class, for example in response to students’ questions or suggestions.
3. More radically, a whole lecture could be presented from within the argument mapping application. Rationale, for example, has an infinitely extendable workspace, on which you can include as many maps as you like; you can zoom and scroll as needed to bring the relevant material to the forefront. Sticky notes can be used to incorporate material which doesn’t naturally fit into an argument map.
4. Instead of just requiring students to read some text before a class, have them try to map the core argument(s) being presented. This gives them a task with a goal, which will help them engage with the text better. (They’ll find this activity very hard at first, but with your guidance they’ll gradually get better at it.)
5. Require students to work up an argument map of their own argument or arguments they’re presenting in their essays. Have them hand the map in with the essay. This will (a) lead them to be much more explicit about what exactly their argument is; (b) give them a logical skeleton on which to hang their essay; and (c) give you a fast way of understanding what they are trying to argue (and, in many cases, whether they are hopelessly confused).

That’s just a few ideas; no doubt there are lots of other good ways to use argument mapping. After all, philosophy (at least in the “Anglo-American analytic” tradition) is heavily focused on understanding and evaluating arguments, even at introductory levels (e.g., Descartes’ classic arguments for the distinctness of mind and body). If we’ve got a better way of displaying and manipulating argument structures, it must surely find many uses.

Argument cartoons

There was a state election in Victoria recently. As you’d expect we were getting a lot of political junk mail in our mailbox, including this postcard*:

Actually, it is a bit unfair to call this “junk” mail, since it appears to be an first-rate piece of graphical communication – an excellent use of what Bob Horn calls visual language. It is presenting a serious argument, but in a cartoon format. Obviously the format makes the somewhat dull subject-matter (how the election system works, and why that means your vote for the Greens is not wasted) much more engaging.

It reminds me of another excellent argument cartoon, by Scott McCloud.

From a theoretical standpoint, the postcard is also interesting as an illustration of how the order of presentation of claims is generally not the same as the logical order among the claims.

What does this mean?

Well, the main point the card wants to make is that the claim, which apparently many believe, that

(1) A vote for the Greens is a wasted vote.

is wrong – i.e., it is objecting to that claim.

Now, if presentation order was the same as logical order, you’d expect the main objection to the claim – the thing which is “closest” to it, logically speaking – to be also closest on the page.

However, what we see next is, in simplified form:

(2) In the first count of ballot papers most often no one hits 50% first time.

But that isn’t actually the main objection to (1). On its own, it doesn’t seem to make any difference to (1).

The main objection is actually quite a bit further down – the claim we might paraphrase as

(3) A vote for the Greens has double the influence [of a vote for a major party].

The text in between (1) and (3) is actually subordinate to (3), which then refutes (1). And there is some logical complexity already in the material between (1) and (3).

It might be clearer if we lay this out in a diagram:

Notice how, as step down the logical order, claim (1) is the last claim we reach – whereas in the order of presentation, it was the first thing mentioned after the contention at issue.

There’s one more complication here – the final claim,

A higher vote for the Greens sends a strong message.

This is another objection to the main contention, and so appears at the top level:

This illustrates the relative strengths and weaknesses of argument maps versus other forms of presentation. When done really well, other forms, such as the cartoon postcard discussed here, can be more engaging, and can convey the gist of a complex argument quite effectively. However they generally present the logic in a quite convoluted order, which often makes it difficult to determine exactly what the argument is.

An argument map, by contrast, is rather spartan; it presents just the claims and their logical relationships. But it does this in a totally transparent and unambiguous way. If your concern is getting the argument exactly right – perhaps because you want to know, with great confidence, just how good it is – then the argument map format is the best one.

A lot more could be said about this argument. The maps here are just a simple “first pass” laying out of the argument. In particular, I haven’t made any mention of the various assumptions being made, and where they fit on the map. A topic, perhaps, for another entry.

* Reproduced without permission – though I figure this is OK since I’m helping spread the Green message

Exploitation, not Augmentation

A recent Boston Globe piece, Souls of a New Machine, has been getting some attention around the traps. In it Chris Spurgeon describes the interesting phenomenon in which some complex computer system takes advantage of human thinking to produce an intelligence result. For example,

The Google image labeler (images.google .com/imagelabeler) is an addictive online game that takes advantage of the fact that it’s very easy for a human to recognize the subject matter of an image (“That’s a puppy!” “That’s two airplanes and a bird!”) but virtually impossible for a computer. The game teams up pairs of strangers to assign keywords to images as quickly as possible. The more images you can label in 90 seconds, the more points you get. Meanwhile, Google gets hundreds of people to label their images with keywords, something that would be impossible with just computer analysis.

Unfortunately, the article calls this phenomenon “intelligence augmentation”. Which it aint.

Using the term this way is inconsistent with established usage. And it muddies the waters. These points are closely related.

The thinker most closely associated with the concept of intelligence augmentation, and who is often credited with having coined the term, is Douglas Engelbart. Engelbarts’ obsession was making human beings smart enough to handle the enormous problems we have to deal with.  This may mean making tools help us be more intelligent.

Thus in his writings (see, e.g., his famous tech report Augmenting Human Intellect) what is being augmented is the intelligence of the human. Some kind of external system is used to make a human smarter. The external system itself might be completely stupid. (Analogy: a shovel can help me dig far more effectively. The shovel itself cannot do any digging.)

In the systems described by Spurgeon, by contrast, it is the external systems which are being made smarter. Human intelligence is being exploited in these systems, but the humans involved are not themselves becoming smarter in any interesting way.

Thus, the systems described by Spurgeon are quite different in the most central way from those which interested Engelbart.

In using the term Intelligence Augmentation to describe these new systems, Spurgeon is effectively lumping together under one heading systems which differ in a crucial respect.

Not a good idea.

It is clear in Spurgeon’s article that he’s interested in the contrast between these intelligence-exploiting systems and standard AI systems, in which the external systems themselves are (supposedly) made intelligent.

There is certainly a very important difference between computer systems which are intelligent “on their own” and those which are only intelligent because there are humans inside the box, so to speak.

That important difference should be marked by using a different term.

Its just that its a mistake to take an existing term which already means something else and to misapply it.

When there’s a genuinely new and interesting phenomenon, why not mark that with an appropriate new term?

“Intelligence Exploitation” works for me.

So, we have three distinct phenomena:

1. Artificial Intelligence (AI) is making computers smart on their own, i.e., with no human “in the box.”
2. Intelligence Augmentation (IA) is using external systems, particularly computers, to make humans smarter.
3. Intelligence Exploitation (IE) is making computer systems smart by extracting and redeploying human intelligence, i.e., by including humans “in the box.”

Why do I care about this? Am I just a verbal pedant? Admittedly, with a background in analytic philosophy, I do have a taste for semantic niceties and their relationship to clear thinking.

But I’m no longer a philosopher, at least in the standard academic sense. These days, Engelbart’s mission is what excites me.

Rationale is all about Intelligence Augmentation – not AI or IE, though I expect that Rationale will eventually incorporate both AI and IE in some way.

Critical thinking in the secondary classroom

An inspiring account from Kylie Sturgess of the Methodist Ladies College in Perth, Western Australia.  Kylie was runner-up in the 2006 Australian Skeptics‘ Prize for Critical Thinking.

Argument mapping in legal contexts – conference

Argument mapping is gradually building momentum – not just in education, but in professional contexts.

This is hardly surprising. After all, the idea of producing diagrams of complex reasoning is very simple and, in retrospect, very obvious.

A strong sign that a topic is starting to “come of age” is when professionals in the area start holding conferences. This often takes a while because a genuinely new topic is likely to be multi-disciplinary. Interesting mutations in intellectual life-forms tend to arise in the gaps or overlaps between existing fields, where constraints of orthodoxy are weakened and variety leads to fertile interactions.

One of the first major conferences in argument mapping is coming up in January. Peter Tillers has put together Graphic and Visual Representations of Evidence and Inference in Legal Settings, at which a fascinating range of speakers will be coming at this topic from various angles.

Last week I put together an abstract for my presentation at that conference:

Rationale – A Generic Argument Mapping Tool

This talk will cover some of the “philosophical” issues involved in designing Rationale as a generic argument mapping software tool. These points will be illustrated with Rationale itself. Themes to be covered will include:

Educational vs Professional. The two main roles of the software – educational (helping people aquire reasoning skills) and professional (helping people perform “on the job”). The design challenges created by the competing requirements of these two roles.

Intelligence augmentation. In helping people perform on the job, the software is intended to augment human intelligence (cf Englebart) rather than to be a reasoning engine. It is intelligence augmentation (IA) as opposed to artificial intelligence (AI). Hence the omission of various “features” which could in theory be added.

Complementing human cognition. In order to augment human intelligence, the software is designed to complement our “native” cognitive strengths and weaknesses. The software should handle those tasks which brains are not good at, and help brains to do what they are good at. In particular, brains are not good at holding complex structures in short term memory. The software is good at maintaining information, but has to make it possible for brains to effortlessly (a) access and (b) interact with that information. The software is in other words intended to become part of the “extended mind”.

Pre-conscious awareness. With a view to making the communication of information from map to brain, and its subsequent incorporation into thinking, as efficient as possible, the software exploits the brain’s capacity for pre-conscious awareness and processing. Specifically, the software makes use of pre-cognitively processed attributes such as colour, position and shape to convey information.

Semi-formality. The software operates in the “semi-formal” domain. Human reasoning almost always takes place in an informal mode, and this is the source of many of its problems. Formal logic and mathematics are formal, don’t suffer many of the problems of informal reasoning, but have little practical application to real-world reasoning problems. Rationale is based on the idea that the “sweet spot” where human reasoning achieve its best results is in the semi-formal domain – more structured and constrained than ordinary informal discourse, but allowing considerably more roughness, vagueness, flexibility etc. than formal modes.

Scaffolding vs straightjacket. In attempting to hit the semiformal sweetspot, the software design has to walk a fine line between providing structure or scaffolding, on one hand, and providing a confining straightjacket, on the other. Users don’t like to be forced to do things one very particular way, even if, in theory, doing things that way would make their thinking better. In practice they will not use a tool that that is highly constraining (unless they have to). Hence a practical tool must be somewhat forgiving.

Focus vs context. Our attention, in reasoning, generally focuses on particular considerations, or small sets of considerations. However it does so in the context of a complex web of reasoning. Somehow, and imperfectly, we maintain focus and understanding of context simultaneously. Software should support this essential feature of our cognitive processing (cf Tillers, Picturing Inference). Rationale does this by providing “Show Path” and “Show Context” features, in which the focus of attention is enhanced and the context is recessed.

Lots means Lots

How do you help your students to achieve really worthwhile gains in critical thinking skills?

We worked on this problem for about five years at the University of Melbourne. We wanted a method for improving critical thinking skills which demonstrably achieves substantial results.

I’ll add now that we wanted a method which reliably acheives these results, i.e, gets them year after year, and in a variety of different contexts.

We think that we succeeded in this. The Reason method, as we called it, achieved gains of about 0.8 standard deviations semester after semester with University of Melbourne students.

We’ll soon be releasing a comprehensive review of the empirical literature (a “meta-analysis”) which compares our results with results found in other studies. Looking at the charts of the data, there certainly appears to be something special about the Reason method.

Increasingly, teachers and researchers around the world are doing their own studies to see if they can obtain the kind of good results showing up in our studies.

That’s great. It is crucial that the results be independently tested and (we hope) verified.

However, any independent attempt at replication should attempt to recreate the essential ingredients of the method being tested.

If you do a study which drops some of the essential ingredients, it doesn’t tell us much about the method.

Unfortunately that’s what we’re seeing. Again and again, attempts by third parties to find out if the Melbourne argument-mapping-based method “really works” don’t really test that method. They drop out a crucial ingredient – and then, usually and predictably, they find that they don’t achieve the same good results.

There are two crucial ingredients to the method we devised.

The first and most important is practice. Lots of practice. The Reason method, in a nutshell, is an application of the Ericsson theory that high levels of skill in any field come from lots of “deliberate practice.” Our idea (hardly very original or brilliant) is that the same will be true of reasoning or critical thinking skills.

The second ingredient comes out of that notion “deliberate.” Basically, deliberate means “good quality”. The challenge we confronted was – how do you get students to do LOTS of “good quality” practice?

Our insight was that you could improve the quality of practice students are doing by putting that practice into a good environment. In particular, we came to believe that argument mapping is a far better context for practice of reasoning skills than typical “prose”-based contexts (such as the typical university lecture, discussion section, book etc. which makes little or no use of argument diagrams).

So the second crucial ingredient in our method is using argument mapping. Specifically, doing one’s practice using argument mapping software.

Let me repeat that for emphasis. The method consists of

1. LOTS of practice
2. using argument mapping software

We used to call the method, in more technical language, “DPAM” – which stood for “deliberate practice using argument mapping.” Not very catchy.

Yanna Rider, one of the Austhink team, came up with the much better acronym LAMP. The method is Lots of Argument Mapping Practice.

Now, whether or not you use argument mapping, doing LOTS of practice is going to demand of a lot of institutional resources. Crudely put, it is going to take a lot of time and effort from staff, or time and effort from a lot of staff.

That’s a problem. Educational institutions are usually stretched pretty thin already, and putting MORE resources into some teaching exercise is a “big ask.”

What they are more often looking for is some way to get results with LESS resources.

So, what we usually find in independent attempts to “replicate” our results is that, when you look closely at how the method is being implemented, the focus is on argument mapping. the LOTS of PRACTICE has been downplayed or ignored.

Our prediction of course is that, to the extent that you don’t do the practice – the extent that you do AM rather than the full LAMP – you won’t get results as strong as ours.

The good news in all of this is that it is possible to achieve substantial gains. But you have to be prepared to do what it takes.

If you find out about an argument mapping study whose results were less impressive than ours, ask – were they really doing enough? Or does it look like they were hoping that argument mapping is some kind of magic bullet?

We believe that an argument-mapping based method is more efficient than other methods, because it offers a better quality of practice. So, for the same amount of resources or practice, you’ll get better results. But if the amount of practice your students are doing is negligible, the results will also be negligible.

One of our goals is to help educational institutions have their students do lots of argument-mapping-based practice without imposing significant extra resource requirements on those institutions. So a teacher can use the LAMP method without creating a lot of extra work for herself.

In a corporate context…

 The note below was sent by a Rationale user in a major Australian corporation, who had received some coaching from Austhink’s Jane Lewis.

It arrived soon after I had finished the previous post suggesting that for more effective thinking, what we need is not more conscious thinking, or to leave things to our unconscious, but rather systematic processes supplemented by external resources which complement our inborn cognitive strengths. Case in point:

I have only been using Rationale for a very short time but, with your help, have been able to quickly learn the basics of argument mapping and been able to use argument maps to make important decisions and influence my management in their decision making. I know that I am developing a valuable skill.

My use of Rationale has been in 3 phases: organising arguments, interacting with peers and stakeholders to develop the argument, and presenting the argument to management. The first two tend to form an iterative process. Sometimes management feedback leads to another iteration series. I suspect there is scope for considerable value in doing more than I have done so far in the interaction phase.

The disciplines of capturing the elements of the argument; organising them in an argument map and then “abstracting up and filling down” leads me to a better and clearer understanding of my argument. It exposes shortcomings, occasionally leading to a re-evaluation of the value of a position. It also exposes openings into which new ideas can emerge.

The argument map is a wonderful communication tool – my peers can quickly see how I am thinking and provide relevant feedback.

Having assembled an argument, clarified it through organising it in a map, expanded it with new ideas and improved it with the feedback from my peers, I can present it to management. They can immediately see the entire argument on a single page. It is organised in terms of the key strategic drivers of the business (“abstracted up”) and the strengths and weaknesses of the argument are immediately apparent. They can quickly reach a position from which they can ask good questions or make valid criticisms. A key management skill is making good decisions quickly on minimal information – the argument map makes this easy.

Let me sketch out how argument mapping with Rationale has helped with a business decision of importance for my department.

The department owns several assets but one of these is not important to our core business objectives. Our company is doing well and a key goal for us is to keep focussed on work that delivers maximum value. Managing unimportant assets is a low-value activity but external constraints prevent simple disposal. I constructed an argument map in support of the proposition that we should trade this asset for an option over other more valuable assets.

Organising the map by abstracting up allowed me to focus on the key issues of COST, BUSINESS FOCUS, COMPETITIVE ADVANTAGE, RISK MANAGEMENT and OPTIONALITY. The arguments for and against the proposition were easily organised in terms of these themes with Rationale. Then I discovered a clear space in the map and immediately a whole new option for our business emerged. I realised that there was completely different way to acquire new options which leads to an elegant method for determining the value of those options. Valuing options is crucially important in our business and good valuations provide a key advantage in negotiations. Mapping the argument gave me a powerful new insight.

I described the proposition to my manager (without showing him the map) – his initial response was negative and he gave his reasons but the mapping process had prepared me. I was able to easily refute his reasoning and describe the value in my proposition. Within 5 minutes he was persuaded and enthusiastically in favour of the idea.

He took the proposition up to his manager and was asked to write a 4 page memo to support the proposition. My manager and I spent many hours honing the memo to present a clear argument. Once it was sent and read, the reply was a long set of questions and criticisms. It was clear that we had failed to communicate our ideas; senior management simply do not have the time to spend thinking through an argument – it is easier for them to send off their immediate impressions and move to the next issue.

I sent my manager my argument map – the entire argument presented clearly in an organised way on a single page. We spent a little time further refining the map and then he was able to present it to senior management over breakfast and see comprehension dawn!

Next week we have a meeting at which we hope to have our proposition signed off!

[Reproduced with permission of the author.]