Gordon Rugg's Blog, page 14

Monday mood lifter: The case of the sinister buttocks

By Gordon Rugg

Poetic justice can be a wonderful thing. Mano Singham at Freethought Blogs has a delightful account of what happens when students attempt to outwit plagiarism detection software by using a thesaurus. It doesn’t end well for them…

http://freethoughtblogs.com/singham/2014/08/18/how-rogeting-leads-to-sinister-buttocks/

 

The mathematics of desire

By Gordon Rugg

When I was an undergrad, back in the day, a lot of the campus graffiti looked as if it had been written by someone who had dropped acid shortly beforehand. One example read: “The Tao that can be expressed in words is not the eternal Tao”.

Another said: “Tell me what you want, and I will give you what you need”. That particular concept stuck in my mind, and it’s one I still use in my work on requirements.

What do people want, and what do they crave, and what do they need, and what are the implications? Those are questions central to our world and our values, and they’ve been around for millennia, but they’ve never been properly answered. In recent years, though, research has produced some fascinating new insights into these old questions.

As usual, the ancient Greeks feature prominently in the story. As usual, they identified some really interesting phenomena, and as usual, they came up with ideas that were half-right and horribly plausible and that led everyone off in the wrong direction for the next couple of millennia.

The ancient Greeks spotted that there were regularities in what people liked, and that a lot of those regularities were mathematical. One batch of regularities related to music; another related to visual proportions. The usual example is the golden ratio, which is generally accepted to be the most visually pleasing ratio for a wide range of purposes. As an example, the length and breadth of the rectangle below conform to the golden ratio.

https://en.wikipedia.org/wiki/Golden_ratio#mediaviewer/File:SimilarGoldenRectangles.svg

There’s some heavy and elegant mathematics behind the golden ratio. A lot of other aesthetic regularities also have elegant and heavy mathematics behind them, such as musical harmonies, so the Greeks reckoned that they were onto something significant. From that promising start, they then headed off into mystical wibblespace, blazing a golden trail as they went.

The next part of the story also follows a familiar schema. When nineteenth century researchers started heavy-duty, boring, data collection and data crunching, they found that the reality was different from what the Greeks had assumed. There’s a whole discipline of psychophysics, which deals with regularities in human perception; for instance, measuring just noticeable differences in human pitch perception, and seeing whether those differences change size at very high or very low pitches.

Also as usual, the beautiful theories of the ancient Greeks were brought down by the ugly facts from this type of research. For instance, tt turns out that people do like the golden ratio, but it isn’t as clear-cut a preference as originally claimed.

This modern research also uncovered various regularities that the ancient Greeks had missed, and confirmed that some of the Greek claims were fairly true, but not invariable universals. There’s now an entire field of neuroaesthetics, and a related field of computational aesthetics, looking at the underlying neurological and computational regularities of aesthetics.

Two modern researchers, Ramachandran and Hirstein, produced a fascinating paper that brings together various strands of modern work on aesthetics, psychophysics and neurophysiology and applied them to art. Its story is a microcosm of the tension between these new fields and traditional approaches to aesthetics. This paper went down like a lead balloon with the art world, who have their own ideas about how aesthetics should be studied; Ramachandran and Hirstein decided that it might be wiser to return to their own fields, and to leave the arts people to continue as before. It was a sensible decision, but the art world was the loser in the episode, because Ramachandran and Hirstein had brought together a powerful assemblage of concepts and methods that could transform the way we think about aesthetics.

The original Ramachandran and Hirstein paper is available online here. It’s well worth reading. Ramachandran and Hirstein are extremely able, insightful researchers.

I won’t try to give a complete overview of recent work in this area; instead, I’ve picked out a few significant themes that particularly interest me, and that particularly relate to knowledge modelling.

Symmetry, balance and asymmetry

Most people, though not all, prefer symmetry to balance, and balance to asymmetry.

It’s tempting to attribute this chain of preferences to some deep mystical cause, but recent research kicks the props out from under that temptation; it turns out that insects also prefer symmetry. Insects aren’t usually associated with deep mystical Platonic insights into the nature of mathematics and aesthetics.

The cause is probably related to mental processing load; symmetry is computationally easier to process than balance, and balance is easier to process than asymmetry. This is a theme that occurs in a wide range of contexts; the human brain tries to keep mental load within comfortable limits.

This bias towards symmetry probably leads to a lot of invisible errors, in the form of missed opportunities.

In the case of missed opportunities, for instance, there’s no inherent need for aircraft to be symmetrical; a few designers such as Burt Rutan have produced deliberately balanced but asymmetrical aircraft, making use of the asymmetry to do things that would be difficult in a symmetrical design. Most designers, though, don’t tend to think that way. I’ve discussed this theme, and other implications, in more detail in Blind Spot (details at the end of this article).

How much is too much? About three standard deviations…

One interesting feature of modern work on aesthetics is that it has discovered new ways of quantifying regularities.

For instance, there’s the old cliché of the desirable hero being “tall, dark and handsome”. How tall is “desirably tall” and how tall is “too tall” – or is it even possible to be “too tall”?

If you apply some basic descriptive statistics to people’s preferences, you find regularities. Usually, there’s a “sweet spot” about one to two standard deviations from the mean. In the case of adult male height, this translates to somewhere between about six feet tall and six feet two inches tall. There have been several pieces of research that looked at how height correlates with status, income, etc, and the outcome from that research is that male height does correlate with those variables, up to a peak at about six foot two, after which there’s a steady decline.

Sometimes this effect works only in one direction (e.g. only for a sweet spot above the average value) and sometimes it works in both directions (i.e. one sweet spot below the average, and another above it).

There’s a separate tendency in some people towards “more is better” without any cut-off point, as in competitive sports.

The full story, and the full set of implications, are fascinating; I’m planning to blog about them later, when the legendary spare moment occurs.

Novelty and homeostasis; variation within a frame

So far, this article has mainly focused on regular trends in what humans like. There’s another trend, though, which cuts across those regularities and appears to contradict them. It’s the regular trend for people to like novelty.

When you look beneath the surface, though, there are regularities within that liking for novelty. People usually like the uncertainty and the novelty to occur within a well-bounded frame. This leads into the issue of entertainment.

We as a species spend a fortune on entertainment and pastimes; sports and games, movies and music, hobbies and passions. That pattern holds true across time and across cultures; art and music and games are pretty much universal, as far back as they can be traced in the archaeological record.

When you look at popular entertainment, you soon start seeing regularities. Sports and games have tightly defined and tightly enforced rules, so the unpredictability of what happens within an individual sporting event fits within a highly predictable set of boundaries. It’s the same with music and movies; there are regularities that keep each individual example within known boundaries.

There’s a strong argument that this is a manifestation of sensory homeostasis. In other words, we as a species regulate our levels of sensory arousal by selecting activities that raise our arousal level if we’re not getting enough input, or that reduce our arousal level if we’re getting too much input. It’s exactly the same principle as a thermostat cutting in to adjust the temperature of a room by switching on the heating if the room gets too cold, and switching on the air conditioning if the room gets too hot.

As with a thermostat, people appear to vary in terms of how fine-grained the adjustments are; some appear to like keeping their range of arousal within narrow bounds, whereas others vary between bouts of low arousal and bouts of high arousal. Some thrill seekers prefer to have their arousal levels consistently high; some people prefer to keep their arousal levels low.

There’s still a lot of research waiting to be done on this topic. It’s an immensely important topic, because it’s almost certainly a major issue in a wide range of social problems, where individual strategies for sensory self-regulation clash with laws or with the lives of people affected by those strategies, as in the case of alcohol abuse.

We can’t know what we don’t know; life-changing experiences

The issue of what people want out of life takes us back to a topic that has featured frequently in previous articles, namely that people often don’t know and can’t know what they really want.

That’s a clear problem in the case of knowing what the client’s requirements are for a particular product. There has been a lot of good work on this topic, and there are some clean, simple and cheap methods for tackling the problem.

There’s been less work on applying those methods systematically to finding out what people really want out of their lives.

This leads into another topic that has huge implications but which has been seriously under-investigated. Autobiographies often include accounts of a key event in the writer’s life where they encountered something for the first time, and knew immediately that this was what they wanted to do with their lives. Often, this happens when the person is still very young, but they stay with that topic for the rest of their lives, and continue to view it as the thing that they were put on this earth to do.

What’s going on there? I wish I knew. It seems to be a real, powerful effect. Those accounts raise the question of whether that effect can only work for a lucky few, or whether everyone could have an experience like that. If it could apply to everyone, is there some way of making it happen more often, so that more people can know just what they want to do with their lives? I’m fairly sure that it could be done, by adapting some well-established techniques from requirements engineering; I’d love to know the answers.

Concluding thoughts

So what happens when we join up these concepts, and see what emerges?

One theme is that it’s possible to model key concepts systematically, with solid numbers for most of those concepts. For instance, the desire for novelty can be modelled using information theory to put numbers onto the degree of novelty.

Many of the issues involved in aesthetics join up with concepts from other areas that have featured in our articles, such as categorisation. An example is the concept of the “uncanny valley”. This was originally described in robotics, where there’s a tendency for robots to be perceived as more attractive as they become more human-like, up to a point where it’s no longer immediately clear whether something is a robot or a human. People feel very uncomfortable about robots and images that are in that uncanny valley.

I’ve argued elsewhere that this is part of a wider issue about categorisation generally. When something doesn’t fit neatly into a category, that imposes more cognitive load on the viewer. This is acceptable in some situations, where the ambiguity can even be attractive (e.g. my earlier article about parsing ambiguous images). In most situations, though, it’s perceived as hard work, and often as potentially threatening.

If this is a broader phenomenon, then it would tend to establish and reinforce clear gaps between different categories; this could be one explanation for the emergence of genres in media, where human cognitive biases would nudge media types into fairly clearly-defined separate categories.

This leads into another phenomenon, namely second order effects. So far, I’ve focused on popular media, sports etc. However, with most media, sports, etc, there are experts who are well aware of the usual regularities, and who want to go beyond those regularities and explore new possibilities. The result has been described with terms such as “music for musicians” or “art for other artists,” where the product only makes full sense if the listener or viewer is already familiar with the usual conventions, and can understand how the new product builds on those conventions and goes beyond them. These outputs are often perceived by ordinary audiences as obscure or inaccessible or unattractive, even though the same outputs may receive critical acclaim from other specialists.

One motivation for producing second order music etc is genuine expert desire for novelty. Another possible motivation is the desire for attention. This leads into the issues of status and of conspicuous consumption, with regard to what people want. Again, there are regularities; for instance, high status is usually associated with display of rare and/or expensive and/or highly visible status markers. Also, there are regularities in the form that these markers take; for instance, status markers usually enhance the apparent height of the individual, consistent with the correlation between height and status described earlier. These issues have been fairly thoroughly studied in anthropology and sociology and disciplines dealing with popular culture, such as media studies.

The theme of sensory homeostasis brings us back to education and the workplace. The typical teaching environment seriously reduces the scope for sensory stimulation, making it difficult for many students to achieve a tolerable (to them) level of self-regulation; from their perspective, the system is subjecting them to torture via sensory deprivation. Similarly, the inherent nature of bureaucracies, caused by game theory and system theory, predispose bureaucracies towards being highly structured and predictable, which will make them uncomfortable enviroments for much of the population.

At one level, these issues have been well known for a long time. At another level, though, these issues are typically viewed as inevitable, rather than as a tendency that we need to counteract via deliberate intervention to make the learning environment and the work environment fit for human beings.

In my next article, I’ll write about how systems theory and games theory and the mathematics of desire combine, with particular regard to how people view the world, and to the implications for education, policy and human happiness.

Notes and links

If you like thoughtful grafitti, here’s the classic:

http://sbisson.wordpress.com/2005/04/20/far-away-is-close-at-hand-in-images-of-elsewhere/

If you’d like to know more about insect preferences for symmetry, then you might like this paper:

Rodriguez, I., Gumbert, A., de Ibarra, N.H., Kunze, J. & Giurfa, M. (2004). ‘Symmetry is in the eye of the ‘beeholder’: innate preference for bilateral symmetry in flower-naïve bumblebees’, Naturwissenschaften 91, pp 374-377.

There’s an entire chapter about the mathematics of desire in my book with Joe D’Agnese, Blind Spot:

http://hydeandrugg.wordpress.com/2013/04/28/new-book-blind-spot/

http://www.amazon.com/Blind-Spot-Solution-Right-Front/dp/0062097903

Monday mood lifter: Alaskan flat tyre

The title says it all…

https://www.pinterest.com/pin/416653402997501398/

Compassionate readers will be reassured to know that no animals were harmed during the making of this image – the grin on the face of the man on the sledge is a giveaway that this is just another case of huskies being huskies. If you want to know what “huskies being huskies” means, then you could try doing an image search for “Moon Moon”. The results will be suitable for work, but might make you spit coffee over your keyboard, so be careful…

Barbara Cartland meets H.P. Lovecraft, Episode 5

By Gordon Rugg

This article is the concluding part of a serial inspired by the concept of Dame Barbara Cartland writing with H.P. Lovecraft. In it, sentences from a Dame Barbara novel and from a Lovecraft short story have been stitched together into a startling new creation by an anonymous narrator. We have seen the two authors’ styles mesh seamlessly together in the previous episodes, but how will they handle the transition from depictions of anguished fear into the gentler climes of love?

The story so far…

In arguably the greatest love story since Twilight, the Earl of Rockbrook has been tempted by the wicked Lady Louise Welwyn. Convalescing in a nearby manor house after a riding accident, he falls in love with the beautiful Purilla, and asks her to marry him, so that they can return to his estate and live happily ever after. Will her response leave him as damaged emotionally as he was damaged physically by the fall? Or will she reveal a passion that matches his? What searing emotions will be revealed by her answer, and will the story end with the two living happily ever after, or will it have a twist of eldritch horror?

The Shunned Lioness and the Lily House

Episode 5: Purilla’s reply

“Yes.”

The rest is shadowy and monstrous.

The End

Notes

In this series, I’ve alternated between sentences from Dame Barbara Cartland’s The Lioness and the Lily and H.P. Lovecraft’s The Shunned House. The sentences from The Lioness and the Lily are not consecutive, but they are in chronological order. The sentences from The Shunned House are not in chronological order. The plot, such as it is, is a mixture of both stories.

I’ve used the Project Gutenberg edition of The Shunned House.

http://gutenberg.org/ebooks/31469

I’m using both texts under fair-use terms, as limited quotations for humorous purposes.

The photo of The Lioness and the Lily is one that I took, of my own copy of the book. I’m using it under fair use policy (humour, and it’s an image of a time-worn cover).

The other photos come from the locations below. I’ve slightly cropped them to fit, and given a faint pink wash to the pictures of Lovecraft and Cthulhu to make them more in keeping with the Cartland ethos.

https://en.wikipedia.org/wiki/Cthulhu#mediaviewer/File:Cthulhu_sketch_by_Lovecraft.jpg

https://en.wikipedia.org/wiki/H._P._Lovecraft#mediaviewer/File:Lovecraft1934.jpg

https://en.wikipedia.org/wiki/Barbara_Cartland#mediaviewer/File:Dame_Barbara_Cartland_Allan_Warren.jpg

Game theory

By Gordon Rugg

I’m interested in game theory for various reasons. One reason is that it makes sense of a wide range of phenomena which otherwise look baffling.

Another is that it can be combined with approaches such as Transactional Analysis and script theory, to provide systematic and rigorous analyses of how individual people view the world, and what the likely outcomes will be when those views collide with other people’s views, or with the things that life throws at us.

It’s a powerful technique, and it often produces unexpected and counter-intuitive results.

Background

If there was ever a competition for the most easily misunderstood name for a concept, then game theory is likely to finish in the top ten. The “game” part suggests that it’s something frivolous, or just about games, but it’s neither of those. The “theory” part suggests to non-researchers that it’s just an unproven idea, which is also wrong, on multiple levels. It would be more accurately described as something like strategy payoff matrix analysis, but that probably wouldn’t catch on.

Game theory is about assessing the likely outcomes from a particular course of action. It gets its name from its origins a couple of centuries ago in games of chance, where card players used it to work out the chance of winning with a given hand of cards. Professional gambling is a serious business, and from those beginnings, game theory was adopted in a range of other serious fields, such as evolutionary ecology, where it was used to work out which strategies would lead to a species surviving or dying, and warfare, where the US armed forces used it in the Vietnam War to assess the outcomes from different bombing strategies. Military use and abuse of game theory left the approach tainted by association in some disciplines; in other disciplines, it’s a core part of how research is done.

Here’s an example of the underlying principle.

Imagine that you’re a hungry fox, searching for food on a snowy winter day. You’re approaching a roadside picnic site, and you see an abandoned hamburger on one of the tables.

You’re about to trot over to the table when you spot an eagle flying down towards the hamburger. You now have to make a decision. Do you try to scare off the eagle, or do you forget about the hamburger and move on to somewhere else? It’s not an easy decision. A hamburger would be enough food for the day, which is a serious consideration in winter. There’s a sporting chance that the scaring-off tactic would work. However, there’s also a real risk that the eagle would refuse to be scared off, and would fight for the food. A fox and an eagle are fairly well matched, so the fight would probably result in injuries to both animals.

In game theory, you can plot the options and the possible outcomes as a matrix. The matrix below shows the strategies and the outcomes from the fox’s point of view. The usual convention in game theory is to show the outcomes from both viewpoints within a single matrix, but that makes the matrix less easy to understand if you’re new to game theory, so I’m just showing one viewpoint, namely the fox’s, in the matrix below.

The upper row of outcomes in the matrix shows what happens if the eagle isn’t in the mood for a fight; the lower row of outcomes shows what happens if the eagle is aggressive. I’ve unpacked some issues about these outcomes in more detail below.

From the fox’s point of view, the “go in aggressively” strategy is the only one that has a chance of getting the food. However, it’s also the only strategy that could result in the fox being injured. The key question now is whether the loss from the injuries will outweigh any benefits. If the fox loses the fight with the eagle, the injuries will be a straight loss, with no gains to show; if the fox wins the fight, it will have gains from the food, but losses from the injuries sustained in the fight.

So is there some way of measuring the gains and losses in this type of matrix? In many fields, there is a way of doing just that.

For the example above, an evolutionary ecologist could quantify the potential gain in terms of the calory value of the food, and could quantify the losses from the “abandon burger” strategy in terms of the calories expended in finding the next meal. Measuring the losses from injury is trickier, but possible; for instance, the calories expended in finding the next meal would probably be higher for an injured animal, or you could measure the average calorie value of the food that the animal found while it was recovering from the injuries, which would probably be lower than the average value after it had recovered.

There’s a whole body of research on foraging theory which deals with exactly this type of problem. The classic work was on topics such as strategies used by bees to maximise the amount of pollen and nectar they could gather relative to the energy they expended flying between flowers.

That may sound a bit esoteric, but the same underlying principles apply to a wide range of areas, including consumer behaviour, and online search behaviour, which is of considerable interest to companies such as Google. For instance, one strategy that works well for some types of problem is to do a lot of foraging in a small area, and then make a large move to a new location, where you then repeat the strategy of foraging within a small area around that new location. This has very different implications, in terms of understanding consumer behaviour, from the strategy of moving steadily in one direction while foraging, or the strategy of moving in random directions for random distances.

Core concepts

In this article, I’ll discuss some core concepts from game theory, namely :

Zero sum games
Mimimax and other payoff types
Repeated encounters versus single encounters
Stochastic game theory
Evolutionarily Stable Strategies
Strategies
Currencies

These aren’t the only significant concepts in game theory, but they’re concepts that particularly interest me from a knowledge modelling viewpoint, and that have far-reaching implications in other fields.

Zero sum games

In some interactions, one person’s losses become another person’s gains; the gains and losses exactly cancel each other out. This type of interaction is technically known as a zero sum game, because the losses and the gains sum (i.e. add up) to zero.

Not all interactions are zero sum games; some interactions are non-zero sum games. A classic example is biological systems, where both parties can benefit from an interaction – for instance, insects getting nectar from plants (benefitting the insects) and in the process pollinating the plants (which benefits the plants).

There’s a plausible story that when US politicians first started using game theory experts as advisors during the Cold War, the game theorists were horrified to discover that the politicians viewed all interactions between the West and the Soviet bloc as a zero sum game.

Zero sum games crop up in a wide range of places. Performance league tables, for instance, are zero sum games. This can have a chilling effect on the spread of best practice, since in a zero sum game each player has a strong incentive to keep their good ideas secret, rather than sharing them.

There’s an insightful discussion of this issue, in relation to education league tables, performance related pay, and medical innovation, here:

http://iteachmaths.blogspot.co.uk/2014/08/is-prp-good-thing.html

In a nutshell, the author shows that you can either have league tables, or you can have rapid spread of best practice innovations, but it’s normally an either/or choice.

Mimimax and other payoff types

There are names for the different types of payoffs, relating to the loss and the gain associated with each strategy – for instance, some strategies minimise the likely loss, but also minimise the likely gain (minimin) whereas others risk the maximum loss, but maximise the gain if they succeed (maximax). Bureaucracies usually favour minimin, whereas entrepreneurs tend to be comfortable with maximax.

An example of minimum risk and maximum payoff is buying a lottery ticket, which will at worst cost the price of the ticket, and at most will win the lottery. Businesses normally favour this minimax strategy when possible, but it isn’t always possible.

Examples of maximum risk and minimum payoff tend to involve young males and the instruction “Hold my drink and watch this”…

It’s useful to know about these four strategies, since they make it easier to assess possible strategies systematically. For instance, if you’re dealing with a large bureaucracy, then there’s not much point in just emphasising the possible gain from a new strategy; what’s more salient to the bureaucracy is whether the strategy would be minimum risk or maximum risk, so you would need to discuss this question explicitly in your pitch.

Repeated encounters versus single encounter

You might be wondering whether the choice of strategy is affected by whether the interaction is a one-off, or whether there’s a sequence of interactions.

The answer is that this does indeed make a difference. Repeated interactions with the same individual or the same situation take you into a different area of game theory, which has been extensively studied.

Repeated interactions also take you into some other interesting areas outside game theory. One particularly far-reaching issue involves being able to recognise specific individuals or situations, so that you can use knowledge from previous encounters to help you decide how to handle the current interaction. There’s been a lot of work on reciprocal altruism, where individuals build up a relationship of trust with each other via a series of interactions. This occurs in species as varied as vampire bats and wasps, so it’s pretty ubiquitous. Conversely, if the fox in our opening example had previously tangled with the same eagle, and knew that the eagle was aggressive, then the fox would have a better chance of choosing the best strategy available.

A related issue is how many different individuals you can recognise, and how long you can remember them. Again, this has been studied in some depth. An example is Dunbar’s number, which is a figure for how many people an individual can maintain social links with (about one or two hundred). There’s a related concept of familiar strangers, i.e. people whom you know by sight, but not personally. In a small organisation, you can know everyone by sight; in a large organisation, you can’t.

This has implications for things such as the social visibility of strangers, and for social dynamics in small villages versus towns, for example. This is one reason that some types of criminals, such as pickpockets and confidence tricksters, tend to gravitate towards towns and cities, where they’re able to blend into an anonymous crowd.

There’s a fascinating discussion of repeated interactions in relation to “tells” in poker on Ed Brayton’s blog:

http://freethoughtblogs.com/dispatches/2013/11/16/poker-psychology-and-the-science-of-tells/#more-23895

Stochastic game theory

A further refinement of strategy choice is to switch between two or more strategies on an arbitrary basis – for instance, the fox might use an aggressive strategy 80% of the time, and a non-aggressive strategy 20% of the time. Stochastic game theory deals with this area, which is fascinating.

For brevity, I won’t go into detail about this area, but it’s a topic that makes a lot of sense of behaviours that might otherwise look contradictory.

Evolutionarily Stable Strategies

Some strategies might work well in the short term, but won’t survive in the long term, either because the statistical odds work against them in the long term, or because other individuals remember them, and use different strategies against them in later encounters. High-risk/high gain strategies, for instance, often perform well in the short term, but turn out to be disastrous later on (for instance, if the fox tries to scare off the eagle, but is killed by the eagle).

A strategy that’s sustainable in the long term is technically known as an ESS (Evolutionarily Stable Strategy). The full story is more complex, and overlaps with the concept of the Nash Equilibrium that features in the movie A Beautiful Mind. For our purposes, though, this definition gets the key point across.

It’s an important concept, because many attractive-looking political theories turn out not to be an ESS. An example is trying to introduce new ideas into government bureaucracies from business, on the assumption that businesses are more innovative and dynamic than bureaucracies.

The flaw in that reasoning is that the most visibly successful businesses at any given moment are likely to be the ones who are currently reaping the benefits of a high-risk/high gain strategy. When that strategy fails disastrously, as it will in time, the company involved goes out of business. That’s part of the natural cycle of business, where over a third of new companies fail in their first year, but it’s not an option for something like a national health or education service.

Large bureaucracies are usually risk-averse for very good reasons, so attempting to change their strategies via policies derived from the very different context of business is usually not a wise idea.

Strategies

The word “strategy” in everyday English often has implications of sophisticated overviews and long-term planning. However, it doesn’t have those implications in game theory.

The strategies in game theory don’t need to be explicit strategies that can be put into words. For instance, in evolutionary ecology, and in foraging theory in particular, there’s been a lot of work on the strategies used by insects.

Human beings can also use strategies that aren’t explicit or verbalised. This is an area where game theory overlaps with fields such as counselling and clinical psychology, in terms of how a person behaves in relation to other people. Berne’s model of Transactional Analysis, for instance, is best known from his book Games People Play. The mention of games in the title is no accident; Berne explicitly uses games as a model for the sorts of regular structures of interactions found in human behaviour.

I find Transactional Analysis particularly interesting because it uses the same underlying concepts to examine the complete range of strategies, from very small scale interactions (another of Berne’s books is called What do you say after you say Hello?) up to the scale of an entire human livespan. This has obvious overlaps with script theory, which I’ll examine in another article.

Currencies

I opened with the example of a fox looking for food. The reason for this example is that it makes the point that “currency” doesn’t always mean “money”.

This is a very important point. It may look obvious once you’ve started thinking about calories as a currency, but it’s a point that’s often overlooked. This is a particular issue in relation to human behaviour, where there’s a strong tendency for economic models to translate everything into the currency of money (for instance, calculating the effects of a potential disaster in terms of financial cost).

This distinction can make sense of many behaviours that don’t make much sense in terms of traditional economics.

For instance, if you offer research participants a cup of good coffee and an upmarket chocolate biscuit as an incentive, they’re more likely to respond favourably than if you offer them enough money to buy a cup of the same coffee and an entire packet of the same biscuits.

If you assess this behaviour in terms of money, it’s illogical. If, however, you assess it in other currencies, it’s often the more logical choice. For instance, if you measure it in the currency of time or the currency of hassle, then choosing the money option would be more costly in terms of the time or the effort needed to go out and buy the coffee and biscuits. Similarly, if you measure the decision in the currency of social signals, the money is impersonal and low-value, whereas the coffee and biscuit are modestly valuable signals of friendship and courtesy.

Closing thoughts

Game theory is a powerful approach. The core concepts are elegant; however, that elegance can tempt some people to over-simplify the issues (for example, by ignoring currencies other than money).

It’s an approach that should be more widely known, and that can provide significant new insights into a wide range of phenomena.

Notes

You’re welcome to use Hyde & Rugg copyleft images for any non-commercial purpose, including lectures, provided that you state that they’re copyleft Hyde & Rugg.

There’s more about the theory behind this article in my latest book:

Blind Spot, by Gordon Rugg with Joseph D’Agnese

http://www.amazon.co.uk/Blind-Spot-Gordon-Rugg/dp/0062097903

Related articles and links:

https://en.wikipedia.org/wiki/Evolutionary_game_theory

A classic book, showing how game theory can be applied to evolutionary ecology:

http://www.amazon.com/Evolution-Theory-Games-Maynard-Smith/dp/0521288843

Books about Transactional Analysis:

http://www.amazon.com/Games-People-Play-Transactional-Analysis/dp/0345410033

http://www.amazon.com/What-you-say-after-hello/dp/0394479955

Monday Mood Lifter – YMCA in Cantonese

By Gordon Rugg

If you’re tired and jaded, and even fish rubbing or hunting stuffed moose can’t bring a sparkle into your life, then fear not, since help is at hand.

This is the inimitable George Lam version of YMCA. It’s completely suitable for work; the only thing it lacks is a video to do justice to the unique qualities of this cover. Though, thinking about it, I’m not sure whether any video could do justice to it…

Anyway, here it is; I hope it brightens your day.

https://www.youtube.com/watch?v=NUye5UxO-54

PS: As an added bonus, if you liked that, you could go on to try his cover of Uptown Girl (with suitable-for-work video of a live performance, on a Segway, sung and subtitled in English and Cantonese). You’re unlikely ever to see anything else quite like it.

https://www.youtube.com/watch?v=FoUkRYDLbNQ

 

 

 

Barbara Cartland meets H.P. Lovecraft, Episode 4

By Gordon Rugg

This article is the penultimate instalment of a serial inspired by the concept of Dame Barbara Cartland writing with H.P. Lovecraft. In it, sentences from a Dame Barbara novel and from a Lovecraft short story have been stitched together into an unhealthy palimpsest recounted by an anonymous narrator. Previously, we have seen the inner torment of the hero, inimitably recounted by the two authors playing to their own unique strengths. How will they depict romance, when it enters the tale?

The story so far…

The Earl of Rockbrook is torn between the pure true love he craves and the barren, gnarled and terrrible fate which lurks before him, in the sensuous form of Lady Louise Welwyn. To distract himself from that eldritch horror he has gone riding, but has been knocked unconscious when his horse trips in a rabbit hole.

The Shunned Lioness and the Lily House

Episode 4: A room, but in which house?

He was in a room that he had never seen before. The small-paned windows were largely broken, and a nameless air of desolation hung round the precarious panelling, shaky interior shutters, peeling wall-paper, falling plaster, rickety staircases, and such fragments of battered furniture as still remained.

“I knows, Miss Purella, what’s wrong and what’s right.” Free from unwarranted superstition though I am, these things produced in me an odd sensation, which was intensified by a pair of widely separated newspaper cuttings relating to deaths in the shunned house–one from the _Providence Gazette and Country-Journal_ of April 12, 1815, and the other from the _Daily Transcript and Chronicle_ of October 27, 1845–each of which detailed an appallingly grisly circumstance whose duplication was remarkable.

There was someone standing at the window looking out, and the sunshine seemed to glint on a golden head and a slim body was silhouetted against the light. Above the anthropomorphic patch of mold by the fireplace it rose; a subtle, sickish, almost luminous vapor which as it hung trembling in the dampness seemed to develop vague and shocking suggestions of form, gradually trailing off into nebulous decay and passing up into the blackness of the great chimney with a fetor in its wake.

Vaguely the Earl thought that this must be Purilla. It was truly horrible, and the more so to me because of what I knew of the spot.

Perhaps Purilla could help him? His fancy had not gone so far as mine, but he felt that the place was rare in its imaginative potentialities, and worthy of note as an inspiration in the field of the grotesque and macabre.

Now he could see his future more clearly, and there was not the darkness he had envisaged or the slough of despond from which he had fancied there was no escape. In this kaleidoscopic vortex of phantasmal images were occasional snap-shots, if one might use the term, of singular clearness but unaccountable heterogeneity.

Then he said quietly: “We have not known each other very long Purilla, but I would be very honoured if you would be my wife, and I will do my best to make you happy.”

And all the while there was a personal sensation of choking, as if some pervasive presence had spread itself through his body and sought to possess itself of his vital processes.

In next week’s final episode: Purilla’s reply. Will it be marriage and happiness ever after, or eldritch horror beyond the capacity of the human mind to imagine?

Notes

The spelling “Purella” is in the original, and appears to be a misprint for “Purilla” which is used consistently elsewhere in The Lioness and the Lily.

In this series, I’ve alternated between sentences from Dame Barbara Cartland’s The Lioness and the Lily and H.P. Lovecraft’s The Shunned House. The sentences from The Lioness and the Lily are not consecutive, but they are in chronological order. The sentences from The Shunned House are not in chronological order. The plot, such as it is, is a mixture of both stories.

I’ve used the Project Gutenberg edition of The Shunned House.

http://gutenberg.org/ebooks/31469

I’m using both texts under fair-use terms, as limited quotations for humorous purposes.

The photo of The Lioness and the Lily is one that I took, of my own copy of the book. I’m using it under fair use policy (humour, and it’s an image of a time-worn cover).

The other photos come from the locations below. I’ve slightly cropped them to fit, and given a faint pink wash to the pictures of Lovecraft and Cthulhu to make them more in keeping with the Cartland ethos.

https://en.wikipedia.org/wiki/Cthulhu#mediaviewer/File:Cthulhu_sketch_by_Lovecraft.jpg

https://en.wikipedia.org/wiki/H._P._Lovecraft#mediaviewer/File:Lovecraft1934.jpg

https://en.wikipedia.org/wiki/Barbara_Cartland#mediaviewer/File:Dame_Barbara_Cartland_Allan_Warren.jpg

 

Systems Theory

By Gordon Rugg

Systems theory is about what happens when individual items are connected and become a system. “Items” in this context can be anything physical and/or abstract, which gives you a pretty huge scope. Systems are ubiquitous. Examples include mechanical systems such as vehicles; social systems such as organisations or countries; and logical systems, such as software. Many of these systems can cause disasters when they fail, as in the examples of nuclear power plant safety systems or autopilot systems in aircraft; systems are important.

There are regularities in how systems behave, and some of those regularities are both counter-intuitive and extremely important. That’s a potentially dangerous combination.

If you understand systems theory, then the world makes a lot more sense, particularly if you combine it with game theory, which will be the topic of one of my next articles. Most questions that start with “Why don’t they…?” can be answered either with “Resources” or “Systems theory” or “Game theory”.

In this article, I’ll look at some core concepts from systems theory.

The usual definition of a system is along the lines of “two or more interconnected and interacting entities”. I’m deliberately not going to spend much time discussing detailed definitions; Instead, I’ll focus on four core concepts:

Properties of systems and entities
Feedback loops
Lag
Improving sub-systems won’t necessarily improve the system, and may actually make it worse

Properties of systems and entities

The first core concept is that a system consists of entities that are interconnected and interacting. It’s a simple concept, but it leads into some concepts with very far-reaching implications.

Here’s an example.

The picture above shows three entities, namely an arrow, a bow and a bowstring. Each of these entities has properties – for example, they all have a length and a weight.

If we combine these entities, they now form a system, as in the picture below.

This system can do things that the individual entities couldn’t do. The most obvious example is that the system can shoot the arrow at speed for a significant distance.

Although this is a system with very few components, it illustrates some profound points.

Systems within systems

One point is that systems can be nested within other systems, as in the diagram below, where each box is a system or subsystem.

Often, this nesting is many layers deep. The image below shows the same system and subsystems as in the previous image, shown vertically separated into four layers so that the levels of nesting are easier to see.

Readers familiar with archery will probably already have spotted that the bow itself (as opposed to the bow plus bowstring system) is a system, composed of a layer that is strongly elastic (the back of the bow) and a layer that is strong in compression (the belly of the bow). Similarly, the arrow is itself a system, composed of the head (which affects the aerodynamics) and the shaft (whose properties affect how the arrow behaves when leaving the bow) and the fletching (the feathers, whose shape and position and other properties have a major effect on how the arrow behaves in flight). In both cases, the sub-components need to be combined in a particular way to produce a working system.

Emergent properties

One key point about systems is that a system will almost certainly have properties that its individual component entities don’t have. For example, the system of bow plus bowstring plus arrow has properties such as draw weight (the amount of force needed to pull the bow back for the length of the arrow shaft) and range (the distance that the bow can shoot the arrow). Neither of these concepts can meaningfully be applied to the components of this system on their own.

Similarly, using a bigger-scale example, the system of a Land Rover has properties such as speed that can only be applied to the system as a whole, not to the component parts in isolation.

If you’re dealing with a deeply nested set of systems, then each layer of the overall system will probably have different properties from the ones above and below. In the case of a Land Rover, for instance, the engine sub-system will have properties that can’t be meaningfully applied to the chassis sub-system, such as maximum revolutions per minute.

Properties that emerge at different levels of nesting are usually referred to as emergent properties.

This concept overlaps considerably with the very useful concept of range of convenience, i.e. the range of contexts within which a particular term can meaningfully be applied.

The concept of emergent properties has often been misunderstood in relation to the concept of reductionism.

One interpretation of reductionism argues that you can understand a complex system, such as a pack of wolves, by looking at each of the nested levels of subsystem involved until you reach the level of individual atoms, and by understanding the properties of each subsystem; this tells you everything that there is to know. This is shown in the image below as a set of coloured bands, one for each layer of subsystem. Only by combining the information from all the layers will you have a complete understanding of the system and its component subsystems.

Another interpretation of reductionism, usually either as a straw man or as a misunderstanding, is the idea that you only need to know the properties of the lowest-level systems, and that you will then know everything there is to know about the higher levels.

This issue has generated a lot of anger among those who believe that science is a reductionist enterprise in the latter sense, which implicitly views activities such as art and music and altruism as being nothing more than atoms interacting with each other. In reality, though, science is very much about the other model of reductionism, where it’s essential to understand the properties specific to the level(s) of nesting on which your research is focused, not just the properties of the lowest level.

In the case of the wolf pack, for instance, there would be a layer of attributes such as pack size or pack hunting strategy that could only apply meaningfully to the pack as a whole, and then other attributes such as sex that could only be applied meaningfully to each individual wolf, and still other attributes that could only be applied meaningfully to the organs of an individual wolf, such as its lung capacity, and so on via the cellular level to the molecular and atomic level.

Back to systems theory proper…

Feedback loops

Another key feature of systems is that they often include feedback loops, which have a habit of producing unpleasant and unexpected results.

Before we get into a detailed analysis of feedback loops, an important point to note is that some of the key concepts involved have been widely adopted in vernacular English, but with very different meanings. This frequently leads to deep misunderstandings. I’ll pick up these differences as they arise.

A feedback loop involves two or more components within a system affecting each other in a loop. In the simplest case, component A affects component B; component B then affects component A, which then affects component B, and so on. This can either go on forever, or go on until something breaks the loop.

We can show this process diagrammatically, as in the image below.

There’s a curving arrow symbol from A to B, showing that A affects B, and there’s a similar (but deliberately not identical) arrow from B to A, showing that B affects A. It’s a loop, with no specified mechanism for breaking the loop.

I’ve included a couple of small boxes labelled L1 and L2 at the start of each arrow symbol, deliberately different from each other in size and colour, to represent lag in the system; I’ll discuss the concept of lag in the next section.

There’s a reason that I’ve deliberately not made the diagram symmetrical. It’s because the way that A affects B isn’t necessarily the same as the way that B affects A. It may happen to be the same, but it doesn’t have to be. This can have far-reaching implications for how the system works, and for how the system can fail. This is a big issue when designing safety-critical systems such as autopilot systems in aircraft, or systems that affect very large numbers of lives, such as an education system.

A simple example of this asymmetry is an electric bell. One design involves using an electromagnet to pull the bell hammer in one direction, and a mechanical spring to pull it in the other direction. These are two very different mechanisms, but they’re closely linked to each other within the system.

The next issue to consider is how A and B affect each other.

The loop between A and B can take four significant forms:

A increases B and B increases A
A increases B and B decreases A
A decreases B and B decreases A
A decreases B and B increases A

All of these cases are known technically as feedback loops.

Unfortunately, the concept of feedback has been picked up in vernacular English, and used with very different meanings, generating a lot of potential for confusion. I’ll discuss these issues as they arise.

A increasing B, and B increasing A

Here’s an example of one type of feedback loop. In the technical sense, it’s known as a positive feedback loop. This means something very different from the vernacular sense of “positive feedback”. I’ll discuss the differences and their implications below.

In the image above, A is causing an increase in B, and B is causing an increase in A. It’s a positive feedback loop, but “positive” in this technical sense does not mean “good” or “encouraging”. Instead, it just means “increasing”. Whether human beings would like or dislike that increase is a completely different issue. “Positive feedback” in its original systems theory sense is a completely different concept from “positive feedback” in the vernacular sense of the term.

This would be a bad enough source of confusion on its own. However, the full story is worse. In systems theory, positive feedback loops usually mean trouble. Here’s an example.

In a forest fire, the flames generate heat, which makes the heated air rise. This rise causes more air to be sucked in from the surrounding area, producing winds, which make the fire burn more fiercely. This in turn increases the amount of heated air rising from the fire, which in turn increases the speed at which more air is sucked in from the surrounding area, which in turn makes the fire burn even more fiercely. This process of self-perpetuating increase will continue until something makes it break down.

Most positive feedback loops contain the potential for this type of escalation. So what about other types of loop?

A decreasing B, and B decreasing A

You can have a system where A and B are each causing the other to decrease further in turn. This is also often not a good thing. A classic example is breakdown of trust between two people or two groups, where each action by one provokes a counter-action by the other, leading to a downward spiral in trust. It’s a situation well known to marriage guidance advisors and to industrial relations mediators. However, it can be a good thing, as in political de-escalation, where tensions decrease step by step between the parties. The difference between this and the previous case is largely a matter of semantics – a decrease of tension could be re-phrased as an increase in calm, for instance.

A and B affecting each other in opposite directions

Another common type of loop involves A and B affecting each other in opposite directions. In these cases, an increase in A will lead to a decrease in B, or vice versa. This type of loop can cause stability within the system, by keeping any increases limited to a manageable level.

There’s a feedback loop of this sort that can affect forest fires. Sometimes, the air that the fire sucks in is moist. In such cases, the rising air can eventually produce rainclouds, and the resulting rain can decrease or put out the fire.

A wide range of systems deliberately include stabilising loops of this sort. In political systems, the concept of checks and balances within a constitution is an example; aircraft autopilot systems are an example of a mechanical system that uses this principle to increase safety.

I’ll briefly discuss autopilot systems, since these illustrate some other important points about systems theory.

In brief, an autopilot works by checking actual direction and height against the planned direction and height. If the aircraft has drifted too far to the left, then the autopilot nudges it to the right until it’s back within an acceptable range; similarly, if the aircraft has drifted too high, then the autopilot will reduce its altitude until the altitude is acceptable.

The core concept is that simple. One huge advantage of this simplicity is that it works regardless of the complexity of the surrounding environment. The autopilot doesn’t have to try modelling the enormously complex weather systems that could blow the plane off course; instead, it just modifies the course until the modification has compensated for whichever winds are blowing.

The implications for other systems, such as economic systems, are obvious and enormous. If you can find and build in the appropriate feedback loops into the system, then you can probably keep the system stable, even if you can’t predict what the wider world will throw at it, and even if you don’t yet fully understand the complete system. (Yes, that’s still a big “if,” but the principle is sound, as demonstrated by the autopilot versus the weather system.)

Autopilot systems demonstrate another important concept. The autopilot only makes a course or altitude correction when the aircraft has drifted more than a particular distance off course. There’s a very practical and sensible reason for this. If you didn’t build in this deliberate delay, then the autopilot would be fussing around with tiny adjustments every second, which wouldn’t be good in terms of wear and tear on the mechanical components, and also wouldn’t make much difference in overall accuracy. Anyone working in the health service or education will be all too familiar with what happens when governments fuss around with drastic re-organisations before the dust from the previous intervention has settled. It’s usually not a good idea.

This delay between event and response is technically known as lag. In some fields, such as computer games, lag is viewed as a huge problem. In systems theory, however, lag is value-neutral. Sometimes it’s a bad thing, but surprisingly often, lag is very useful indeed.

Lag

Lag has a lot of similarities to concepts such as slack and spare capacity and redundancy in organisational theory and information theory respectively. All of these concepts are usually viewed as a bad thing by novices; all of them are in reality much more complex and multi-faceted, and all of them can be extremely useful when applied properly.

Experts in safety-critical system design become very twitchy when they see a design that has little lag in it. Experts in organisational behaviour react similarly when they’re told that an organisation is efficient or lean or that it has little waste. Why do they react that way? It all makes sense if you focus on what happens when things go wrong, rather than on what happens when things are going right.

If something goes wrong in a system that has very little lag in it, then the problems will escalate very quickly indeed. That’s not a situation that anyone would want to be in. Anyone with sense would prefer a situation where the problem takes more time to become serious, so that the humans involved have a chance to fix it before it gets too bad.

Similarly, if you’re in an organisation which is lean and efficient, what happens when there’s an outbreak of flu and staff are staying home because they’re ill? Because the organisation is lean and efficient, there’s no spare capacity to handle the sudden shortfall. That’s a major problem, but it’s a completely avoidable one, and this concept has been well known in organisational theory for a century or more – it’s one of the key findings from the work of Max Weber. Short-term efficiency can be the enemy of long-term efficiency; delays in response can make a system more stable.

As an example of these concepts in practice, John Seddon has done a lot of excellent work in this area. A good introduction to his work is his California Faculty Association lecture, which is on YouTube, in several short parts; this link is to the second part, where he starts getting into the detail of his topic.

Sub-system improvements don’t always improve the system, and may make it worse

This is one of the most counter-intuitive findings to emerge from systems theory; it has major implications for any attempt to improve a system, such as the education system or the health system.

At first sight, it might appear obvious that improving sub-systems within a system will automatically and inevitably bring about improvements in the system as a whole. This assumption is often a central feature of high-level policy. However, it simply isn’t true.

Often, improving sub-systems has no effect on the quality of the system as a whole, whether that system is mechanical or organisational or software. Quite often, improving sub-systems actually reduces the quality of the system as a whole.

I’ve written about this in some detail here. In brief, there are several ways that this effect can occur. One way is that improvements in one sub-system can bring problems for other sub-systems; for instance, fitting a more powerful engine into a car can cause problems for the brakes sub-system, the fuel sub-system and possibly the suspension sub-system. Another possibility is that sub-systems improve at the expense of the system as a whole – for instance, departments in an organisation might all improve their productivity by referring all customer complaints to the head office, meaning that the complaint handling becomes much more cumbersome and expensive to the organisation as a whole, since it’s now being handled by people who aren’t familiar with the relevant specific details.

As an example of getting it right, here’s Roy Lilley elegantly, eloquently and humorously discussing this principle with regard to healthcare purchasing policy:

http://is.gd/WMKXEJ

The converse principle also applies; making a system as a whole more efficient can have no effect on individual sub-systems, or can make sub-systems less efficient.

This issue has major, extremely practical, implications for policy, but it’s not widely known. The result is that policy is often driven by assumptions that are simply wrong, and that make matters worse rather than better. It’s a particular risk when someone is peddling a clear, simple, big-picture solution; such proposed solutions are often clear and simple because they’re simply ignoring the inconvenient realities which doom those proposed solutions to inevitable failure, causing financial and human pain along the way.

Closing thoughts

This article has looked at some key concepts from systems theory. There’s a lot more detail that I haven’t discussed, for brevity. I haven’t gone into concepts such as soft systems and hard systems, or sources and sinks, or homeostasis, for example.

Systems are important, and ubiquitous, and they often behave in ways which are actually quite simple, but which are very different from what most people would expect. Systems theory is powerful, but it can appear very paradoxical at first sight.

This has profound implications for anyone attempting to improve a system, particularly a huge, complex system such as a national health system or a national education system. Often, ideas that look simple and attractive are actually disastrously wrong, because they have failed to consider basic issues from systems theory. Conversely, often it’s possible to fix apparently intractable problems by using some very simple concepts from system theory.

In my next article in this mini-series, I’ll look at game theory, and how that interacts with systems theory and with real-world systems problems. I’ll then look at the mathematics of desire, and how our biases steer us towards some possibilities and away from others. Finally, I’ll bring these themes together in an examination of belief systems and their implications for education and related fields.

Notes

You’re welcome to use Hyde & Rugg copyleft images for any non-commercial purpose, including lectures, provided that you state that they’re copyleft Hyde & Rugg.

There’s more about the theory behind this article in my latest book:

Blind Spot, by Gordon Rugg with Joseph D’Agnese

http://www.amazon.co.uk/Blind-Spot-Gordon-Rugg/dp/0062097903

 

Monday Mood Lifting Muppets

By Gordon Rugg

To help your Monday get off to a better start, here’s the academic pecking order, explained via the Muppets. Whoever put this together clearly knows their subject matter well…

https://twitter.com/AcademicsSay/status/497230061482041344/photo/1

Barbara Cartland meets H.P. Lovecraft, Episode 3

By Gordon Rugg

For reasons that seemed good at the time, I’m writing a serial inspired by the concept of Dame Barbara Cartland collaborating in writing with H.P. Lovecraft. In the previous episodes, we have seen the two inimitable talents working in harmony, with the underlying dark mysteries in Cartland’s classic plot being masterfully elaborated by Lovecraft’s unique style. In this episode, we see this harmony continue, as the story swells to thrilling new heights…

The story so far…

The Earl of Rockbrook has succumbed to the blighted charms of Lady Louise Welwyn, and faces the prospect of having to marry her, even though he does not particularly like her as a person. Now, as he ponders the consequences, his mind turns to the gulf between the pure true love he craves and the barren, gnarled and terrrible fate which lurks before him.

The Shunned Lioness and the Lily House

Episode 3: A purer love

Thinking it over, he knew exactly what he required of the woman who would bear his name. No sane person had ever seen it, and few had ever felt it definitely.

She would be tall, dignified and capable of doing justice to the Rockbrook diamonds. Such a thing was surely not a physical or biochemical impossibility in the light of a newer science which includes the theories of relativity and intra-atomic action.

Secondly, the Earl on considering the hypothetical woman to whom he was not yet prepared to give a name, was certain he would not wish to marry anyone who aroused in him the sort of emotions which he considered rather embarrassing. The anthropomorphic patch of mold on the floor, the form of the yellowish vapor, and the curvature of the tree-roots in some of the old tales, all argued at least a remote and reminiscent connection with the human shape; but how representative or permanent that similarity might be, none could say with any kind of certainty.

He went upstairs to change into his riding-clothes and he knew that his Army batman for some years, was aware that he was in a black mood, and had no wish to add to it. The young soldier’s return was not a thing of unmitigated happiness.

He gave the horse its head after they were clear of the trees in the Park and galloped across country at a speed which made it impossible to think of anything but the demands on his horsemanship. There was a suggestion of queerly disordered pictures superimposed one upon another; an arrangement in which the essentials of time as well as of space seemed dissolved and mixed in the most illogical fashion.

The unexpectedly when he was still in full gallop the horse stumbled and the Earl knew he had caught his hoof in a rabbit-hole. It was of this world, and yet not of it–a shadowy geometrical confusion in which could be seen elements of familiar things in most unfamiliar and perturbing combinations.

Then almost quicker than thought he found himself falling, felt the impact as he hit the ground and the crack of his collar-bone breaking. The rest is shadowy and monstrous.

In next week’s stirring episode: A room, but in which house…?

Notes

In this series, I’ve alternated between sentences from Dame Barbara Cartland’s The Lioness and the Lily and H.P. Lovecraft’s The Shunned House. The sentences from The Lioness and the Lily are not consecutive, but they are in chronological order. The sentences from The Shunned House are not in chronological order. The plot, such as it is, is a mixture of both stories.

I’ve used the Project Gutenberg edition of The Shunned House.

http://gutenberg.org/ebooks/31469

I’m using both texts under fair-use terms, as limited quotations for humorous purposes.

The photo of The Lioness and the Lily is one that I took, of my own copy of the book. I’m using it under fair use policy (humour, and it’s an image of a time-worn cover).

The other photos come from the locations below. I’ve slightly cropped them to fit, and given a faint pink wash to the pictures of Lovecraft and Cthulhu to make them more in keeping with the Cartland ethos.

https://en.wikipedia.org/wiki/Cthulhu#mediaviewer/File:Cthulhu_sketch_by_Lovecraft.jpg

https://en.wikipedia.org/wiki/H._P._Lovecraft#mediaviewer/File:Lovecraft1934.jpg

https://en.wikipedia.org/wiki/Barbara_Cartland#mediaviewer/File:Dame_Barbara_Cartland_Allan_Warren.jpg