Concept maps and visualizing things

CmapTools map

Concept maps are cool & useful

I’ve been advocating for the use of concept maps for years. I’ve even written papers about it. But I’ve also spent most of my time writing plain, linear text. Scholarly papers, courseware, grant applications – these are all the basics of academic communication, and they’re all just strings of words. So it’s been hard to practise what I preach.

Recently, though, something happened that really opened my eyes to the very significant benefits of diagrams in general and concept maps in particular. So significant was this experience, that I want to share it in the hope that I can help others who are also struggling with the confines of linear text.

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Form can inform content. Sometimes.

Changing the “look and feel” of my blog made me reconsider the tagline, what it really meant, and how I could express it best.

You may have noticed, I’ve changed the “theme” of my blog.  I like to keep things simple, and though I will probably add a touch of colour here and there, I hadn’t noticed this particular theme, called Hemingway, before.  Not that I’m a big fan of Hemingway, the writer, but this theme really appeals to my sense of simplicity.

But there was one problem: the tagline, that sound bite-ish blurb that describes the blog.  It was originally a couple of dozen words long.  It fit nicely in the old theme (Redoable Lite), but in Hemingway, it just didn’t render properly because it was too long.

I could have tried to mess with the template for Hemingway, but there was no guarantee that I could alter the bits of CSS needed to render the tagline better.  So maybe, I reasoned, I should consider a shorter tagline.

I ended up with “design is essential, but it isn’t normal.”  Kind of makes you wonder, doesn’t it?

I like this new, much shorter, tagline because it connects better to the name of my blog, and also says something interesting (hopefully) about the content.  In a world that seems obsessed with very superficial and naive design (witness, virtually any of the design shows on television these days), I want to bring home the point that design is not something that we (North Americans) are really used to at all, while also emphasizing how important I think design is for the world generally.

It may not be the perfect tagline, but I think it’s better than the old one.

The interesting thing is, though, that what drove me to think up a tagline that is – in my mind at least – very noticeably better than the old one is a simple rendering/positioning/visual feature of my blog.  This is interesting, I think, because there are many people who think that design is only superficial when it deals with simple appearances.  But here, I hope, I’ve shown that if you think about it properly, even what might be thought of as superficial can lead to rather deeper considerations.

Don’t get me wrong: I still firmly believe that form must follow function.  But sometimes, if the form is there already, it can really help figure out new forms to fit function or, in this case, content, better.

The salary pyramid

Here’s a new* way to visualize some characteristics of corporations.

One of the big, current news items is the notion of bailing out the Big 3 North American automakers. But there are certain characteristics of the Big 3 that make me wonder whether we’re doing more harm than good by just giving them money. I’d accumulated some data about the relative performance of the Big 3 versus other popular automakers, but I couldn’t figure out how to present what little data I had in a meaningful way.

One of the tidbits of information I had was that the CEO’s of Japanese companies make about 10 times the salary of their company’s lowest level worker, whereas this ratio is far higher in the USA.

It turns out that it’s not that simple. A quick check of Google suggests there’s no clear answer, but some definite trends.

  • According to the Fair Economy website, the current ratio is over 400.
  • According the the google excerpt of a questia report from 1995, the median CEO in a survey conducted by Business Week earned more than 94 times what a factory worker earned, whereas the ratio in Japan was between 20 and 30.
  • In 2005, alternet.org reported that the ratios were 500 in USA, 45 in Mexico, 25 in England, and 10 in Japan. (Although I failed to find any evidence of background research on this.)
  • Michael Moore’s blog reports (in October 2008) that the ratios as over 400 for USA, 28 in Britain (which is not the same as England), and 17 in Japan.
  • In 2000, bnet reported that the ratios were 476 in USA, 13 in Germany, and 11 in Japan.

…you get the picture.

Anyways, I was wondering about how CEO salary compared to the total corporate costs, and thinking this obviously related to the number of employees. And then suddenly the notion of the pyramid popped into my head.

It was an unconscious cognitive act that generated the idea – that’s why it seemed to appear fully formed in my mind – so I can’t positively say how it came to me. But I strongly suspect it was a case of analogical reasoning (which I believe strongly is the key cognitive act in designing things). I’m well-aware of the visualization of the corporate pyramid, with the CEO at the apex and all the lowly workers ranged out at base. The height of the pyramid represents the level of an employee in the hierarchy. One just has to change the vertical axis to get a salary pyramid.

If one uses the horizontal axis to represent the number of employees at a given salary level, then one can construct pyramid shapes that model the distribution of compensation through the company in a simple, systems-wide way.


Figure 1: Salary pyramids for
Toyota (red) and GM (blue).

It then occurred to me that the resulting shapes might only be pyramidoid, and that the shapes themselves might be interesting. Consider the following examples.

Figure 1 show the rather absurd salary pyramids for Toyota (in red) and GM (in blue). The figures used to build these pyramids are as follows. GM has 266,000 employees, average total worker compensation of $75/hr, and a CEO salary ratio of about 400. Toyota has about 316,000 employees, average total worker compensation of $45/hr, and a CEO salary ratio of 15.

Note that the vertical axis is uniform for both GM and Toyota; that is, the difference in the height of the pyramids is accurate to the data. The total area of the pyramids is a representative measure of the total cost of all salary in the corporation. It should be clear that there’s definitely something very wrong at GM – considering that Toyota is doing just fine.

The bottoms of the two pyramids in Figure 1 are not at the same level, but at the scale shown here, the difference is not visible. Because of the interesting features that can you can capture in a pyramid, let’s make up a couple of companies with different characteristics and look at their pyramids. I’ve done this in Figure 2.


Figure 2: Some basic differences
between salary pyramids.

In Figure 2, we show two salary pyramids. The vertical axis is in units of currency (for salary) and the width is in units of “employees.” The wider the triangle, the more people are earning that corresponding salary.

The green triangle represents a company where the CEO salary ratio is relatively small; that company also has a relatively shallow hierarchy (assuming greater salary corresponds to higher level in the corporate structure) – i.e. it’s relatively light on middle management.

The yellow triangle has roughly the same area as the green one, but it represents a company with a worse paid workforce (lower base), a better paid CEO (the top of the triangle is quite high) and because the base is smaller but the triangle is taller, we can say with confidence that a greater fraction of salary cost goes to management (than for the company represented by the green triangle).

This means we can use salary pyramids to compare companies as well as looking for specific characteristics in single companies.

What is not represented accurately in Figure 1 is the shape of the sides of the pyramids. That’s why I call these shapes pyramidoid: the sides aren’t necessarily straight. Interestingly, the shape of the sides can possibly tell us interesting things too.


Figure 3: Two different kinds of
corporations: one with very little
middle management, and one with a lot of
middle management.

Figure 3 shows two pyramidoids. Since their bases are equally wide and have the same offset from the horizontal, we know they have the same size of equally paid workers. Since both shapes have the same height, we know the CEOs of both companies are paid the same with respect to their workers.

The pyramidoid on the left is quite skinny through the middle. Since width indicates number of employees at a given (vertical) salary level, this figure tells us that most employees make relatively little – or that only very few employees make more than the workers. Assuming that one can reasonably map low salary to workers and high salaries to executives, then this figure represents a company with a very light layer of middle management.

The pyramidoid on the right is rather fat. This says that there are, for most salary levels, more employees in (presumably) middle management than there are low-paid workers. Depending on the nature of the company, this could be a very serious problem. One interpretation would be that this company has more managers than workers. This may not make sense, but so few things these days do….

I don’t have any real data for an organization, to see what a real salary pyramid would look like – at least not right now. But I hope I’ve suggested that this very simple visualization can not only indicate important corporate characteristics, but also provide an easy way to compare corporations.

* I did try to google a few alternatives – like “compensation pyramid” – but couldn’t find anything that lined up with my idea. So, to the best of my knowledge, this is a new way to visualize certain features of corporate structures.