17 April 2009

Ternary graphs and what they do for you

Yes, yet another in the series of absolutely esoteric concepts that may actually play a role in your life!

You have to love this stuff, no?

Ternary graphs are graphs that utilize three major axes and can then have additional correlated lines added in to follow other information. Just so you get an idea, a basic ternary piece of graph paper looks like this:

Ternary Graph Paper

Today it is ternary graphing which we used in geology class to help classify the mineral content of rocks that had three primary mineral types so that you could identify the melting temperature of that rock based on mineral composition. Yes, pure esoterica! The good folks at Tulane have an example of this at their Petrology course, and it gives you a nice example of the multiple mineral types and differing melt temperatures associated with them. First would be a 3-D representation of crystallization temperatures utilizing the different percentages of minerals:


Now that just looks horrible! But, if you project it onto ternary graph paper, you get this:


Note that the crystallization temperatures now become boundary curves, so you can start to figure out what crystals are forming when and how long they have to develop. This is great stuff!

In geography you can use it to plot things like changes in neighborhood status due to demogrpahics, as seen at the Geography Field Work site looking at the impact of gentrification on a neighborhood.


How does this have applicability to the real world beyond the rocks beneath your feet?

As if those weren't important...

The reason it has applicability is via the other great ternary problem that crops up in all sorts of places. The first great example of the exclusionary ternary problem rule is NASA that started to show up in the 1980's, and as a result its fallout is described like this (Source: Space.com, 13 MAR 2000) and I will highlight the words that are critical:

WASHINGTON - A former NASA manager issued a critical report Monday of the agency's "faster, better, cheaper" approach that has pushed the agency's engineers and scientists to crank out more frequent, low-cost and stripped-down missions since the early 1990s.

The report was written by Tony Spear, who worked on several missions and headed up much of the Pathfinder mission that successfully air-bagged its way onto the Red Planet in July 1997 on a relatively modest budget.


"As with any major human endeavor, there have been successes and failures in the stress and strain of venturing onto new ground, trying new things, taking risk to gain significant return," the report said.

However, "failing due to mistakes is not tolerable," it concluded, particularly when contrasted to failures occurring due to use of exotic technology or a spacecraft that encounters a strange, unknown environment.

In my mind this is the 3-axis exclusionary rule because that is what it came down to during this period. The quip about NASA projects was: faster, better, cheaper... choose two out of three.

Ahhh... now you begin to see that if you put faster on one axis, better on another and cheaper on a third you can start to see what the cost trade-offs are on a project. Well, that was the idea, in reality you can't do that as getting something that is, say, faster and cheaper ends up meaning, engineering-wise, that you are low-balling the work, fast-tracking it and thus don't have time to invest in better technology. Which means you can get a known, proven, low cost sensor platform out the door fast and a low cost. All well and good.

Now if you need better sensors you have a trade-off: you can try to push for faster design work, which costs a hell of a lot, or go for slower design work at lower cost. What you can't get is a new sensor on a new platform done cheaply and quickly. If you are used to thinking in the 3-axis graph you would think that these would not be mutually exclusive and offer trade-offs between them. The world does not work like a neat ternary graph for new engineering designs.

An old design, however (not better) can be faster and cheaper. A new design is one or the other, not both.

If you can afford a long time to delivery, then you can get it cheaper and better. A faster track means one or the other.

Do you see how this works?

The ternary graph is very good for plotting mutually dependant parts of a system, but when each part has individual parameters that act on their own, you can't plot them on the graph as a change in one of the independent variables has a non-dependant variable change in ways that are outside the plotting realms.

Three interdependent variables are great for ternary graphs, and when a system can be found that has something going on like that, it allows for good interpolation of what happens if any single variable changes: you are looking at dependencies which reflect each other and, so, are known as part of a system.

So with two different ways of looking at three-variable problems, what else can this apply to?

Interestingly enough I think a good case can be made for health care!

Really there are three major determining factors that we all want from health care, and the debate about them really is quite interesting. Let me put them down as I see them:

1) Cost - Everyone wants 'affordable' health care. Well price varies along with many things, but affordability is a basic concept to deal with. So Cost is a definite part of the problem.

2) Availability - This, too, is necessary. Everyone wants there to be enough providers and such, and this turns out to be a major concern witnessing how other systems that are State run or supported soon start to make it less available. So Availability is part of the problem.

3) Quality - Good quality health care has been a mandatory part of the American system and we work very hard to sue the dickens off of poor providers of health care. One mistake and you're out. So this is part of the problem, too, as it is an expectation of the system.

Now are these interdependent, like crystallization points for minerals or how changes in immigration and gentrification and services are interlinked? Or are there independent variables that change in ways not easily told by these three things that everyone wants, which is the NASA concept?

The US system has two major periods that typify it: 1) immediate post-WWII era (1946-60), 2) increased presence of health insurance as a major feature of working life (1961-present).

Era 1 is typified by high availability, good quality and moderate cost. There were very few complaints about the health care system coming into the baby boom era when all the babies were being born and families were expanding at a fast clip. What had once been a wartime benefit to encourage older workers to get to work in the factories during the war (health insurance) continued its subsidized way beyond that necessity, but hadn't shown up as part of the labor/management landscape.

Era 2 is typified by increasing utilization of health insurance subsidies as a negotiating lever between labor and management and saw a swelling of rolls for families getting health insurance. Plus the Boomers would start to appear in the equation, causing an increase in the number of people getting health insurance due to the demographic change they represent. This era is typified by high availability (no one is turned away), high quality and moderate to increasingly high cost.

Just as a rough 'hand-waving' concept, US health care is demonstrating that increased utilization with subsidies added in will increase quality of care, but also increase cost.

This points to an interdependence where cost goes up with higher quality and larger subsidized utilization, and is lower with somewhat lower quality and less subsidization. As subsidization is part of what changes the system, it must be examined.

The UK was in similar circumstances post-WWII, but went from an Era 1 to a different scenario, call it Era 3.

Era 3 is typified by State control of the system, universal availability for citizens and higher taxation. The result for the UK is high to moderate and declining availability of health care services, good to low moderate quality, and low cost. The universal experiment there is pointing to a relative decline in availability (rationing) and a slow lowering of quality standards. Part of the reason for that lowering is the ever increasing dependence of the UK on foreign born doctors due to British citizens not seeing medical practice as a good occupation.

Canada is in a similar boat, most likely due to the similarity of government systems, and is seeing increased rationing (low availability) for what people in the US would consider 'standard' tests and procedures.

Germany is a different case, and gets its own designation as Era 4. It is typified by a low productivity economy, high taxation and mandatory subscription to health care services unless you earn enough to opt-out. Additionally you lose much of the patient choice of physician in the German systems (save at the high end) and this causes patients to 'hop' from available doctors quickly amongst queues. For the amounts paid into the system, Germans are satisfied by their system, but are seeing different problems show up.

Era 4 is typified by high taxation, low productivity, non-choice of physicians (as we know it in the US, but similar to the HMO model for ability to switch due to wait length), and near universal availability of health care. In Germany the cost is hidden in the tax system and doctors only bill directly if you are part of a non-State plan. Thus there is no indication of cost valuation available in the German system. This is a major factor that then distorts the examination of systems, but there are telling points that Germany is moving away from the full State system and encouraging competition and alternative plans to the State one. One does not do that if you are getting good cost valuation, and as the government has so much of the burden and it is trying to get competition, the Cost portion must be reaching unacceptable levels for the government. It does have high medical availability and moderate to high quality (although Germany doesn't do a good job measuring this), and attempts to ensure that everyone has options while maintaining a minimum standard of health care for everyone. But the lack of cost metrics, the low productivity of individuals and high taxes for such a system, are indicators that while the State can maintain a minimum it cannot guarantee good valuation for the cost it has to pay. In essence the government is the purchaser of last resort for the poor and that cost isn't something it wants to continue on with.

There are non-dependent problems that show up in health care between the major variables, which means it is NOT the easy ternary graph... uh-oh. That leaves us with the NASA model.

How would that work?

Cost, Availability, Quality: choose 2 out of 3.

In the case of Germany, UK, Canada and other Nations we can see that if you get low cost you can have available but moderate to low quality health care (UK) or low availability but moderate quality health care (Canada). Or you can get high availability and moderate to high quality, but the cost becomes unacceptable to the payer (Germany).

There are, of course, other models, like the failed Soviet and Cuban ones, that have universal availability, low cost and low quality, but that is unlikely to be acceptable to Americans.

The non-representative factors in the Cost, Availability and Quality model is demographics and type of society the US has in comparison to Europe or other parts of the world. The US has a high productivity society, an expanding population and increasing standard of living for the entire society. Those European nations that have full or major State involvement in health care are now typified by stagnant productivity, contracting population and a standard of living that is only slowly increasing due to general penetration of technology, but the non-use of such technology at the workplace for increasing productivity. Thus to get a social 'good' productivity of the economy to support that 'good' is sacrificed: no one feels the need to achieve greater income to get better care or any of the other State-mandated offerings of social welfare.

As a tool the ternary graph offers many opportunities to examine systems with high degrees of interdependence and also to weed out those that have other factors at play. It is also good to examine changes in such things as demographics where a two axis graph wouldn't show up trends clearly, but a three axis one does. Plus by projecting a fourth set of boundary layers, one can learn how changes in the interdependent variables effect the overall system.

Luckily the NASA system also has its limits, as demonstrated by health care, but its utility does demonstrate that the 'lock-out' of one factor by the other two can show up in other systems that are highly complex. That factor is independent of the areas sought to be measured, thus changing them asymmetrically when that factor is impacted. So even with extremely complex systems, like health care, you can work to isolate three factors that can tell you what the repercussions of the system are even if there is no great 1:1 co-incidence of 'lock-out'. Even without that, however, the Cost, Availability,Quality aspect of health care is telling and has many chilling and deeply similar aspects to the NASA new project Faster,Better,Cheaper system.

That should be very, very worrying for those examining health care and trying to get high availability, high quality and low cost.

No system exhibits that so far. None.

Until we get something like the AutoDoc from Larry Niven's Known Space works, and we have a great trust in fully automated medicine all the way to major surgery, this will not change. It can, with very advanced technology and automated treatment systems, but those aren't past the 'wish we could do it' stage. That will change how we get medical care, by getting people out of the provisioning part of it... and that will have profound changes for society. Automation tends to do that to a system.

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