Proofs for Yesterday's Post

Surviving Entropy

My 'for-fun' research project is on survival strategies for complex systems.  I found an interesting result last night regarding systems survival.  To make sense of it, you need to understand the context.  The big picture is a system (think biological organism or intelligent civilization) that moves through time trying to maintain a state--surviving, in other words.  The system is made up of components that degrade via entropy.  As a simpler analogy, imagine a satellite that has an on-board computer, but has lost all but the most basic programming.  All that the thing can do is upload and run a new program you send it.  See the amazing graphic below.  This is like a system moving through time and being subject to random internal changes.  The program as it it sent is the original version, and the program as it arrives is the one after some time has gone by.

To simulate entropy, imagine that the satellite's radios cannot do any kind of error correction or detection--you have to build that into the code of the program you send.  This is a very difficult challenge--to write a program that can detect and correct errors in itself.  It can't be done with any kind of certainty because the functionality of the program may be corrupted by the very errors it needs to correct. 

To do the math, we need some definitions, which the graphic below is intended to help.  The rows below are the symbols we send to the satellite's computer, comprising a program.  In the illustration the rows are 28 blocks long, representing 28 symbols (very short for a real program).  Each one of these is vulnerable to corruption due to noise in the channel.  The received code is marked red in a block if transmission error has caused the wrong symbol to be received.  Our first parameter n is the number of symbols.  So n=28 in the illustrations.

If the probability of a symbol arriving intact is p, and the probabilities are independent of one another, then the probability of all of them arriving intact is

Because I'm really interested in what happens in nature as survival systems are subjected to entropy, we need not restrict ourselves to sending a single copy of the program.  Nature is massively parallel, so imagine now that we have lots of computers running simultaneously and we can send several copies (call that parameter k).  In the graphic below, k=5, since there are five layers (five mutually redundant copies).

The probability of at least one program surviving is given by

Now imagine that our program can be broken up into self-contained chunks. Each segment has the property that it can detect if it is broken some of the time (I call this the Am I Me? test) and the ones that are working correctly can tell detect and incapacitate copies of their chunk that aren't working (the Are You Me? test). All we need is one surviving chunk from each type. This is illustrated below, with the vertical dividers showing chunks. Dark green blocks are members of chunk-instances that survive. The number of chunks is parameter m.

In the simplest case where all the chunks are the same size (m divides n), the probability of survival is now

As you would guess,when k is larger the probability of survival (correct uploading of the program) increases, and a m grows the same is true.  What's interesting is that the best trade-off between the two is different, depending on whether p is near zero or near one.  When the probability p of any one symbol arriving correctly is small, the advantage of the segmented transmission (m >1) over unsegmented (m = 1) is

This means that for unreliably transmission of symbols, once k is modestly large, it pays to concentrate on building up m because of the way exponents work.  So more segments is the best survival strategy.  On the other hand, if the chances of an individual symbol arriving intact are high, we have

[Edit: actually the limit is for (1-seg)/(1-unseg), which is a comparison of the chance of NOT surviving, but the rest of the conclusions hold.  See proofs.) The proofs of these limits are too long to include in the margins of this blog.  Notice the symmetry?  The situation is now reversed, and once we have a modest number of segments, we're better off building more redundancy in them.  Also notice that the number of program steps n is not present in either limit.  This means that the strategies are scalable. 

I'm looking for real world examples of this phenomenon, either in human-designed systems or biological ones.  For example, in comparing molecules to cells in the human body, we can assume that molecular mechanism are very reliable, with high probability of persisting across time (p close to one).  Cells have both Am I Me? and Are You Me? tests (programmed cell death and the immune system, respectively), so they qualify as components made up of molecules.  Many cells of different types make up a body, so the number of types is m and the number of each type is k.  Without further assumptions, the model above would predict that we would see many more copies of each cell type than number of cell types.  This seems to be the case: there are trillions of cells and hundreds of cell types.

How robust is this?  Are there other examples?  I'd like to find an example where p is low.

Survival Strategies

Speculation is rife that the brick and mortarboard, chalk and talk higher education establishment has reached senescence. The particular charge is, that Edusaurus rex has grown thick-limbed on the richly oxygenated air of heavy government subsidies and cannot survive the change in economic conditions, which now favor the fleet-footed Cyberdon meme, which potentially can deliver the same product much more cheaply and conveniently. Let me elaborate on this cataclysm with a (cue crashing thunder)...

Worst Case Scenario. Imagine an unholy union, birthed on a Friday the thirteenth midnight in a graveyard, between University of Phoenix and Wal-Mart. Because continued exposure to "that which cannot be named" may have unpleasant physiological effects, let us call it Yoyo U to disguise this chimera in polite conversation*, or more formally as Cyberdon yoyo.

The trough of state and federal money for higher education is deep and broad and as untouchable as a third rail. The bricks and mortarboard institutions have gobbled it up, burped, and said "more please!" before even using a napkin. To get into the feeding pen and belly-up to the rich public broth, one must first pass through the baleful gaze of the accreditors and weather their harsh words and blows from compliance prods. Imagine though that Cyberdon yoyo passes this gate, slips in unannounced, and proceeds to feed. And reproduce.

As a rule of thumb, provided that you can talk your students into taking out loans, you can count on about $10K per student per year without them having to dip much into their own pockets. In fact, the way the loans are set up, they can sometimes take out extra money and buy a bass boat too. I've actually heard "College Eks is paying me to go to school." But yoyo is bred for value, and manages to wholesale price its educational product at subsidy level: any student--particularly PELL-eligible students with high enough GPAs to qualify for some state-based merit aid--can attend nearly for free. To be sure, this requires a very clever financial aid digestive system on the part of the Cyberdon, but this is a worst-case scenario, remember.

Of the 170 or so small private liberal arts institutions, I suspect many of them depend on bread and butter students like the ones described: some need, good credentials. More generally, any institution that depends on state and federal aid would see fierce new competitor gobbling up part of their PELL and potato stew as true discount education comes to the masses.

At first, Edusaurus laughs at the scrawny little unattractive furry beast. It makes jokes about the quality of the product, and mocks the labor standards. But by and by, the weather turns chilly, and there are suddenly a LOT of little yoyos running around, gobbling up all the best parts of the stew.

Eventually, because of shear scale, Cyberdon yoyo can offer services that Edusaurus can't dream of. Free textbooks for class, and high quality ones too. A massive online library. A return policy that can't be beat. Gift cards for a PhD. True, the selection may not be as great as one would like: there are no Masters of Applied Ambiguities degrees or Historiogragraphy of Post-Colonial Xenobiology courses, but you can find what you need, and it's cheap. And you can get a degree while working full time! Heck, all you need is a smart phone--you can take classes while driving down the interstate!

What happens to the small colleges that then have their customers staying away in droves? I think it's safe to say that if this scenario plays out, many venerable institutions will face unplanned obsolescence. The ones that survive this K-T boundary, like the alligator, need to find an undisturbed ecological niche.

There are still bookstores. Amazon.com and bn.com didn't kill the traditional bookstore. You'll notice that you pay a lot more in Borders or Barnes and Noble stores than you do online, but you can buy coffee and hobnob with other customers. It's a social activity to shop for books in person. The bandwidth is higher in real life (see my last post), which allows for a richer experience, and some people will pay a premium for it. That gives us our main question to drive survival of the small privates.

What's special about being here? Don't look at things you'd wish to be different as much as what you do well. Close to the beach? How can you take advantage of that? In a major city? What unique benefit can you leverage for your students? What is it that's worth paying a premium for?

A perhaps less palatable question is this: how can you subsidize your traditional program with cheap-to-operate secondaries like online and evening school? The latter has a built-in advantage over yoyo because of locality--if it's convenient and customer service is excellent. Online programs probably need to be limited to a very few, very good ones--something you can specialize in . Maybe the Masters of Applied Ambiguities is your niche.

If it's liberal arts you're into, it's a lousy brand. Fix it. I'm not saying the product is bad, but the marketing generally is. Answer the question: what does liberal arts mean in terms of the graduate's career? See my post about the mismatch between expectations and reality here:

The bottom line is that we discovered that many of our students don't understand the product they're buying, and we don't understand them very well either. It's not the kind of thing one can slap a bandaid fix on, but will require a complete re-think of many institutional practices.

Get some young people involved. Youth may be wasted on the young, but only they understand exactly how it's being wasted. If your strategic planning group is all over 22, you have a problem.

In general, survival means always looking for an edge to increase the probability of making it one more year (details). This will become critical if the easy meals become harder to find. I heard someone say once that success is a big predictor of failure. The point was that complacency is not conducive to increasing those probabilities. At this point, I think there's plenty of opportunity to find a niche. But there are only so many niches, and to mix metaphors, the music will stop at some point leaving a bunch of Edusaurus species with growling tummies.

[Edit: I changed cybercodon to cyberdon as easier to say and arguably more accurate]

Update 10/8/2009: See "Served, Yes, But Well-Served?" from Inside Higher Ed. Quote:

The list published by the Student Lending Analytics blog last month jumped off the computer screen: Of the 10 colleges and universities whose students received the most Pell Grant funds in 2008-9, 7 were for-profit institutions.

The article goes on to speculate about the meaning of this, but one thing is clear: Cyberdon is through the gate. The big players in the online market aren't heavy discounters aiming for the best students--that's not where the easy money is to be made right now. Judging from the article (and looking at the Pell grant numbers), the opposite may be the case: find students who have trouble getting into bricks and mortarboard institutions because of their own qualifications or because of overcrowding at two-year schools. It's a kind of captive audience. Squeeze out all the subsidies and loans you can, and keep the price high. As long a students are willing to take out loans, there's no downward price pressure.

See also: "Scaling Higher Education" and "End of the World, Etc."

---

*I mean no disrespect to either institution, nor to the idea of low cost ed. I got the moniker like this: University of Walmart = U of W = U of (UU) = (UU) U, but You-You is easier to say as Yo Yo, hence Yo-Yo You. Logical, no?

Unplanned Obsolescence

On a morning bike ride here in Düren, I returned to the abandoned military post I'd discovered last week, this time with the camera along. The entrance to the installation is shown below, with what I presume to be a guard house.
According to our host Hans, this was originally a WWII era site that was then taken over by the Belgians and not truly abandoned until 10-15 years ago. He has a lot of stories about the Belgians, their two official languages, and the state of their equipment. Whatever the case then, the buildings are falling apart now, aided by local vandals. It's silent and spooky to walk around in these modern ruins.
Part of this large installation has been turned into a nature preserve, and a large chuck is now occupied by commercial interests. AVIS has a car park there, on the other side of the overgrown road I biked in on. It's fenced off, but the cars surround what look like barracks. I stuck the lens between the chain links and snapped the photo below. There are rows of identical buildings, in much better shape than the abandoned ones.
I'm thinking back, but I don't think I've ever visited an abandoned university. They surely exist, and one can easily find photos of them courtesy of your favorite search engine. Here are some links, none of which I've verified, so caveat emptor:

• Some lovely photos on Flickr, but location and name of university unspecified.
• One in Greece
• Institute de Chemie et Metallurgi in Belgium, according to the text and pictures.
• University of Brazil expansion, according to the text.
• Flickr photos of Morristown College, then Knoxville College, now abandoned campus. According to Wikipedia, the college closed in 1994 and has several historical buildings at the site.

The bricks and mortar of established campuses represent substantial costs to operate and maintain, and unless the summer has a good enrollment or other forms of income, 25% of the year many buildings aren't earning their keep. We might compare the established way of delivering education to the now-established ways of running those same institutions using big expensive software packages like Datatel or SCT Banner or Jenzabar products. The installation time is about the same as a building project, and costs of maintenance are probably comparable.

The bricks and mortar approach has been under pressure to change from online-only institutions. Similarly, the big-iron approach to college administrative software is under pressure from open source competition. I'd heard about the Kuali project before reading this article in InsideHigherEd today. The big news (to me at least) is that major universities are converting to the open source software, with Colorado State University and San Joaquin Delta College being live on the system according to the article, and The University of Arizona and Michigan State University soon to follow.

I've often made the point in these blag posts that sometimes the only reasonable approach to a hard problem is an evolutionary one. In fact, we might call this the ultimate creative endeavor. A combination of either random or inspired input, combined with a rational weeding-out process can over time differentiate ideas that work from ones that don't. I argued more technically in "Survival Strategies" that in the long run this is probably the only route to long term survival in a changing environment. In terms of the topic at hand, that means that open source software is better positioned to survive than commercial software because of the evolutionary approach of the first, compared to what I called a monolithic entity in the paper--a one path to success model, that commercial software companies have to follow. It's not practical for Microsoft to create 100 different versions of Windows to see which one is most popular. Open source software, by contrast, thrives with that model. Of course most open source projects fail--that's really the whole point--that's how evolution works, by leaving a lot of bad ideas in the software cemetary.

But I don't want to write about software; the point is a broader one. The very same process is now beginning to play out in the general realm of higher education. Competition for bricks and mortar colleges from online universities is only the beginning. The means to deliver education conveniently in electronic forms creates a whole new environment that is different from the one that universities and colleges have grown up in. Open source software to run a college is small potatoes. Imagine the whole educational product from start to finish as evolutionary instead of monolithical, plodding beasts.

To embark on this excursion, we'll need to consider what the obstacles are currently to success for a university. This is first and foremost: money. Mammon is the oxygen of higher education, and it's the pursuit of it that creates a natural environment for larger and larger beasts. As with any economy of scale problem, there are efficiencies that come from size. The barriers to even functioning as a basic higher education provider are substantial. There are state and federal entities who have a hand in because of the money they dump into financial aid. There are accreditors of all kinds, the costs of finding and processing potential students, and the large bureaucracy that is needed to support the whole edifice. Doing this on a small scale can be done, but there's no room for error.

That is the Jurassic model of large lumbering beasts living in an oxygen-rich enviroment, but what's the open-sourcy alternative? What is it that prospective students really get out of higher education? If the answer is allegiance to a football team, or a brand name diploma, or making great contacts for their future careers, that's one thing. If it's actually learning to think and communicate, that's another. The two are not mutually exclusive, of course, but the point is that the teaching part can be done in an entirely different way that doesn't involve vast amounts of money. It already is. You can download free courseware from MIT and other places, for example. But let's suppose that education requires interaction with teachers and fellow students. This can clearly be done online, as with University of Phoenix Online, for example. But their model serves just to rake in as much financial aid and loan money as possible--essentially porting to the old bricks and mortar model to the digital age without changing much, in the same sort of way that the first cars resembled the horse-drawn carriages they were to replace.

Instead of a big online university, with all the same problems of accreditation and such, imagine something more like eBay for education. In this model, a match-making service pairs up students and teachers online. Probably the course slots are actually bid for in an auction. A ratings system tracks feedback from customers (students), and the prices students would be willing to pay for a particular instructor would serve as another kind of rating. The eBay-like service would provide a minimal administrative structure in return for a percentage. This could, for example, include a minimal standardization of courses, or at least suggestions, for different areas of study. Students ideally would continue to take courses as a life-long process, something the dinosaria can only preach but not really deliver. Why? Because of the money. It would be far, far cheaper to deliver courses in this way. As a first order calculation, imagine that the service provider takes 10% for overhead. This itself would be subject to competition, which would drive the price to some reasonable level, since there's no reason only one such service could exist.

So I as a math professor decide to offer a Digital Logic class, with an enrollment of 20. I'll teach three sections simultaneously, which may be less than a face to face load, but online is more time consuming, so let's call it even. How much do I need to get in tuition to have a reasonable lifestyle? Two semesters worth is a maximum of 120 nominal tuitions T. If I charged $1000 each, that's $120K less the administrative cost. Even at $500 per student, I could afford to live nicely in lots of places, and still have three months a year free. The more specialized the course, the more in demand the professor, the more comfortably he or she could make a living.

Meanwhile, the administrative eBay-like service doesn't have to worry about processing student loans, applications, or accreditation. It doesn't have to build and maintain a lot of buildings, nor hire a football coach. It can run at full speed twelve months per year. And of course, it can do lots of this with open-source software, using Moodle as a course-delivery platform, for example.

I searched for such a service, but haven't found anything like it. If you read this and know of one, please let me know.

The downside is an erosion of standardization, the obsolescence of the 'major' and many other conventions of higher education. That's the nature of evolutionary change, and it's ultimately the marketplace of careers and ideas that decides if it works. Because of the drastically reduced cost of such a model, it's a good bet that something similar already exists or will soon. Whether or not it, or something similar eventually takes root is an open question. But I think it's a good bet that in the long run a lot of old buildings with neo-classical fascades will have weeds growing around them.

How to Make it Last

I just finished an article Survival Strategies (pdf), which is a theoretical examination of how something--anything--can survive an indefinitely long period. There are some practical bits of wisdom to be gleaned from this for higher education or any business enterprise.

First, longevity requires one to 'be many' or 'be smart.' The former case works well for biological life, which can multiply and fill every evolutionary niche available. The latter is the only strategy open to an individual subject. It has to constantly work to increase its probability chances in two ways.

External threats and opportunities have to be anticipated in order to be successful. This means doing something like science: observation, experimentation, and creation of inductive hypotheses. The more you understand and can predict and control the environment, the better your odds are.

The second way in which an organization needs to improve its odds is internal. There is always some chance of self-destruction. For a college this might mean the decision to close the institution down because of lack of funds. It's hard to imagine an institution doing this except out of necessity, but there are other ways in which it can become self-destructive. As a case in point, this article describes a nearby college that made some bad decisions about who to let manage its endowment.

The point is that in addition to being able to anticipate and take advantage of external conditions, an institution ought to be continually striving to make its decision-making better as well. We see bits and pieces of this with an emphasis on assessment, TQM, and the whole idea of institutional effectiveness. We audit expenses assiduously. Why don't we audit decisions? If there were such a thing as documentation and retrospective analysis of decision-making, it would lead to better decisions down the road (my opinion). It's the difference between being curious and self-reflective and being stubborn and blind to the past. We would probably accept this description for individual humans, but it's not commonly discussed, in my experience, for institutions.

Update: The paper is now on the arXiv science preprint server here.