The Long View

In "On Design," I gave three versions of designing for an outcome: soft, forward, and inverse, in increasing degree of difficulty. The question "how difficult is inverse design?" is of utmost importance when we consider complex systems. As a real example, consider how the government of the United States is "designed." By this I mean, the way laws and policies are created and enforced. Because of conflicting goals of different constituents and the inherent difficulty of the project, there is no complete empirical language to describe a state of affairs, let alone do a forward simulation to see the status of the nation in, say, three years. And even if we did have such a language, we would be limited to simulation and prediction of only the "easiest" parameters. And even these would subject to the whims of entropy, a subject I'll take up later.

I submit that individual governments, as well as companies, universities, and militaries use soft design with bits and pieces of forward and inverse design thrown in (for example trying to forecast near term economic conditions to help determine monetary policy).

Government in the general sense has been "designed" by the process of being tossed into the blender of fate, to be tested by real events. See the following video of the history of Europe to see what I mean.

Natural selection would seem to be be at work here, weeding out the worst designs. But it's not Darwinian  because the countries change rapidly over time with the population and minds of leaders. One truly spectacular bad idea (like invading Russia, apparently) can bring down a whole nation. So what we are left with is a very temporary list of "least bad designs." Of course, many other factors are important, such as geography, natural resources, and so on. Even so, the people who live there still have to make use of such advantages. If Switzerland abandoned its natural mountain fortress and invaded Russia, it likely wouldn't end well.

Darwinian evolution is different from this national evolution. In the former, good solutions can be remembered and reused through genes or any other information passed from generation to generation. Diversity is created through recombination, mutation, population isolation, and so on. Darwinian evolution comes with an empirical language that we partly understand. To make a metaphor of it, "programs" are written in phenotypes and these "are computed by" the laws of physics and chemistry using the design and environment as "inputs." The fact that scientists can discover this language and use it to make predictions should be appreciated for the miracle that it is: we are witnesses to a dynamic but understandable problem-solving machine of enormous scope that has worked spectacularly well at producing viable designs with only an empirical language. Evolution does not use predictive techniques (that is anticipating that a critter will need wings and therefore building them--for a dramatic example of this, see this video). But there do exist creatures who do use forward and inverse design to plan their day. If you throw a ball at target, you're predicting. If you go to the fridge to get food, you're using the inverse technique: starting with the outcome (get food) and working back to the solution. But this still isn't good enough.

Here's the rub: forward design isn't enough to guarantee any more than short term outcomes, and our ability to do inverse thinking is very limited. Let me pose a problem:

What present actions will lead to [insert subject]  existing in a healthy state 100 years from now? 1000 years from now? 10,000 years from now?

The question is posed as an inverse design problem, starting with the goal and asking what needs to be done to achieve that goal. If we had a good language with which to describe the states, we could at least imagine an evolutionary approach, shown in the diagram below, with the red dot being the desired goal.

We're asking "where do we need to be NOW in order to end up where we want to be AFTER?" The forward design approach is to simulate lots of "befores" and see where then end up "after," and choose the best solution we can find. If we are lucky, we can use a Darwinian approach, combining partially successful solutions or tweaking "near misses" to home in on the best solution we can find. This depends on the sort of problem we're trying to solve, and specifically whether or not it is continuous in the right way. Sometimes being close isn't any good--those "a miss is as good as a mile" problem. All of this highlights the importance of the empirical language, which must have rules precise and reliable enough to allow this kind of prediction and analysis. Clearly in the case of governments, companies, universities, or even our own selves, this is not possible.

With only forward design techniques and lacking a good empirical language, we can still solve the problem with massive brute force: by actually creating a host of alternatives and seeing what happens in real time. A computer game company could do this, for example. Rather than spending a lot of money to find the bugs in its game, it could just begin selling it with the knowledge that the game will be reproduced on many different systems and display many kinds of problems. With this data in hand, it can begin to debug. This seems to be a real strategy. This sort of solution obviously won't work for a government, although in a democracy we have a non-parallel version: swapping out one set of leadership for another routinely, to see what works best (in theory at least).

Paying it Backward. What would it look like if we had all the tools to solve the inverse problem? We could pose it precisely, work forward simulations like the one pictured above, and we would have a huge advantage, shown in the graphic below.

Again, the red dot is where we've decided we want to be after a while. The inverse solver shows us all of our possible starting places in the now. There are multiple ones if we have not completely specified the eventual outcome, which tells us what opportunities we have now to optimize other things than the one we were thinking about when we posed the problem.

Example: An artillery officer is given the task of attacking a distant building. The locations of his guns and the target are fixed. Using ballistics equations we can work backwards to show all the possible solutions: e.g., a high arcing shell like a mortar, or a flat trajectory. This decision will determine how much powder is used.

The inverse solver illuminates "free" parameters and allows us to customize our solution.

Conclusions. For the real-world messy problems we face in complex human organizations, it's fair to say that we are not very good at long-term planning. In some cases it may be impossible because the forward simulators simply don't exist--there are no reliable cause and effect mechanisms. Trying to predict the stock market might fall into that category. In other areas, short-term goals are given preference over long term goals. This is reasonable for at least two reasons. First, the longer out the prediction is, the more likely it is wrong. Second, as individual humans our ability to affect events is a narrow window (e.g. a term for a legislator), and most of us want positive feedback now, not 1000 years from now.

As a very real example of our collective difficulty with long-term planning, consider the issue of human-caused climate change. With the terminology given in these two posts, it's easy to dissect the arguments:

• Empirical language. The basic facts about temperature change and CO2 levels are accepted by the scientific community, but still debated as a political matter. 
• Forward design: Cause and effects are challenged in the political discourse, computer simulations are therefore called into question. Unaccounted-for causes are conjured to explain away data that is (to some extent) agreed on.
• Inverse design: Prescriptions about what to do now to affect the future climate are attacked as being too detrimental to the present, and/or useless.

The question of what happens to the climate is scientific--this is the arena where we are best at design. If we can't understand and act on such threats intelligently, it's very hard to make the argument that we have any long-term planning ability collectively. Note that I'm not neutral on this particular question. The evidence is overwhelming that the risk to our decedents is very high. But go read the experts at RealClimate.org. 

Higher Education. This isn't a climate change blog; what does this analysis have to do with your day to day job in the academy? Everything. From the oracle at Delphi: "Know Thyself." What functional aspects of your institution are understood? How many are understood well enough to make predictions? How many are understood well enough to make inverse predictions?

We work backwards all the time. Suppose budgetary concerns have pushed up freshman enrollment targets, so the admissions office is tasked with bringing in 1000 new students for the fall. This is posed as an inverse problem, and with the standard empirical language of admissions we can build basic predictors. This is the "admissions funnel" prospects->applicants->accepted->enrolled (this is the simplified version). We usually have historical data on the conversion rates between these stages. If the universe is kind, we can use Darwinian methods--keep what works, assuming what works last time will work again, tweak to see if we can make it better. If there's a significant discontinuity (suppose state grants suddenly dried up, or we have a new competitor) the old solutions may not work anymore.

We can and should work hard to create an empirical language and use it to simulate our futures, trying to end up in a good one. This isn't enough.

Short term optimization leads to long-term optimization sometimes, but not as a rule. Think of it as a maze you're trying to escape. If at every junction you choose a path that takes you closer to the opposite wall of the maze, you may make smart moves in the short term only to discover there's no exit there: a long-term failure.

(original image by Tiger Pixel ) 

Even though we can't solve the inverse problem entirely, we may find that we have enough empirical vocabulary to make some important decisions. What do we want the demographics of the student body to look like in 10 years? Answering this question about the future puts constraints on how we operate now, even if they are fuzzy and inexact. Forget about solving the problem exactly--that's impossible--and think about what constraints are imposed in the big picture. Do we want a strong research program, or a large endowment, a national reputation for X? More idealistically, what do we want to be able to say about our alumni in a decade or two? How much does their success matter, and what sort of success are we talking about? Work backwards. I'll finish with an example.

Example: Student Success. If we focus on a goal for our ultimate accomplishment: the education of students, what does this reveal? How exactly do we want our students to benefit from their education? Some possibilities:

• Happiness with life
• Being good citizens
• Being successful financially
• Being loyal to their alma mater
• Getting a job right out of school

The overwhelming narrative in the public discourse is that we want students to be "globally competitive" and "get well-paying jobs." But that's a means to some end. What is the ultimate aim? On a national scale, the answer might be better national security and a stronger economy. For an institution, the answer might be that we want our products strongly identified with our brand, or that we want them to donate lots of money in the annual campaign. I think it's important to start there and ask "why do we care?" You could follow that up with lots of activities, like telling the students themselves why you care, if that's appropriate.  

Suppose that we care because we want the institution to be able to rely on an international body of alumni who will contribute back in money, connections, expertise, and other intangibles. This will enable the university to grow by presenting global options that may not be apparent now, but also establish an exponentially-growing revenue stream through an expanding endowment as successful alumni give large gifts back to the institution. Working backwards, we might identify several tracks to success:

• The state department track--prepare students for high-level international government positions
• The military track--ditto for the miltary
• The global entrepreneur track--help them achieve independence
• The big corporate track--give students the skills to compete and succeed within vast multi-nationals
• The wildcard track--for those students who don't fit the mold, are intelligent and creative, but don't want to be entrepreneurs or work in a cubical. This could include scientists, philosophers, and artists of all stripes.

If we keep working backwards, even without exact solutions, we can make some good guesses as to the curriculum each track needs, and the type of faculty mentors we need. This neatly sidesteps the drift toward vocational education that the public narrative implies, and gives the institution a raison d'être. There's nothing wrong with telling students "we want you to succeed so that you'll help us succeed." This sort of pseudo-altruism is what keeps the population going, after all. Thanks, mom and dad.

Think Backwards. Short term forward planning is like beer: it's obviously a good idea at the time, but watch out for the hangover.

On Design

A couple of day ago I had occasion to think about the difference between finding solutions randomly or by design. You might not think that random searching is the best way to find something, but this is essentially what has produced the stunning variety of life on Earth over the last three and a half billion years, especially in the last 600 million or so. This evolutionary approach is characterized by massive trial and error (usually in parallel) with success, or fitness, ascertained by the system. Unfit results are thrown away. Fit results are tinkered with randomly to create new experiments.

Evolutionary trial and error is a good way to solve a complex problem, as I tell my students. Yesterday we did a big review of all our integration techniques in Calculus 2, and one of the problems was $\int\sin x\cos xdx$. The official way to do this is by substitution, but someone yelled out to use integration by parts. I always try to follow these suggestions to the bitter end, even if I know they'll fail, because I want them to get used to the idea of trying things that don't work: it's a the heart of the creative/inductive approach of solving problems like evolution does. Even if your calculus skills are rusty, you can appreciate the following sequence.

Following the student's suggestion, we get $\int\sin x\cos xdx=\sin^{2}x-\int\sin x\cos xdx$

Now notice something cool--the original problem reappeared on the right side. If we move it to the other side to double up and then divide by two we get the solution:

$\int\sin x\cos xdx=\frac{\sin^{2}x}{2}+C$

In the process, the students discovered another useful trick for solving integrals. It's so cute they wanted to try it on the other problems (none of which worked).

Trial and error leads us down all sorts of unexpected pathways. Organizing this idea to work on computers is done routinely, including genetic programming and simulated annealing. More speculatively, artificial life simulations attempt to study biological-type interactions between agents in a simplified computational setting.

The original Tierra artificial life simulation shown above. Image courtesy of Wikipedia. (I have my own version of this that I use to research survival of complex systems. You can find the original code here.)

So what about design? The word is used for different purposes, but in this case I don't mean art design, like creating a new logo for your company, but designing for a function. Abstractly, imagine we want to create a design D of some object or process so that we obtain some attribute A. It might be a bridge that can support 100 tons at once, or a liberal arts curriculum designed to create open-minded graduates. There's a clear task at hand and a clear goal at the end.  I propose that for the most pure form of design to occur, and guarantee a successful outcome, that we need the following positivist ingredients:

1. Language. Definitions of the task and the outcome in unambiguous terms and in a common "empirical" language. By that I mean that we can take precise descriptions in this language and actual implement them without room for error. Think of specifications on a mechanical gear, for example. 
2. Forward Analysis or Simulation. A way to deterministically go take the specification D and ascertain if A applies or not. For example, we could take the plans for the bridge, with materials and all specifications considered, and determine if it can support the desired weight load. With 1 and 2 together we can use evolutionary methods to find solutions. Perhaps not the overall best solution, but it's a good way to search. 
3. Backward Analysis or Inverse Prediction. Here we take the attribute and work backwards to get the design. This is much faster than trial and error using forward analysis, but it requires a much deeper knowledge of the subject.

As a simple example, if I want an exponential function to model the growth rate of some phenomenon I'm studying, I can specify the problem precisely.

1. Description. At time 0 the population is 20 units. At time 10 it is 35 units. Find the exponential function that exactly fits this data.
2. Simulation. I can solve the forward problem for any candidate solution. I someone proposes $P=10e^{.3t}$, we can just  let t=10 and compute the population to be about 201 at time 10--not close to the observed value.
3. Inverse Prediction. Because this problem is well-understood, I can solve the backwards problem and design a solution: $P=20e^{.056t}$. We can go back to the forward analysis and simulate the population at time 10 to be modeled as 35.01.... We can get as close as precision dictates to the measurements.

Backward analysis or inverse prediction (my terms) is very powerful. If I don't have enough information to determine a design, this inverter will tell us that D isn't unique given the constraints. This inverse predictor grants us a deep understanding of the structure of the problem. It's also very hard to come by.

For convenience, let me attempt definitions that solidify the foregoing discussion and delineate the different ways of going from specification to design.

• Soft Design. Language is not empirical, outcomes will not be certain and cannot be reliably simulated, but is generally a D -> A evolutionary approach based on experience or preference. Example: designing a new letterhead for your company.
• Forward Design. This requires an empirical language that permits simulation of D -> A. An evolutionary approach guided by experience homes in on a reasonable solution. Example: designing a lawn irrigation system.
• Inverse Design. Successfully determines A -> D through proven deterministic rules that completely model the attribute A and design constraints. Example: designing a computer algorithm to invert a matrix.

Finding inverses such that we can compute A->D is hard. There is no general way of doing it--this is guaranteed by Rice's Theorem--so solving the Inverse Design problem is itself a Forward Design problem. What?

Let me try that again: in subjects where we don't already have a workable theory, the only way to find one is with an empirical language and trial and error. Of course, if there are connections to know theories like physics, we can get a good head start. But one doesn't have to find complicated examples. Here's a simple one:

The Collatz Conjecture is easy to state. Take any positive whole number, like 34. If it's even, divide by two. Otherwise multiply by three and add one. Repeat this process. The conjecture is that you always end up back at one. No one knows if it is true. If you take a moment to look at the Wikipedia page linked above you'll find that an amazing number of mathematical tools have been tried on it to no avail. This is evidence of an evolutionary Forward Design process that's trying to crack the problem. Assuming it's solved one day, it will create a body of theory that broadens the scope of the Inverse Design problems we can solve.

Most problem domains do not enjoy the complete ability to do inverse prediction. I would go further and say that most of the design work done on practical problems is soft or forward design, with bits of inverse design thrown in here and there for the most well-understood and well-defined problem types. 

"Think like the designer" is something I often tell my daughter when she's working with a computer program or trying to find a water fountain in a building, or otherwise in the middle of someone else's design. What were they trying to achieve, and what constraints did they face? This is an informal attempt at inverse thinking on the fly. Sometimes it works: water fountains are often near the bathrooms because it saves on plumbing.

Applying this to learning outcomes assessment is straightforward. We usually don't have good definitions of what it is we're trying to achieve, so most course design, assessment design, program design, curriculum design, and so on is soft. In cases where, e.g., standardized testing attempts to pin down the definition of "learning," there is no only the problem of the validity of those tests, but the top-down mentality that goes with it. It seems to me that there is an assumption that good definitions are enough to grant us the ability to do inverse design. This is obviously absurd: we have good measurements of stock market data, but that doesn't guarantee we can pick winners.

Even if standardized tests are a great definition of learning, one would still have to apply a forward design process, employing trial and error, to find best practices. In higher education, there are many obstacles to this, and because of demographic differences, comparisons across institutions are not automatically valid. It's a hard problem. For my part, I'm not satisfied that the empirical language is developed well enough to even dream of an inverse design. The creation of a good empirical language over time goes hand in hand with the solution to the forward design problem, which is itself a forward design problem...

Next: "The Long View"

Creating Word Clouds

I just came across Wordle for creating word clouds out of a text source. It's very neat, flexible, and free. As an example, I took a chapter for a book I wrote on authentic assessment and pasted it into the Wordle input. Here's the result.

This could be used with program plans or reports, curriculum maps, or other input sources to create attention-getters that also have some content--the larger words are the ones most frequent in the source.

You can change fonts, colors, formating, and even eliminate words (by clicking on them) to adjust the output.

I created another one on the blog for my novel that you can see here. For that I took an entire novella and pasted it into the input.