Running Local

This Train of Thought Makes All Stops

Archive for the ‘Mathematics’ Category

Where Are the Wizards?

Posted by Bob Kohm on March 17, 2009

It has been said that the line between magic and technology is located where the common person can look at a system and have no idea of not just how it functions, but why it functions. I cannot build an internal combustion engine (hell, I can barely change a spark plug), but I can look at one and figure out how it works, at least in broad strokes. Looking at a circuit board, however, isn’t going to provide and spark in my brain that will tell me how the computer I’m writing this on works, how my 46″ big screen is showing Handy Manny at this moment, or how I can talk to someone in Peru or Vietnam by dialing 13 digits into the phone the board may have come from. It is complex beyond my ability to ascertain, and I must simply rely upon it to work, to reply upon others to provide the networks upon which it draws, and to build be a new one when this one fails. Before it was retired in April of 2008, Air Force pilots had to rely upon their computers to make constant adjustments to the flight surfaces of their Stealth Fighters to keep the unaerodynamic Nighthawks in the air. Think about that– is there a higher presumed expert on the science and craft of flying than a trained US Air Force pilot? Even their skills and expertise could not keep an F-117 in the air; they had to rely upon a system with more expertise than they could ever hold. The trust inherent in relying upon these gadgets and systems of gadgets is awesome when you consider it, especially in those cases when even the “experts” are outside of their capacity in understanding and manipulating them, as in the Air Force example.

But is that trust warranted?

Much like my laptop and the Internet (series of tubes…?) themselves, our financial system is complex beyond simple understanding, even by the “experts”. The derivative nightmares that have crashed our economy were not the product of a bunch of execs sitting in a room trying to come up with a better way to make money but rather the end product of extraordinarily complex mathematical formulae that redefined risk in a way so out of keeping with realistic definitions of the concept as to have made these bundled junk loans look like an asset worthy of investment. Take those instruments and throw them into a milieu that sees incredibly complex markets interacting with complex personal decisions and trending, with overseas financial and security needs and philosophies, with complex logistical realities mandated by our “just in time” systems of inventory management amongst a host of other complexities and intangibles. Once you’ve done that, take a look at some of our experts on that overarching economic system– say Alan Greenspan, Paul Krugman, Larry Summers, Zhou Xiaochuan, and Daniel McFadden– and understand that they have wildly divergent opinions of not only how to fix the system but in fact on how the system works and exists at all.

This is a system so complex that, although we rely on it for fundamentals such as food delivery, power generation and medical care, nobody does completely– can completely– understand it. We are assured by many “experts” that they have a handle on this thing, that they can tame and manipulate it to our universal benefit, that they can shield us from its temper tantrums and benefit us from its soaring successes… they think.

The same is true of so many systems in the world in which we live– can the President be expected to understand and process the self-interests of the many nations on the planet when they are all just guessing at their own self-interests? And if we can not hold that expectation, then are we prepared to accept that judgements made on war and peace are made in a manner that must ultimately be accepted as uniformed?

We are at a point in our societal evolution where our artificial systems have merged with natural systems with ultimately unpredictable and uncontrollable outcomes becoming more the norm; it has long been a favored chestnut of science fiction writers, but the reality is truly emerging now into the public consciousness as a result of the financial crisis. What the implication of that will be for the future remains to be seen, but we cannot get to that point until we accept the concept that experts on these systems are not wizards and that while they can make educated guesses, they cannot speak with the authority that an expert on civil engineering can speak on bridge construction; to take anything they say as a firm prediction of probability may be a stretch; taking them as gospel is insanity.

It seems we have extended and expanded our reality right back to the point of trial and error. Welcome to the Nineteenth Century, circa 2009.

Posted in American History, Cultural Phenomena, Economy, education, Mathematics | 3 Comments »

A New Priesthood

Posted by Bob Kohm on January 26, 2009

The story of my academic life in middle & high school was my distaste inability to “show all work”. Arriving at a correct answer was never a problem for me, whether it was in algebra or trig, biology or the rudimentary computer science we studied back in the dark ages of the mid-Eighties. Showing all work though– there was nothing more frustrating than getting back a math exam with an 80 on it when every damned answer was correct but I had neglected to adequately translate my thought process in reaching that answer into a discernible, codifiable process. Actually there were a couple of young ladies who were considerably more frustrating, but that’s life as a teen-aged boy.

It’s that inability to show work, though, that intrigues me right now. I employed all of the standard dodges– what does it matter as long as I’m right, who will ever need this crap anyway (a mantra I recalled a couple of years back while trying to lay a triangular pattern of tile in my entryway), blah blah blah. The good Franciscan Brothers were, if you’ll pardon the phrase, hell bent on getting us to show all work.

They were, however, not quite so interested in process and practice in the humanities. Yes, there were papers to do in some of the Social Studies classes and essay questions on some of the Lit tests, but there were a surprising number of multiple choice, fill in the blank, true/false types of questions, too. For some reason the approach and execution of the thinker are less important in those topics, at least to the minds of some. The answer was adequate.

I’ve learned to appreciate, if not always execute, the description of systems over the intervening years. Its inherent value becomes apparent as one progresses through life, as the need to apply flexible process to rigid situations exerts and unveils itself. It is curious, then, that as we proceed further into an age in which we are told that mathematics and science are the raisons d’etre for education that very knowledge of process in falling by the wayside.

As computers run our algorithims and processors compute our runs, one can actually make the case that the display of work is an anachronism.  I play a game at a free site that requires deducing by eye the end results of a gravitational field– the math behind it is mind-boggling to me, but simple enough that whoever created the game gave away the result for free. Perhaps the time has come then when not only do we not need to show work, but we, the general populace, can not.

Why, then, is the Navy still teaching navigation by sextant at Annapolis? It’s an arcane and extraordinarily complex process involving taking sightings on the sun and stars. It is a technology surpassed what, five times over before we even reach GPS… yet it is still relevant. You must have the technical knowledge to navigate your ship if your systems are down, and, int he world of Academy graduates, the basic knowledge of taking a sighting and computing your position off of it underlies so many other integral processes that you need it to formulate the next generations of technology.

Those Middies with their deep knowledge are still a pace behind the diminution of process, however. There’s is a complex but approachingly ancient technology, whereas mathematical knowledge now proceeds into areas that support technologies beyond the understanding of most. Anyone can explain the construction of the internal combustion engine, even if you can’t build one yourself. Explain to me, however, how the computer you are reading this on is engineered and is working, or how the signals generated by the buttons I’m pressing are translating into the blog you’re reading somewhere else in the world right now. Yes, of course we all know the basics– integrated circuits, binary code, etc.– but the workings, the actual workings? Show all work with your answer.

It is very current to talk about societal divides– the digital divide, the economic divide, racial divides, education divides. I think they’re all about to be superseded.  We face a knowledge divide, a mathematical divide that can really only be described in the language of mathematics that itself forms the divide, thus becoming an intractable problem for the majority of the planet. While we all enjoy the fruits of mathematics– your Wii, your car, your bank account or the box you’re reading this on– we can’t describe its workings and have reached a point where it is both too complicated to do so for the majority of the planet… but also not necessary to do so either.

There are those in the world who can still show all work. Are they ascending to a different societal plane, a new priesthood that directly communes with the divine technology? The Maya priests were the leaders of their society because they understood the comings and goings of the sun and concocted a societal construct around that knowledge. Are we not doing the same with our technology?

Posted in American History, Autobiographical, Cultural Phenomena, education, History, Mathematics | Tagged: , , , , , | 5 Comments »

 
%d bloggers like this: