Michael Jackson dead at 50

There aren’t any pop artists I’ve grown attached to over the years. There have always been songs I’ve liked for a time, sometimes intensely, but then they fade. I really like revisiting them after 10 years or so. Certain songs bring back memories of my childhood or when I was a teen, or going through college. So it is with Michael Jackson. I heard about his passing yesterday, and I felt a bit sad, but not overwrought. He’s been a fixture in my life, a bit hard to avoid. When I was a teen his music was wildly popular and was on the radio all the time. His music and performance art were significant and innovative in pop culture. When he “exploded on the scene” in the early 1980s he really stood on his own. There was no one else like him. I was really struck by his music videos. They were innovative and captured my attention. Some would say later that he made the music video an art form worth paying attention to. There were music videos around before he really made it big, but they were amateurish.

Before all that I didn’t really know about him, but I’d heard him, as part of the Jackson 5. A couple of their songs were big favorites of mine when I was a kid in the 1970s, ABC (video), and I Want You Back (video). Michael was the child lead singer of the group. I liked this music because it was simple and catchy, and Michael’s voice sounded like a child’s, which I could relate to instantly.

I watched The Wiz when it came on TV. It was a reimagining of The Wizard of Oz in the mold of Motown. Michael Jackson was in it along with Diana Ross. Only thing was I barely noticed him under the costume and make-up.

As a young teen I remember I liked Shake Your Body Down (video) by The Jacksons (the Jackson brothers changed their name in 1975) off of their Destiny album, Don’t Stop ‘Til You Get Enough (video) from Michael’s solo album Off The Wall, and Human Nature (video) from Thriller. Around this time I started hearing about Michael Jackson a bit as a solo artist. He didn’t leave an indelible imprint on my imagination until he produced his Beat It (video), Billie Jean (video), and Thriller (video) music videos, all from his Thriller album. They had an epic quality. They were like small movies. Of these three the only one I really liked as a song was “Billie Jean”.

As with anyone who’s famous, Weird Al Yankovic had to make parodies of his music (imitation being the sincerest form of flattery): “Eat It” (Beat It), and “Fat” (Bad).

These are some other videos and songs that Michael Jackson (or “The Jacksons”) made that were favorites of mine:

Can You Feel It by The Jacksons from their Triumph album - This is going to sound crass, but President Obama could’ve used this song as an anthem for his campaign. Seriously.

From Michael’s album Bad: Another Part of Me, Man in the Mirror, and I Just Can’t Stop Loving You

Black or White from his album Dangerous – Out of all the music videos he made this is my favorite. It’s brimming with creativity. I loved the line, “I’m not going to spend my life being a color.” The end of it features a technology that was very new at the time, computer morphing. This video was produced in 1991.

You Rock My World from his album Invincible – This was the latest one I really liked. It just feels so easy to dance to. The video has some great creative elements in it. What’s funny is Chris Tucker keeps dropping names of older Michael Jackson songs, and phrases he’s used. I love watching Tucker dance in it. I don’t know for sure but this may have been the last time Marlon Brando appeared on film before he died.

I had never bought one of Jackson’s albums before, but I felt like getting this one when this song came out in 2001. I listened to the album at the store and was disappointed. This was the only good song on it. A lot of albums had that problem back then (maybe they still do?).

It really seemed like Jackson’s career was winding down when his last album was released. I didn’t expect anything new out of him. I thought he would change focus and do something else with his life, and perhaps he did. I heard yesterday, though, that he was planning a European tour, before the fateful day.

Artistic influences

Doing my research last night I learned that there have been many artists who’ve used samples of his music, or have done covers of his songs. I heard a few many years ago. A song called Love Will Be Right Here by Sisters With Voices used a sample of “Human Nature”. A rap called O.P.P. by Naughty by Nature used two samples from the Jackson 5: “ABC” and “I Want You Back”. A few artists I’ve seen who’ve done covers are Mariah Carey with I’ll Be There (video) (here’s the original song by the Jackson 5), Alien Ant Farm with Smooth Criminal (video) (an homage to all things Jackson. Here’s the original (video)), and a band simply named “V” with Can You Feel It (video).

I check out YouTube regularly as I sometimes find some real interesting stuff on it. I happened to find some videos made by someone who goes by the name of “Cat From Japan” that give you a real sense of where Michael Jackson got some of his artistic ideas, and they come from a rich heritage.

A dance move that Jackson became known for when his career was exploding in the early 80s was the “Moonwalk”.

I think I heard recently that it used to be called “the back slide”. He popularized it, but he certainly didn’t invent it. Here’s a video called “Origins of the Moonwalk”

Here’s a video CFJ did combining the music from Jackson’s “Smooth Criminal” with footage from two movies Fred Astaire starred in, The Band Wagon and Daddy Long Legs. Both Astaire movies were choreographed by Michael Kidd. If you compare this video to “Smooth Criminal” you’ll see the influence. You can even see it a little in “You Rock My World”. There came a point when I realized you could compare Jackson’s dancing with Astaire’s later work (towards the end of his career). This video makes the case pretty well.

Here’s another video CFJ produced showing the influence of West Side Story on Jackson’s videos “Beat It” and “Bad”.

Feel free to leave comments. If you’ve got some favorite songs/videos, go ahead and share them.

President Obama gets the “nerdcore” test

I watched a bit of the TV and Radio Correspondents’ dinner this past weekend and saw this routine by John Hodgman. I couldn’t pass it up. I really enjoyed it. We’re all I’m sure familiar with this comedian. He’s been on The Daily Show, The Colbert Report, and all of those Apple Mac ads (he’s the “PC”).

“We are wary, Mr. President…”

As I was watching the thought kept running through my head “Come on! Ask Obama a Monty Python question!” It didn’t happen. I really liked the Dune questions though, because Hodgman acted like he knew the details like the back of his hand. Perfect! Though he never gave the answers. I know them, but I’ll leave them for my readers to ponder.

Anyway, when he got to the end my mind raced immediately to one of the most famous sequences in sci-fi cinema, from Star Trek: The Wrath of Khan:

“Of all the souls I have encountered in my travels, his was the most…human!”

The beauty of mathematics denied

“So, so you think you can tell
Heaven from Hell,
blue skies from pain.
Can you tell a green field from a cold steel rail?
A smile from a veil?
Do you think you can tell?”
– from “Wish You Were Here” by Pink Floyd

I’ve taken some time to get back into the subject of mathematics, and secondarily math education. This is partly because I’ve had this niggling feeling that math is pertinent to my study of computing. I was always told that math was important to computer science, but in my work I didn’t feel it had relevance beyond algebra and discrete structures. The thing is, with the exception of a couple math classes I had in high school I didn’t find the presentation of math that interesting, nor did I feel like I was really grasping it. Nevertheless there was always some part of me that was interested in math generally for some reason.

Alan Kay helped steer me towards some interesting things about mathematics last year, and I’m grateful for that. This started when I watched a video of a presentation he did called “What is Squeak?” (video) and I became intrigued when he said that students aren’t learning what real mathematics is in most American schools. I went to good public schools, but I figured since he talked about most schools I probably wasn’t taught this either. I asked him about this last year, and I realized quickly that no, I wasn’t taught what real mathematics was.

He believes that students should be taught to think of mathematics as mathematicians do, even if they don’t go into it professionally. He’s seen examples of how this can be done. The reason is that math is not about the numbers, arithmetic, symbols, and algebra that we learned in school. It’s a way of thinking. It’s just a matter of translating this mode of thought into forms that children can understand and work with. There’s a good introductory video he did for math education with children called “Doing With Images Makes Symbols” (video). At first I thought it was going to be about ideas for the GUI, but it’s not. It’s really about pointing out a flaw in traditional pedagogy, that teachers try to teach math the way adults understand it, using logic and symbols, and this is part of what makes math hard for children to understand. The other part, which he doesn’t discuss in the video, is that most math teachers don’t teach the fundamental ideas of math, nor how to think in mathematics the way mathematicians do. Instead they teach aspects of mathematical thinking through what we call “math classes”.

For the rest of this post I’ll be talking about a book called The Art of Mathematics, written by Jerry King, who is a professor of mathematics at Lehigh University. This isn’t a book report. He talks about a bunch of things in greater detail than I’ll cover here. So please do read it. I’ll just be talking about what really grabbed me.

It’s a very interesting book. In it King lays bare what is rarely acknowledged, that typically schools and universities do not teach the full depth, the beauty of mathematics. In a typical scenario a student is not exposed to real mathematics until their junior or senior year in college, if they take math courses for that long. Up until then they are fed a steady diet of procedures and techniques for solving math problems, but they don’t get to the essence of what mathematics is. The end result has been generations of students who for the most part fall into two categories (à la C. P. Snow).

There are those who became skilled in some aspects of mathematics for its utility in science and engineering, but have missed its beauty. Then there are those he calls “humanists” who have felt like math isn’t for them. They’ve felt forced to do it in school. They left it by the side of the road as soon as they had the chance, hoping to never deal with it again. They are educated but they are so distant from what mathematics is they don’t recognize it, much less its beauty. We see them out in society all the time. They say, “I’m not good at math,” and they say it with no stigma at all. Most of the rest of society would say, “Yeah, me neither. What was the point?”

None of us would say, “I can’t read” without feeling a profound sense of shame and deprivation, which goes to show that mathematics is not seen as essential in order for people to function in our society. But is that view correct? I think there’s reason to believe it’s not. There are some common everyday reasons I can imagine where having “a taste for mathematics”, as Alan Kay calls it, would be advantageous to all sorts of people in ordinary life (again, I’m not talking about algebra, but mathematical thinking). But more importantly, Kay has also said that in order for our civilization to realize the potential of the computer as a new medium it is essential that we understand (real) mathematics and science. He’s also said for years that “computers form a new kind of math”, a kind that doesn’t fit into the confines of classical math categories.

Jerry King wishes that mathematics would be upgraded to the status of a subject that students should be literate in to be considered educated. He explains why mathematics education at universities has not been good for decades, and touches on some essential ideas that every mathematician knows, which the typical math student is not shown.

Mathematics at its essence is a way of thinking about relationships of abstractions. It’s also a creative/discovery process, something that most math pedagogies don’t teach.

From this one can see right away that math is valuable to science, since deeply embedded in it is the study of the relationships between things. It also has value in computer programming, since in order to get our programs to work we have to understand the concept of abstraction, and understand something about the relationships between things in our code, and entities that are created in a running program.

Bertrand Russell said that mathematics is “p implies q“, and as King explains in his book this point of view allows us to take assumptions and reason about their implications. For example, “If p is true then q is also true”.

Beyond the reasoning skills it engenders, King says there’s also beauty in it which you can experience once you get to the real essence of mathematics. For mathematicians this is the reason they do it. I would say the same is true of computing. It’s the reason I got into it, and still pursue it, though as a field I would not be so bold as to say we know yet what its true essence is.

What King’s book reveals is that mathematicians do not merely have a more advanced knowledge of math in terms of how most of us understand it. They have a very different perspective on it than we do. Mathematicians believe that this perspective is impossible to teach. You either “get it” innately, or you don’t, no matter how you’ve been taught. King is the exception. He contends that everyone has the potential to understand this perspective, and that it would do us good to do so. If only mathematicians could find it in themselves to have a passion for teaching what they really know.

What follows are summaries from my notes, and quotes from his book. I’ll try to make it clear when I’m talking about my own thoughts.

Aesthetics

In my estimation the most important chapter in his book is called “Aesthetics”. King says that mathematicians do mathematics for aesthetic reasons, but the aesthetics of mathematics are not defined anywhere, either in the field or outside it. For mathematicians it’s a personal experience.

The crux of his book is explaining why most people are never exposed to the beauty of mathematics, and it’s a tough problem to solve:

Deeply embedded in our culture lies the notion that mathematics can be truly comprehended only by a gifted minority. Because so few members of the otherwise educated public possess even the rudiments of mathematical knowledge, mathematics has been assigned a special status. Unique among the collection of disciplines–such as philosophy, history, and literature–which in times past formed the basis of both the concepts of liberal education and the core curriculum, mathematics may be set aside under ordinary conditions without social or intellectual consequence.

…

Behind all this stands the concept–widely held and deeply believed–that there exists in a certain few members of the human race a type of “mathematical mind” which allows them to understand the logical complexities of mathematics. It is believed that just as there are only a few people capable of running 100 meters in less than ten seconds there are only an analogous few capable of understanding mathematics. And just as the inability to sprint at world-class level carries with it no social stigma, neither does the inability to understand mathematics.

Mathematical talent comes to you exactly as does sprinting talent: God either gives it to you or he does not. Or so it is believed.

Such beliefs provide comfort. Through them, members of the public can justify their often awesome mathematical ignorance. And because of them, mathematicians can rationalize their failure to teach–in a way such that the knowledge sticks–even the basics of the glorious discipline which occupies every moment of their conscious thought and almost every ounce of their energy. You cannot be expected to understand mathematics–so goes the myth–unless nature has provided to you the kind of mind necessary for the subject’s comprehension. Nor can you be expected to teach mathematics to people who lack the basic mental equipment for it, just as Minnesota Fats lacks the physical equipment to run the Olympic Trials.

Comforting they may be, but these beliefs have no more validity than astrology.

He speculates that a sense of aesthetics may really make mathematicians who they are, as opposed to the developed senses of logic, precision, the ability to manipulate symbols, or the ability to deal with layers of abstraction. Jules-Henri Poincaré, a French mathematician, believed…

that an “aesthetic sensibility” for mathematics defined the very soul of the mathematician. It acted as a “delicate sieve” without which no one in mathematics can become a “real creator”.

…

Poincaré is right as rain about beauty and every mathematician knows he is right. You have inside you an aesthetic sensibility toward mathematics which acts on your intuitive mind as a delicate sieve sorting out the elegant and harmonious ideas from those which are merely useless combinations of other ideas. You have it, that is, or you are not a mathematician.

Poincaré, however, did not extend the notion of the aesthetics of mathematics to teaching. He did not believe that students could understand the beauty of mathematics through the educational process, but King is hopeful.

Perhaps Poincaré was wrong. Maybe the notion extends. Perhaps you can bring students to mathematics early on by emphasizing its aesthetic value rather than its utility or its applicability. … I don’t know. But one thing is certain. We will do no harm by trying. For what we do now has failed. Mathematics as understood by mathematicians remains unknown to everyone else. … To the humanist–and to everyone else in the other culture–the subject is something to be shunned.

I refuse to believe that this is the nature of things, that mathematics must remain forever beyond all but a tiny minority of our citizens. The notion that there exists a large subset of the populace who are capable of appreciating and understanding music, art, and literature but are somehow innate mathematical cripples seems to be simultaneously arrogant, apologetic, and just plain wrong. … We can do ourselves no harm … by presenting to our students early on those characteristics of mathematics which, in Poincaré’s words, contain “this character of beauty and elegance, and which are capable of developing in us a sort of aesthetic emotion.”

…

Instead of aesthetics, the schools give us drill and tedium–and immediately forgettable techniques aimed at unwanted and unwelcome applications.

The other side of this problem is we need to understand…

why people are driven to do important and difficult things for the sake of beauty. We need to understand what Mr. Keats had in mind when he wrote:

“Beauty is truth, and truth beauty–that is all
Ye know on Earth, and all ye need to know.”

In the book King notes an interesting correlation between the beauty of mathematics and scientific and engineering ideas, derived from mathematics, that have been recognized as being very useful. He suggests that perhaps in the case of mathematics beauty brings more than just pleasure, but also advancements in our ability to make new discoveries and build things that work. That would be pretty cool if it was true. King also says that mathematics IS a kind of art.

He says that unfortunately there has been no formal study of aesthetics (he suggested philosophy is the appropriate venue for this) which might help the academic community better understand what mathematics is, because philosophers don’t consider art and aesthetics as serious subjects, since they provide amusement and enjoyment. To them serious subjects like truth, justice, and reality are the things worth spending time on.

[S]erious people–most of them–do not deal professionally with matters of amusement and enjoyment. But they ought. Because there is more at stake than understanding what kind of art appeals to whom and why it does. … We need to understand why people are driven to do important and difficult things for the sake of beauty and for its own sake alone.”

My own sense of the reason King says this is it would help educators understand how to teach mathematics so that people understand it, and convey why it’s important.

Quoting Seymour Papert, King says:

[W]hen mathematics is taught in the schools, students are asked to “forget the natural experience of mathematics in order to learn a new set of rules.” Moreover, as we all know, the existing “rule learning process” does not work, has not worked, and–in my view–cannot work.

What is needed is a real understanding of the mathematician’s “personal experience” with his subject. At the highest levels, there can be no doubt that this experience is largely aesthetic. What we must learn first are the characteristics of mathematical aesthetics so that we can talk about mathematical elegance in more than a descriptive manner.

He says this will require rethinking classical aesthetics to include theories (to be developed) that apply to mathematics. It will require bringing teachers into math classrooms in primary and secondary schools who have been touched deeply by their own personal sense of mathematical beauty, so they can communicate that to their students. The problem here is:

We are not … headed that way. The future seems to hold, for mathematics instruction, an increased dependence on technology in the form of computers, hand-held calculators, and video presentation. Surely, I cannot be the only person to notice the clear correlation between the declining mathematical abilities of American students and the aggressive introduction of these technologies into the mathematics classroom. The decline began as the technology came in.

At the university level it will require bringing research mathematicians back to teaching. The problem here, he says, is that mathematicians think their only job in life that’s worth doing is mathematics. If a mathematician talks about mathematics (rather than doing it) they are considered “on their way out”, a former mathematician. In the profession it’s seen as beneath one’s stature, even shameful, to talk about it in descriptive terms. Thankfully there are a few like King who don’t care about that.

Technology and math education

Alan Bradley: Some programs will be thinking soon.
Dr. Walter Gibbs: Won’t that be grand? All the computers and the programs will start thinking and the people will stop.

— Tron (1982)

I want to take a detour here to address King’s point about technology entering the math curriculum in primary and secondary schools. His aversion to technology in the educational setting is understandable, but I think he’s narrowing the focus of his blame too much. In much the same way that college mathematics is taught as a set of rules and techniques, so it is in primary and secondary school. The quality of instruction would be improved somewhat if the technology were taken away, but not a great deal.

I had a wonderful conversation with an engineering professor from Duke University in March. One of the topics we discussed was how math is taught in secondary schools, from her own experience either observing it, or hearing second-hand accounts. It gave me a sinking feeling in my stomach. She said that students are required to buy a specific TI calculator model, and teachers use it as an integral part of their “math” instruction. She used the example of inverting a matrix. Rather than teaching what one is really doing when one inverts a matrix, students are taught to enter the matrix into the calculator and to hit the “invert” button. That’s it. They are not taught where the principle comes from, why they would want to do this, or what it represents. It’s a continuation of the procedural mindset that King criticizes. From this perspective I can see its folly now.

I said to the professor, “That’s not teaching math. That’s teaching how to use the calculator.” Yet the educational system has deluded itself into thinking they are teaching mathematics by doing this. Obviously one needs to know about arithmetic operations, but that’s not all we need to know.

Later I remembered that some academics used to say, “Someday we won’t have to teach math. We will have calculators and computers that will do the math for us.” First of all, as I’m increasingly becoming aware, this displays a fundamental misunderstanding of what math is, and its importance. It’s also widespread. What it reveals is the mistaken notion that mathematics has nothing to contribute to human reasoning, and is only useful for science and engineering where math is used to express ideas and figure things out. And why would it be useful to the general population to understand mathematics? It’s just symbol manipulation and calculation after all, isn’t it? Something that machines are fully capable of doing by themselves.

We can see how the educational establishment, and the “humanists” as King calls them, view mathematics. I’m not saying that calculation and symbol manipulation are unnecessary skills, but let’s be clear (for once!). Calculation is a product of arithmetic, not mathematics. Arithmetic is an outgrowth of mathematics, but they are not the same thing. Symbol manipulation is a part of mathematics, but it’s only a skill within it. It’s like knowing how to write in that realm. Having it does not mean that one understands mathematics.

I disagree with King that technology is at fault for the decline in math education. What he and the professor from Duke are seeing is an extension of the way math has been taught in our school system and in our universities all along! Now, I’ve heard the claims that the current standard in public education in the U.S. (No Child Left Behind) requires teachers to “teach to the test”, and other things. That’s not my point. Procedural thinking in math education has been around for decades.

The perceived role of technology also has something to do with this. If teachers and those who create curriculum believe that progress means machines do more of the thinking for us, then this is what you get.

There’s nothing wrong with a computer or calculator making some tasks easier. It can enhance our work. What we should not do is use it as a crutch, making it automate as much as possible so we no longer have to think, because then we’re really robbing ourselves. Technology should be brought in consciously with an eye towards where it helps us think.

Theory

King gets into some foundational concepts, theory and forms, which he uses later to illustrate what mathematical aesthetics is like.

He says a theory is a framework or set of rules which prescribes the collection of allowable sentences one can make about whatever objects are under consideration.

A theory, therefore, gives you a framework for talking about the objects of the theory. More precisely, it gives you rules of inference from which you can prove theorems about the objects. Truth about the objects consists of sentences about them which are either assumed in the theory or else are provable within the framework of the theory.

Just an aside, but this almost sounds like a description of a programming language on a computer, minus the stuff about theorems and proofs. Could programming languages represent theories of computation? Hmm…something to consider. Anyway…

Extending this idea of mathematical theory a bit King says:

Plato, you will recall, asserted that what one has knowledge of are abstractions, which he called Forms. Roughly, what Plato did was replace real-world objects by their Forms in his epistemology. Each real-world object–say an apple–is a temporal thing which undergoes constant change. The Form of the apple, however, lives in an ideal realm and is eternal and unchanging. It is the Form of the apple and not the apple, said Plato, about which we can have knowledge. Moreover, because Plato’s truth could be known only about Forms and not about real-world objects the Forms were to him more real than the actual objects. … Plato argued, in fact, that Forms represented the only true reality since it was only Forms about which one could have knowledge.

An example of real mathematics

King takes a stab at defining aesthetics in mathematics, in formal terms. I’m not going to cover that here. Read the book. From my own sense of the aesthetics of mathematics I think he defined it well.

He presents a couple of proofs to demonstrate the aesthetics. I’m going to use one of them as a way to discuss what real mathematics is like. It also demonstrates a foundational principle of mathematics: p implies q (also expressed as p=>q, using “=>” as a double-lined arrow). The symbol p represents a hypothesis, and q represents a conclusion.

He puts forward the problem: Without leaving the room let’s set out to prove that there are at least two trees in the world with the same number of leaves.

To make a proof we start with a hypothesis. “The hypothesis is what we assume, the conclusion is what we deduce.” The hypothesis needs to be minimal. This is part of the aesthetics.

Whatever we mean by “trees” and “leaves” it seems obvious that there are more trees in the world than there are leaves on any single tree (probably many more). … So, for our hypothesis, we will assume that the number of trees exceeds the number of leaves on any single tree by some positive number. It is sufficient to assume that the excess is only 1.

If this were written as a typical math problem I had in school it would have been rendered as: “Given t trees in the world and a maximum of m leaves on any one tree, prove that there are at least two trees with the same number of leaves,” and I would’ve felt stuck, because my math training taught that we should only draw knowledge from prior math material (formulas and proofs), and whatever the problem statement gave us.

What I find interesting is that King approaches the problem differently than I would have, and probably most other math students. He uses the ideas about forms and theory to get an idea about how to approach the problem, and he thinks about the relationships of “trees” to “leaves”. What I find interesting and pleasant about the mathematician’s approach is that our imagination, intuition, common sense, and experience can play a part in solving math problems.

We can imagine forms of different trees. We’ve seen hundreds of them in our life. So we have a fair idea of their structure and what they look like. The theory is that there are t trees in the world and a maximum of m leaves on any tree. Using the forms of “trees” and “leaves”, and this theory, we can explore its ideas.

He starts with an idea that fits easily into our notions of the relationships. When I looked at King’s hypothesis I thought, “Of course. I can imagine that,” but I wouldn’t have come up with it, because I wasn’t taught to think of math in these terms.

If I had understood the notions of theory and forms, and their use in mathematics, I might’ve come up with the same assumption right away. Or I could’ve experimented with other ones, and through a process of discarding the theories that didn’t serve the objective of the proof maybe I would’ve eventually hit upon the one King used. I remember Alan Kay saying that children who are learning to think like mathematicians go through a kind of scientific process, trying out ideas and seeing which ones succeed and which ones don’t. Research mathematicians go through the same process.

I believe it was King who also said something I have heard from those in the math reform movement for years, that it’s the process that matters, not the result, and I think I’m beginning to understand this. Math education has been results-oriented for as long as I can remember, creating a system where the only acceptable goal is to get from Point A to Point B as efficiently as possible. What King indicates is that this mindset is part of the problem.

I think, however, there’s been a misunderstanding of “it’s the process that matters” when the math reform agenda has been implemented. Logic matters in mathematics. This implies that there needs to be room for criticism and correction of logical flaws, something that reform-minded teachers have discarded in the name of protecting self-esteem. This is not a small omission. I think the idea needs to be that how you get to something that’s logically consistent need not be a straight A-to-B process. “The right answer” is the end result of creating something that’s logically consistent. It’s an afterthought. The goal is to reason about the ideas under consideration, and to wonder about the implications of those ideas (not necessarily in that order).

It’s become apparent to me that in addition there are circumstances in the realm of mathematics where a precise answer is not desirable, because it gets in the way of exploring and thinking about ideas and how those explored ideas fit into a logical structure.

This brings to mind a story I heard years ago about a female executive interviewing for a position at Microsoft with Bill Gates. It’s been a while, so I may not have this word for word, but it basically went like this. Gates asked her point blank during the interview, “How many gas stations are there in the United States?” The woman responded, “I don’t know.” He pressed her further about why she didn’t know, and she said, “I would need to collect data to find an answer to that question.” Gates got frustrated and asked her, “Are you stupid?”

I heard commentary about this incident from others who had been associated with Microsoft, and what they said was Gates wasn’t expecting her to recall a fact, an exact figure on the number of gas stations. He was looking for a reasonable estimate, and he would’ve looked for a justification of it–a proof, perhaps–without her leaving the room. What was said about this and other “Microsoft questions” is “they really want to see how you think.” My guess is in this instance he was testing the candidate’s understanding of mathematics. I’m also guessing that she had a math education that was similar to mine. I would’ve given the same response.

I talked to Sanjoy Mahajan, a theoretical physicist at MIT who was a panelist at this year’s Conference on World Affairs at the University of Colorado at Boulder. We were talking about math education and he spoke about the ability to estimate, and that this is an important skill in mathematics. He used an example that a math teacher used with students (I can’t remember the name). He said the teacher would ask, “How many trees could fit in this room?” without bringing a single physical tree into it. He wanted the students to visualize, based on the trees they’d seen, about how many would fit, and they’d discuss it.

The setup for the proof on “two trees with the same number of leaves” is similar. In terms of mathematics we don’t have to go out and look at every tree and count their leaves and come up with a maximum. We just make a reasonable estimate, based on our experience with how many trees are, say, in a single forest, and how many leaves we’ve seen on a single tree, and our knowledge that there are many forests in the world. We estimate that there are more trees than leaves on a tree. It seems to work, and that’s our assumption.

Here’s the theorem statement from the book: Let t denote the number of trees in the world and let m denote the maximum number of leaves on any single tree. If t exceeds m + 1, then there exist at least two trees with the same number of leaves.

Just to make the mapping to “p implies q” more obvious I’ll break it down: p = “t exceeds m + 1″, implies = “then”, q = “there exist at least two trees with the same number of leaves”.

Here’s the proof from the book: Since m denotes the maximum number of leaves on any one tree, each tree will possess either 0, 1, 2, 3, … or m leaves. Imagine m + 1 boxes sitting in a row on your floor, each tagged, in order, with the numbers 0, 1, 2, …, m. Now imagine bringing the world’s trees one by one into your room (suspend disbelief). Place each tree in the box which bears the label equal to that tree’s number of leaves (thus, a bare tree goes into box number 0, a tree with one leaf goes into box number 1, etc.).

We have only m + 1 boxes and, by our hypothesis, we have more than this number of trees. Hence, some box must contain at least two trees when trees have been brought into the room. Thus, at least two trees must have the same number of leaves.

Q.E.D.

The reason we were able to prove this was because of our knowledge of combinatorial math, but it’s so simple it even works intuitively.

Aesthetic distance

He introduced this topic of “aesthetic distance” from a philosopher’s perspective on how audiences appreciate art. He then put mathematics in the situation of being the object of appreciation. He said there are people who are too close to mathematics, and those who are too far away. The ones who are too close are scientists and engineers. They have quite a bit of knowledge around mathematics, but “their nose is pressed up against it”. They work with it all the time, but they don’t have sufficient distance from it to understand it and appreciate its beauty. They understand the rules and formulas they were taught, but they don’t really understand what mathematics is. Most others are so far away from mathematics that they have no comprehension of it at all and therefor cannot appreciate its beauty either.

In “the middle” between these two groups are the mathematicians, who are at a sufficient distance to understand what they are looking at, and to appreciate its beauty, and they are a small group compared to the others. With the way things are set up, only mathematicians can experience its beauty, and they aren’t doing anything to change the situation. They’ve locked themselves into their own “room”, so to speak, and they aren’t letting anyone else in.

King discusses at length the reasons why this has happened. To sum it up, it wasn’t always like this. There was a time when mathematics departments actually taught what they knew about math, rather than just procedures and techniques. King says that after 1957, our “Sputnik moment”, math departments at universities were seen as essential and no longer had to compete for money and students. They were even encouraged to engage in more research, for Cold War purposes, rather than teach. This fit in well with what mathematicians really wanted to do anyway–research. Math education, however, deteriorated. The change made mathematicians feel privileged, even superior. The privilege that mathematicians enjoy is in essence the cause of the problem with math education at universities to this day.

Conclusion

This book was an eye opener for me, mainly because it revealed that what I thought was math was not real mathematics, but rather aspects of math (deduction, reduction, symbol manipulation) and techniques derived from math (arithmetic, procedural tricks for solving problems, pattern matching). My sense is my math education in public school was better in terms of quality than what I got in college, but that isn’t necessarily saying much. College math was like how King described it: mostly techniques taught by rote, conveying no understanding. At least in the public schools I attended I got some sense of the aesthetics of mathematics.

I expected to get a sense of “the art of mathematics” from this book. Instead it talks about the subjects I discuss above, and more. I didn’t get a sense of the beauty of mathematics, but then King did say the purpose of the book was to talk about the subject, not delve into it. Nevertheless it is a good introduction for the uninitiated. He came out with a new book just a few months ago called Mathematics in 10 Lessons: The Grand Tour. I have it on my reading list. My sense of it is he gets into the actual subject of mathematics in that book.

—Mark Miller, http://tekkie.wordpress.com

Post updates

I’ve updated a few old posts:

• Added some touch-ups to “Reminiscing, Part 1″ and “My Journey, Part 1″.
• Added a video of a model Space Shuttle (w/ tank) rocket to “Steve Eves Lives The Dream”. Very cool!
• Added some informational material to “Our economic future”.

Boulder High students protest teacher layoff

video courtesy of The Daily Camera newspaper, Boulder, CO.

Boulder High School (or perhaps it’s the Boulder Valley School District) has laid off a social studies teacher, Chris Barnes, because of budget cuts. Such are the inevitable and in this case cruel losses of a severe recession. Apparently he’s not just any teacher. This is a video of his students protesting his layoff. They really like the guy. It’s not everyday that you see this. Even if he were to stay they probably wouldn’t have another class with him. So the fact that these students would take time out to do this means a lot.

I had a similar experience many years ago. I attended Casey Jr. High School (now Casey Middle School) in Boulder in the early 1980s. I had a government (civics) teacher who was great. He taught us the traditional stuff (out of the textbook) about how our government works, but he also had us carry out exercises of a couple different major governmental functions as a group, so we could enter those worlds ourselves and see how it really works, not just the ideal of how it should work. He got kids who most teachers would’ve given up on as trouble makers to participate in these exercises, and they became genuinely interested and engaged. I saw a side of these kids I didn’t know existed, and he proved the point that every child is interested in learning. Those were valuable experiences.

He taught us discernment skills in political rhetoric. We watched and read current, real political material and we evaluated what they said–how much was content, and how much was just air. Were they just giving us one side of the issue? What’s the other side? Do they make a good argument?

He encouraged us to watch C-SPAN, to see government in action, and to see political figures unfiltered; and a couple specific news programs, which covered news at length, not in little bites.

He decided to leave Casey after our course, of his own accord. He had taken up another job in the private sector. Somehow the rumor got around that he had been forced out because the assistant principal didn’t like him, or something. Soon after some of the students in his class, plus some kids who just didn’t like the assistant principal, went outside with signs and protested the assistant principal and the fact that our civics teacher was leaving. Some were passionate. Some were disciplined by the school for disruptive behavior. I never thought I’d see the day when students would protest in favor of a school teacher! It kind of brings to mind a movie I saw years ago called “Dead Poets Society” (video).

I still remember that teacher’s government class to this day (though as you can tell I can’t remember his name). I see him as someone who made me a fully engaged citizen of the United States. Seeing the video from Boulder High brought back memories, and it’s good to see that there are still public school teachers out there who are good enough that students are willing to protest for them.

Inexcusable: BVSD teachers walk out just before finals

I don’t have a dog in this fight, since I graduated high school more than 20 years ago, and I don’t have kids in school. I am a citizen who’s concerned about educational issues though. So I thought I’d weigh in.

I saw this story yesterday that 80 BVSD teachers in Broomfield, CO. had called in and said they were not showing up for work for the day. Students were planning on attending review sessions with their teachers for finals next week. Oh well. The school district hurriedly found substitute teachers to replace the ones who didn’t show up (apparently there was no advance notice of this event). Kids either sat in class with no activities, or “watched movies” as a few put it.

What was behind the walkout was a contractual dispute with the school district. From what I can surmise from the comments that followed the article (follow the above link), contract negotiations were in progress. The understanding of the teachers was that the district was going to be fully funded with no cuts, but the district kept coming back with lower offers for the teachers (in terms of raises), and possibly beefy offers for administrators (I’m not clear on that part). The fact that administrators were making more than the teachers wasn’t surprising to me. I knew this was the case 16 years ago. As far as I’m concerned this is the way it’s been and the way it always will be in public schools. Some commenters said that in a few cases teachers make more than administrators (if the teacher has upped their pay with higher credentials, and the principal is new, for example).

Anyway the teachers reacted, and in my opinion the students suffered for it. Finals are an important and stressful time for students as things are. For teachers to do this at this time just adds to the stress, not to mention some confusion. They don’t need this right now.

From the way teachers were describing the situation, they’ve been feeling financially stressed, and to boot they were feeling shafted. Well in my estimation they shafted their students and caused them stress yesterday. How about we leave the students out of the dispute, okay? They don’t deserve this. It’s apparent to me these teachers were not thinking about how their actions would affect students. There’s a time and a place for this sort of thing, and now is not it.

Edit 5/20/09: More “sick outs” have been happening this week, now in Boulder, to protest contract negotiations. Here’s an editorial in the Denver Post about it which echoes my sentiments.

Steve Eves lives the dream

Steve Eves launched a 1/10th scale model of the Saturn V rocket on April 25 in a field in Maryland. It was 36 feet tall and weighed 1,600 lbs. It flew to an altitude of about 4,000 ft. and returned safely. Here’s video I found that shows a bit of Steve’s story, and the launch.

This was awsome to see, even just on video! Steve succeeded in setting the world record. This flight will be recorded in the Guinness Book.

Seeing this reminded me of when I once launched a 6 ft. tall Estes rocket called “Mean Machine” with some friends more than 20 years ago, out in a field that’s a block away from where I live now. I remember it used a D-size solid rocket engine and when it launched it was loud, sounding like a jet engine. It flew up so high we could barely see it. It looked like a small dot in the huge sky. I had launched many smaller, less powerful model rockets before this. They flew up between 50 and 200 ft. I had never seen one go up this high (the instructions from Estes always said “check for low flying aircraft before launch”, and of course power lines)! For a bit I wondered if I’d ever see it again, or if a wind current had caught it and blown it away. It came back down…without its parachute about 20 yards away from where it was launched. The 24″ parachute with a light plastic nose cone attached seemed to take forever to come down. It landed right near where I live now. The “launch lug”, I believe it was called, The shock cord mount, which attached the parachute to the fuselage, had separated from the rocket body. I had built the rocket 2 or 3 years before I launched it. The glue that held it on had gotten old and brittle. My interest in model rockets was waning. It had been overtaken by my interest in computers. It was the last rocket I launched.

Back when I was really into model rockets (elementary and jr. high school) I imagined building and launching ones like the one Steve built; how neat that would be. It’s really gratifying to see someone do it.

Edit 5/28/09: I found this video today of a Space Shuttle model rocket and I could not pass up including it here. The boosters detach in mid-flight, and at apogee the Shuttle detaches and ignites it’s own engine for a few seconds. The Shuttle looks like it’s radio controlled from its flight pattern, and it comes in for a smooth landing! WOW! I imagine this is homemade. I doubt it came as a kit. I have no idea who made it though. The description on the video at YouTube didn’t say.

Getting an education in America

I like keeping myself informed about what’s going on with education. I’ve been increasingly alarmed about what is happening at our universities. It began first with a sense of alarm several years ago when I read that at universities like Princeton and Harvard, going back to the 1980s, the arts and humanities had been taken over by post-modern thought, and rather than studying the classics and history, they critiqued them, turning out people who were not taught to care what the masters of the arts, literature, and history thought, but to instead criticize them from their own uninformed vantage point. I’ve since heard that Princeton has made a positive change, bringing back classical liberal arts.

I started hearing accounts of CS graduates who can (not) (program). Around the same time I was hearing complaints from universities about the inadequate high school education their incoming freshmen were getting, and how they required a lot of remediation. I saw M. J. McDermott’s presentation about “reformed math”, and I heard about a new Applied Computing major the undergrad CS department at my alma mater was starting up, and it was more popular than the traditional CS major. I definitely got a sense that gradually over time there’s been an almost imperceptible movement towards watering down, some would call it “dumbing down”, university education, with some bright spots that run counter to the trend.

What’s gradually dawned on me in the last few months is that our universities at the undergrad level are slowly being turned into vocational schools. I’ve pondered the question, “Why is this happening?” and I’ve done a little research here and there. It turns out this has been going on for a long time, since at least the early part of the 20th century. Captains of industry back then believed that a university education was useless because graduates didn’t have any skills that could be put to work in industry immediately. In my grandparents’ generation college was seen as the ticket to a high paying professional career. My experience is in my parents’ generation it was seen as a path to a good paying career, but not stratospheric. This POV has not been lost on universities that want to recruit students. So there’s been pressure to tailor curricula towards teaching vocational skills that can be of use right away in industry and specific professions.

Last summer I read an account from an anonymous English/Literature professor at a “no name” college, who taught night classes to non-traditional aged students, called In the Basement of the Ivory Tower. It provides much needed commentary about a movement that started in the 1990s towards “universal access” to higher education. The professor said he flunks most of his students. Why? Most of his students do not have the requisite skills for his class. No matter. The university keeps recruiting the unqualified in the name of “universal access”. Most of his students come to his university to enhance their career prospects. They need the college credit, or a degree, to meet the qualifications for a better paying job, but they’re unqualified to be there in the first place. He said some of his students would be better off going back to high school. What’s heartening is the author refuses to water down his curriculum, and has received no pressure to do so by the administration. He is fortunate in that respect. I’ve heard from another professor that’s felt some pressure to water down what he teaches.

The anonymous author of the article couldn’t help the feeling that it’s all pointless, though. He said he would’ve loved to have taught students who could learn the material, but most of the ones he gets can’t.

College is the new high school

There’s another force at work. Foreign students who graduate from their high schools are farther along in their education than our high school students. A couple years ago I heard a few first-hand accounts from foreign students who have gone to our universities for their undergraduate education, and they said a lot of what they learned in college was REVIEW for them! This brought home a little story Alan Kay told in a video that was made out of an interview with him called Education in the Digital Age, made in 1998. In it he said he attended a dinner party in the UK and a woman came up to him and said, “You Americans have the best high school education in the world.” Kay was taken aback. She chided, “Too bad you have to go to college to get it.” Ah,…British humor, but it’s the truth. A high school education used to be enough to get a job that paid enough to support a family in this country. Today this is no longer the case by and large. Has anyone asked why that is? Why is it seen as necessary that in order to compete in a globalized world we must send more students to college just to maintain parity? It isn’t that more foreigners are college educated than we are. It’s that our undergraduate education in many cases is like their high school. And it would appear that we are slowly but surely turning undergraduate education into a high school educational experience, minus the standardized tests for measuring aptitude. The big difference is with college, parents and students have to pay tuition.

John Stossel produced an eye-opening 20/20 segment called College: Worth the Price of Admission?. In it he indicts many of our universities for suckering unwitting parents and students into a system that will ultimately make them financially worse off than if the students had just gone to work right out of high school. He says for these students vocational training is often enough for them to get jobs that pay well enough to have a decent standard of living. This can be done at the community college level, or at centers where students can apprentice.

Why are universities doing this? Maybe it’s greed, or perhaps a misguided commitment to universal access. It used to be that universities were picky about which students they admitted. With many this is apparently no longer the case. According to the show universities are recruiting from the bottom 40% of the high school class in addition to the students who would normally qualify. Why? They figure most of them will not graduate college, but they’ll spend a year or two trying. During that time they pay tuition which goes into the university’s coffers. Some people excuse this saying that even some college is beneficial to students as they pursue their careers. What gets swept under the rug is that many parents and students don’t understand that a college education is just that. It’s a more rigorous education, one that hopefully expands one’s horizons and perception. It doesn’t necessarily get you a higher paying job. That’s the truth. There are always some who get that four-year degree, who end up not being able to find work that pays enough to live on and pay the crippling student loan debt they’ve accrued, because they majored in “basket weaving” (I’m using this as a generic metaphor. If you majored in basket weaving and are well off, I apologize). The show profiled some college grads who are making the same wages as high school graduates.

According to Stossel what many universities are selling is an illusion, that a “university education”, no matter what students study, will help them earn “a million dollars more on average” in their careers than if they just tried to get work with a high school diploma. What Stossel’s segment points out is that if you look at the stats in a broad sense this is true, but there are some high-powered individuals that skew the average. It’s reasoned that these people would be earning more than the average person even if they never went to college. What makes the difference is ambition and drive, not a college education.

When I went to college to get my BSCS in the late 1980s there was some of this mentality around, that a college education was going to lead to a good paying career. I remember some students training to be engineers talking smack about history, philosophy, English majors, etc., saying the only thing they’re going to be able to do with their degrees is become college professors teaching other students who will go on to get “real jobs”. I remember seeing a large poster being sold at the student bookstore that had a luxurious home up on a hill, with a detached stylish garage just a little ways below it with about ten sparkling, expensive sports cars in it, and in big bold letters at the bottom saying something like, “THE VALUE OF HIGHER EDUCATION”. At the time I almost believed it. Somehow I must’ve gotten the message that a college degree would bring me a hefty salary. I even saw this poster in a couple students’ rooms. A nice vaccine for me against this sort of marketing was that I enjoyed computers for what they were. I wasn’t taking CS for the money, though I knew students who were. I had misperceptions about my career prospects, but they were my own, and were not strongly influenced by popular perceptions.

In summary, I’ve gotten a sense that our educational system is eroding under our feet. I think a big reason for this is the raison d’etre of education has been lost or confused. The classic purpose of education in our country was to shoot for an ideal of having an educated citizenry, and ultimately a few who would become educated leaders. Universities were not designed to be vocational schools. That’s why as a rule they suck at it. Let’s stop trying to make them into what they are not.

I personally believe that the problem is our system of middle and high schools. Our students start falling behind our international competitors in middle school, and fall further behind in high school. Bill Gates said several years ago that our high school system is “obsolete”. By this he meant that even if our high schools totally functioned as they were designed they would still be inadequate. He didn’t say this as a slam against high school, but as a 2 x 4 across the forehead to get people to pay attention to the fact that we shouldn’t be satisfied with what we have. It can be much better.

A modest proposal

I can’t say I know how to fix this, but I have a few ideas. We Americans have this tendency to believe that education is made up of facts and techniques, things which have been discovered and need to be conveyed. Once students have acquired the requisite facts and techniques they are considered educated. Our educational system’s approach to standardized testing reflects this.

Morris Kline said, “The logic of discovery is more interesting than the logic of the discovered.” I reflected on this a bit. Why was the movie “The Matrix” so fascinating, and its sequels kind of flat? The reason was that in the first movie we were discovering along with Neo who he really was, and the truth of the reality he existed in. The sequels were kind of boring, because there wasn’t much new to discover. They mostly dealt with the “big ideas” that we as the audience had already discovered. What was new was mostly new characters and flashy new action sequences.

What Europeans learn at their top schools is the important ideas; concepts, ways of thinking, and how to build relationships between them, not just facts. This is a more powerful form of learning. Facts can be applied to problems, but they don’t help solve problems beyond the obvious. Techniques are useful shortcuts in solving problems, but they are brittle. If all you understand is a set of techniques, what do you do when you encounter a problem outside of them? Are you better off knowing a set of facts and techniques, or knowing how to be a skilled and flexible thinker and learner? Are you better off learning “how to” manipulate quadratics, “how to” solve them, “how to” program, “how to” balance atomic formulas,”how to” write an essay, “how to” paint, “how to” draw, or “how to” play an instrument? Or are you better off discovering your inner mathematician, scientist, modeler, writer, and artist? Technique is helpful. I’m not saying that “how to” content is worthless, but it doesn’t get to what’s powerful about the subject matter. What’s powerful about education is the development of our faculties, and trying to replicate the same realizations that masters from our past have achieved (while making it easier for students to realize than it was for the masters), not pasting a bunch of “post it” notes all over students’ minds. Some factual reference points are good to have, but I think our educational system should use facts (and techniques) wisely, not with abandon as it has done for decades.

There’s a catch though. I believe that teaching this way requires that teachers are actually competent in their subjects, and this means in part that they’ve already discovered their inner mastery of their own faculties. I’ve heard in recent years for example that we often have P.E. teachers teaching math. Having a fact and technique-based educational system is amenable to this sort of setup. A teacher can follow an education guide for teaching a subject, give assignments by number, and grade against a key. This will not do if we want to improve the quality of education our students receive.

The benefits of CO2

“We will restore science to its rightful place”
                 — President Barack Obama at his inaugural address

I heard this past weekend that the EPA has classified carbon dioxide as a pollutant that is hazardous to public health, and therefor needs to be regulated. What I feel is being left out of the discussion is that this much maligned gas is plant food. I assume we all learned about the process of photosynthesis in high school biology. In our society we apparently talk a lot about being “green”, but it appears to me that the EPA’s decision is actually anti-green. Watch these videos to see why.

Here’s a refresher on the process of photosynthesis

Carbon dioxide is essential for plant growth

More carbon dioxide means greater biomass in plants (more plant growth)

There are a couple interesting things to note. One is that CO2 is heavier than air, so it has a tendency to sink towards the Earth. The Greenhouse Effect takes place in the upper atmosphere. I imagine there’s a bit of CO2 up there. The amount of it in the atmosphere as a whole is minute, about 380 parts per million. Here’s a decent article on the chemical composition of the atmosphere, and what’s known about its evolution since the Earth was first formed. It’s a bit old (it said CO2 was (currently) at 360 PPM).

Secondly, the chemical equation displayed in the first video shows that an equal amount of oxygen is produced from the amount of carbon dioxide that was introduced into the photosynthetic process. So more CO2 at the start will eventually produce a more oxygen-rich environment.

I understand there are concerns about global warming stemming from rising CO2 levels, but this side of the science is left out of the discussion, and it shouldn’t be. CO2 has a good side as well, and what these videos show in the small is that our biosphere has a natural response to higher carbon dioxide levels. It is absorbed into the bodies of plants and more oxygen is produced. We can think of plants as our natural carbon scrubbers. More than that, more plant growth leads to more food for us and animal life.

Our economic future

“We all believed in socialism because we were children of a different generation. Then I realized that if you want to irradicate poverty you don’t do it by redistribution of existing wealth. You have to create new wealth.”

— Narayana Murthy, Chairman and CEO of Infosys, circa. 2002

I’m stepping into an area fraught with politics, which I usually try to avoid as I think it distracts from the main mission of my blog, but I feel as though I need to say something because I get a strong feeling we as a country are repeating some mistakes of the past, and we shouldn’t be. The above quote is from a series produced in 2002 by PBS called Commanding Heights: The Battle for the World Economy. It explains the evolution of economic theory in the 20th century, from globalized trade (early 20th century), to Keynesian economics, to a return of free markets, and then globalization.

I hear the refrain from those in power now that “We’ve tried that and it didn’t work”, regarding free markets. To the extent that misplaced regulation caused our current mess, I agree, but a prevailing attitude I’m seeing develop among Democrats concerns me. I see what they are proposing now and I say, “We’ve tried this as well and it didn’t work.” Just look at our history. Does anyone remember the 1970s (I’m referring to President Nixon’s, Ford’s, and Carter’s economic policies)? It was the product of Keynesian ideas in a changed world that was no longer compatible with it, and they are still incompatible.

(Update 6/2/2009: I had to revise the paragraph below with updated info. since my AP newswire link disappeared)

The sheer magnitude of spending that is being proposed is mind boggling: A budget of $3.55 trillion for next year, with plans for future spending, along with projected deficits totaling $7.1 trillion from 2010-2019. That’s in addition to the $1.8 trillion deficit we’ve accrued this year alone. That’s a total of $8.9 trillion added to the debt in 10 years. To provide some perspective it took us 28 years, 1980-2008, to rack up an $11 trillion debt. So Obama is talking about increasing the debt by 81% in 36% of the time.

I could understand the necessity of setting up TARP (Troubled Asset Relief Program) to rescue the financial system while it was collapsing quickly last year, but the news I’ve been hearing lately says that even the Bush Administration overdid it a little. Now the Obama Administration is proposing a new round of TARP financing. Maybe it’s necessary, but it may backfire on us. Banks overfilled their reserves from the last TARP. They are keeping their powder dry, and have been stingy about lending. The question we should ask is why. Are they being greedy or are they just getting more conservative, trying to avoid high risk investments? Finding out which it is makes a big difference in terms of how to approach this.

I’ve gotten a sense that the election of Obama was not a vote for the future in terms of economics, but an attempt to arrest the present and reach into the past for salvation. I get a sense that we’re saying, “Stop this train. I want to get off!” It was a vote for “Remember the good old days? Let’s bring them back!” Too bad that’s a dream that’s not possible. The world has changed. It’s time to craft a new future. I know this sounds really anachronistic given that the Obama campaign used up-to-date technology, and continues to use it. The economic and budgetary solutions put forward, however, are from several decades in the past.

I’ve been paying close attention to financial analysis of our economy over the past several months. The sense I get is that we are preparing to repeat some old mistakes, and we will achieve similar results. The way I see it we can look forward to the following over the next few years:

1. Inflation: caused by higher energy prices, and the classic “too much money chasing too few goods” phenomenon due to the fact that we’ve been printing money at an accelerated rate, and given the current proposals we’re going to accelerate it even more because we’re not going to be able to borrow all the money we need. I’m sure inflation feels good now, since we’ve been in a deflationary cycle. Given the slowness of government to react to any situation, and a consistently prevailing attitude of “If it works don’t fix it” (no matter who’s in power) we can predict with certainty that the government will overcorrect. Secondly, whenever the economy recovers, banks will draw from their excess reserves and increase the money supply even more. Saving will continue to be low, because it doesn’t pay to save money in an inflationary economy. Investors will put their money abroad in an attempt to increase their wealth instead of losing it letting it sit in a bank account (more on this below).
2. Higher interest rates. From what I’m hearing we’ve nearly tapped out our borrowing capacity, at least with what foreign bond holders are willing to buy into. We’ll need to increase interest rates to make bond holding more attractive. This is going to have consequences for all of us. Initially we may not feel it, due to excess capacity that will be built up in the banking system, but eventually we will.
3. Slow domestic economic growth caused by #1 and #2, and government borrowing crowding out private borrowing. I think however we will see a “jobless recovery”. Even though foreign countries appear to be in worse shape now than we are, if they stay true to market principles I think they will recover faster than we will, and will grow faster. Their crashing stock markets mean things are getting cheaper over there. Our current economic policies are not encouraging investment in our economy. Money will flow where it is welcomed, despite many people’s notions of where it “should” go. So I think we can look forward to a stock market recovery down the road (maybe next year), but I don’t get a sense that we will have robust job growth. The key to all of this happening is for our government and financial system to somehow untangle the derivatives mess of mortgage-backed securities and CDO’s.
4. A trend towards slow, lumbering gigantism in the private sector. With economic conditions not conducive to domestic investment, and therefor the creation of few competitors in the marketplace I think we’ll see a trend towards conglomeration, and perhaps more regulated monopolies. This will contribute to our slow economic growth because these giants are not going to be too competitive internationally. If they survive it’ll be because they participate in government contracts, and they can get pretty far on their inertia alone.
5. Your future is a government job. With all the government spending that’s going to take place, probably the best place to find a good paying job will be working for the federal government, or a major corporation that does government contracting. Government is not as efficient in creating jobs as the private sector is, but there will definitely be growth there. And it’ll likely be secure. Despite the efforts of past administrations, it’s been relatively rare when government jobs get cut. The federal government has grown continuously no matter who’s been in charge. It’s just been a matter of where the growth has occurred.

Having said all that I hope I’m wrong. I hope that we will come out of this with a robust domestic economy with good private sector job growth in the years ahead. I just don’t see that happening given what I’ve learned about our past history doing what we’re doing now.

Ending on a light-hearted note, The Onion discusses “Closing the money hole”. Though I haven’t seen pundit discussions that are nearly this silly (there’s expressions of muted surprise, but it’s amazing to me there’s not more alarm), the public discussion among citizens has felt pretty close to this… I haven’t posted warnings about foul language in videos I’ve posted in the past, because just about every video I post now has a little of it, and I got tired of warning people off, but there’s a bit of it here:

 
Edit 6/2/2009: I found this May 31 interview with Niall Ferguson and Joshua Ramo (video) on Fareed Zakaria’s CNN show “GPS”. Unfortunately I can’t embed this video, so follow the link. What Niall says agrees with what I said above. Both Niall and Joshua widen the picture of the consequences of what the federal government is doing now, and what it still needs to do. I agree with Joshua’s premise that we live in a “revolutionary time”, but I disagree with his examples. It’s true that we have “upstarts” around the world filling the void created by discredited leadership, but my point here is the solutions that are being offered, that I’ve heard, are also old, discredited solutions, but in new packaging. Unfortunately we’ve chosen something “new” that’s really not. I guess the thinking is that since one old idea apparently doesn’t work, let’s try a different old idea. Sorry, that’s not going to work either. Best come up with something new, though let’s not throw out the baby with the bathwater. Some of the old ideas still hold true. Let’s not forget what we’ve learned that works (and what doesn’t), but acknowledge that we have more to learn about how a globalized economy works.

—Mark Miller, http://tekkie.wordpress.com