I came upon this video recently titled “Dangerous Knowledge”, produced by the BBC. It profiles the life and times of three mathematicians (Georg Cantor, Kurt Gödel, and Alan Turing) and one scientist (Ludwig Boltzmann). For some reason it drew me in.
The show makes allusions to an atheism which I find difficult to relate to this subject. Commentators keep making reference to this idea that “God is dead”. It feels irrelevant to me. The important thing going on in the story is the destruction of the concept of the Newtonian mechanical universe. Perhaps this is a European idea. Their concept of God, as it’s portrayed in the show, seemed to be deeply tied to this idea of certainty. Since these four people (not to mention the world around them) were destroying the idea of certainty, their concept of God was being destroyed as well.
“Dangerous Knowledge”
This was also about the limits of some of our mental perceptual tools, math and science.
I had heard of Cantor when I read “The Art of Mathematics”, by Jerry King. He talked about how Cantor had come up with this very controversial idea that there were infinities of different sizes, using the mathematical concept of sets. He proved the paradoxical idea, for example, that the infinite set of even (or odd) numbers was the same size as the infinite set of natural numbers.
What’s interesting to me is that through this program you can see a line of thought, beginning with Cantor, running through several decades, to some of the first baby steps of computer science with Turing. Turing’s inspiration for his mathematical concept of the computer (the Turing machine) came from the work of Gödel, and another mathematician named Hilbert. The work of Gödel’s that Turing was specifically interested in was inspired by the paradoxes raised by Cantor.
The video below is from the television production of “Breaking the Code”, which was originally written as a play by the same name. It’s about Turing’s life and work deciphering the Nazis’ Enigma encoding/decoding system, and his ideas about computing. The TV production puts the emphasis on Turing’s homosexuality and how that put him in conflict with his own government. The play got much more into his ideas about computing. There are a couple scenes in the TV version that talk about his ideas. This is one of them. I think it’s a perfect epilogue to “Dangerous Knowledge”:
A couple clips of the play, starring the same actor (Derek Jacobi), are shown in the first episode of “The Machine That Changed The World”, called “Great Brains”. There’s a whole section in it on Turing starting at 43:45 in the video.
I went to see the movie Julie & Julia yesterday, and I really liked it, way more than I expected. I remember Julia Child from her TV show when I was a kid. I can’t remember. Either my mom or my grandmother (or both) used to watch her show regularly. I wanted to see the movie because I thought it was about her life (which it is), but what blew me away was the story of Julie, who takes on a project of going through all of Julia’s recipes and blogging about it. The experience she has doing this matches my own blogging experience in some ways. I am also following my inspiration where it leads, and I also struggle with my own ignorance. What’s comforting and inspiring about the movie is it shows that 1) those who inspire us went through their own struggles and doubts, and 2) we tend to idealize/idolize our inspirations. In a Platonic way (after Plato) these idealized versions we hold within ourselves are really “forms”, and they’re our inspiration, not what we think are our inspiration. We come to own our inspiration using the illusion that it all comes from someone else to make the inspiration stronger within us at first.
The movie is based on two books: My Life in France, by Julia Child, and Julie and Julia: 365 Days, 524 Recipes, 1 Tiny Apartment Kitchen, by Julie Powell, which is based on her blog The Julie/Julia Project. The movie skillfully interweaves the two stories to show parallels in the lives of these two people–and perhaps idealizes them as well.
Coming out of ignorance and teaching others
Speaking of Plato, I came upon a video recently showing Plato’s allegory of ”The cave”. It describes well an aspect of the journey I feel I’ve been on, based on my experience. It was meant as a way of expressing the process that one goes through to reach enlightenment, the responsibility of the enlightened to try to help fellow members of society to go on their own enlightenment journeys, and the obstacles they face in doing it.
There’s a morbid aspect to this allegory. Plato says that those who return to the “prisoners” to try to free them risk death, for those inside do not wish to leave their unenlightened state. I think I read that this allegory was Plato’s way of describing the significance of the life and death of Socrates, and that this allusion to “the danger of death” to the enlightened was an oblique reference to his Athenian trial and death sentence. I don’t feel that this applies today, but I have sometimes seen the mocking and dismissive resistance that Plato described when I’ve tried to share in the “troubles and honors” of fellow developers, and present an expanded viewpoint of computing.
This story is more than 2,000 years old, and it shows that the process of becoming enlightened, and the difficulties in helping others do the same are part of the human condition.
I’ve turned on a feature on WordPress called “e-mail replies”. I’m not really sure what it is. I’ve seen some other blogs that are set up so that when you comment on a blog post it will e-mail you if anyone else has come along and commented, making conversations more convenient. I’m giving it a whirl. If I get complaints about it I’ll turn it off.
Update 8-17-09: I’ve revised this post a bit to clarify some points I made.
I received a request 2-1/2 weeks ago to write a post based on video of a speech that Alan Kay gave at Kyoto University in February, titled “Systems Thinking For Children And Adults”. Here it is. The volume in the first 10 minutes of the video is really low, so you’ll probably need to turn up your volume. The volume in the video gets readjusted louder after that.
On the science of computer science
Kay said what he means by a science of computing is the forward-looking study, understanding, and invention of computing. Will the “science” come to mean something like the other real sciences? Or will it be like library and social science, which means a gathering of knowledge? He said this is not the principled way that physics, chemistry, and biology have been able to revolutionize our understanding of phenomena. Likewise, will we develop a software engineering that is like the other engineering disciplines?
I’ve looked back at my CS education with more scrutiny, and given what I’ve found I’m surprised that Kay is asking this question. Maybe I’m misunderstanding what he said, but for me CS was a gathering of knowledge a long time ago. The question for me is can it change from that to a real science? Perhaps he’s asking about the top universities.
When I took CS as an undergraduate in the late 80s/early 90s it was clear that some research had gone into what I was studying. All the research was in the realm of math. There was no sense of tinkering with architectures that existed, and very little practice in analyzing it. We were taught to apply a little analysis to algorithms. There was no sense of trying to create new architectures. What we were given was pre-digested analysis of what existed. We didn’t study it. So it had gotten as far as exposing us to the “TEM” parts, but only in a narrow band. The (S)cience was non-existent. (Update 8-31-2009: I apologize. I just realized that I didn’t fully explain myself here. See “What would computing as a real science by like?” (below) for an explanation on “TEMS” (Technology, Engineering, Mathematics, Science).)
What we got instead is what I’d call “small science” in the sense that we had lots of programming labs where we experimented with our own knowledge of how to write programs that worked; how to use, organize, and address memory; and how to manage complexity in our software. We were given some strategies for doing this, which were taught as catechisms. The labs gave us an opportunity to see where those strategies were most effective. We were sometimes graded on how well we applied them.
We got to experience a little bit of how computers could manipulate symbols, which I thought was real interesting. I wished that there would’ve been more of that.
One of the tracks I took while in college was focused on software engineering, which really focused on project management techniques and rules of thumb. It was not a strong engineering discipline backed by scientific findings and methods.
When I got out into the work world I felt like I had to “spread the gospel”, because what IT shops were doing was ad hoc, worse than the methodologies I was taught. I was bringing them “enlightenment” compared to what they were doing. The nature and constraints of the workplace broke me out of this narrow-mindedness, and not always in good ways.
It’s only been by doing a lot of thinking about what I’ve learned, and my POV of computers, that I’ve been able to see this that I’ve been able to see that what I got out of CS was a gathering of knowledge with some best practices. At the time I had no concept that I was only getting part of the picture even though our CS professors openly volunteered with a wry humor that “computer science is not a science”. They compared the term “computer science” to “social science” in the sense that it was an ill-defined field. There was the expectation that it would develop into something more cohesive, hopefully a real science, later on. Given the way we were taught though, I guess they expected it to develop with no help from us.
Kay has complained previously that the commercial personal computing culture has contributed greatly to the deterioration of CS in academia. I have to admit I was a case in point. A big reason why I thought of CS the way I did was this culture I grew up in. Like I’ve said before, I have mixed feelings about this, because I don’t know if I would be a part of this field at all if the commercial culture he complains about never existed.
What I saw was that people were discouraged from tinkering with the hardware, seeing how it worked, much less trying to create their own computers. Not to say this was impossible, because there were people who tinkered with 8- and 16-bit computers. Of course, as I think most people in our field still know, Steve Wozniak was able to build his own computer. That’s how he and Steve Jobs created Apple. Computer kits were kind of popular in the late 1970s, but that faded by the time I really got into it.
When I used to read articles about modifying hardware there was always the caution about, “Be careful or you could hose your entire machine.” These machines were expensive at the time. There were the horror stories about people who tried some machine language programming and corrupted the floppy disk that had the only copy of their program on it (ie. hours and hours of work). So people like me didn’t venture into the “danger zone”. Companies (except for Apple with the Apple II) wouldn’t tell you about the internals of their computers without NDAs and licensing agreements, which I imagine one had to pay for handsomely. Instead we were given open access to a layer we could experiment on, which was the realm of programming either in assembly or a HLL. There were books one could get that would tell you about memory locations for system functions, and how to manipulate features of the system in software. I never saw discussion of how to create a software computer, for example, that one could tinker with, but then the hardware probably wasn’t powerful enough for that.
By and large, CS fit the fashion of the time. The one exception I remember is that in the CS department’s orientation/introductory materials they encouraged students to build their own computers from kits (this was in the late 1980s), and try writing a few programs, before entering the CS program. I had already written plenty of my own programs, but as I said, I was intimidated by the hardware realm.
My education wasn’t the vocational school setting that it’s turning into today, but it was not as rigorous as it could have been. It met my expectations at the time. What gave me a hint that my education wasn’t as complete as I thought was that opportunities which I thought would be open to me were not available when I looked for employment after graduation. The hint was there, but I don’t think I really got it until a year or two ago.
What would computing as a real science be like?
I attended the 2009 Rebooting Computing summit on CS education in January, and one of the topics discussed was what is the science of computer science? In my opinion it was the only topic brought up there that was worth discussing at that time, but that’s just me. The consensus among the luminaries that participated was that historically science has always followed technology and engineering. The science explains why some engineering works and some doesn’t, and it provides boundaries for a type of engineering.
We asked the question, “What would a science of computing look like?” Some CS luminaries used an acronym “TEMS” (Technology, Engineering, Mathematics, Science), and there seemed to be a deliberate reason why they had those terms in that order (in other circles it’s often expressed as “STEM”). Technology is developed first. Some engineering gets developed from patterns that are seen. Some math can be derived from it. Then you have something you can work with, experiment with, and reason about–science. The part that’s been missing from CS education is the science itself: experimentation, an interest and proclivity to get into the guts of something and try out new things with whatever–the hardware, the operating system, a programming language, what have you–just because we’re curious. Or, we see that what we have is inadequate and there’s a need for something that addresses the problem better.
Alan Kay participated in the summit and gave a description of a computing science that he had experienced at Xerox PARC. They studied existing computing artifacts, tried to come up with better architectures that did the same things as the old artifacts, and then applied the new architectures to “everything else”. I imagine that this would test the limits of the architecture, and provide more avenues for other scientists to repeat the process (take an artifact, create a new architecture for it, “spread it everywhere”) and gain more improvement.
To give you a “starter” idea of what this process is like, read the introduction to Design Patterns, by Gamma, Helm, Johnson, and Vlissides, and take note of how they describe coming up with their patterns. Then notice how widely those patterns have been applied to projects that have nothing to do with what the Gang of Four originally created with the patterns they came up with.
The problem is more often than not, there’s been no study of the other technologies where these patterns have been applied. When the Xerox Learning Research Group came up with Smalltalk (object-orientation, late-binding, GUI), Alan Kay expected that others would use the same process they did to improve on it, but instead people either copied OOP into less advanced environments and then used them to build practical software applications, or they built applications on top of Smalltalk. It’s just as I described with my CS education: The strategies get turned into a catechism by most practitioners. Rather than studying our creations, we’ve just kept building upon and using the same frameworks, and treating them with religious reverence–we dare not change them lest we lose community support. Instead of looking at how to improve upon the architecture of Smalltalk, people adopted OOP as a religion. This happened and continues to happen because almost nobody in the field is being taught to apply scientific principles to computing, and there’s little encouragement from funding sources to carry out this kind of research.
There are degrees of scientific thinking that software developers use. One IT software house where I worked for a year used patterns on a regular basis that we created ourselves. We understood the essential idea of patterns, though we did not understand the scientific principles Kay described. Everywhere else I worked didn’t use design patterns at all.
There has been more movement in the last few years to break out of the confines developers have been “living” in, to try and improve upon fundamental runtime/VM architecture, and building better languages on top of it. This is good, but in reality most of it has just recapitulated language features that were invented decades ago through scientific approaches to computing. There hasn’t been anything dramatically new developed yet.
The ignorance we ignore
“What is the definition of ignorance and apathy?”
“I don’t know, and I don’t care.”
A twentieth century problem is that technology has become too “easy”. When it was hard to do anything whether good or bad, enough time was taken so that the result was usually good. Now we can make things almost trivially, especially in software, but most of the designs are trivial as well.
A fundamental problem with our field is there’s very little appreciation for good architecture. We keep tinkering with old familiar structures, and produce technologies that are marginally better than what came before. We assume that brute force will get us by, because it always has in the past. This is ignoring a lot. One reason that brute force has been able to work productively in the past is because of the work of people who did not use brute force, creating: functional programming, interactive computing, word processing, hyperlinking, search, semiconductors, personal computing, the internet, object-oriented programming, IDEs, multimedia, spreadsheets, etc. This kind of research went into decline after the 1970s and has not recovered. It’s possible that the brute force mentality will run into a brick wall, because there will be no more innovative ideas to save it from itself. A symptom of this is the hand-wringing I’ve been hearing about for a few years now about how to leverage multiple CPU cores, though Kay thinks this is the wrong direction to look in for improvement.
There’s a temptation to say “more is better” when you run into a brick wall. If one CPU core isn’t providing enough speed, add another one. If the API is not to your satisfaction, just add another layer of abstraction to cover it over. If the language you’re using is weak, create a large API to give it lots of functionality and/or a large framework to make it easier to develop apps. in it. What we’re ignoring is the software architecture (all of it, including the language(s), and OS), and indeed the hardware architecture. These are the two places where we put up the greatest resistance to change. I think it’s because we acknowledge to ourselves that the people who make up our field by and large lack some basic competencies that are necessary to reconsider these structures. Even if we had the competencies nobody would be willing to fund us for the purpose of reconsidering said structures. We’re asked to build software quickly, and with that as the sole goal we’ll never get around to reconsidering what we use. We don’t like talking about it, but we know it’s true, and we don’t want to bother gaining those competencies, because they look hard and confusing. It’s just a suspicion I have, but I think mathematics education is important for all this. We can’t get to better architectures without it. Nobody else seems to mind the way things are going. They accept it. So there’s no incentive to try to bust through some perceptual barriers to get to better answers, except the sense that some of us have that what’s being done is inadequate.
In his presentation in the video, Kay pointed out the folly of brute force thinking by showing how humungous software gets with this approach, and how messy the software is architecturally. He said that the “garbage dump” that is our software is tolerated because most people can’t actually see it. Our perceptual horizons are so limited that most people can only comprehend a piece of the huge mess, if they’re able to look at it. In that case it doesn’t look so bad, but if we could see the full expanse we would be horrified.
This clarifies what had long frustrated me about IT software development, and I’m glad Kay talked about it. I hated the fact that my bosses often egged me on towards creating a mess. They were not aware they were doing this. Their only concern was getting the computer to do what the requirements said in the quickest way possible. They didn’t care about the structure of it because they couldn’t see it. So to them it was irrelevant whether it was built well or not. They didn’t know the difference. I could see the mess, at least as far as my project was concerned. It eventually got to the point that I could anticipate it, just from the way the project was being managed. So often I wished that the people managing me or my team, and our customers, could see what we saw. I thought that if they did they would recognize the consequences of their decisions and priorities, and we could come to an agreement about how to avoid it. That was my “in my dreams” wish.
Kay said, “Much of the applications we use … actually take longer now to load than they did 20 years ago.” I’ve read about this (h/t to Paul Murphy), and the following video illustrates it pretty well. A few people did a side-by-side test of a 2007 Vista laptop with a dual-core Intel processor (I’m guessing 2.4 Ghz) and 1 Gig. RAM vs. a Mac Classic II with a 16 Mhz Motorola 68030 and 2 MB RAM. My guess is the Mac was running a SCSI hard drive (the only kind you could install on a Mac when they were made back then). I didn’t see them insert a floppy disk.
They said in the video that the Mac is “1987 technology”. Even though the Mac Classic II was introduced in 1991, they’re probably referring to the 68030 CPU it uses, which came out in 1987. Note that the volume in this video is pretty loud, so you may want to turn down your volume:
The Mac completed the contest in 1 minute, 42 seconds, 25% faster than the Vista laptop, which took 2 minutes, 17 seconds. You can tell when the Mac is “off” when the white dialog box on the black background comes up. At that point it is ready to be shut off manually. It didn’t have an auto-shutoff.
Someone else posted a demonstration (video) in 2009 of a Vista desktop PC which completed the same tasks in 1 minute, 18 seconds–23% faster than the old Mac. I think the difference was that the laptop vs. Mac demo likely used a slower processor for the laptop (vs. the 2009 demo), and probably a slower hard drive. The thing is though, it probably took a 4 Ghz dual-processor (or quad core?) computer, faster memory, and a faster hard drive to beat the old Mac.
To be fair, I’ve heard from others that the results would be much the same if you compared a modern Mac to the old Mac. The point is not which platform is better. It’s that we’ve made little progress in responsiveness.
The wide gulf between the two pieces of hardware (old Mac vs. Vista PC) is dramatic. The hardware got about 15,000-25,000% faster via. Moore’s Law (though Moore’s Law only applied to transistors, not speed), but we have not seen a commensurate speed up in system responsiveness. As you can see, in some cases the newer software technology is slower than what existed 22 years ago.
When Kay has elaborated on this in the past he’s said this is also partly due to the poor hardware architecture which was adopted by the microprocessor industry in the 1970s, and which has been marginally improved over the years. Quoting from an interview with Alan Kay in ACM Queue in 2004:
Neither Intel nor Motorola nor any other chip company understands the first thing about why that architecture was a good idea [referring to the Burroughs B5000 computer].
Just as an aside, to give you an interesting benchmark—on roughly the same system, roughly optimized the same way, a benchmark from 1979 at Xerox PARC runs only 50 times faster today. Moore’s law has given us somewhere between 40,000 and 60,000 times improvement in that time. So there’s approximately a factor of 1,000 in efficiency that has been lost by bad CPU architectures.
The myth that it doesn’t matter what your processor architecture is—that Moore’s law will take care of you—is totally false.
Another factor is the configuration and speed of main and cache memory. Cache is built into the CPU, is directly accessed by it, and is very fast. Main memory has always been much slower than the CPU in microcomputers. The CPU spends the majority of its time waiting for memory, or data to stream from a hard drive or internet connection, if the data is not already in cache. This has always been true. It may be one of the main reasons why no matter how fast CPU speeds have gotten the user experience has not gotten commensurately more responsive.
The revenge of data processing
The section of Kay’s speech where he talks about “embarrassing questions” from his wife (the slide is subtitled “Two cultures in computing”) gets to a complaint I’ve had for a while now. There have been many times while I’m writing for this blog when I’ve tried to “absent-mindedly” put the cursor somewhere on a preview page and start editing, but then realize that the technology won’t let me do it. You can always tell when a user interaction issue needs to be addressed when your subconscious tries to do something with a computer and it doesn’t work.
Speaking about her GUI apps. his wife said, “In these apps I can see and do full WYSIWYG authoring.” She said about web apps., “But with this stuff in the web browser I can’t–I have to use modes that delay seeing what I get and I have to start guessing,” and, “I have to edit through a keyhole.” He said what’s even more embarrassing is that the technology she likes was invented in the 1970s (things like word processing and desktop publishing in a GUI with WYSIWYG–aspects of the personal computing model), whereas the stuff she doesn’t like was invented in the 1990s (the web/terminal model). Actually I have to quibble a bit with him about the timeline.
“The browser = next generation 3270 terminal” 3270 terminal image from Wikipedia.org
The technology she doesn’t like–the interaction model–was invented in the 1970s as well. Kay mentioned 3270 terminals earlier in his presentation. The web browser with its screens and forms is an extension of the old IBM mainframe batch terminal architecture from the 1970s. The difference is one of culture, not time. Quoting from the Wikipedia article on the 3270:
[T]he Web (and HTTP) is similar to 3270 interaction because the terminal (browser) is given more responsibility for managing presentation and user input, minimizing host interaction while still facilitating server-based information retrieval and processing.
Applications development has in many ways returned to the 3270 approach. In the 3270 era, all application functionality was provided centrally. [my emphasis]
It’s true that the appearance and user interaction with the browser itself has changed a lot from the 3270 days in terms of a nicer presentation (graphics and fonts vs. green-screen text), and the ability to use a mouse with the browser UI (vs. keyboard-only with the 3270). It features document composition, which comes from the GUI world. The 3270 did not. Early on a client scripting language was added, Javascript, which enabled things to happen on the browser without requiring server interaction. The 3270 had no scripting language.
There’s more freedom than the 3270 allowed. One can point their browser anywhere they want. A 3270 was designed to be hooked up to one IBM mainframe, and the user was not allowed to “roam” on other systems with it, except if given permission via. mainframe administration policies. What’s the same though is the basic interaction model of filling in a form on the client end, sending that information to the server in a batch, and then receiving a response form.
The idea that Kay brought to personal computing was immediacy. You immediately see the effect of what you are doing in real time. He saw it as an authoring platform. The browser model, at least in its commercial incarnation, was designed as a form submission and publishing platform.
Richard Gabriel wrote extensively about the difference between using an authoring platform and a publishing platform for writing, and its implications from the perspective of a programmer, in The Art of Lisp and Writing. The vast majority of software developers work in what is essentially a “publishing” environment, not an authoring environment, and this has been the case for most of software development’s history. The only time when most developers got closer to an authoring environment was when Basic interpreters were installed on microcomputers, and it became the most popular language that programmers used. The old Visual Basic offered the same environment. The interpreter got us closer to an authoring environment, but it still had one barrier: you either had to be editing code, or running your program. You could not do both at the same time, but there was less of a wait to see your code run because there was no compile step. Unfortunately with the older Basics the programmer’s power was limited.
People’s experience with the browser has been very slowly coming back towards the idea of authoring via. the AJAX kludge. Kay showed a screenshot of a more complete authoring environment inside the browser using Dan Ingalls’s Lively Kernel. It looks and behaves a lot like Squeak/Smalltalk. The programming language within Lively is Javascript.
We’ve been willing to sacrifice immediacy to get rid of having to install apps. on PCs. App. installation is not what Kay envisioned with the Dynabook, but that’s the model that prevailed in the personal computer marketplace. You know you’ve got a problem with your thinking if you’re coming up with a bad design to compensate for past design decisions that were also bad. The bigger problem is that our field is not even conscious that the previous bad design was avoidable.
Kay said, “A large percentage of the main software that a lot of people use today, because it’s connected to the web, is actually inferior to stuff that was done before, and for no good reason whatsoever!”
I agree with him, but there are people who would disagree on this point. They are not enlightened, but they’re a force to be reckoned with.
What’s happened with the web is the same thing that happened to PCs: The GUI was seen as a “good idea” and was grafted on to what has been essentially a minicomputer, and then a mainframe mindset. Blogger Paul Murphy used to write, from a business perspective, about how there are two cultures in computing/IT that have existed for more than 100 years. The oldest culture that’s operated continuously throughout this time is data processing. This is the culture that brought us punch cards, mainframes, and 3270 terminals. It brought us the idea that the most important function of a computer system is to encode data, retrieve it on demand, and produce reports from automated analysis. The other culture is what Murphy called “scientific computing”, and it’s closer to what Kay promotes.
The data processing culture has used web applications to recapitulate the style of IT management that existed 30 years ago. Several years ago I heard from a few data processing believers who told me that PCs had been just a fad, a distraction. “Now we can get back to real computing,” they said. The meme from data processing is “The data is more important than the software, and the people.” Why? Because software gets copied and devalued. People come and go. Data is what you’ve uniquely gathered and can keep proprietary.
I think this is one reason why CS enrollment has fallen. It’s becoming dead like Latin. What’s the point of going into it if the knowledge you learn is irrelevant to the IT jobs (read “most abundant technology jobs”) that are available, and there’s little to no money going into exciting computing research? You don’t need a CS degree to create your own startup, either. All you need is an application server, a database, and a scripting/development platform, like PHP. Some university CS departments have responded by following what industry is doing (h/t to a user named “DHCDBD” over at TechRepublic.com) in an effort to seem relevant and increase enrollment (ie. keep the department going). The main problem with this strategy is they’re being led by the nose. They’re not leading our society to better solutions.
What’s natural and what’s better
Kay tried to use some simple terms for the next part of his talk to help the audience relate to two ideas:
“new” — for a new outlook that changes one’s perception. He gets into this idea of “outlook” later.
He gave what I think is an elegant graphical representation of one of the reasons things have turned out the way they have. He talked about modes of thought, and said that 80% of people are outer-directed and instrumental reasoners. They only look at ideas and tools in the context of whether it meets their current goals. They’re very conservative, seeking consensus before making a change. Their goals are the most important thing. Tools and ideas are only valid if they help meet these goals. This mentality dominates IT. Some would say, “Well, duh! Of course that’s the way they think. Technology’s role in IT is to automate business processes.” That’s the kind of thinking that got us to where we are. As Paul Murphy has written previously, the vision of “scientific computing”, as he calls it, is to extend human capabilities, not replace/automate them.
Kay said that 1% of people look at tools and respond to them, reconsidering their goals in light of what they see as the tool’s potential. This isn’t to say that they accept the tool as it’s given to them, and adjust their goals to fit the limitations of that version of the tool. Rather, they see its potential and fashion the tool to meet it. Think about Lively Kernel, which I mentioned above. It’s a proof of this concept.
There’s a symbiosis that takes place between the tool and the tool user. As the tool is improved, new ideas and insights become more feasible, and so new avenues for improvement can be explored. As the tool develops, the user can rethink how they work with it, and so improve their thinking about processes. As I’ve thought about this, it reminds me of how Engelbart’s NLS developed. The NLS team called it “bootstrapping”. It led to a far more powerful leveraging of technology than the instrumental approach.
The “80%” dynamic Kay described happened to NLS. Most people didn’t understand the technology, how it could empower them, and how it was developed. They still don’t. In fact Engelbart is barely known for his work today. Through the work that was done in the early days of Xerox PARC, a few of his ideas managed to get into technology that we’ve used over the years. He’s most known now for the invention of the mouse, but he did much more than that.
In the instrumental approach the goals precede the tools, and are actually much more conservative than the approach of the 1-percenters. In the instrumental scenario the goals people have are similar whether the tools exist or not, and so there’s no potential for this human-tool interaction to provide insight into what might be better goals.
Kay talked about this subject at Rebooting Computing, and I think he said that a really big challenge in education is to get students to shift from the “80%” mindset to one of the other modes of thought that have to do with deep thinking, at least exposing students to this potential within themselves. I think he would say that we’re not predisposed to only think one way. It’s just that left to our own devices we tend to fall into one of these categories.
I base the following on the notes Kay had on his slides in his speech:
He said that in the commercial computing realm (which is based on the way mainframes were sold to the public years ago) it’s about “news”: The emphasis is on functionality, and people as components. This approach also says you get your hardware, OS, programming language, tools, and user interface from a vendor. You should not try to make your own. This sums up the attitude of IT in a nutshell. It’s not too far from the mentality of CS in academia, either.
The “new” in the 1970s was a focus on the end-user and whether they can learn and do. “We should design how user interactions and learning will be done and work our way down to the functions they need!” In other words, rather than thinking functionality-first, think user-first–in the context of the computer being a new medium, extending human capabilities. Aren’t “functionality” and “user” equally high priorities? Users just want functionality from computers, don’t they? Ask yourself this question: Is a book’s purpose only to provide functionality? The idea at Xerox PARC was to create a friendly, inviting, creative environment that could be explored, built on, and used to create a better version of itself–an authoring platform, in a very deep sense.
Likewise, with Engelbart’s NLS, the idea was to create an information sharing and collaboration environment that improved how groups work together. Again, the emphasis was on the interaction between the computer and the user. Everything else was built on that basis.
By thinking functionality-first you turn the computer into a device, or a device server, speaking metaphorically. You’re not exposing the full power of computing to the user. In the typical IT mentality that’s the idea. It’s too dangerous to expose the full power of computing to end users, so the thinking goes. They’ll mess things up either on purpose or by mistake. Or they’ll steal or corrupt proprietary information. Such low expectations… It’s like they’re children or illiterate peasants who can’t be trusted with the knowledge of how to read or write. They must be read to aloud rather than reading for themselves. Most IT environments believe that they cannot be allowed to write, for they are not educated enough to write in the computer’s complex language system (akin to hieroglyphics). Some allow their workers to do some writing, but in limited, and not very expressive languages. This “limits their power to do damage”. If they were highly educated, they wouldn’t be end users. They’d be scribes, writing what others will hear. Further, these “illiterates” are never taught the value of books (again, using a metaphor). They are only taught to believe that certain tomes, written by “experts” (scribes), are of value. It sounds Medieval if you ask me. Not that this is entirely IT’s fault. Computer science has fallen down on the job by not creating better language systems, for one thing. Our whole educational/societal thought structure also makes it difficult to break out of this dynamic. Chris Crawford has a great essay on this if you’d like to explore this analogy further.
The “news” way of thinking has fit people into specialist roles that require standardized training. The “new” emphasized learning by doing and general “literacy”.
We’re in danger of losing it
Everyone interested in seeing what the technology developed at ARPA and Xerox PARC (the internet, personal computing, object-oriented programming) was intended to represent should pay special attention to the part of Kay’s speech titled “No Gears, No Centers: ARPA/PARC Outlook”. Kay told me about most of this a couple years ago, and I incorporated it into a guest post I wrote for Paul Murphy’s blog, called “The tattered history of OOP” (see also “The PC vision was lost from the get-go”). Kay shows it better in his presentation.
I think the purpose of Kay’s criticism of what exists now is to point out what we’ve lost, and continue to lose. Since our field doesn’t understand the research that created what we have today, we’ve helplessly taken it for granted that what we have, and the method of conservative incremental improvement we’ve practiced, will always be able to handle future challenges.
Kay said that because of what he’s seen with the development of the field of computing, he doesn’t believe what we have in computer science is a real field. And we are in danger of losing altogether any remnants of the science that was developed decades ago. This is because it’s been ignored. The artifacts that are based on that research are all around us. We use them every day, but the vast majority of practitioners don’t understand the principles and outlook that made it possible to create them. This isn’t a call to reinvent the wheel, but rather a qualitative statement: We’re losing the ability to make the kind of leap that was made in the 1970s, to go beyond what that research has brought us. In fact, in Kay’s view, we’re regressing. The potential scenario he paints reminds me of the science fiction stories where people use a network of space warping portals for efficient space travel and say, “We don’t know who built it. They disappeared a long time ago.”
I think there are three forces that created this problem:
The first was the decline in funding for interesting and powerful computing research. What’s become increasingly clear to me from listening to CS luminaries, who were around when this research was being done, is that the world of personal computing and the internet we have today is an outgrowth–you could really say an accident–of defense funding that took place during the Cold War–ARPA, specifically research funded by the IPTO (the Information Processing Techniques Office). This isn’t to say that ARPA was like a military operation. Far from it. When it started it was staffed by academics and they were given a wide berth in which to do their research on computing. An important ingredient of this was the expectation that researchers would come up with big ideas, ones that were high risk. We don’t see this today.
The reason this computing research got as much funding as it did was because of the Sputnik launch. This got Americans to wake up to the fact that mathematics, science, and engineering were important, because of the perception that they were important for the defense of the country. The U.S. knew that the Soviets had computer technology they were using as part of their military operations, and the U.S. wanted to be able to compete with them in that realm.
In terms of popular perception there’s no longer a sense that we need technical supremacy over an enemy. However computing is still important to national defense, even taking the war against Al Qaeda into account. A few defense and prominent technology leaders in the know have said that Al Qaeda is a very early adopter of new technologies, and an innovator in their use for their own ends.
In 1970 computing research split into part government-funded and part private, with some ARPA researchers moving to the newly created PARC facility at Xerox. This is where they created the modern form of personal computing, some aspects of which made it into the technologies we’ve been using since the mid-1980s. The groundbreaking work at PARC ended in the early 1980s.
The second force, which Kay identified, was the rise of the commercial market in PCs. He’s basically said that computers were introduced to society before we were ready to understand what’s really powerful about them. This market invited us in, and got us acquainted with very limited ideas about computing and programming. We went into CS in academia with an eye towards making it like Bill Gates (never mind that Gates is actually a college drop-out), and in the process of trying to accommodate our limited ideas about computing the CS curriculum was dumbed down. I didn’t go into CS for the dream of becoming a billionaire, but I had my eye on a career at first.
It’s been difficult for universities in general to resist this force, because it’s pretty universal. The majority of parents of college-bound youth have believed for decades that a college degree means a secure economic future–meaning a job, a career that pays well. It’s not always true, but it’s believed in our culture. This sets expectations for universities to be career “launching pads” and centers for social networking, rather than institutions that develop a student’s faculties, their ability to think, and expose them to high level perspectives to improve their perception.
The third force is, as Paul Murphy wrote, the imperative of IT since the earliest days of the 20th century, which is to use technology to extend and automate bureaucracy. I don’t see bureaucracy as a totally bad thing. I think of Alexander Hamilton’s quote about public debt, rephrased as, “A bureaucracy, if not excessive, will be to us a blessing.” However, in its traditional role it creates and follows rules and procedures formulated in a hierarchy. There’s accountability for meeting directives, not broad goals. Its thinking is deterministic and algorithmic. IT, being traditionally a bureaucratic function, models this (we should be asking ourselves, “Does it have to be limited to this?”). My sense of it is CS responded to the economic imperatives. It felt the need to lean towards what industry was doing, and how it thinks. The way it tried to add value was by emphasizing optimization strategies. The difference was it used to have a strong belief in staying true to some theoretical underpinnings, which somewhat counter-balanced the strong pull from industry. That resolve is slipping.
Kay and I have talked a little about math and science education. He said that our educational system has long viewed math and science as important, and so these subjects have always been taught, but they haven’t understood their significance. So the essential ideas of both tend to get lost. What the computer brings to light as a new medium is that math (as mathematicians understand it, not how it’s typically taught) and science are essential for understanding computing’s potential. They are foundations for a new literacy. Without this perspective, and the general competencies in math and science to support it, both students and universities will likely continue the status quo.
Outlook: The key ingredient
Kay’s focus on outlook really struck me, because we have such an emphasis in our society on knowledge and IQ. My view of this has certainly evolved as I’ve gotten into my studies.
Whenever you interview for a job in the IT industry you get asked about your knowledge, and maybe some questions that probe your management skills. In technology companies that actually invent stuff you are probed for your mental faculties, particularly at tech companies that are known as “where the tech whizzes work”. I had an interview 5 years ago with a software company where the employer gave me something that resembled an IQ test. I have not seen nor heard of a technology company that asks questions about one’s outlook.
Kay said,
What outlook does is give you a stronger way of looking at things, by changing your point of view. And that point of view informs every part of you. It tells you what kind of knowledge to get. And it also makes you appear to be much smarter.
…
Knowledge is ’silver’, but outlook is ‘gold’. I dare say [most] universities and most graduate schools attempt to teach knowledge rather than outlook. And yet we live in a world that has been changing out from under us. And it’s outlook that we need to deal with that. And in contrast to these two, IQ is just a big lump of lead. It’s one of the worst things in our field that we have clever people in it, because like Leonardo [da Vinci] none of us is clever enough to deal with the scaling problems that we’re dealing with. So we need to be less clever and be able to look at things from better points of view.
This is truly remarkable! I have never heard anyone say this, but I think he may be right. All of the technology that has been developed, that has been used by millions of people, and has been talked about lo these many years was created by very smart people. More often than not what’s been created, though, has reflected a limited vision.
Given how society’s perception of computing has been, I doubt Kay’s vision of human-computer interaction would’ve been able to fly in the commercial marketplace, because as he’s said, we weren’t ready for it. In my opinion it’s even less ready for it now. But certainly the internal and networked computing vision that was developed at PARC could’ve been implemented in machines that the consuming public could’ve purchased decades ago. I think that’s where one could say, “You had your chance, but you blew it.” Vendors didn’t have the vision for it.
What’s needed in the future
One of Kay’s last slides referred to Marvin Minsky. I am not familiar with Minsky, and I guess I should be. He said that in terms of software we need to move from a “biology of systems” (architecture) to a “psychology of systems” (which I’m going to assume for the moment means “behavior”). I don’t really know about this, so I’m just going to leave it at that.
In a chart titled “Software Has Fallen Short” Kay made a clearer case than he has in the past for not idolizing the accomplishments that were made at ARPA/Xerox PARC. In the past he’s tried to discourage people from getting too excited about the PARC stuff, in some cases downplaying it as if it’s irrelevant. He’s always tried to get people to not fall in love with it too much, because he wanted people to improve upon it. He used to complain that the Lisp and Smalltalk communities thought that these languages were the greatest thing, and didn’t dream of creating anything better. Here he explains why it’s important to think beyond the accomplishments at PARC: It’s insufficient for what’s needed in the future. In fact the research is so far behind that the challenges are getting ahead of what the current best research can deal with.
He said that the PARC stuff is now “news”, and my guess is he means “it’s been turned into news”. He talked about this earlier in the speech. The essential ideas that were developed at PARC have not made it into the computing culture, with the exception of the internet and the GUI. Instead some of the “new” ideas developed there have been turned into superficial “news”.
Those who are interested in thinking about the future will find the slide titled “Simplest Idea” interesting. Kay threw out some concepts that are food for thought.
A statement that Kay closed with is one he’s mentioned before, and it depresses me. He said that when he’s traveled around to universities and met with CS professors, they think what they’ve got “is it”. They think they’re doing real science. All I can do is shake my head in disbelief at that. Even my CS professors understood that what they were teaching was not a science. For the most part what’s passing for CS now is no better than what I had–excepting the few top schools.
Does computer science have a future? I think as before, computing is going to be at the mercy of events, and people’s emotional perceptions of computing’s importance. This is because the vast majority of people don’t understand what computing’s potential is. Today we see it as “current” not “future”. I think that people’s perception of computing will become more remote. Computing will be in devices we use every day, as we can see today, and we will see them as digital devices, where they used to be analog.
“Digital” has become the new medium, not computing. Computing has been overlayed with analog media (text, graphics, audio, video). Kay has said for a while now that this is how it is with new media. When it arises, the generation that’s around doesn’t see its potential. They see it as the “new old thing” and they just use it to optimize what they did before. Computing for now is just the magical substrate that makes “digital” work. The essential element that makes computing powerful and dynamic has been pushed to the side, with a couple of exceptions, as it often has been.
Kay didn’t talk about this in the video, but he and I have discussed this previously. There used to be a common concept in computing, which has come to be called “generative technology”. It used to be a common expectation that digital technology was open ended. You could do with it what you wanted. This idea has been severely damaged by the way that the web has developed. First, commercial PCs, which were designed to be used alone and in LANs, were thrust upon the internet using native code and careless programming, which didn’t anticipate security risks. In addition identities became more loosely managed, and this became a problem as people figured out how to hide behind pseudonyms. Secondly, the web browser wasn’t designed initially as a programmable medium. A scripting language was added to browsers, but it was not made accessible through the browser. The scripting language was not designed too well, either.
Many security catastrophes ensued, each eroding people’s confidence in the safety of the internet, and the image of programming. People who didn’t know how to program, much less how the web worked, felt like they were the victims of those who did know how to program (though this went all the way back to stand-alone PCs as well when mischievous and destructive viruses circulated around in infected executables on BBSes and floppy disks). Programming became seen as a suspicious activity, rather than a creative one. And so as vendors put up defensive barriers to try to compensate for their own flawed designs, it only reinforced the initial design decision that was made when the commercial browser was conceived: that programming would be restricted to people who worked for service providers. Ordinary users should neither expect to gain access to code to modify it, nor want to. It’s gotten to the point we see today where even text formatting on message boards is restricted. HTML tags are restricted or banned altogether in favor of special codes, and you can’t use CSS at all. Programming by the public on websites is usually forbidden, because it’s seen as a security risk. And most web operators don’t see the value of letting people program on their site.
Kay complained that despite the initial idealistic visions of how the internet would develop, it’s still difficult or impossible to send a simulation to somebody on a message board, or through e-mail, to show the framework for a concept. What I think he had envisioned for the internet is a multimedia environment in which people could communicate in all sorts of media: text, graphics, audio, video, and simulations–in real time. Specialized software has made this possible using services you can pay for, but it’s still not something that people can universally access on the internet.
To get to the future we need to look at the world differently
I agree with the sentiment that in order to make the next leaps we need to not accept the world as it appears. We have to get out of what we think is the current accepted reality, what we’ve put up with and gotten used to, and look at what we want the world to be like. We should use that as inspiration for what we do next. One strategy to get that started might be to look at what we find irritating about what currently exists, what we would like to see changed, and think about it from a fundamental, structural perspective. What are some things you’ve tried to do but given up on because when you tried to use the tools or resources available they just weren’t up to the task? What sort of technology (perhaps a kind that doesn’t exist yet) do you think would do the job?
Edit 8-21-2009: A reader left a comment to an old post I wrote on Lisp and Dijkstra, quoting a speech of Dijkstra’s from 10 years ago, titled “Computing Science: Achievements and Challenges”. Towards the end of his speech he bemoaned the fact that CS in academia, and industry in the U.S. had rejected the idea of proving program correctness. He attributed this to an increasing mathematical illiteracy here. I think his analysis of cause and effect is wrong. My own CS professors liked the discipline that proofs of program correctness provided, but they rejected the idea that all programs can and should be proved correct. Dijkstra held the view that CS should only focus on programs that could be proved correct.
I think Dijkstra’s critique of anti-intellectualism in the U.S. is accurate, however, including our aversion to mathematics, and I found that it answered some questions I had about what I wrote above. It also gets to the heart of one of the issues I harp on repeatedly in my blog. His third bullet point is most prescient. Quoting Dijkstra:
The ongoing process of becoming more and more an amathematical society is more an American specialty than anything else. (It is also a tragic accident of history.)
The idea of a formal design discipline is often rejected on account of vague cultural/philosophical condemnations such as “stifling creativity”; this is more pronounced in the Anglo-Saxon world where a romantic vision of “the humanities” in fact idealizes technical incompetence. Another aspect of that same trait is the cult of iterative design.
Industry suffers from the managerial dogma that for the sake of stability and continuity, the company should be independent of the competence of individual employees. Hence industry rejects any methodological proposal that can be viewed as making intellectual demands on its work force. Since in the US the influence of industry is more pervasive than elsewhere, the above dogma hurts American computing science most. The moral of this sad part of the story is that as long as computing science is not allowed to save the computer industry, we had better see to it that the computer industry does not kill computing science. [my emphasis]
I wrote a post a year ago talking about how a Tron sequel was “possible”, given that a Tron “test reel” (video) was shown by some people from Disney at last year’s ComicCon. I’ve been reading updates (there are newer updates here as well) over at Tron 2.0 News, and a Tron movie sequel has definitely been in the works. A couple months after the “test reel” was shown at ComicCon it was announced that Jeff Bridges had signed on, to reprise his role as Kevin Flynn. Bridges said that shooting for the sequel would begin in Spring 2009. Later several more actors were announced, including Bruce Boxleitner, reprising his role as Alan Bradley (no word yet on whether the character “Tron” will be making an appearance). A new generation of main characters was introduced, played by twenty-something actors, one of them being Flynn’s son.
One of the early announcements was that the film was going to be shown in 3D. That’s a hot trend right now.
An interesting story that Tron 2.0 News talked about just recently was that the “test reel” was never supposed to have been shown at ComicCon, or anywhere else in the first place. As of last July, Disney was on the fence about making a sequel. They didn’t want the “test reel” shown to anybody because they didn’t want to raise expectations and then disappoint their audience. It really was just a test to see if the technology could handle the vision, and it was supposed to be “inside Disney only”. It sounds like a few renegade executives at Disney snuck it into ComicCon in hopes of forcing Disney’s hand. According to the story some people at Disney got taken to the woodshed for this. It didn’t take long for them to decide, though, to go ahead with the sequel, probably because of the excitement generated by the “sneak preview” at ComicCon, and the bootleg video of it that was taken there, which went viral on the internet.
Disney created an unreleased test reel for the first “Tron” film back when it was first being developed. It was just a test to show the capabilities of the gels, backlighting, and rotoscoping techniques that were going to be used in the final film. It had a story line which was not in the released film, of a character inside a computer fighting a bad guy and then freeing another character from prison.
Tron 2.0 News revealed a while back that John Lasseter, who came back to Disney once Pixar merged with them, was instrumental in getting the sequel “test reel” made. It sounded like he had to really push for it hard, even working on it semi-secretly with an outside CGI firm. Lasseter was blown away by the original “Tron” movie when he worked at Disney back then. He’s been famously quoted as saying that if Tron hadn’t been made “there would’ve been no Toy Story”. “Toy Story” being Pixar’s first feature film. In the end us Tron fans may have Lasseter to thank for doing what needed to be done to get Disney to make the sequel.
According to the latest news I’ve read, shooting for the sequel just got wrapped up about a week ago in Canada. The post-production CGI work is projected to take another year. The early projection is that the movie will be released during Christmas 2010, but I could easily imagine the release being pushed back to 2011. An exciting tidbit is that IMAX might be looking at making an IMAX version of it. That would be very cool!
The current buzz is Disney is going to release an “updated” teaser trailer for it at this year’s ComicCon. Hopefully it’ll be released on the internet. I’ll be looking for it!
Another piece of news is that Disney is working on a video game to be released with the movie…a different one from “Tron 2.0″…and they’re finally getting the release of the two right this time! A PC/Mac game called “Tron 2.0″ was released several years ago by Disney, which had a sequel story line. An XBox version eventually came out as well, to lackluster reviews. It was supposed to be released with a movie sequel that Disney had planned for release around 2003/04, but the project died. The game was released, oddly, without a movie to go with it.
The plot of the game was that Alan Bradley and Dr. Lora Baines (having gotten married) had a son, Jet, played as a twenty-something in the game. Lora suffered some mysterious death (not shown in the game, just talked about by the characters), but Alan preserved her consciousness in an AI sub-system, called “ma3a”. Alan was still alive and working for Encom. I forget what happened to Flynn. There might’ve been some story line about how he “rezzed” himself inside of Encom’s computers, but he doesn’t show up in the game at all.
Jet is the main character in the game. He gets sucked into Encom’s computer system (through the “laser process”) when a corruption in the system is detected. The theme of virus corruption plays prominently in the game. Jet is immediately considered part of the system corruption by the system’s guards, and so he has to fight the system, while pleading his case that he’s not a threat. He meets up with “ma3a” to try to fight the corruption. A mystery emerges about “ma3a”, but in the process of trying to discover what it is, tragedy strikes. In my opinion this is the reason to play the game. It’s a real interesting plot twist. Jet continues trying to fight the corruption and find his way out of the computer world, with some help from his father when he’s able to make contact with him. Along the way Jet has some powerful flashbacks that reveal his family’s past.
Meanwhile in the real world an evil, thuggish corporation takes over Encom, and the higher ups imprison Alan to get him to give up some technology secrets. Jet discovers what’s been happening in the real world (and Alan discovers what happened to Jet) and uses the computer system to help his father escape captivity. In turn his father is more able to help him from the outside.
I thought the story line that was put into the game was really interesting, and made it worthwhile to play it all the way through. Everything was great…until the ending. It was written like an afterthought. It sucked. Still, I like the game. I’ve been a fan of it for a long time. There’s a good story, some great “eye candy”, and some good “retro” parts that took me back years.
Bruce Boxleitner and Cindy Morgan lent their voices to their game characters, Alan Bradley and “ma3a”. Syd Mead designed a new light cycle, and perhaps some of the other stuff for the game.
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A bit of the plot has been revealed for the movie sequel. This is obviously spoiler material, so you may wish to skip it.
The backstory is that Flynn disappeared into the Encom system years ago and has been missing ever since. In the present day Flynn’s son investigates his father’s disappearance and along the way gets sucked into the Encom system. He finds his father inside the system, and along with a female character they go on a journey that’s much more perilous than the one that Flynn, and Tron and Yori (computer programs written by Alan and Lora) embarked on in the first movie. Obviously Alan Bradley plays a part in the story somehow, but that has not been revealed yet.
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The producers of the sequel say that while it will pay homage to the first film, in parts, they’re creating it as a stand-alone movie. The audience will not need to have seen the first film to understand it. This makes sense as it’ll have been nearly 30 years since the first film was made. It reminds me of the way that the newer Battlestar Galactica series was done. There were a few references to things from the original TV series, though it was disorienting the way they cast it as “the first war”. I always thought it would’ve been better if they had just left the old references out of it and cast the series as a remake. For the most part they created it anew.
For those who are interested there’s an IMDB news page that’s been set up for the movie sequel, which has a lot of news on it, but there’s lots of good “inside scoop” info. on Tron 2.0 News that you won’t find on IMDB.
Edit 7-27-09: Disney has released an updated version of the “test reel” that they showed at Comic-Con 2008, on YouTube. As you might expect it looks and sounds A LOT clearer than the out-of-focus, fuzzy, bootleg version that’s been on the internet for a year! The title they seem to be going with for the movie is “Tron Legacy”. And they say right on it that they expect the movie to be released in 2010. They also mention “IMAX 3D”. Awesome! They did not give permission to embed the video, so follow the “test reel” link above to view it.
Here’s a slideshow of Tron Legacy concept art that was shown at Comic-Con:
“A man must learn on this principle, that he is far removed from the truth” – Democritus
Science is a way of thinking. As Neil deGrasse Tyson has said, “It is a philosophy of discovery.” I reflected recently on what being a scientist is really all about. Good scientists are constantly trying to change their perception of reality. No, they’re not using psychedelic drugs (hopefully). They are rather like art appreciators trying to see what the artist is saying more clearly, except that their method is to guess at what the “artist meant” and then test the guess by going out and using instruments to help them observe the object of the guess more clearly than our native senses can. They share their observations with other scientists so that they can be validated or invalidated by peer review. Think of it as a “sanity check” on what you’ve found. It’s really like reverse-engineering nature if you think about it. I don’t mean to mislead with these analogies. I’m not trying to say that I know there is an “artist” of the world, or an “engineer”. I have my own opinions about that. Science has not found a creator for the world and since I’m talking about science I will respect that here. I’m trying to convey how scientists discover and use different perspectives to try to get at what’s really going on in our world and universe. They try to get beyond what the untrained eye and mind can see.
In our everyday lives we have a saying, “If it’s too good to be true it probably is.” Scientists try to get beyond the obvious, because they know that if it looks obvious it probably isn’t in reality. Scientists are natural skeptics. I’ve heard the saying that the best scientists are people who are always trying to prove themselves wrong. The most succinct description I’ve heard for how scientists come up with guesses (hypotheses) is that they must come up with something that can be “falsified”. In other words, it must be something that can be observed and/or measured so that others can say, “I came up with the same thing” or “No, this is not right. You missed ‘this’, and/or you did not consider ‘that’.” Most hypotheses are proved wrong in some way. There is a constant process of “debugging” our own notions of what’s happening. If a hypothesis cannot be falsified it is not science.
Even if a hypothesis turns out to be valid, scientists try to find the limits of its validity. This is commonly called “error”. It’s a reflection of what scientists think is the confidence level of their result(s), and there is always some error in science. The way I view it is to think of yourself inside a partially opaque sphere. You can see through it some, but the shapes of the objects outside of it look foggy, unclear. Science is the process of wiping away bits of what’s obscuring the image. You create a “window” through which you can see a bit of reality, but not all of it. Part of being a good scientist is understanding where there is a decent level of clarity and what the boundaries of it are. There is always a limit on it. Even scientific instruments have the potential to introduce error into observations, and scientists must be aware of these limitations. Science is about the process of trying to expand that “window” more and more, sometimes in small steps, sometimes big ones, to see reality more clearly.
Recently I’ve begun to wonder if our schools are teaching science correctly. A week or two ago I began having a debate with a newspaper columnist by the name of Mike Ellis at the Daily Camera, Boulder, Colorado’s daily newspaper. We’d chat in various comment sections on the Daily Camera web site whenever the issue of global warming came up. At the time Ellis asserted that CO2 levels had remained very consistent for thousands of years, and had only recently begun to change to levels not seen for a very, very long time (hundreds of thousands of years, I believe he said). I’ve also seen him say that prior to the Industrial Revolution climate change happened because of changes in Earth’s orbit. One could throw in continental drift as well, in all seriousness. He said that the CO2 levels correlate very well with the trend we’ve seen of rising temperature since the Industrial Revolution, and that CO2 is entirely responsible for this. I had been paying attention to the debate on this issue off and on for several years. From what I’ve heard from the proponents of the theory of anthropogenic global warming (AGW–climatic warming caused by human activity), even they don’t make such a claim. They would say that CO2 is a significant contributor to the rise in temperature, but not that it’s responsible for all of it. I asked over at WattsUpWithThat.com about this argument he made and they were struck by it. One commenter said, “Not even the IPCC makes that claim.” What bugged me is Ellis made such a hard and fast scientific claim based on a correlation he said he saw in the data. Correlations in data can be deceiving. They can make you think you’ve found a relationship between phenomena when you haven’t. The question is what is the relationship, if any? It must be tested scientifically by observation before the relationship can be legitimately claimed to be realistic. It turns out it has been tested, but the scientific conclusion is unclear to me now. For now I’m taking the position that it’s not settled, at least in my own mind. I’ll need to look into this further.
I came upon an article in the opinion section of the Daily Camera web site titled “Global warming whodunit”, written by Ellis. He is a blogger and his credit says that he studies climate change as a hobby. Okay, so he’s not a professional scientist. I read through most of the article and thought he used an interesting literary framework for making the argument. He puts CO2 “on trial”. However, when I got to the last three paragraphs I thought, “Wait a minute. There’s something wrong here.” Ellis asserts:
Still not convinced? I loaded as much publicly available data as I could into Microsoft Excel. The result? An 88 percent correlation between global temperatures and atmospheric CO2 concentration. The temperature correlation peaks about 12 years after the CO2 stimulus, and falls off slowly over decades. This is huge evidence that CO2 drives temperatures, and that the oil we burn today causes the most warming 10 to 15 years from now. [my emphasis]
Notice his use of the term “evidence”. I thought surely he had some scientific source to back up what is unmistakably a scientific claim. It sounded kind of like the arguments we had earlier, but this time he added this 10-15 year delay factor. I and others asked Ellis in the comments section (I’m “mmille10″ in the comments) to show how he came up with this conclusion. He posted the URL to a blog posting where he asserted the same thing, showing charts he had produced in Excel, created from combining two data sets (for CO2 and global average temperature) and shifting the temperature data set 12 years to show the correlation in higher relief. Take a look at them. The correlation he talks about looks quite beautiful…and obvious. In his article he talked about other correlations he tried with other purported causes, such as sun spots, but they were not as good of a fit as CO2 to temperature. The implication he leaves the reader with is that CO2 is most definitely the “culprit”.
Ellis admitted in the comments that he had no scientific source to back up his claim that there was this 10-15 year relationship between CO2 and temperature (though he did reference scientific information which he said proved that CO2 causes global warming), and that he had seen nothing that contradicted his “results” (hah!), but that it didn’t matter because it was an opinion column. That’s just a cop out. There’s an old saying I’ve heard in journalism: “We have the right to our own opinions, but we do not have the right to our own facts.” Ellis used his own statistical analysis, had the audacity to dress it up as a scientific claim, and then used it as fact in his argument. This is pseudo-science at its most brazen. It’s not even that hard to figure out that he’s doing it. His whole column hinges on this claim. He doesn’t even give the old saw of, “Most of the world’s scientists believe this is true.” He could’ve used that instead and it would’ve had more legitimacy than this red herring.
Ellis’s whole point is about the correlation that matches up so well. He begs his readers, “What else could it be?” (I’m paraphrasing) Well that’s the thing. It could be something else. The only way to eliminate or diminish that possibility is to test the relationship out in nature. I’ll ignore for the moment that Ellis said this was “evidence”, which it most certainly is not. At best it is a hypothesis, but is it falsifiable?
Leaving his pseudo-science aside, I think where Ellis made an error is he assumes that there can only be one or two major factors that affect temperature. A thought I had was maybe one of the data sets that he threw out, due to the fact that it doesn’t correlate well by itself against temperature, might actually correlate well if he put in other factors and events which climatologists also think affect temperature. Just doing a simple-minded analysis is not good enough for science.
I respect Ellis’s right to his opinions, but I think it goes beyond the pale for even an opinion columnist to mislead the reading public using the platform of a newspaper of record. I haven’t read him extensively so I can’t speak to the quality of his other work. I’m talking about this one article, but due to the platform he has I found his article and his ignorance of the scientific method offensive. The Daily Camera should try for better quality than this in a city that has three major science labs (NOAA, NIST, and NCAR) and one of the premiere science and engineering universities in the country (C.U. Boulder). Publishing this drivel was an insult to our intelligence.
I kind of understand what’s going on here. Newspapers are really hurting right now financially. The Rocky Mountain News, a paper that’s been around for more than a century, went out of business a few months ago. Newspapers are desperate to find avenues to seem more relevant in order to attract readers. In this case the Camera has brought in a blogger. It hasn’t helped the quality of what they publish. I can tell you that much.
On the use of computers in science
I’m including some material here on science education and computers, because this has implications for what I talk about above. Here’s a speech by Alan Kay I’ve cited in a previous post. It’s called What is Squeak?. Incidentally, Kay graduated with a B.A. in molecular biology and mathematics from the University of Colorado, back in the 1960s I believe. He received his masters and doctorate in computer science from the University of Utah. In addition to being a pioneer in computing, he’s done a lot of pioneering work in developing math and science education principles, using computers for childhood education, outside of academia.
Despite the title what he talks about is teaching real mathematics and real science, using computers, but in a very specific way.
If you want to skip to the part where he discusses science move the slider to 42:00.
He gave his talk using a “slide show” (he was actually using the Squeak system to do it), but unfortunately the camera that recorded this was stationary. So you can see him speak, but you can’t see the slides, demos, and videos he described. If you want to see this stuff, which he’s used often in other presentations, I’d suggest looking Kay up on Google Video. They have other presentations he’s done where at least some of this material is shown. The reason I picked this video is he really focuses in on how to teach science using computers. He does talk about math and computers as well, and what he had to say about “real math” is valuable, but I don’t think this part was as clear, since he references multimedia quite a bit for it.
One thing I would like readers to pay attention to in this video is the section where he describes the appropriate way to approach teaching scientific principles to children using computers, which is to create simulations. This is important, because doing it backwards is pseudo-science. Quite a bit of the Q&A period after his talk is on this subject. He said:
You can’t do science on a computer or with a book, because [with] the computer–like a book, like a movie–you can make up anything. We can have an inverse cube law of gravity on here, and the computer doesn’t care. No language system that we have knows what reality is like. That’s why we have to go out and negotiate with reality by doing experiments.
I couldn’t hear the question exactly, but I think a questioner asked whether a simulation that Kay had up on screen was pseudo-science. Kay said, “This is a model. If you present it to the kids as fact, it is pseudo-science.” The idea being that a model is something that the kids should construct after having experienced the actual phenomenon in order to explore what they have just observed. By the way, scientists who are using computers properly to create simulations use the same process. By going through it students and scientists can learn something more: the mechanics of more about what they have observed, and come up with insights that lead to new questions. Kids also get the added benefit of learning some mathematical principles in the process. He makes a big point about not taking a pre-existing model and just showing it to kids as if it was fact, because then you lose what science is about as a thought process.
After watching this I began wondering about how computers are used by professional scientists. For example, meteorologists use computer models as part of their weather prediction process. I don’t know for sure but I feel fairly certain that they didn’t create these models themselves. They may alter parameters that go into the model. I don’t know enough about meteorological practice to say that for sure. So are they participating in pseudo-science? I’d say one difference is meteorologists do not just say, “The computer models says X, so that’s our prediction.” They actually use several prediction models at once, because there’s not just one “right” model–they come up with different results. From what I’ve heard about this process they use them to set boundaries for what could happen, within a certain boundary of error (I’m doing some hand waving here). One question I have is do these models have an error rating? It seems to me this could theoretically be established with time, comparing a long series of model predictions with what actually happened. The question is can the error be measured?
Meteorologists use their own skills, gathering data like temperature, humidity, barometric pressure, etc., in addition to looking at the models to make a prediction. Even so, due to the chaotic nature of the atmosphere, the only weather prediction you can have some confidence in is the one for the next day.
I don’t know for sure but I feel fairly certain that computers are used by NASA to try to determine the flight paths of the spacecraft they launch, taking gravity wells into consideration. Even there the science is not exact, which I think is proven out by the number of failed landings that NASA has had on Mars. There have also been a number of times when NASA has had to make unplanned corrections to the flight path of a spacecraft in flight, which had nothing to do with equipment malfunctions.
What about using a computer model to demonstrate what has been found scientifically? I think if the computer is just used to display scientifically gathered data (it could be in any form: a chart, an animation, etc.), that’s different from running a model that’s actually computing its way through a process (a simulation) and saying, “This is reality.” Even if they are used in prediction, I can tell you from experience that there is some error involved, as is true of any scientific instrument. Having said this, I think if a computer is used in a scientific presentation of observed data there should be accompanying materials which demonstrate the error in the observations. People have a perception that computers are precise, exacting, and therefor reveal absolute truth. It can be a challenge to try to convey error through a demonstration on a computer.
Bringing this full circle, one might think that Mike Ellis in his article did what I just described, using a computer to display data. The difference is he drew unwarranted conclusions from the “data display” and parlayed it as “huge evidence”. It would’ve been scientifically valid for Ellis to point out that a data correlation exists between CO2 and temperature. That’s interesting. It could be used as a hypothesis, which could be used as motivation to do scientific research on it. The point where he stepped into pseudo-science was when he said this correlation showed a strong relationship existed between the two. He did tried to do “science on a computer”, as Kay would put it.
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”. 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 (video) by The Jacksons (the Jackson brothers changed their name in 1975) off of their Destiny album, “Don’t Stop ‘Til You Get Enough” 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”, 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). Michael even got in on the fun by making his own cute parody of “Bad”, called Badder (video), in his movie Moonwalker.
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.
- “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.
Edit 7-8-2009: I watched portions of the memorial service for Michael Jackson last night. It was pretty good. I really liked Jermaine Jackson’s rendition of “Smile” written by Charlie Chaplin. It was heartfelt. Brook Shields said it was Michael’s favorite song of all. Chaplin wrote this music for his 1936 movie Modern Times.
Hearing Jermaine sing it last night took me back to the ending of the movie Chaplin starring Robert Downey Jr. The song plays as the movie describes what happened to the people portrayed in the movie. There’s a piece written by John Barry (he wrote the score for the movie) that plays just as the credits start to roll that’s really beautiful as well!
I’ve done a little research into “Smile”. It sounds like it originally didn’t have a name. Chaplin just used it in his movie without a credit. Lyrics were added to it in 1954 by John Turner and Geoffrey Parsons and it was given the name “Smile”. It was obviously rearranged as well. It looks like Nat King Cole was the first to sing it. From what I’ve heard, Jermaine got the lyrics a bit mixed up, but that’s okay. They were in mourning, so who cares. Here’s Michael Jackson’s rendition of “Smile”.
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!”
“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 The conventional wisdom among mathematicians is 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.
(Update 7-7-2009: I modified the two paragraphs below because I realized I was making some pedagogical points that were perhaps inappropriate. What I wanted to emphasize in the first paragraph was the importance of criticism in the education of math students. In the second, I did not want to diminish the importance of precision. It’s just a matter of where it’s applied.)
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, as does the concept of relationships between things. Depending on where students are pedagogically, one subject or both might be good to emphasize. This implies that there needs to be room for criticism and correction of flaws in thinking, 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 (though precision within proofs is essential), 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.
They did not give permission to embed the video, so follow the “test reel” link above to view it.
