# Coming to grips with a frustrating truth

I’d heard about Mensa many years ago, and for many years I was kind of interested in it. Every once in a while I’d see “intelligence quizzes,” which were supposed to get one interested in the group (it worked). Mensa requires an IQ test, and a minimum score, to join. I looked at some samples of the discussions members had on topics related to societal issues, though, and it all looked pretty mundane in terms of the thought processes exhibited. It wasn’t the intelligent discussion I expected, which was surprising.

I came upon the following video by Stefan Molyneux recently (it was made in 2012), and it seems to explain what I’ve been seeing generally for more than ten years in the same sort of societal discussions (though I can’t say what the IQ level of the participants was). I’ve frequently run into people who seem to have some proactive mental ability, and yet what they come out with when thinking about the society they live in is way below par. I see it on Quora all the time. Most of the answers to political questions are the dregs of the site–really bad. I’ve had no explanation for this inconsistency, other than perhaps certain people with less than stellar intelligence are drawn to the political questions, until I saw this analysis. Molyneux said it’s the result of a kind of cognitive abuse.

The reason I’m bothering with this at all is seeing what he described play out has bothered me for many years, though I’ve assumed it’s due to popular ignorance. It’s part of what’s driven my desire to get into education, though now I feel I have to be more humble about whether that’s really a good answer to this.

I found his rational explanation for this confusing. I’ve needed to listen to it a few times, and take notes. I’ll attempt to summarize.

This is a generalization, but the point is to apply it to people who are more intelligent than average, but who refuse to allow inquiry into their beliefs about society:

Children who are in the “gifted” categories of IQ are told a certain moral message when they’re young, about how they are to behave. However, when those same children try to apply that morality to their parents, and the adults around them–in other words, demand consistency–they are punished, humiliated, and/or shamed for it. They eventually figure out that morality has been used to control them, not teach them. (This gave me the thought, based on other material by Molyneux, that perhaps this is one reason atheism is so prevalent among this IQ category. Rather than morality being a tool to uplift people to a higher state of being, it’s seen purely as a cynical means of control, which they understandably reject.) As soon as they try to treat morality as morality, in other words, as a universal set of rules by which everyone in their society is governed, they are attacked as immoral, uncaring, brutish, wrong, and are slandered. This is traumatic to a young mind trying to make sense of their world.

The contradiction they encounter is they’re told they’re evil for not following these rules as a child, and then they’re told they’re evil for attempting to apply those same rules to other adults when they grow up. They are punished for attempting to tell the truth, even though they were told when they were young that telling the truth is a virtue (and that lying is evil). If they attempt to tell the truth about their society, they are punished by the same adults who cared for them.

The image he paints is, to me, analogous to Pavlov’s dog, where all of its attempts to follow its instincts in a productive way are punished, leading to it quivering in a corner, confused, afraid, and despondent, unable to respond at all in the presence of food. In this case, all attempts to apply a moral code consistently are punished, leading to a disabled sense of social morality, and a rejection of inquiry into this battered belief system, in an attempt to protect the wound.

Molyneux comes to an ugly truth of this situation. This inability to question one’s societal beliefs is the product of a master-slave society: In slave societies, rules are applied to the slaves that are not applied to the masters. They operate by a different set of rules. Morality that is dispensed to the ignorant is used as a cynical cover for control. Those subjected to this inconsistent reality deal with it by trying their best to not look at it. Instead of pushing through the shaming, and demanding consistency, risking the rejection that entails from the society they grew up in, they blindly accept the master-slave dichotomy, and say, “That’s just the way it is.” Those who question it are attacked by these same people, because engaging in that leads them back to the pain they suffered when they did that themselves.

He also addressed a psychological phenomenon called “projection.” He said,

… they must take the horrors of their own soul and project them upon the naive and honest questioner. Every term that is used as an attack against you for engaging in these conversations is an apt and deeply known description of their own souls, or what’s left of them.

I also found this summary video helpful in understanding motivated reasoning, why we’re wired to reject rational thought, and evidence, and to prefer beliefs that are inculcated and reinforced through our social groups, and their authority figures.

Molyneux sort of addressed the evolutionary reasons for it, but I have liked Jonathan Haidt’s explanation for it better, since he gets into the group dynamic of shared beliefs, and justifies them, saying that they played some role in the survival of our species, up until recently: Those who had this group-belief trait lived to reproduce. Those who did not died out. That isn’t to say that it’s essential to our survival today, but that it deserves our respectful treatment, since it was a trait that got what we are here.

What’s also interesting is that Molyneux relates the trait of motivated reasoning to the practice of science, quoting Max Planck (I’ve heard scientists talk about this) in saying that science really only advances when the older generation of scientists dies. This creates room for other ideas, supported by evidence, and critical analysis, to flourish, perhaps setting a new paradigm. If so, it becomes a new sort of orthodoxy in a scientific discipline for another generation or so, until it (the orthodoxy), too, dies away with the scientists who came up with it, repeating the cycle.

Related posts:

Psychic elephants and evolutionary psychology

“What a waste it is to lose one’s mind”

The dangerous brew of politics, religion, technology, and the good name of science

# A word of advice before you get into SICP

If you’ve been reading along with my posts on exercises from Structure and Interpretation of Computer Programs” (SICP), this is going to come pretty late. The book is a math-heavy text. It expects you to know the math it presents already, so for someone like me who got a typical non-math approach to math in school, it seems abrupt, but not stifling. If you’re wondering what I mean by “non-math approach,” I talked about it in “The beauty of mathematics denied,” James Lockhart also talked about it in “A Mathematician’s Lament.”

I’ve been reading a book called, Mathematics in 10 Lessons: The Grand Tour,” by Jerry King (I referred to another book by King in “The beauty of mathematics denied”), and it’s helped me better  understand the math presented in SICP. I could recommend this book, but I’m sure it’s not the only one that would suffice. As I’ve gone through King’s book, I’ve had some complaints about it. He tried to write it for people with little to no math background, but I think he only did an “okay” job with that. I think it’s possible there’s another book out there that does a better job at accomplishing the same goal.

What I recommend is getting a book that helps you understand math from a mathematician’s perspective before getting into SICP, since the typical math education a lot of students get doesn’t quite get you up to its level. It’s not essential, as I’ve been able to get some ways through SICP without this background, but I think having it would have helped make going through this book a little easier.

A couple questions have bugged me for ages about rational numbers:

1. Why is it that we invert and multiply when dividing two fractions?
2. Why is it that when we solve a proportion, we multiply two elements, and then divide by a third?

For example, with a proportion like:

$\frac {3} {180} = \frac {2} {x}$

the method I was taught was to cross-multiply the two numbers that are diagonally across from each other (2 and 180), and divide by the number opposite x (3). We solve for x with $x = \frac {2 \times 180} {3}$, but why?

These things weren’t explained. We were just told, “When you have this situation, do X.” It works. It produces what we’re after (which school “math” classes see as the point), but once I got into college, I talked with a fellow student who had a math minor, and he told me while he was taking Numerical Analysis that they explained this sort of stuff with proofs. I thought, “Gosh, you can prove this stuff?” Yeah, you can.

I’ve picked up a book that I’d started reading several years ago, “Mathematics in 10 Lessons,” by Jerry King, and he answers Question 1 directly, and Question 2 indirectly. I figured I would give proofs for both here, since I haven’t found mathematical explanations for this stuff in web searches.

I normally don’t like explaining stuff like this, because I feel like I’m spoiling the experience of discovery, but I found as I tried to answer these questions myself that I needed a lot of help (from King). My math-fu is pretty weak, and I imagine it is for many others who had a similar educational experience.

I’m going to answer Question 2 first.

The first thing he lays out in the section on rational numbers is the following definition:

$\frac {m} {n} = \frac {p} {q} \Leftrightarrow mq = np, where\: n \neq 0,\, q \neq 0$

I guess I should explain the double-arrow symbol I’m using (and the right-arrow symbol I’ll use below). It means “implies,” but in this case, with the double-arrow, both expressions imply each other. It’s saying “if X is true, then Y is also true. And if Y is true, then X is also true.” (The right-arrow I use below just means “If X is true, then Y is also true.”)

In this case, if you have two equal fractions, then the product equality in the second expression holds. And if the product equality holds, then the equality for the terms in fraction form holds as well.

When I first saw this, I thought, “Wait a minute. Doesn’t this need a proof?”

Well, it turns out, it’s easy enough to prove it.

The first thing we need to understand is that you can do anything to one side of an equation so long as you do the same thing to the other side.

We can take the equal fractions and multiply them by the product of their denominators:

$nq (\frac {m} {n}) = (\frac {p} {q}) nq$

by cancelling like terms, we get:

${mq = np}$

This explains Question 2, because if we take the proportion I started out with, and translate it into this equality between products, we get:

${3x = 2 \times 180}$

To solve for x, we get:

$x = \frac {2 \times 180} {3}$

which is what we’re taught, but now you know the why of it. It turns out that you don’t actually work with the quantities in the proportion as fractions. The fractional form is just used to relate the quantities to each other, metaphorically. The way you solve for x uses the form of the product equality relationship.

To answer Question 1, we have to establish a couple other things.

The first is the concept of the multiplicative inverse.

For every x (with x ≠ 0), there’s a unique v such that xv = 1, which means that $v = \frac {1} {x}$.

From that, we can say:

$xv = \frac {x} {1} \frac {1} {x} = \frac {x} {x} = 1$

From this, we can say that the inverse of x is unique to x.

King goes forward with another proof, which will lead us to answering Question 1:

Theorem 1:

$r = \frac {a} {b} \Rightarrow a = br, where\; b \neq 0$

Proof:

$b (\frac {a} {b}) = rb$

by cancelling like terms, we get:

${a = br}$

(It’s also true that $a = br \Rightarrow r = \frac {a} {b}$, but I won’t get into that here.)

Now onto Theorem 2:

$r = \frac {\frac {m} {n}} {\frac {p} {q}}, where\; n \neq 0, p \neq 0, q \neq 0$

By Theorem 1, we can say:

$\frac {m} {n} = r (\frac {p} {q})$

Then,

$\frac {m} {n} \frac {q} {p} = r (\frac {p} {q}) \frac {q} {p}$

By cancelling like terms, we get:

$\frac {m} {n} \frac {q} {p} = (r) 1$

$r = \frac {m} {n} \frac {q} {p}$

Therefor,

$\frac {\frac {m} {n}} {\frac {p} {q}} = \frac {m} {n} \frac {q} {p}$

And there you have it. This is why we invert and multiply when dividing fractions.

Edit 1/11/2018: King says a bit later in the book that by what I’ve outlined with the above definition, talking about how if there’s an equality between fractions, there’s also an equality between a product of their terms, and by Theorem 1, it is mathematically correct to say that division is just a restatement of multiplication. Interesting! This does not mean that you get equal results between division and multiplication: $\frac {a} {b} \neq ab$, except when b equals 1 or -1. It means that there’s a relationship between products and rational numbers.

Some may ask, since the mathematical logic for these truths is fairly simple, from an algebraic perspective, why don’t math classes teach this? Well, it’s because they’re not really teaching math…

Note for commenters:

WordPress supports LaTeX. That’s how I’ve been able to publish these mathematical expressions. I’ve tested it out, and LaTeX formatting works in the comments as well. You can read up on how to format LaTeX expressions at LaTeX — Support — WordPress. You can read up on what LaTeX formatting commands to use at Mathematical expressions — ShareLaTeX under “Further Reading”.

HTML codes also work in the comments. If you want to use HTML for math expressions, just a note, you will need to use specific codes for ‘<‘ and ‘>’. I’ve seen cases in the past where people have tried using them “naked” in comments, and WordPress interprets them as HTML tags, not how they were intended. You can read up on math HTML character codes here and here. You can read up on formatting fractions in HTML here.

Related post: The beauty of mathematics denied

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

# SICP: Chapter 3 and exercises 3.59, 3.60, and 3.62

### Prologue

SICP reaches a point, in Chapter 3, where for significant parts of it you’re not doing any coding. It has exercises, but they’re all about thinking about the concepts, not doing anything with a computer. It has you do substitutions to see what expressions result. It has you make diagrams that focus in on particular systemic aspects of processes. It also gets into operational models, talking about simulating logic gates, how concurrent processing can work (expressed in hypothetical Scheme code). It’s all conceptual. Some of it was good, I thought. The practice of doing substitutions manually helps you really get what your Scheme functions are doing, rather than guessing. The rest didn’t feel that engaging. One could be forgiven for thinking that the book is getting dry at this point.

It gets into some coding again in Section 3.3, where it covers building data structures. It gets more interesting with an architecture called “streams” in Section 3.5.

One thing I will note is that the only way I was able to get the code in Section 3.5 to work in Racket was to go into “Lazy Scheme.” I don’t remember what language setting I used for the prior chapters, maybe R5RS, or “Pretty Big.” Lazy Scheme does lazy evaluation on Scheme code. One can be tempted to think that this makes using the supporting structures for streams covered in this section pointless, because the underlying language is doing the delayed evaluation that this section implements in code. Anyway, Lazy Scheme doesn’t interfere with anything in this section. It all works. It just makes the underlying structure for streams redundant. For the sake of familiarity with the code this section discusses (which I think helps in preserving one’s sanity), I think it’s best to play along and use its code.

Another thing I’ll note is this section makes extensive use of knowledge derived from calculus. Some other parts of this book do that, too, but it’s emphasized here. It helps to have that background.

I reached a stopping point in SICP, here, 5 years ago, because of a few things. One was I became inspired to pursue a history project on the research and development that led to the computer technology we use today. Another is I’d had a conversation with Alan Kay that inspired me to look more deeply at the STEPS project at Viewpoints Research, and try to make something of my own out of that. The third was Exercise 3.61 in SICP. It was a problem that really stumped me. So I gave up, and looked up an answer for it on the internet, in a vain attempt to help me understand it. The answer didn’t help me. It worked when I tried the code, but I found it too confusing to understand why it produced correct results. The experience was really disappointing, and disheartening. Looking it up was a mistake. I wished that I could forget I’d seen the answer, so I could go back to working on trying to figure it out, but I couldn’t. I’d seen it. I worked on a few more exercises after that, but then I dropped SICP. I continued working on my history research, and I got into exploring some fundamental computing concepts on processors, language parsing, and the value of understanding a processor as a computing/programming model.

I tried an idea that Kay told me about years earlier, of taking something big, studying it, and trying to improve on it. That took me in some interesting directions, but I hit a wall in my skill, which I’m now trying to get around. I figured I’d continue where I left off in SICP. One way this diversion helped me is I basically forgot the answers for the stuff I did. So, I was able to come back to the problem, using a clean slate, almost fresh. I had some faded memories of it, which didn’t help. I just had to say to myself “forget it,” and focus on the math, and the streams architecture. That’s what finally helped me solve 3.60, which then made 3.61 straightforward. That was amazing.

### A note about Exercise 3.59

It was a bit difficult to know at first why the streams (cosine-series and sine-series) were coming out the way they were for this exercise. The cosine-series is what’s called an even series, because its powers are even (0, 2, 4, etc.). The sine-series is what’s called an odd series, because its powers are odd (1, 3, 5, etc.). However, when you’re processing the streams, they just compute a general model of series, with all of the terms, regardless of whether the series you’re processing has values in each of the terms or not. So, cosine-series comes out (starting at position 0) as: [1, 0, -1/2, 0, 1/24, …], since the stream is computing a0x0 + a1x1 + a2x2 …, where ai is each term’s coefficient, and some of the terms are negative, in this case. The coefficients of the terms that don’t apply to the series come out as 0. With sine-series, it comes out (starting at position 0) as: [0, 1, 0, -1/6, 0, 1/120, …].

What’s really interesting is that exercises 3.59, 3.61, and 3.62 are pretty straightforward. Like with some of the prior exercises, all you have to do is translate the math into stream terms (and it’s a pretty direct translation from one to the other), and it works! You’re programming in mathland! I discovered this in the earlier exercises in this section, and it amazed me how expressive this is. I could pretty much write code as if I was writing out the math. I could think in terms of the math, not so much the logistics of implementing computational logic to make the math work. At the same time, this felt disconcerting to me, because when things went wrong, I wanted to know why, computationally, and I found that working with streams, it was difficult to conceptualize what was going on. I felt as though I was just supposed to trust that the math I expressed worked, just as it should. I realize now that’s what I should have done. It was starting to feel like I was playing with magic. I didn’t like that. It was difficult for me to trust that the math was actually working, and if it wasn’t, that it was because I was either not understanding the math, and/or not understanding the streams architecture, not because there was something malfunctioning underneath it all. I really wrestled with that, and I think it was for the good, because now that I can see how elegant it all is, it looks so beautiful!

### Exercise 3.60

This exercise gave me a lot of headaches. When I first worked on it 5 years ago, I kind of got correct results with what I wrote, but not quite. I ended up looking up someone else’s solution to it, which worked. It was kind of close to what I had. I finally figured out what I did wrong when I worked on it again recently: I needed to research how to multiply power series, but in a computationally efficient manner. It turns out you need to use a method called the Cauchy product, but there’s a twist, because of the way the streams architecture works. A lot of math sources I looked up use the Cauchy product method, anyway (including a source that covers power series multiplication that I cite below), but the reason it needs to be used is it automatically collects all like terms as each term of the product is produced. The problem you need to work around is that you can’t go backwards through a stream, except by using stream-ref and indexes, and I’ve gotten the sense by going through these exercises that when it comes to doing math problems, you’re generally not supposed to be doing that, though there’s an example later in SICP where they talk about a method Euler devised for accelerating computation of power series where they use stream-ref to go backwards and forwards inside a stream. I think that’s an exception.

Here are a couple sources that I found helpful when trying to work this out:

Formal Power Series, from Wikipedia. Pay particular attention to the section on “Operations on Formal Power Series.” It gives succinct descriptions on multiplying power series, inverting them (though I’d only pay attention to the mathematical expression of this in Exercise 3.61), and dividing them (which you’ll need for Exercise 3.62).

Edit 6/4/2018: I originally had a video here, which I thought gave a good illustration of what the Cauchy product accomplishes. It also provided a nice visual aide that pointed me toward a solution to this problem in SICP. Unfortunately, the video has disappeared from YouTube. So, I’ll substitute a presentation of the Cauchy product that I used as a tool for figuring out how to do this exercise. This will not give you the answer for how to do this exercise, but it’s on the way to the answer I got.

Let A and B be power series that we’re going to multiply. We will use ai to represent the coefficients for A, and bi to represent the coefficients for B:

A = a0x0 + a1x1 + a2x2 + …

B = b0x0 + b1x1 + b2x2 + …

Multiplying these series creates a new series, C, made by creating a sum of products from terms in A and B:

A x B = C

C0 = a0x0b0x0

C1 = a1x1b0x0 + a0x0b1x1

C2 = a2x2b0x0 + a1x1b1x1 + a0x0b2x2

C3 = a3x3b0x0 + a2x2b1x1 + a1x1b2x2 + a0x0b3x3

C4 = …

A x B = C0 + C1 + C2 + C3 + C4 + …

You’ll note that, with the exception of the very first term, as we progress to computing each term, we start with the ith term in series A, and go down to the 0th term, but with series B, we start with the 0th term, and go upward to the ith term.

To reiterate, you can’t use the stream architecture in SICP to compute the product for this exercise using the exact method I’ve outlined above (when I thought about trying to do that, it get extremely convoluted, and it’s not worth pursuing), but there is a way to compute the product series that allows you to go through both streams from left to right.

What helped me find a succinct way to implement mul-series was to just focus on the coefficients:

a0b0
a1b0 + a0b1
a2b0 + a1b1 + a0b2
a3b0 + a2b1 + a1b2 + a0b3

A couple hints I’ll give are:

• There is a way to do the Cauchy product without using mutable state in variables, nor is it necessary to do anything particularly elaborate. You can do it just using the stream architecture.
• Think about how addition is commutative, as you look at the above pattern of computation.

The solution is a little counterintuitive, but once you find it, it’s pretty neat.

It is crucial that you get the solution for this exercise right, though, because the next two exercises (3.61 and 3.62) will give you no end of headaches if you don’t. Exercise 3.61 builds on what you create for this one, and 3.62 builds on what you create for 3.61.

Exercise 3.60 says you can try out mul-series using sin(x) and cos(x), squaring both, and then adding the product series together. This should give you a result of 1. How is “1” represented in streams, though? Well, it makes sense that it will be in the constant-term position (the zeroth position) in the stream. That’s where a scalar value would be in a power series.

There is a related concept to working with power series called a unit series. A unit series is just a list of the coefficients in a power series. If you’ve done the previous exercises where SICP says you’re working with power series, this is what you’re really working with (though SICP doesn’t mention this). It’s why in Exercise 3.61 SICP has you writing a function called “invert-unit-series”.

The unit series equivalent for the scalar value 1 is [1, 0, 0, 0, 0, …].

### A note about Exercise 3.62

The exercise talks about using your div-series function to compute tan-series. Here was a good source for finding out how to do that:

Trigonometric Functions

The unit series for tan-series should come out as: [0, 1, 0, 1/3, 0, 2/15, 0, 17/315, …]

# The beauty of mathematics denied, revisited: Lockhart’s Lament

Vladislav Zorov, a Quora user, brought this to my attention. It is a worthy follow-up to Jerry King’s “The Art of Mathematics,” called Lockhart’s Lament. Lockhart really fleshes out what King was talking about. Both are worth your time. Lockhart’s lament reminds me a lot of a post I wrote, called The challenge of trying to get a real science of computing in our schools. I talked about an episode of South Park to illustrate this challenge, where a wrestling teacher is confronted with a pop culture in wrestling that’s “not real wrestling” (ie. WWE), as an illustration of the challenge that computer scientists have in trying to get “the real thing” into school curricula. The wrestling teacher is continually frustrated that no one understands what real wrestling is, from the kids who are taking his class, to the people in the community, to the administrators in his school. There is a “the inmates have taken over the asylum” feeling to all of this, where “the real thing” has been pushed to the margins, and the pop culture has taken over. The people who see “the real thing,” and value it are on the outside, looking in. Hardly anybody on the inside can understand what they’re complaining about, but some of them are most worried that nothing they’re doing seems to be enough to make a big dent in improving the lot of their students. Quite the conundrum. It looks idiotic, but it’s best not to dismiss it as such, because the health and welfare of our society is at stake.

Lockhart’s Lament — The Sequel is also worth a look, as it talks about critics of Lockhart’s argument.

Two issues that come to mind from Lockhart’s lament (and the “sequel”) is it seems like since we don’t have a better term for what’s called “math” in school, it’s difficult for a lot of people to disambiguate mathematics from the benefits that a relative few students ultimately derive from “math.” I think that’s what the critics hang their hat on: Even though they’ll acknowledge that what’s taught in school is not what Lockhart wishes it was, it does have some benefits for “students” (though I’d argue it’s relatively few of them), and this can be demonstrated, because we see every day that some number of students who take “math” go on to productive careers that use that skill. So, they will say, it can’t be said that what’s taught in school is worthless. Something of value is being transmitted. Though, I would encourage people to take a look at the backlash against requiring “math” in high school and college as a counterpoint to that notion.

Secondly, I think Lockhart’s critics have a good point in saying that it is physically impossible for the current school system, with the scale it has to accommodate, to do what he’s talking about. Maybe a handful of schools would be capable of doing it, by finding knowledgeable staff, and offering attractive salaries. I think Lockhart understands that. His point, that doesn’t seem to get through to his critics, is, “Look. What’s being taught in schools is not math, anyway! So, it’s not as if anyone would be missing out more than they are already.” I think that’s the sticking point between him and his critics. They think that if “math” is eliminated, and only real math is taught in a handful of schools (the capacity of the available talent), that a lot of otherwise talented students would be missing out on promising careers, which they could benefit from using “math.”

An implicit point that Lockhart is probably making is that real math has a hard time getting a foothold in the education system, because “math” has such a comprehensive lock on it. If someone offered to teach real math in our school system, they would be rejected, because their method of teaching would be so outside the established curriculum. That’s something his critics should think about. Something is seriously wrong with a system when “the real thing” doesn’t fit into it well, and is barred because of that.

I’ve talked along similar lines with others, and a persistent critic on this topic, who is a parent of children who are going through school, has told me something similar to a criticism Lockhart anticipated. It goes something like, “Not everyone is capable of doing what you’re talking about. They need to obtain certain basic skills, or else they will not be served well by the education they receive. Schools should just focus on that.” I understand this concern. What people who think about this worry about is that in our very competitive knowledge economy, people want assurances that their children will be able to make it. They don’t feel comfortable with an “airy-fairy, let’s be creative!” account of what they see as an essential skill. That’s leaving too much to chance. However, a persistent complaint I used to hear from employers (I assume this is still the case) is that they want people who can think creatively out of the box, and they don’t see enough of that in candidates. This is precisely what Lockhart is talking about (he doesn’t mention employers, though it’s the same concern, coming from a different angle). The only way we know of to cultivate creative thinkers is to get people in the practice of doing what’s necessary to be creative, and no one can give them a step-by-step guide on how to do that. Students have to go through the experience themselves, though of course adult educators will have a role in that.

A couple parts of Lockhart’s account that really resonated with me was where he showed how one can arrive at a proof for the area of a certain type of triangle, and where he talked about students figuring out imaginary problems for themselves, getting frustrated, trying and failing, collaborating, and finally working it out. What he described sounds so similar to what my experience was when I was first learning to program computers, when I was 12 years old, and beyond. I didn’t have a programming course to help me when I was first learning to do it. I did it on my own, and with the help of others who happened to be around me. That’s how I got comfortable with it. And none of it was about, “To solve this problem, you do it this way.” I can agree that would’ve been helpful in alleviating my frustration in some instances, but I think it would’ve risked denying me the opportunity to understand something about what was really going on while I was using a programming language. You see, what we end up learning through exploration is that we often learn more than we bargained for, and that’s all to the good. That’s something we need to understand as students in order to get some value out of an educational experience.

By learning this way, we own what we learn, and as such, we also learn to respond to criticism of what we think we know. We come to understand that everything that’s been developed has been created by fallible human beings. We learn that we make mistakes in what we own as our ideas. That creates a sense of humility in us, that we don’t know everything, and that there are people who are smarter than us, and that there are people who know what we don’t know, and that there is knowledge that we will never know, because there is just so much of it out there, and ultimately, that there are things that nobody knows yet, not even the smartest among us. That usually doesn’t feel good, but it is only by developing that sense of humility, and responding to criticism well that we improve on what we own as our ideas. As we get comfortable with this way of learning, we learn to become good at exploring, and by doing that, we become really knowledgeable about what we learn. That’s what educators are really after, is it not, to create lifelong learners? Most valuable of all, I think, is learning this way creates independent thinkers, and indeed, people who can think out of the box, because you have a sense of what you know, and what you don’t know, and what you know is what you question, and try to correct, and what you don’t know is what you explore, and try to know. Furthermore, you have a sense of what other people know, and don’t know, because you develop a sense of what it actually means to know something! This is what I see Lockhart’s critics are missing the boat on: What you know is not what you’ve been told. What you know is what you have tried, experienced, analyzed, and criticized (wash, rinse, repeat).

On a related topic, Richard Feynman addressed something that should concern us re. thinking we know something because it’s what we’ve been told, vs. understanding what we know, and don’t know.

What seems to scare a lot of people is even after you’ve tried, experienced, analyzed, and criticized, the only answer you might come up with is, “I don’t know, and neither does anybody else.” That seems unacceptable. What we don’t know could hurt us. Well, yes, but that’s the reality we exist in. Isn’t it better to know that than to presume we know something we don’t?

The fundamental disconnect between what people think is valuable about education and what’s actually valuable in it is they think that to ensure that students understand something, it must be explicitly transmitted by teachers and instructional materials. It can’t just be left to chance in exploratory methods, because they might learn the wrong things, and/or they might not learn enough to come close to really mastering the subject. That notion is not to be dismissed out of hand, because that’s very possible. Some scaffolding is necessary to make it more likely that students will arrive at powerful ideas, since most ideas people come up with are bad. The real question is finding a balance of “just enough” scaffolding to allow as many students as possible to “get it,” and not “too much,” such that it ruins the learning experience. At this point, I think that’s more an art than a science, but I could be wrong.

I’m not suggesting just using a “blank page” approach, where students get no guidance from adults on what they’re doing, as many school systems have done (which they mislabeled “constructivism,” and which doesn’t work). I don’t think Lockhart is talking about that, either. I’m not suggesting autodidactic learning, nor is Lockhart. There is structure to what he is talking about, but it has an open-ended broadness to it. That’s part of what I think scares his critics. There is no sense of having a set of requirements. Lockhart would do well to talk about thresholds that he is aiming for with students. I think that would get across that he’s not willing to entertain lazy thinking. He tries to do that by talking about how students get frustrated in his scheme of imaginative work, and that they work through it, but he needs to be more explicit about it.

He admits in the “sequel” that his first article was a lament, not a proposal of what he wants to see happen. He wanted to point out the problem, not to provide an answer just yet.

The key point I want to make is the perception that drives not taking a risk is in fact taking a big risk. It’s risking creating people, and therefore a society that only knows so much, and doesn’t know how to exceed thresholds that are necessary to come up with big leaps that advance our society, if not have the basic understanding necessary to retain the advances that have already been made. A conservative, incremental approach to existing failure will not do.

Related post: The beauty of mathematics denied

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

# The Babbage Difference Engine at the Computer History Museum is going away

Hat tip to Christina Engelbart at Collective IQ

I was wondering when this was going to happen. The Difference Engine exhibit is coming to an end. I saw it in January 2009, since I was attending the Rebooting Computing Summit at the Computer History Museum, in Mountain View, CA. The people running the exhibit said that it was commissioned by Nathan Myhrvold, he had temporarily loaned it to the CHM, and he was soon going to reclaim it, putting it in his house. They thought it might happen in April of that year. A couple years ago, I checked with Tom R. Halfhill, who has worked as a volunteer at the museum, and he told me it was still there.

The last day for the exhibit is January 31, 2016. So if you have the opportunity to see it, take it now. I highly recommend it.

There is another replica of this same difference engine on permanent display at the London Science Museum in England. After this, that will be the only place where you can see it.

Here is a video they play at the museum explaining its significance. The exhibit is a working replica of Babbage’s Difference Engine #2, a redesign he did of his original idea.

Related posts:

Realizing Babbage

The ultimate: Swade and Co. are building Babbage’s Analytical Engine–*complete* this time!

# Psychic elephants and evolutionary psychology

Peter Foster, a columnist for the National Post in Canada, wrote what I think is a very insightful piece on a question that’s bedeviled me for many years, in “Why Climate Change is a Moral Crusade in Search of a Scientific Theory.” I have never seen a piece of such quality published on Breitbart.com. My compliments to them. It has its problems, but there is some excellent stuff to chew on, if you can ignore the gristle. The only ways I think I would have tried to improve on what he wrote is, one, to go deeper into the identification of the philosophies that are used to “justify the elephantine motivations.” As it is, Foster uses readily identifiable political labels, “liberal,” “left,” etc. as identifiers. This will please some, and piss off others. I really admired Allan Bloom’s efforts to get beyond these labels to understanding and identifying the philosophies, and the mistakes that he perceives were made with “translating” them into an American belief system that were at the root of his complaints, the philosophers who came up with them, and the consequences that have been realized through their adherents. There’s much to explore there.

Foster also “trips” over an analogy that doesn’t really apply to his argument (though he thinks it does) in his reference to supposed motivations for thinking Earth was the center of the Universe, though aspects of the stubbornness of pre-Copernican thinking on it, to which he also refers, apply.

He says a lot in this piece, and it’s difficult to fully grasp it without taking some time to think about what he’s saying. I will try to make your thinking a little easier.

He begins with trying to understand the reasons for, and the motivational consequences of, economic illiteracy in our society. He uses a notion of evolutionary psychology (perhaps from David Henderson, to whom he refers), that our brains have been in part evolutionally influenced by hundreds of thousands of years (perhaps millions. Who knows how far back it goes) of tribal society, that our natural perceptions of human relations, regarding power and wealth, and what is owed as a consequence of social status, are influenced by our evolutionary past.

Here is a brief video from Reason TV on the field of evolutionary psychology, just to get some background.

Edit 2/16/2016: I’ve added 3 more paragraphs relating to another video I’m adding, since it relates more specifically to this topic.

The video, below, is intriguing, but I can’t help but wonder if the two researchers, Cosmides and Tooby, are reading current issues they’re hearing about in political discourse into “stone age thinking” unjustifiably, because how do we know what stone age thinking was? I have to admit, I have no background in anthropology or archaeology at this point. I might need that to give more weight to this inference. The topic they discuss here, about a common misunderstanding of market economics, relates back to something they discussed in the above video, about humans trying to detect and form coalitions, and how market mechanisms have the effect of appearing to interfere with coalition-building strategies. They say this leads to resentment against the market system.

What this would seem to suggest is that the idea that humans are drastically changing our planet’s climate system for the worst is a nice salve for that desire for coalition building, because it leads one to a much larger inference that market economics (the perceived enemy of coalition strategies) is a problem that transcends national boundaries. The constant mantra of warmists that, “We must act now to solve it,” appears to demand a coalition, which to those who feel disconnected by markets feels very desirable.

One of the most frequent desires I’ve heard from those who believe that we are changing our climate for the worst is that they only want to deal with market participants, “Who care about me and my community.” What Cosmides and Tooby say is this relates back to our innate desire to build coalitions, and is evidence that these people feel that the market system is interfering, or not cooperating in that process. What they say, as Foster says, is this reflects a lack of understanding of market economics, and a total ignorance of the benefits its effects bring to humanity.

Foster says that our modern political and economic system, which frustrates tribalism, has only been a brief blink of an eye in our evolutionary experience, by comparison. So we still carry an evolutionary heritage that forms our perceptions of fairness and social survival, and it emerges naturally in our perceptions of our modern systems. He says this argument is controversial, but he justifies using it by saying that there is an apparent pattern to the consequences of economic illiteracy. He notices a certain consistency in the arguments that are used to morally challenge our modern systems, which does not seem to be dependent on how skilled people are in their niche areas of knowledge, or unskilled in many areas of knowledge. It’s important to keep what he says about this in mind throughout the article, even though he goes on at length into other areas of research, because it ties in in an important way, though he does not refer back to it.

He doesn’t say this, but I will. At this point, I think that the only counter to the natural tendencies we have (regardless of whether Foster describes them accurately or not) is an education in the full panoply in the outlooks that formed our modern society, and an understanding of how they have advanced since their formation. In our recent economy, there’s a tendency to think about narrowing the scope of education towards specialties, since each field is so complex, and takes a long time to master, but that will not do. If people don’t get the opportunity to explore, or at least experience, these powerful ways of understanding the world, then the natural tendency towards a “low-pass filter” will dominate what one sees, and our society will have difficulty advancing, and may regress. A key phrase Foster uses is, “Believing is seeing.” We think we see with our eyes, but we actually see with our beliefs (or, in scientific terms, our mental models). So it is crucial to be conscious of our beliefs, and be capable of examining and questioning them. Philosophy plays a part in “exercising” and developing this ability, but I think this really gets into the motivation to understand the scientific outlook, because this is truly what it’s about.

A second significant area Foster explores is a notion of moral psychology from Jonathan Haidt, who talks about “subconscious elephants,” which are “driving us,” unseen. We justify our actions using moral language, giving the illusion that we understand our motivations, but we really don’t. Our pronouncements are more like PR statements, convincing others that our motivations are good, and should be allowed to move forward, unrestricted. However, without examining and understanding our motivations, and their consequences, we can’t really know whether they are good or not. Understanding this, we should be cautious about giving anyone too much power–power to use money, and power to use force–especially when they appeal to our moral sensibility to give it to them.

Central to Foster’s argument is that “climate change” is a moral crusade, a moral argument–not a scientific one, that uses the authority that our society gives to science to push aside skepticism and caution regarding the actions in “climate policy” that are taken in its name.

Foster excuses the people who promote the hypothesis of anthropogenic global warming (AGW) as fact, saying they are not frauds who are consciously deceiving the public. They are riding pernicious, very large, “elephants,” and they are not conscious of what is driving them. They are convinced of their own moral rightness, and they are honest, at least, in that belief. That should not, however, excuse their demands for more and more power.

I do not mean what I say here to be a summary of Foster’s article. I encourage you to read it. I only mean to make the complexity of what he said a bit more understandable.

Related posts: Foster’s argument has made me re-examine a bit what I said in the section on Carl Sagan in “The dangerous brew of politics, religion, technology, and the good name of science.”

I’m taking a flying leap with this, but I have a suspicion my post called “What a waste it is to lose one’s mind,” exploring what Ayn Rand said in her novel, “Atlas Shrugged,” perhaps gets into describing Haidt’s “motivational elephants.”

# Reviving programming as literacy

I came across this interview with Lesley Chilcott, the producer of “An Inconvenient Truth” and “Waiting For Superman.” Kind of extending her emphasis on improving education, she produced a short 9-minute video selling the idea of “You should learn to code,” both to adults and children. It addresses two points: 1) the anticipated shortage of programmers needed to write software in the future, and 2) the increasing ubiquity of programming in all sorts of fields where people would think it wouldn’t exist, such as manufacturing and agriculture.

The interview gets interesting at 3 minutes 45 seconds in.

Michelle Fields, the interviewer, asked what I thought were some insightful questions. She started things off with:

It seems as though the next generation is so fluent in technology. How is it that they don’t know what computer programming is?

Chilcott said:

I think the reason is, you know, we all use technology every day. It’s surrounding us. Like, we can debate the pro’s and con’s of technology/social media, but the bottom line is it’s everywhere, right? So I think a lot of people know how to read it. They grow up playing with an iPhone or something like that, but they don’t know how to write it. And so when you say, “Do you know what this is,” specifically, or what this job is–and you know, those kids are in first, second, fifth grade–they know all about it, but they don’t know what the job is.

I found this answer confusing. She’s kind of on the right track, thinking of programming as “writing.” I cut her some slack, because as she admits in the interview, she’s just started programming herself. However, as I’ve said before, running software is not “reading.” It’s really more like being read to by a machine, like listening to an audio book, or someone else reading to you. You don’t have to worry about the mental tasks of pronunciation, sentence construction, or punctuation. You can just listen to the story. Running software doesn’t communicate the process that the code is generating, because there’s a lot that the person using it is not shown. This is on purpose, because most people use software to accomplish some utilitarian task unrelated to how a computer works. They’re not using it to understand a process.

The last sentence came across as muddled. I think what she meant was they know all about using technology, but they don’t know how to create it (“what the job is”).

There was this study which found that 56% of students would rather eat broccoli than learn math. Do you think that since computer programming is somewhat related to math, that that’s the reason children and students shy away from it?

Chilcott said:

It could be. That is one of the myths that exist. There is some, you know, math, but as Bill Gates and some other people said, you know, addition, subtraction–It’s much more about problem solving, and I think people like to problem-solve, they like mysteries, they like decoding things. It’s much more about that than complicated algorithms.

She’s right that there is problem solving involved with programming, but she’s either mistaken or confusing math with arithmetic when she says that the relationship between math and programming is a “myth.” I can understand why she tries to wave it off, because as Fields pointed out, most students don’t like math. I contend, as do some mathematicians, this is due to the way it’s taught in our schools. The essence of math gets lost. Instead it’s presented as a tool for calculation, and possibly a cognitive development discipline for problem solving, both of which don’t communicate what it really is, and remove a lot of its beauty.

In reality math is pervasive in programming, but to understand why I say this you have to understand that math is not arithmetic–addition, subtraction, like she suggests. This confusion is common in our society. I talk more about this here. Having said this, it does not mean that programming is hard right off the bat. The math involved has more to do with logic and reasoning. I like the message in the video below from a couple of the programmers interviewed: “You don’t have to be a genius to know how to code. … Do you have to be a genius to do math? No.” I think that’s the right way to approach this. Math is important to programming, but it’s not just about calculating a result. While there’s some memorization, understanding a programming language’s rules, and knowing what different things are called, that’s not a big part of it.

The cool thing is you can accomplish some simple things in programming, to get started, without worrying about math at all. It becomes more important if you want to write complex programs, but that’s something that can wait.

My current understanding is the math in programming is about understanding the rules of a system and what statements used in that system imply, and then understanding the effects of those implications. That sounds complicated, but it’s just something that has to be learned to do anything significant with programming, and once learned will become more and more natural. I liken it to understanding how to drive a car on the road. You don’t have to learn this concept right away, though. When first starting out, you can just look at and enjoy the effects of trying out different things, exploring what a programming environment offers you.

Where Chilcott shines in the interview above is when she becomes the “organizer.” She said that even though 95% of the schools have computers and internet access, only 10% have what she calls a “computer science” course. (I wish they’d go back to calling it a “programming course.” Computer science is more than what most of these schools teach, but I’m being nit-picky.) The cool thing about Code.org, a web site she promotes, is that it tries to locate a school near you that offers programming courses. If there aren’t any, no problem. You can learn some basics of programming right inside your browser using the online tools that it offers on the site.

The video Chilcott produced is called “Code Stars” in the above interview, but when I went looking for it I found it under the name “the Code.org film,” or, “What Most Schools Don’t Teach.”

Here is the full 9-minute video:

If you want the shorter videos, you can find them here.

The programming environment you see kids using in these videos is called “Scratch.”

Gabe Newell said of programming:

When you’re programming, you’re teaching possibly the stupidest thing in the entire universe–a computer–how to do something.

I see where Newell is going with this, but from my perspective it depends on what programming environment you’re using. Some programming languages have the feel of you “teaching” the system when you’re programming. Others have the feel of creating relationships between simple behaviors. Others, still, have the feel of using relationships to set up rules for a new system. Programming comes in a variety of approaches. However, the basic idea that Newell gets across is true, that computers only come with a set of simple operations, and that’s it. They don’t do very much by themselves, or even in combination. It’s important for those new to programming to learn this early on. Some of my early experiences in programming match those of new programmers even today. One of them is, when using a programming language, one is tempted to assume that the computer will infer the meaning of some programming expression from context. There is some context used in programming, but not much, and it’s highly formalized. It’s not intuitive. I can remember the first time I learned this it was like the joke where, say, someone introduces his/her friend to a dumb, witless character in a skit. He/she says, “Say hi to my friend, Frank,” and the dummy says, “Hi to my friend Frank.” And the guy/gal says, “NO! I mean…say hello,” making a hand gesture trying to get the two to connect, and the dummy might look at the friend and say, “Hello,” but that’s it. That’s kind of a realization to new programmers. Yeah, the computer has to have almost everything explained to it (or modeled), even things we do without thinking about it. It’s up to the programmer to make the connections between the few things the computer knows how to do, to make something larger happen.

Jack Dorsey talked about programming in a way that I think is important. His ultimate goal when he started out was to model something, and make the model malleable enough that he could manipulate it, because he wanted to use it for understanding how cities work.

Bill Gates emphasized control. This is a common early motivation for programmers. Not necessarily controlling people, but controlling the computer. What Gates was talking about was what I’d call “making your own world,” like Dorsey was saying, but he wanted to make it real. When I was in high school (late 1980s) it was a rather common project for aspiring programming students to create “matchmaking” programs, where boys and girls in the whole school would answer a simple questionnaire, and a computer program that a student had written would try to match them up by interests, not unlike some of the online dating sites that are out there now. I never heard of any students finding their true love through one of these projects, but it was fun for some people.

Vanessa Hurst said, “You don’t have to be a genius to know how to code. You need to be determined.” That’s pretty much it in a nutshell. In my experience everything else flowed from determination when I was learning how to do this. It will drive you to learn what you need to learn to get it, even if sometimes it’s subject matter you find tedious and icky. You learn to just push through it to get to the glorious feeling at the end of having accomplished what you set out to do.

Newell said at the end of the video,

The programmers of tomorrow are the wizards of the future. You’re going to look like you have magic powers compared to everybody else.

That’s true, but this has been true for a long time. In my professional work developing custom database solutions for business customers I had the experience of being viewed like a magician, because customers didn’t know how I did what I did. They just appreciated the fact that I could do it. I really don’t mean to discourage anyone, because I still enjoy programming today, and I want to encourage people to learn programming, but I feel the need to say something, because I don’t want people to get disillusioned over this. This status of “wizard,” or “magician” is not always what it’s cracked up to be. It can feel great, but there is a flip side to it that can be downright frustrating. This is because people who don’t know a wit of what you know how to do can get confused about what your true abilities are, and they can develop unrealistic expectations of you. I’ve found that wherever possible, the most pleasurable work environment is working among those who also know how to code, because we’re able to size each other up, and assign tasks appropriately. I encourage those who are pursuing software development as a career to shoot for that.

A couple things I can say for being able to code are:

• It makes you less of a “victim” in our technology world. Once you know how to do it, you have an idea about how other programs work, and the pitfalls they can fall into that might compromise your private information, allow a computer cracker to access it, or take control of your system. You don’t have to feel scared at the alarming “hacking” or phishing reports you hear on the news, because you can be choosey about what software you use based on how it was constructed, what it’s capable of, how much power it gives you (not someone else), and not just base a decision on the features it has, or cool graphics and promotion. You can become a discriminating user of software.
• You gain the power to create the things that suite you. You don’t have to use software that you don’t like, or you think is being offered on unreasonable terms. You can create your own, and it can be whatever you want. It’s just a matter of the knowledge you’re willing to gather and the amount of energy you’re willing to put into developing the software.

Edit 5-20-2013: While I’m on this subject, I thought I should include this video by Mitch Resnick, who has been involved in creating Scratch at MIT. Similar to what Lesley Chilcott said above, he said, “It’s almost as if [users of new technologies] can read, but not write,” referring to how people use technology to interact. I disagreed with the notion, above, that using technology is the same as reading. Resnick hedged a bit on that. I can kind of understand why he might say this, because by running a Scratch program, it is like reading it, because you can see how code creates its results in the environment. This is not true, however, of much of the technology people use today.

Mark Guzdial asked a question a while back that I thought was important, because it brings this issue down to where a lot of people live. If the kind of literacy I’m going to talk about below is going to happen, the concept needs to be able to come down “out of the clouds” and become more pedestrian. Not to say that literacy needs to be watered down in toto (far from it), but that it should be possible to read and write to communicate everyday ideas and experiences without being super sophisticated about it. What Mark asked was, in the context of a computing medium, what would be the equivalent of a “note to grandma”? I remember suggesting Dan Ingalls’s prop-piston concept from his Lively Kernel demos as one candidate. Resnick provided what I thought were some other good ones, but in the context of Mother’s Day.

### Context reversal

The challenge that faces new programmers today is different from when I learned programming as a child in one fundamental way. Today, kids are introduced to computers before they enter school. They’re just “around.” If you’ve got a cell phone, you’ve got a computer in your pocket. The technology kids use presents them with an easy-to-use interface, but the emphasis is on use, not authoring. There is so much software around it seems you can just wish for it, and it’s there. The motivation to get into programming has to be different than what motivated me.

When I was young the computer industry was still something new. It was not widespread. Most computers that were around were big mainframes that only corporations and universities could afford and manage. When the first microcomputers came out, there wasn’t much software for them. It was a lot easier to be motivated to learn programming, because if you didn’t write it, it probably didn’t exist, or it was too expensive to get (depending on your financial circumstances). The way computers operated was more technical than they are today. We didn’t have graphical user interfaces (at first). Everything was done from some kind of text command line interface that filled the entire screen. Every computer came with a programming language as well, along with a small manual giving you an introduction on how to use it.

PC-DOS, from Wikipedia

It was expected that if you bought a computer you’d learn something about programming it, even if it was just a little scripting. Sometimes the line between what was the operating system’s command line interface, and what was the programming language was blurred. So even if all you wanted to do was manipulate files and run programs, you were learning a little about programming just by learning how to use the computer. Some of today’s software developers came out of that era (including yours truly).

Computer and operating system manufacturers had stopped including programming languages with their systems by the mid-1990s. Programming languages had also been taken over by professionals. The typical languages used by developers were much harder to learn for beginners. There were educational languages around, but they had fallen behind the times. They were designed for older personal computer systems, and when the systems got more sophisticated no one had come around to update them. That began to be remedied only in the last 10 years.

Computer science was still a popular major at universities in the 1990s, due to the dot-com craze. When that bubble burst in 2000, that went away, too. So in the last 18 years we’ve had what I’d call an “educational programming winter.” Maybe we’ll see a revival. I hope so.

### Literacy reconsidered

I’m directing the rest of this post to educators, because there are some issues around a programming revival I’d like to address. I’m going to share some more detailed history, and other perspectives on computer programming.

What many may not know is that we as a society have already gone through this once. From the late 1970s to the mid-1980s there was a major push to teach programming in schools as “computer literacy.” This was the regime that I went through. The problem was some mistakes were made, and this caused the educational movement behind it to collapse. I think the reason this happened was due to a misunderstanding of what’s powerful about programming, and I’d like educators to evaluate their current thinking in light of this, so that hopefully they do not repeat the mistakes of the past.

As I go through this part, I’ll mostly be quoting from a Ph.D. thesis written by John Maxwell in 2006 called Tracing the Dynabook: A Study of Technocultural Transformations.” (h/t Bill Kerr)

Back in the late 1970s microcomputers/personal computers were taking off like wildfire with Apple II’s, and Commodore VIC-20’s, and later, Commodore 64’s, and IBM PCs. They were seen as “the future.” Parents didn’t want their children to be “left behind” as “technological illiterates.” This was the first time computers were being brought into the home. It was also the first time many schools were able to grant students access to computers.

Educators thought about the “benefits” of using a computer for certain cognitive and social skills.  Programming spread in public school systems as something to teach students. Fred D’Ignazio wrote in an article called “Beyond Computer Literacy,” from 1983:

A recent national “computers in the schools” survey conducted by the Center for the Social Organization of Schools at Johns Hopkins University found that most secondary schools are using computers to teach programming. … According to the survey, the second most popular use of computers was for drill and practice, primarily for math and language arts. In addition, the majority of the teachers who responded to the survey said that they looked at the computer as a “resource” rather than as a “tool.”

…Another recent survey (conducted by the University of Maryland) echoes the Johns Hopkins survey. It found that most schools introduce computers into the curriculum to help students become literate in computer technology. But what does this literacy entail?

Because of the pervasive spread of computers throughout our society, we have all become convinced that computers are important. From what we read and hear, when our kids grow up almost everyone will have to use computers in some aspect of their lives. This makes computers, as a subject, not only important, but also relevant.

An important, relevant subject like computers should be part of a school’s curriculum. The question is how “Computers” ought to be taught.

Special computer classes are being set up so that students can play with computers, tinker with them, and learn some basic programming. Thus, on a practical level, computer literacy turns out to be mere computer exposure.

But exposure to what? Kids who are now enrolled in elementary and secondary schools are exposed to four aspects of computers. They learn that computers are programmable machines. They learn that computers are being used in all areas of society. They learn that computers make good electronic textbooks. And (something they already knew), they learn that computers are terrific game machines.

… According to the surveys, real educational results have been realized at schools which concentrate on exposing kids to computers. … Kids get to touch computers, play with them, push their buttons, order them about, and cope with computers’ incredible dumbness, their awful pickiness, their exasperating bugs, and their ridiculous quirks.

The main benefits D’Ignazio noted were ancillary. Students stayed at school longer, came in earlier, and stayed late. They were more attentive to their studies, and the computers fostered a sense of community, rather than competition and rivalry. If you read his article, you get a sense that there was almost a “worship” of computers on the part of educators. They didn’t understand what they were, or what they represented, but they were so interesting! There’s a problem there… When people are fascinated by something they don’t understand, they tend to impose meanings on it that are not backed by evidence, and so miss the point. The mistaken perceptions can be strengthened by anecdotal evidence (one of the weakest kinds). This is what happened to programming in schools.

The success of the strategy of using computers to try to improve higher-order thinking was illusory. John Maxwell’s telling of the “life and death of Logo” (my phrasing) serves as a useful analog to what happened to programming in schools generally. For those unfamiliar with it, the basic concept of Logo was a programming environment in which the student manipulates an object called a “turtle” via. commands. The student can ask the turtle to rotate and move. As it moves it drags a pen behind it, tracing its trail.  Other versions of this language were created that allowed more capabilities, allowing further exploration of the concepts for which it was created. The original idea Seymour Papert, who taught children using Logo, had was to teach young children about sophisticated math concepts, but our educational system imposed a very different definition and purpose on it. Just because something is created on a computer with the intent of it being used for a specific purpose doesn’t mean that others can’t use it for completely different, and possibly less valuable purposes. We’ve seen this a lot with computers over the years; people “misusing” them for both constructive and destructive ends.

As I go forward with this, I just want to put out a disclaimer that I don’t have answers to the problems I point out here. I point them out to make people aware of them, to get people to pause with the pursuit of putting people through this again, and to point to some people who are working on trying to find some answers. I present some of their learned opinions. I encourage interested readers to read up on what these people have had to say about the use of computers in education, and perhaps contact them with the idea of learning more about what they’ve found out.

I ask the reader to pay particular attention to the “benefits” that educators imposed on the idea of programming during this period that Maxwell talks about, via. what Papert called “technocentrism.” You hear this being echoed in the videos above. As you go through this, I also want you to notice that Papert, and another educator by the name of Alan Kay, who have thought a lot about what computers represent, have a very different idea about the importance of computers and programming than is typical in our school system, and in the computer industry.

The spark that started Logo’s rise in the educational establishment was the publication of Papert’s book, “Mindstorms: Children, Computers, and Powerful Ideas” in 1980. Through the process of Logo’s promotion…

Logo became in the marketplace (in the broad sense of the word) [a] particular black box: turtle geometry; the notion that computer programming encourages a particular kind of thinking; that programming in Logo somehow symbolizes “computer literacy.” These notions are all very dubious—Logo is capable of vastly more than turtle graphics; the “thinking skills” strategy was never part of Papert’s vocabulary; and to equate a particular activity like Logo programming with computer literacy is the equivalent of saying that (English) literacy can be reduced to reading newspaper articles—but these are the terms by which Logo became a mass phenomenon.

It was perhaps inevitable, as Papert himself notes (1987), that after such unrestrained enthusiasm, there would come a backlash. It was also perhaps inevitable given the weight that was put on it: Logo had come, within educational circles, to represent computer programming in the large, despite Papert’s frequent and eloquent statements about Logo’s role as an epistemological resource for thinking about mathematics. [my emphasis — Mark] In the spirit of the larger project of cultural history that I am attempting here, I want to keep the emphasis on what Logo represented to various constituencies, rather than appealing to a body of literature that reported how Logo “didn’t work as promised,” as many have done (e.g., Sloan 1985; Pea & Sheingold 1987). The latter, I believe, can only be evaluated in terms of this cultural history. Papert indeed found himself searching for higher ground, as he accused Logo’s growing numbers of critics of technocentrism:

“Egocentrism for Piaget does not mean ‘selfishness’—it means that the child has difficulty understanding anything independently of the self. Technocentrism refers to the tendency to give a similar centrality to a technical object—for example computers or Logo. This tendency shows up in questions like ‘What is THE effect of THE computer on cognitive development?’ or ‘Does Logo work?’ … such turns of phrase often betray a tendency to think of ‘computers’ and ‘Logo’ as agents that act directly on thinking and learning; they betray a tendency to reduce what are really the most important components of educational situations—people and cultures—to a secondary, faciltiating role. The context for human development is always a culture, never an isolated technology.”

But by 1990, the damage was done: Logo’s image became that of a has-been technology, and its black boxes closed: in a 1996 framing of the field of educational technology, Timothy Koschmann named “Logo-as-Latin” a past paradigm of educational computing. The blunt idea that “programming” was an activity which could lead to “higher order thinking skills” (or not, as it were) had obviated Papert’s rich and subtle vision of an ego-syntonic mathematics.

The message–or black box–resulting from the rise and fall of Logo seems to have been the notion that “programming” is over-rated and esoteric, more properly relegated to the ash-heap of ed-tech history, just as in the analogy with Latin. (pp. 183-185)

To be clear, the last part of the quote refers only to the educational value placed on programming by our school system. When educators attempted to formally study and evaluate programming’s benefits on higher-order thinking and the like, they found it wanting, and so most schools gradually dropped teaching programming in the 1990s.

Maxwell addresses the conundrum of computing and programming in schools, and I think what he says is important to consider as people try to “reboot” programming in education:

[The] critical faculties of the educational establishment, which we might at least hope to have some agency in the face of large-scale corporate movement, tend to actually disengage with the critical questions (e.g., what are we trying to do here?) and retreat to a reactionary ‘humanist’ stance in which a shallow Luddism becomes a point of pride. Enter the twin bogeymen of instrumentalism and technological determinism: the instrumentalist critique runs along the lines of “the technology must be in the service of the educational objectives and not the other way around.” The determinist critique, in turn, says, ‘the use of computers encourages a mechanistic way of thinking that is a danger to natural/human/traditional ways of life’ (for variations, see, Davy 1985; Sloan 1985; Oppenheimer 1997; Bowers 2000).

Missing from either version of this critique is any idea that digital information technology might present something worth actually engaging with. De Castell, Bryson & Jenson write:

“Like an endlessly rehearsed mantra, we hear that what is essential for the implementation and integration of technology in the classroom is that teachers should become ‘comfortable’ using it. […] We have a master code capable of utilizing in one platform what have for the entire history of our species thus far been irreducibly different kinds of things–writing and speech, images and sound–every conceivable form of information can now be combined with every other kind to create a different form of communication, and what we seek is comfort and familiarity?”

Surely the power of education is transformation. And yet, given a potentially transformative situation, we seek to constrain the process, managerially, structurally, pedagogically, and philosophically, so that no transformation is possible. To be sure, this makes marketing so much easier. And so we preserve the divide between ‘expert’ and ‘end-user;’ for the ‘end-user’ is profoundly she who is unchanged, uninitiated, unempowered.

A seemingly endless literature describes study after study, project after project, trying to identify what really ‘works’ or what the critical intercepts are or what the necessary combination of ingredients might be (support, training, mentoring, instructional design, and so on); what remains is at least as strong a body of literature which suggests that this is all a waste of time.

But what is really at issue is not implementation or training or support or any of the myriad factors arising in discussions of why computers in schools don’t amount to much. What is really wrong with computers in education is that for the most part, we lack any clear sense of what to do with them, or what they might be good for. This may seem like an extreme claim, given the amount of energy and time expended, but the record to date seems to support it. If all we had are empirical studies that report on success rates and student performance, we would all be compelled to throw the computers out the window and get on with other things.

But clearly, it would be inane to try to claim that computing technology–one of the most influential defining forces in Western culture of our day, and which shows no signs of slowing down–has no place in education. We are left with a dilemma that I am sure every intellectually honest researcher in the field has had to consider: we know this stuff is important, but we don’t really understand how. And so what shall we do, right now?

It is not that there haven’t been (numerous) answers to this question. But we have tended to leave them behind with each surge of forward momentum, each innovative push, each new educational technology “paradigm” as Timothy Koschmann put it. (pp. 18-19)

The answer is not a “reboot” of programming, but rather a rethinking of it. Maxwell makes a humble suggestion: that educators stop being blinded by “the shiny new thing,” or some so-called “new” idea such that they lose their ability to think clearly about what’s being done with regard to computers in education, and that they deal with history and historicism. He said that the technology field has had a problem with its own history, and this tends to bleed over into how educators regard it. The tendency is to forget the past, and to downplay it (“That was neat then, but it’s irrelevant now”).

In my experience, people have associated technology’s past with memories of using it. They’ve given little if any thought to what it represented. They take for granted what it enabled them to do, and do not consider what that meant. Maxwell said that this…

…makes it difficult, if not impossible, to make sense of the role of technology in education, in society, and in politics. We are faced with a tangle of hobbles–instrumentalism, ahistoricism, fear of transformation, Snow’s “two cultures,” and a consumerist subjectivity.

An examination of the history of educational technology–and educational computing in particular–reveals riches that have been quite forgotten. There is, for instance, far more richness and depth in Papert’s philosophy and his more than two decades of practical work on Logo than is commonly remembered. And Papert is not the only one. (p. 20)

Maxwell went into what Alan Kay thought about the subject. Kay has spent almost as many years as Papert working on a meaningful context for computing and programming within education. Some of the quotes Maxwell uses are from “The Early History of Smalltalk,” (h/t Bill Kerr) which I’ll also refer to. The other sources for Kay’s quotes are included in Maxwell’s bibliography:

#### What is Literacy?

“The music is not in the piano.” — Alan Kay

The past three or four decades are littered with attempts to define “computer literacy” or something like it. I think that, in the best cases, at least, most of these have been attempts to establish some sort of conceptual clarity on what is good and worthwhile about computing. But none of them have won large numbers of supporters across the board.

Kay’s appeal to the historical evolution of what literacy has meant over the past few hundred years is, I think, a much more fruitful framing. His argument is thus not for computer literacy per se, but for systems literacy, of which computing is a key part.

That this is a massive undertaking is clear … and the size of the challenge is not lost on Kay. Reflecting on the difficulties they faced in trying to teach programming to children at PARC in the 1970s, he wrote that:

“The connection to literacy was painfully clear. It is not just enough to learn to read and write. There is also a literature that renders ideas. Language is used to read and write about them, but at some point the organization of ideas starts to dominate the mere language abilities. And it helps greatly to have some powerful ideas under one’s belt to better acquire more powerful ideas.”

Because literature is about ideas, Kay connects the notion of literacy firmly to literature:

“What is literature about? Literature is a conversation in writing about important ideas. That’s why Euclid’s Elements and Newton’s Principia Mathematica are as much a part of the Western world’s tradition of great books as Plato’s Dialogues. But somehow we’ve come to think of science and mathematics as being apart from literature.”

There are echoes here of Papert’s lament about mathophobia, not fear of math, but the fear of learning that underlies C.P. Snow’s “two cultures,” and which surely underlies our society’s love-hate relationship with computing. Kay’s warning that too few of us are truly fluent with the ways of thinking that have shaped the modern world finds an anchor here. How is it that Euclid and Newton, to take Kay’s favourite examples, are not part of the canon, unless one’s very particular scholarly path leads there? We might argue that we all inherit Euclid’s and Newton’s ideas, but in distilled form. But this misses something important … Kay makes this point with respect to Papert’s experiences with Logo in classrooms:

“Despite many compelling presentations and demonstrations of Logo, elementary school teachers had little or no idea what calculus was or how to go about teaching real mathematics to children in a way that illuminates how we think about mathematics and how mathematics relates to the real world.” (Maxwell, pp. 135-137)

Just a note of clarification: I refer back to what Maxwell said re. Logo and mathematics. Papert did not use his language to teach programming as an end in itself. His goal was to use a computer to teach mathematics to children. Programming with Logo was the means for doing it. This is an important concept to keep in mind as one considers what role computer programming plays in education.

The problem, in Kay’s portrayal, isn’t “computer literacy,” it’s a larger one of familiarity and fluency with the deeper intellectual content; not just that which is specific to math and science curriculum. Kay’s diagnosis runs very close to Neil Postman’s critiques of television and mass media … that we as a society have become incapable of dealing with complex issues.

“Being able to read a warning on a pill bottle or write about a summer vacation is not literacy and our society should not treat it so. Literacy, for example, is being able to fluently read and follow the 50-page argument in [Thomas] Paine’s Common Sense and being able (and happy) to fluently write a critique or defense of it.” (Maxwell, p. 137)

Extending this quote (from “The Early History of Smalltalk”), Kay went on to say:

Another kind of 20th century literacy is being able to hear about a new fatal contagious incurable disease and instantly know that a disastrous exponential relationship holds and early action is of the highest priority. Another kind of literacy would take citizens to their personal computers where they can fluently and without pain build a systems simulation of the disease to use as a comparison against further information.

At the liberal arts level we would expect that connections between each of the fluencies would form truly powerful metaphors for considering ideas in the light of others.

Continuing with Maxwell (and Kay):

“Many adults, especially politicians, have no sense of exponential progressions such as population growth, epidemics like AIDS, or even compound interest on their credit cards. In contrast, a 12-year-old child in a few lines of Logo […] can easily describe and graphically simulate the interaction of any number of bodies, or create and experience first-hand the swift exponential progressions of an epidemic. Speculations about weighty matters that would ordinarily be consigned to common sense (the worst of all reasoning methods), can now be tried out with a modest amount of effort.”

Surely this is far-fetched; but why does this seem so beyond our reach? Is this not precisely the point of traditional science education? We have enough trouble coping with arguments presented in print, let alone simulations and modeling. Postman’s argument implicates television, but television is not a techno-deterministic anomaly within an otherwise sensible cultural milieu; rather it is a manifestation of a larger pattern. What is wrong here has as much to do with our relationship with print and other media as it does with television. Kay noted that “In America, printing has failed as a carrier of important ideas for most Americans.” To think of computers and new media as extensions of print media is a dangerous intellectual move to make; books, for all their obvious virtues (stability, economy, simplicity) make a real difference in the lives of only a small number of individuals, even in the Western world. Kay put it eloquently thus: “The computer really is the next great thing after the book. But as was also true with the book, most [people] are being left behind.” This is a sobering thought for those who advocate public access to digital resources and lament a “digital divide” along traditional socioeconomic lines. Kay notes,

“As my wife once remarked to Vice President Al Gore, the ‘haves and have-nots’ of the future will not be caused so much by being connected or not to the Internet, since most important content is already available in public libraries, free and open to all. The real haves and have-nots are those who have or have not acquired the discernment to search for and make use of high content wherever it may be found.” (Maxwell, pp. 138-139)

I’m still trying to understand myself what exactly Alan Kay means by “literature” in the realm of computing. He said that it is a means for discussing important ideas, but in the context of computing, what ideas? I suspect from what’s been said here he’s talking about what I’d call “model content,” thought forms, such as the idea of an exponential progression, or the concept of velocity and acceleration, which have been fashioned in science and mathematics to describe ideas and phenomena. “Literature,” as he defined it, is a means of discussing these thought forms–important ideas–in some meaningful context.

In prior years he had worked on that in his Squeak environment, working with some educators. They would show children a car moving across the screen, dropping dots as it went, illustrating velocity, and then, modifying the model, acceleration. Then they would show them Galileo’s experiment, dropping heavy and light balls from the roof of a building (real balls from a real building), recording the ball dropping, and allowing the children to view the video of the ball, and simultaneously model it via. programming, and discovering that the same principle of acceleration applied there as well. Thus, they could see in a couple contexts how the principle worked, how they could recognize it, and see its relationship to the real world. The idea being that they could grasp the concepts that make up the idea of acceleration, and then integrate it into their thinking about other important matters they would encounter in the future.

Maxwell quoted from an author named Andrew diSessa to get deeper into the concept of literacy, specifically what literacy in a type of media offers our understanding of issues:

The hidden metaphor behind transparency–that seeing is understanding–is at loggerheads with literacy. It is the opposite of how media make us smarter. Media don’t present an unadulterated “picture” of the problem we want to solve, but have their fundamental advantage in providing a different representation, with different emphases and different operational possibilities than “seeing and directly manipulating.”

### What’s a good goal for computing?

The temptation in teaching and learning programming is to get students familiar enough with the concepts and a language that they can start creating things with it. But create what? The typical cases are to allow students to tinker, and/or to create applications which gradually become more complex and feature-rich, with the idea of building confidence and competence with increasing complexity. The latter is not a bad idea in itself, but listening to Alan Kay has led me to believe that starting off with this is the equivalent of jumping to a conclusion too quickly, and to miss the point of what’s powerful about computers and programming.

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. This is inverse vandalism: the making of things because you can. Couple this to even less sophisticated buyers and you have generated an exploitation marketplace similar to that set up for teenagers. A counter to this is to generate enormous dissatisfaction with one’s designs using the entire history of human art as a standard and goal. Then the trick is to decouple the dissatisfaction from self worth–otherwise it is either too depressing or one stops too soon with trivial results.

Edit 4-5-2013: I thought I should point out that this quote has some nuance to it that people might miss. I don’t believe Kay is saying that “programming should be hard.” Quite the contrary. One can observe from his designs that he’s advocated the opposite. Not that technology should mold itself to what is “natural” for humans. It might require some training and practice, but once mastered, it should magnify or enhance human capabilities, thereby making previously difficult or tedious tasks easier to accomplish and incorporate into a larger goal.

Kay was making an observation about the history of technology’s relationship to society, that the effect on people of useful technology being hard to build has generally caused the people who created something useful to make it well. What he’s pointing out is that people generally take the presence of technology as an excuse to use it as a crutch, in this case to make immediate use of it towards some other goal that has little to do with what the technology represents, rather than an invitation to revisit it, criticize its design, and try to make it better. This is an easy sell, because everyone likes something that makes their lives easier (or seems to), but we rob ourselves of something important in the process if that becomes the only end goal. What I see him proposing is that people with some skill should impose a high standard for design on themselves, drawing inspiration for that standard from how the best art humanity has produced was developed and nurtured, but guard against the sense of feeling small, inadequate, and overwhelmed by the challenge.

Maxwell (and Kay) explain further why this idea of “literacy” as being able to understand and communicate important ideas, which includes ideas about complexity, is something worth pursuing:

“If we look back over the last 400 years to ponder what ideas have caused the greatest changes in human society and have ushered in our modern era of democracy, science, technology and health care, it may come as a bit of a shock to realize that none of these is in story form! Newton’s treatise on the laws of motion, the force of gravity, and the behavior of the planets is set up as a sequence of arguments that imitate Euclid’s books on geometry.”

The most important ideas in modern Western culture in the past few hundred years, Kay claims, are the ones driven by argumentation, by chains of logical assertions that have not been and cannot be straightforwardly represented in narrative. …

But more recent still are forms of argumentation that defy linear representation at all: ‘complex’ systems, dynamic models, ecological relationships of interacting parts. These can be hinted at with logical or mathematical representations, but in order to flesh them out effectively, they need to be dynamically modeled. This kind of modeling is in many cases only possible once we have computational systems at our disposal, and in fact with the advent of computational media, complex systems modeling has been an area of growing research, precisely because it allows for the representation (and thus conception) of knowledge beyond what was previously possible. In her discussion of the “regime of computation” inherent in the work of thinkers like Stephen Wolfram, Edward Fredkin, and Harold Morowitz, N. Katherine Hayles explains:

“Whatever their limitations, these researchers fully understand that linear causal explanations are limited in scope and that multicausal complex systems require other modes of modeling and explanation. This seems to me a seminal insight that, despite three decades of work in chaos theory, complex systems, and simulation modeling, remains underappreciated and undertheorized in the physical sciences, and even more so in the social sciences and humanities.”

Kay’s lament too is that though these non-narrative forms of communication and understanding–both in the linear and complex varieties–are key to our modern world, a tiny fraction of people in Western society are actually fluent in them.

“In order to be completely enfranchised in the 21st century, it will be very important for children to become fluent in all three of the central forms of thinking that are now in use. […] the question is: How can we get children to explore ways of thinking beyond the one they’re ‘wired for’ (storytelling) and venture out into intellectual territory that needs to be discovered anew by every thinking person: logic and systems ‘eco-logic?'” …

In this we get Kay’s argument for ‘what computers are good for’ … It does not contradict Papert’s vision of children’s access to mathematical thinking; rather, it generalizes the principle, by applying Kay’s vision of the computer as medium, and even metamedium, capable of “simulating the details of any descriptive model.” The computer was already revolutionizing how science is done, but not general ways of thinking. Kay saw this as the promise of personal computing, with millions of users and millions of machines.

“The thing that jumped into my head was that simulation would be the basis for this new argument. […] If you’re going to talk about something really complex, a simulation is a more effective way of making your claim than, say, just a mathematical equation. If, for example, you’re talking about an epidemic, you can make claims in an essay, and you can put mathematical equations in there. Still, it is really difficult for your reader to understand what you’re actually talking about and to work out the ramifications. But it is very different if you can supply a model of your claim in the form of a working simulation, something that can be examined, and also can be changed.”

The computer is thus to be seen as a modeling tool. The models might be relatively mundane–our familiar word processors and painting programs define one end of the scale–or they might be considerably more complex. [my emphasis — Mark] It is important to keep in mind that this conception of computing is in the first instance personal–“personal dynamic media”–so that the ideal isn’t simulation and modeling on some institutional or centralized basis, but rather the kind of thing that individuals would engage in, in the same way in which individuals read and write for their own edification and practical reasons. This is what defines Kay’s vision of a literacy that encompasses logic and systems thinking as well as narrative.

And, as with Papert’s enactive mathematics, this vision seeks to make the understanding of complex systems something to which young children could realistically aspire, or that school curricula could incorporate. Note how different this is from having a ‘computer-science’ or an ‘information technology’ curriculum; what Kay is describing is more like a systems-science curriculum that happens to use computers as core tools:

“So, I think giving children a way of attacking complexity, even though for them complexity may be having a hundred simultaneously executing objects–which I think is enough complexity for anybody–gets them into that space in thinking about things that I think is more interesting than just simple input/output mechanisms.” (Maxwell, pp. 132-135)

I wanted to highlight the part about “word processors” and “paint programs,” because this idea that’s being discussed is not limited to simulating real world phenomena. It could be incorporated into simulating “artificial phenomena” as well. It’s a different way of looking at what you are doing and creating when you are programming. It takes it away from asking, “How do I get this thing to do what I want,” and redirects it to, “What entities do we want to make up this desired system, what are they like, and how can they interact to create something that we can recognize, or otherwise leverages human capabilities?”

Characterizing Alan Kay’s vision for personal computing, Maxwell talked about Kay’s concept of the Dynabook:

Alan Kay’s key insight in the late 1960s was that computing would become the practice of millions of people, and that they would engage with computing to perform myriad tasks; the role of software would be to provide a flexible medium with which people could approach those myriad tasks. … [The] Dynabook’s user is an engaged participant rather than a passive, spectatorial consumer—the Dynabook’s user was supposed to be the creator of her own tools, a smarter, more capable user than the market discourse of the personal computing industry seems capable of inscribing—or at least has so far, ever since the construction of the “end-user” as documented by Bardini & Horvath. (p. 218)

Kay’s contribution begins with the observation that digital computers provide the means for yet another, newer mode of expression: the simulation and modeling of complex systems. What discursive possibilities does this new modality open up, and for whom? Kay argues that this latter communications revolution should in the first place be in the hands of children. What we are left with is a sketch of a possible new literacy; not “computer literacy” as an alternative to book literacy, but systems literacy—the realm of powerful ideas in a world in which complex systems modelling is possible and indeed commonplace, even among children. Kay’s fundamental and sustained admonition is that this literacy is the task and responsibility of education in the 21st century. The Dynabook vision presents a particular conception of what such a literacy would look like—in a liberal, individualist, decentralized, and democratic key. (p. 262)

I would encourage interested readers to read Maxwell’s paper in full. He gives a rich description of the problem of computers in the educational context, giving a much more detailed history of it than I have here, and what the best minds on the subject have tried to do to improve the situation.

The main point I want to get across is if we as a society really want to get the greatest impact out of what computers can do for us, beyond just being tools that do canned, but useful things, I implore educators to see computers and programming environments more as apparatus, instruments, media (the computers and programming environments themselves, not what’s “played” on computers, and languages and metaphors, which are the media’s means of expression, not just a means to some non-expressive end), rather than as agents and tools. Sure, there will be room for them to function as agents and tools, but the main focus that I see as important in this subject area is in how the machine helps facilitate substantial pedagogies and illuminates epistemological concepts that would otherwise be difficult or impossible to communicate.

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

# Are we future-oriented?

The death of Neil Armstrong, the first man to walk on the Moon, on August 25 got me reflecting on what was accomplished by NASA during his time. I found a YouTube channel called “The Conquest of Space,” and it’s been wonderful getting acquainted with the history I didn’t know.

I knew about the Apollo program from the time I was a kid in the 1970s. I was born two months after Apollo 11, so I only remember it in hindsight. By the time I was old enough to be conscious of the Apollo program’s existence, it had been mothballed for four or five years. I could not be ignorant of its existence. It was talked about often on TV, and in the society around me. I lived in Virginia, near Washington, D.C., in my early childhood. I remember I used to be taken regularly to the Smithsonian Air and Space Museum. Of all of their museums, it was my favorite. There, I saw video of one of the moon walks, the space suits used for the missions (as mannequins), the Command Module, and Lunar Module at full scale, artifacts of a time that had come and gone. There was hope that someday we would go back to the Moon, and go beyond it to the planets. The Air and Space Museum had an IMAX movie that was played continuously, called “To Fly.” From what I’ve read, they still show it. It was produced for the museum in 1976. I remember watching it a bunch of times. It was beautifully done, though looking back on it, it had the feel of a “demo” movie, showing off what could be done with the IMAX format. It dramatizes the history of flight, from hot air balloons in the 19th century, to the jet age, to rockets to the Moon. A cool thing about it is it talked about the change in perspective that flight offered, a “new eye.” At the end it predicted that we would have manned space missions to the planets.

Why wouldn’t we have manned missions that venture to the planets, and ultimately, perhaps a hundred years off, to other star systems? It would just be an extension of the advancements in flight we had made on earth. The idea that we would keep pushing the boundaries of our reach seemed like a given, that this technological pace we had experienced would just keep going. That’s what everything that was science-oriented was telling me. Our future was in space.

In the late 1970s Carl Sagan produced a landmark series on science called “Cosmos.” He talked about the history of space exploration, mostly from the ground, and how our destiny was to travel into space. He said, introducing the series,

The surface of the earth is the shore of the cosmic ocean. On this shore we’ve learned most of what we know. Recently we’ve waded a little way out, maybe ankle deep, and the water seems inviting. Some part of our being knows this is where we came from. We long to return, and we can…

### Winding down?

As I got into my twenties, in the 1990s, I started to worry about NASA’s robustness as a space program. It started to look like a one-trick pony that only knew how to launch astronauts into low-earth orbit. “When are we going to return to the Moon,” I’d ask myself. NASA sent probes out to Jupiter, Mars, and then Saturn, following in the footsteps of Voyager 1 and 2. Surely similar questions were being asked of NASA, because I’d often hear them say that the probes were forerunners to future manned space flight, that they were gathering information that we needed to know in advance for manned missions, holding out that hope that someday we’d venture out again.

The Space Shuttle was our longest running space program, from 1981 to 2011, 30 years. Back around the year 2000 I remember Vice President Al Gore announcing the winner of the contract to build the next generation space shuttle, which would take the place of the older models, but it never came to be. Under the administration of George W. Bush the Constellation program started in 2005, with the idea of further developing the International Space Station, returning astronauts to the Moon, establishing a base there for the first time, and then launching manned missions to Mars. This program was cancelled in 2010 in the Obama Administration, and there has been nothing to replace it. I heard some criticism of Constellation, saying that it was ill-defined, and an expensive boondoggle, though it was defended by Neil Armstrong and Gene Cernan, two Apollo astronauts. Perhaps it was ill-defined, and a waste of money, but it felt sad to see the Space Shuttle program end, and to see that NASA didn’t have a way to get into low-earth orbit, or to the International Space Station. The original idea was to have the first stage of the Constellation program follow, after the space shuttles were retired. Now NASA has nothing but rockets to send out space probes and robotic rovers to bodies in space. Even the Curiosity rover mission, now on Mars, was largely developed during the Bush Administration, so I hear.

I have to remember at times that even in the 1970s, during my childhood, there was a lull in the manned space program. The Apollo program was ended in the Nixon Administration, before it was finished. There was a planned flight, with a rocket ready to go, to continue the program after Apollo 17, but it never left the ground. There’s a Saturn V rocket that was meant for one of the later missions that lays today as a display model on the grounds of the Kennedy Space Center. I have to remember as well that then, as now, the program was ended during a long drawn out war. Then, it was in Vietnam. Now, it’s in the Middle East.

Manned space flight ended for a time after the SL-4 mission to the Skylab space station in 1974. It didn’t begin again for another 7 years, with the first launch of the Space Shuttle. The difference is the Shuttle was first conceptualized towards the end of the Apollo program. It was there as a goal. Perhaps we are experiencing the same gap in manned flight now, though I don’t have a sense that NASA has a “next mission” in mind. As best I can tell the Obama Administration has tasked NASA with supporting private space flight. There is good reason to believe that private space flight companies will be able to send astronauts into low-earth orbit soon. That’s a consolation. The thing is that’s likely all they’re going to do in the future–launch to low-earth orbit. They’re at the stage that the Mercury program was more than 50 years ago.

What I ask is do we have anything beyond this in mind? Do we have a sense of building on the gains in knowledge that have been made, to venture out beyond what we now know? I grew up being told that “humans want to explore, to push the boundaries of what we know.” I guess we still are that, but maybe we’re directing that impulse in new ways here on earth, rather than into space. I wonder sometimes whether the scientific community fooled itself into believing this to justify its existence. Astrophysicist, and vocal advocate for NASA, Neil deGrasse Tyson has worried about this, too.

I realized a few years ago, to my dismay, that what really drove the creation of the space program, and our flights to the Moon, was not an ambition to push our frontiers of knowledge just for the sake of gaining knowledge. There was a major political aspect to it: beating the Soviets in “the space race” of the 1960s, establishing higher ground for ourselves, in a military sense. Yes, some very valuable scientific and engineering work was done in the process, but as Tyson would say, “science hitched a ride on another agenda.” That’s what it’s often done in human history. Many non-military benefits to our society flowed from what NASA once did, none of which are widely recognized today. Most people think that our technological development came from innovators in the private sector alone. The private sector did a lot, but they also drew from a tremendous resource in our space and defense research and development programs, as I’ve documented in earlier posts.

I’ll close with this great quote. It echoes what Tyson has said, though it’s fleshed out in an ethical sense, too, which I think is impressive.

The great enemy of the human race is ignorance. It’s what we don’t know that limits our progress. And everything that we learn, everything that we come to know, no matter how esoteric it seems, no matter how ivory tower-ish, will fit into the general picture a block in its proper place that in the end will make it possible for mankind to increase and grow; become more cosmic, if you wish; become more than a species on Earth, but become a species in the Universe, with capacities and abilities we can’t imagine now. Nor do I mean greater and greater consumption of energy, or more and more massive cities.

It’s so difficult to predict, because the most important advances are exactly in the directions that we now can’t conceive, but everything we now do, every advance in knowledge we now make, contributes to that. And just because I can’t see it, and I’m an expert at this, … doesn’t mean it isn’t there. And if we refuse to take those steps, because we don’t see what the future holds, all we’re making certain of is that the future won’t exist, and that we will stagnate forever. And this is a dreadful thought. And I am very tired when people ask me, “What’s the good of it,” because the proper answer is, “You may never know, but your grandchildren will.”

— Isaac Asimov, 1973, from the NASA film “Small Steps, Giant Strides”

Then as now, this is the lament of the scientist, I think. Scientists must ask society’s permission to explore, because they usually need funds from others to do their work, and there is no immediate payback to be had from it. It is for this reason that justifying the funding of that work is tough, because scientific work goes outside the normal set of expectations people have about what is of value. If the benefits can’t be seen here and now, many wonder, “What’s the point?” What Asimov pointed out is the pursuit of knowledge is its own reward, but to really gain its benefits you must be future-oriented. You have to think about and value the world in which your children and grandchildren will live, not your own. If your focus is on the here and now, you will not value the future, and so potential future benefits of scientific research will not seem valuable, and therefor will not seem worthy of pursuit. It is a cultural mindset that is at issue.

Edit 12-10-2012: Going through some old articles I’d saved, I came upon this essay about humanity’s capacity for intellectual thought, called “Why is there Anti-Intellectualism?”, by Steven Dutch at the University of Wisconsin-Green Bay. It provides some reasonable counter-notions to my own that seem to confirm what I’ve seen, but will still take some contemplation on my part.

There’s no science in the article. In terms of quality, at best, I’d call this an “executive summary.” Maybe there’s more detailed research behind it, but I haven’t found it yet. Dutch uses heuristics to provide his points of comparison, and uses a notion of evidence to provide some meat to the bones. He asks some reasonable questions that are worth contemplating, challenging the notion that “humans are naturally curious, and strive to explore.” He then makes observations that seem to come from his own experience. Overall, he provides a reasonable basis for answering a statement I made in this article: “I wonder sometimes whether the scientific community fooled itself into believing this to justify its existence.” He comes down on the side of saying, in his opinion (paraphrasing), “Yes, some in the scientific community have fooled themselves on this issue.” He discusses the notion that “humans are naturally curious,” due to the behavior exhibited by children. He concludes by saying that children naturally display a shallow curiosity, which he calls “tinkering.” The harder task of creative, deep thought does not come naturally. It’s something that needs to be cultivated to take root. Hence the need for schools. The question I think we as citizens should be asking is whether our schools are actually doing this, or something else.

# An example of computing as a new medium

Bret Victor, a former designer at Apple, is working on a way to use a computer to make math more meaningful. I can see that he really gets the representational aspect, that the symbols are not the math, just a way to represent it, and it’s not a particularly good way to represent it. This is not the whole of math encapsulated into something that’s easy to understand (math is about assertions and inferences of relationships, which are then proved or disproved), but it’s an alternative to using symbols for representing complex relationships.

Here’s an article talking about Bret’s work on an early version of something he’s working on for the iPad.

Great stuff, and I congratulate him on finding a good use for a computer!