New Website

I have migrated the parts of this blog I felt like saving to my new website, www.colingrove.com. I have, among other things, a new blog there which I intend to be updating on a regular basis.

Eben Alexander, a neuroscientist out of Harvard, recently wrote a book about his "near-death experience". Unfortunately, Alexander took his experience as "Proof of Heaven". Needless to say, I'm skeptical. And now, we hear about researchers at Michigan who have observed an electrical surge in the brain shortly before death which could explain the types of vivid experiences described by Alexander and others. It serves as a reminder of how little we really know about the brain.

Computer-Graded Math Homework: Why Not?

In recent decades there have been more and more efforts to introduce computers into math education, with varying levels of success. The University of Iowa now offers several different computer-based courses, but they have not, for the most part, replaced the traditional lecture and discussion courses that likely look the same as they did fifty years ago. One area that I think is underdeveloped is computer grading.

The first widespread use of computer grading of which I'm aware was the introduction of the 'e-rater' in grading GRE essays. Interest in computer grading has grown recently with interest in Massive Open Online Courses (MOOCs). Grading an essay is not an easy task for a computer, and current algorithms tend to rely on quantitative notions like word count and average word length to score submissions. Many academics consider this somewhat absurd, and I tend to agree with them. Verbosity and use of advanced vocabulary are only helpful when succinct, clear prose won't do.

But I expect that grading math, say, college algebra and possibly calculus, would be considerably easier for computers. There are currently software packages that allow professors to post quizzes in which students are given a box to enter the answer, or possibly multiple-choice options. But I think that computers could actually check and give feedback on work, this being the type of feedback that students actually find useful. Furthermore tools currently in place in computer-grading software for essays could be helpful, such as a process through which students could continually revise their homework and watch how their score changes. This would encourage revision of work, and would encourage students to keep changing their work until they get it right, something that is important in math, but rarely incentivized in a realistic way. These same methods could be used to grade exams, and would probably be an improvement over the current multiple-choice tests given in large universities.

These ideas aren't new, they've been implemented for essay grading. But it seems to me they lend themselves more to grading math.

Two Eternal Tensions

It occurred to me while reading Kevin Kelly's What Technology Wants that there are two constant (related) tensions that play a big role in civilization (by this I do not mean that these are the only forces, I simply am focusing on two of them). One is the tension between the desire for the benefits of government and the desire to be as free as possible. The other is the tension between the desire for the benefits of technology and the desire to have as much control over our lives as possible, to feel that it is we that use technology and not the other way around.

The relationships between these notions are complicated. Government is a type of technology, and ideally enhances freedom in that it enables a civilization in which we have a much wider range of choices, giving us a net gain of freedom. One of Kelly's main points is that this the typical effect of technology. So far, so good.

But reality is more complicated, because government and technology in general both tend to overreach. Government, unchecked, will seek to empower itself at the cost of civil liberties. Technology, unchecked, will seek to empower itself at the cost of our well-being and our environment. However, both are worth the cost, so instead of asking how to do away with government or technology, we must ask how to steer it.

To check government (inevitably world government) will always be a struggle. Desired methods will often go beyond what is legal (civil disobedience) but, at least for the more democratic governments, will rarely approach anything resembling revolt. To check technology, we must simultaneously embrace it and be vigilant against its harms. Kelly makes an argument that the Precautionary Principle, whereby a technology or policy must be proven to do no harm before it can be used, is a terrible notion to apply. Global warming denialists like to latch on to criticism of the Precautionary Principle, but let us not be dissuaded from examining it critically by them. One can't help but assent to the observation that the Precautionary Principle is self-contradictory, since in order to apply it, we would first have to prove that it can do no harm. And this is really Kelly's point, the harm it does is precisely in preventing technological progress. He recommends a program of careful adoption and vigilant oversight.

But to me the parallel is more clear in my day-to-day life, at least on the technological side. I am very into technology but I try to be careful that the technology I use helps me rather than harms me. For example, I've found Twitter to be mostly distracting, something that is too tempting to check every ten minutes, and mostly full of content I don't actually get that much out of. I've tried it a couple times, but I doubt I'll go back for quite awhile. I'm on the fence about RSS readers for the same reason. Of course I'm not always successful, I've gotten sucked into computer games or, worse, television shows, many of which provide mindless entertainment.

So I guess my point is that we benefit greatly from government, even as we (well, some of us) often find it necessary to check its overreach, in the same way that we benefit greatly from technology, even as we struggle to live our lives independent of its grasp.



I have felt the urge to publish various thoughts on matters sparked by What Technology Wants and have chosen not to restrain myself to the book review format, where I put them all in one post. This will probably be how I share my thoughts while reading from now on.

Anti-science sentiment on the Left

It's no secret that many conservatives, or at least their congressional representatives, are at odds with facts on which scientists agree, from evolution to global warming to whether raped women can get pregnant. But the left should hardly claim the scientific high ground without addressing certain anti-science movements in liberal ideology.

One common belief is that we liberals are so in touch with our bodies that we know when something hurts/helps us even when medical science disagrees. Examples of this include the gluten-free movement, advocates in the existence of chronic Lyme disease, and the belief in homeopathy. Intelligent individuals allow advocacy of these unscientific diseases and remedies to become such an integral part of their identity that changing their opinions in the face of contradicting evidence (or lack of supporting evidence) would amount to losing part of their sense of self. I do not have proof that backers of these ideas skew to the left politically, and if presented with evidence that this isn't true, I would have to change my mind. But it's been true in my experience.

Another common belief is that people were better off in the past. Strains of this belief run through a lot of environmentalist thinking. While liberals are all for moral progress, they often are hesitant to support technological progress. Kevin Kelly recently wrote an excellent book on technological progress (review will come when I finish it), which addresses concerns that such progress brings more harm than good. I will defer to him in countering these arguments, but I want to point out that this hesitancy is purely conservative, even if held by liberals. For being "liberal" is not the same as being "progressive".

It seems to me that progressives accept change as inevitable and try to push it in as good a direction as possible, while conservatives try to slow it down or even reverse it (note that by "conservatives" I do not necessarily mean political conservatives, though those groups often do overlap). Note that both groups see a potentially dangerous future which they try to avoid. Historically it seems clear that conservatives cannot succeed, but that does not ensure success for progressives.

Right now the generic liberal position seems to be progressive morally but conservative technologically. This would pair nicely with the (politically) conservative position being conservative morally (which it is) and progressive technologically, but this last position certainly isn't uniform. While capitalism is an element of technological progress, so is the science through which we learn about global warming and evolution, so the (politically) conservative position seems split on technological progress.

This does not seem to bode well. We can only hope that we will do our best to steer the technological stampede, instead of planting ourselves in its way, only to be trampled.

Glasshouse, by Charles Stross

(Originally written for Math Graduate Board Newsletter)

It's the 27th century, but Robin has chosen to wake up from his memory excision in an orthohuman body. You could say he's old-fashioned that way. After all, when death just means reversion to your last backup, it isn't hard to tell the assembler to put you in just about any kind of body you can imagine. Sticking with an orthohuman body isn't just a choice, it's a statement.

But when Robin is recruited to participate in a sociological study recreating the pre-Acceleration dark ages (20th/21st centuries), "orthohuman" gets a little too realistic. There are no assemblers to rearrange her atoms in case of injury or illness, the NPCs there to aid in her transportation drive taxis instead of pointing her to the nearest T-gate, and experimenters have gone to the extreme of making the participants fertile (Robin has been female orthohuman before, but she is not happy with the weakness of her new body, and fertility is just a kick in the stomach). And then there's the society in which she's imprisoned; Were morals really so irrational, customs so arbitrary, life so uncomfortable? But she's got more to worry about when she begins to remember what, through memory excision, she tried so hard to forget...

In Glasshouse, Charles Stross foresees a future in which a mind can be backed up, printed into the physical world in any body and in as many copies as desired. The driving question behind Stross' book, then, is the question of identity. If "you" are not your body, what are "you"? This classic philosophical question gains both complications and insights in Stross' future, in which one's consciousness can be not only split or merged, but also tampered with. If someone reaches in and swaps a few memories, or tweaks a few personality dials, what's left?

Stross manages, as well, to pack in allegories of and commentary on no less than religion, gender roles, death, war, government surveillance, and more, all in what is certainly a page-turner. The best science fiction not only provides a specific vision of the future, it offers sharp critique of the present, and is, if not quite self-fulfilling prophecy, at least a cog in the engine of progress. Glasshouse fits the bill as well as anything.

It's Time

We humans seem to experience time in a very specific way. Our notion of time as linear and oriented (that is, the direction of time matters) is very strong. But is this necessarily the case?

Now first I want to state that I have very little understanding of general relativity, which presumably answers some of my questions about the nature of time. So in my discussion here I will restrict myself to the methodology of thought experiments, without trying to delve into the mathematics of relativity too much. Furthermore I have no doubt that in the process of explaining my thoughts I will expose more ignorance of physics than should be expected of a physics major, but I hope these ruminations will nevertheless be interesting as the simple musings they are.

First, must time be one-dimensional? We certainly experience time as one-dimensional. We are only conscious of tracing out time in a single dimension, and in that dimension, in a single direction. But as we go through our lives, do we not also only trace out a single dimension in space? Our past and future existence in space can be drawn as a line. To use mathematical terminology, it is a one-dimensional manifold immersed in the (locally) Euclidean 3-space. Might our path through time also be a one-dimensional manifold embedded (i.e. we don't seem to experience the same moment twice) in higher dimensions?

These thoughts fail Occam's Razor, unless there is a reason that extra dimensions of time would solve problems presented by physical theories involving just one dimension. Furthermore  it isn't clear to me it matters whether the extra "unseen" dimensions so popular with today's theoretical physicists need to be specifically identified as dimensions of time or space; in fact, I suspect such identification is unnecessary. Time is considered separate specifically because we experience it in the unique way we do, so calling extra dimensions that we do not experience dimensions of time would be confusing.

A perhaps more interesting question, is that if we experience time as an oriented one-manifold (i.e., it looks linear when you zoom in), what kind of one-manifold is it? Assuming it's connected, there aren't that many options. It could be an infinite line (time has no beginning or end), a ray (time has a beginning (or end) but no end (or beginning)), a finite line segment, or a loop.

The Big Bang indicates that 13.7 billion years ago, something important happened, but it isn't clear that was actually the start of time. It could simply be a singularity in the space-time manifold, in which the spatial dimensions collapsed but the time dimension did not. For example, take a donut and squish part of it down to a point. The donut still is 3-dimensional everywhere but the squished point. Suppose now that the dimension that goes around the donut hole is time. As time goes by, we are travelling around the donut. We can see the two spatial dimensions that are perpendicular to the time dimension at any point except for the squished point. This point is a singularity.

If this is what the Big Bang was, there's no real reason to believe the donut is squished in only one place. In fact it isn't clear we will every be able to know anything about the other side of the singularity. But this is my blog, so I'll go ahead and say I like the picture of the once-squished donut. If I'm not mistaken, this is similar to the notion of time proposed by those studying Loop Quantum Gravity. My next question would be, is the loop that describes the time dimension smooth? If it isn't, it would seem that we really have no hope of learning anything about the other side of the singularity.

The primary curiosity about time is why we experience it in such a different way from the other dimensions. I suspect that the squished donut just exists, and that our voyage around it is an illusion. Our existence in the dimension is no different than our existence in each dimension of space, but for some reason while we can look in the mirror and see ourselves from head to toe, we cannot at once see ourselves from birth to death. Even our language doesn't allow it; without a second thought I just stated that we cannot at once see ourselves from birth to death, nearly without perceiving the tautology. An understanding of time such as this would have many fascinating consequences. For example, my death would be no more profound a notion than the top of my head.

But for now we'll have to wait for the neuroscientists to give us a little more to go on. Not that lack of information will stop anyone from philosophizing.