Bob Frankston suggested I post some of my recent remarks and references to Orbital Angular Momentum and its potential value in increasing the capacity of “spectrum” (the word I think misleads everyone, but that’s a subject I’ve talked about a lot). So I did put up a brief page here, with some references also. I believe my comments made it onto Dave Farber’s Interesting People list, though I do not follow that list.
This is part of my general quest to get the wireless community to stop thinking about radio as “colors” and “rays” and “channels”, since they are poor approximations to the physics of EM waves, based on Marconi’s techniques for CW multiplexing of morse code. I wish the regulators were far more cognizant of the fundamental physics and our modern Computational Radio toolkit – the path I started following back in 1994, when I got fascinated with wavelet analysis and UWB Impulse Radio and their bases in physics and connection to information theory.
What do we teach when we teach science in school? And really, why do we teach science that way?
I’ve personally never been quite sure whether I’m more of a scientist, engineer, or mathematician. The public lumps these all together for some reason, perhaps because they all appear to deal with concepts that are expressed in terms that must be learned carefully, because they certainly are not wired into our brains, and they aren’t the basis of popular culture either, unlike literature, art, history, sports, etc.
The science we teach is pretty old. Mostly 19th century ideas about the world around us are taught as “facts” with little but anecdotal data to support it. We teach it via an ontology that replays the history of science, thus the newest and most powerful scientific understandings are viewed as “too advanced”. If it weren’t so widely discredited, we would be teaching K-12 kids about phlogiston first, and general chemical oxidation reactions second, just as one example of that.
We don’t teach kids ancient Greek and French cave drawing first, do we?
I’ve heard lots of reasons for teaching “old” science, and old models and definitions taught as facts, over the years, and the reasonsnever really made a lot of sense. They certainly don’t make sense today. If we rethink the whole enterprise of what we teach as science, we have a real opportunity – perhaps a bigger opportunity than the big postwar drive towards science surrounding the Kennedy space program.
What got me bugged about this issue was reading a really fascinating book I’ve recommended to many people recently: The Blind Spot: Science and the Crisis of Uncertainty by William Byers. In it, as part of Byers’ main theme, he points out that the 20th century was marked by a profound re-learning of much we thought certain scientifically. Yet our school systems teach much of that old science as “certain” today.
Two deep questions about physics will suffice to make my point:
1) Is the Universe’s geometry Euclidean? We teach Euclidean geometry under the unadorned name “Geometry” as if it were foundationally correct. And we teach physics (including elementary astrophysics and cosmology) as if the universe were Euclidean. But by the end of the 20th century it’s become pretty clear that the universe’s geometry is non-Euclidean. That’s what Einstein proposed in the first decade of the 20th century, and more than 100 years later, it’s pretty clear that he was right in rejecting Euclid. Many (but not necessarily all) of the theorems taught in High School geometry also can be derived without using the parallel postulate in their proof – and non-Euclidean geometry need *only* be complicated to people who have learned Euclidean geometry first.. That postulate, however, is almost certainly *scientifically* wrong…. do we teach geometry according to Euclid because it’s always been taught that way? If so, we should put a caveat in the front of the book that we are teaching something that kids should forget about when they learn more about physics? [Euclidean geometry is a consistent formal theory, but teaching it first is profoundly misleading, if our universe is not that way.]
It would be quite easy to start with a course in the Geometry that actually matches the Universe as we know it. Just as rigorous, it still generates the same answers for normal problems, and conceptually it would be much easier to understand cosmology and astrophysics as they are today.
2) Is there nothing? One of the most painful parts of physics teaching these days is the conceit used in its teaching that a true “vacuum” exists or that experiments can be perfectly isolated… Teaching kids the idea that they can create conditions of complete vacuum, with no fields, no matter/energy, … except for, say, a couple of billiard balls representing masses has a real downside. The downside is that we have no evidence that such a vacuum exists or can exist. My own sense is that we got to this place by inventing the “number” zero, and generalizing. However the number zero, and the null set, are *far more complicated* than almost any other concepts we shove down kids throats without explaining them. Worse yet is the idea of “nothing”. When we reason about “nothing” or include it in our models, it creates havoc – just think about this: is “no goats” the same as “no apples”? No goats is a much simpler concept than “nothing”, because it implies goats exist somewhere. “Nothing” implies the absence of real categories of things, and categories of things that cannot be real, and there are clearly far more of those hypothetical things than there are kinds of real things. This is far from science – more like mysticism.
We use “nothing” and “zero” in *very* sophisticated ways, and in actual science, we have to be *very careful* lest we trip up and misuse these concepts. It’s very hard to differentiate “nothing” from “I haven’t found any way to measure all aspects of reality yet, but maybe there is something there that we haven’t managed to notice.”
We have no scientific evidence for “nothing” being real. (and some experimental evidence that the “quantum vacuum” is far from “nothing”, which would call almost all we teach about physics into question…)
Kids tend to be very concrete, of course. If you only provide them with examples of things where everything is simple and fits the “theory du jour”, most kids will assume that their authoritative teachers and textbooks are telling them everything they need to know. But in fact, schools teach a lot of science that is just plain known to be wrong, and even some big howlers at that. It’s not just oversimplification – we teach things we now know to be wrong.
The law of conservation of mass and the law of conservation of energy are known to be wrong. And now that we know how to measure mass and energy, we don’t need nuclear reactions to show it is true. That doesn’t mean we can’t talk about the “engineering” concept of conservation of mass, which is true in most fields of engineering that don’t involve high speeds or nuclear reactions – but it’s not science, it’s engineering. (and don’t get me started on “equilibrium” thinking – the universe is far from equilibrium, as Prigogine showed us – it’s what he calls a dissipative system. Dissipative systems are a far better way to think about biology, work, what the politicians call “energy”, … so we should teach kids science around dissipative systems, not around equilibrium states)
The universe is not laid out in a 3D grid with Cartesian coordinates, either. There is no “0″ point on the axes – no center of the universe, no “omniscient point of view.”
I picked physics. But the same holds for chemistry, biology, …
We teach the notion of “species” in biology as a primary concept. But practicing biologists know that “species” is pretty useless framework for describing biological reality – they are not stable (we’ve demonstrated both Darwinian evolution and Lamarckian evolution are real and common phenomena, once we started looking deeply at more and more of the world), they are not well-defined, and they represent only one perspective on life. When we stop making “species” a central concept, we can see that many kinds of distinctions are more biologically relevant than gamete compatibility.
We teach “genetic determinism” in K-12 biology – but in fact, we know that developmental processes (particularly epigenetic processes of methylation, etc.) play huge roles in all aspects of biology. Is it just the huge egos of Watson and Crick (the same egos that cut Rosalind Franklin out of the Nobel prize) that wanted to call DNA the sole, fundamental “code of life”, inspiring popular culture to invent paranoias about “cloning individuals”? Or was it just an overzealous media that ignored and continues to ignore the evidence that evolution passes information on through means other than DNA? And that DNA is pretty slippery and unreliable stuff (not at all like a computer program)?
We teach that there are “hardwired” parts of physiology and anatomy in every species. Yet we see that “hardwired” things are built by processes that many times don’t work very well. So “hardwired” is actually not hardwired at all. We see only what we want to believe, and science often is the result of removing those blinders by holding our “proof” up to scrutiny.
One great example of completely ignoring what we started learning around the time of the Civil War from James Clerk Maxwell, and on up through the 20th century is the way we teach K-12 kids about electromagnetism and light. Here we fail our kids enormously: we teach kids about the idea that light travels in “rays” from a source like the sun, and can be “bent” by lenses and prisms, while we’ve known for centuries that there is no such thing as a light “ray” at all. What we know is that light is something novel involving electrical and magnetic interactions that behaves like a combination of “waves” and “particles” – but *never* as rays. The experiments that would show this are easy to do for kids, and effective models exist of both (wave tanks and “billiard tables” that vary the speed of “photons” on different areas by having them climb slopes). Rays are a “calculational” device but are not scientific ways to understand light, yet we teach it as if light were “rays” and not something else.
(and of course there’s a great opportunity to combine physics of light with biology and congnitive psychology in exploring how our eyes and mind *actually* perceive things, which is full of opportunity to dispel many “false” facts about “seeing is believing”, replacing them with a better understanding of understanding: “believing is seeing”, a much more scientifically sound notion).
To me, as Byers suggests, we need to embrace *un*-certainty, while learning to understand the cumulative process of discovery and exploration(!) that is Science. This can’t be taught in a way that can be measured by multiple choice tests about *facts*. Here’s a good test question for a science test, if you want to see if a kid gets what science is:
You can even make this “multiple choice”, of course. Instead we have questions like:
Why do all the lawyers in DC assume that “spectrum is like real estate”? I suspect it is because their experience of science in school was to learn a bunch of definitions and metaphors, dumbed down and essentially false, confusing science, engineering, and math thinking with memorizing a list of concepts that can be regurgitated on tests, and memorizing algorithms for solving simple mathematical problems posed as physics and chemistry.
Since more than half of the MIT undergraduates I’ve met in my life are confused about what science is, and they are supposedly the ones most educated in science in the country, I suspect it is an endemic problem… What I do know is that many, many people want to see the US get ahead in STEM. Why not engage that energy? Why not endeavor to teach our kids real science? Today’s science, developed without teaching facts that are known not to be facts. Discuss the way that we struggle with uncovering what we know, the challenges of testing what we think is true (not some sterile “hypothesis” made up so that all kids can pass a test on a “method” that misses the point that science is always subject to revision, but is nonetheless built on hundreds of years of human experience… humanity’s most profound collective, constructive effort).
My view is that there is a *huge* opportunity available to the first culture/country/whatever that actually sets out to create a *real* science curriculum. That is *certainly* not what I see the politicians doing. Sadly, neither are most science educators willing to proceed do do that, though most scientists would probably agree with most of what I’ve just said. The idea of teaching current science is perceived as “too high risk”. Good lord, is teaching a zillion things that “t’aint so” a “low risk”???
Yeah, I know that this makes me sound like a lunatic who doesn’t understand the value of teaching irrelevant, but difficult and formal texts for “critical thinking” purposes. But is it teaching critical thinking to *uncritically* teach a curriculum that makes students learn stuff we know not to be true, then regurgitate it on SATs? That smacks of obscurantism, not at all what science is about!
PS: for the record, I did fantastically on my Physics and Bio SATs and APs, despite my knowing that many of the questions I was being asked were based on things already disproved. But fortunately, I had learned what kind of answers they, the College Board, wanted on the test. So I put myself in the frame of mind of the “science educator community” and spouted the answers they wanted. Got excellent scores. But it’s bass-ackwards to require a student to regurgitate stuff they will have to “un learn” if they go on, as I did, to a career in STEM, and it probably means that most people who pursue non-STEM careers end up learning a lot of things that make it much harder for them to engage with real scientific knowledge when the chance comes up. People accept whatever “just so story” they feel comfortable with about the world, because they have been taught nothing about how discovery and exploration actually work.
Due to a complex double failure, old posts were lost about 9 months ago, and while I’ve reconstructed a couple from network caches, I’ve given up on efforts to reconstruct old blog entries from remnants.
However, I will be posting new material, largely focused on ideas I’m exploring outside of “work” (I’m now at SAP), that some might find interesting, and perhaps a few postings on Internet and radio architecture and policy matters.
One of my grad students (whom I won’t embarrass here) just introduced me to a new UROP student as a fount of Internet know-how by saying that I “invented UDP”. This just seemed odd to me. Perhaps because our culture is so oddly focused on “who” and ignoring the more important “what”. People Magazine is far more appreciated
So I wrote an email back explaining what I thought matters contributions from many groups and a few individuals, all if he could publish it, and upon reflection I decided I should post the note in a place where he could refer to it, but I could ensure its integrity and currency.
The broader point is that what I really care about are the contributions I’ve managed to make to the world – the “what”. I’m not all that humble, but I’d be happy if the ideas I’ve struggled to develop contribute to improving man’s understanding of man and his world. That would be enough. Dayenu (as they say in Hebrew).