7 Gpeople

While at a conference in Istanbul, I went to the İSTANBUL ARKEOLOJİ MÜZELERİ, which was an absolutely fascinating archeology museum. Istanbul has featured prominently in the growth of civilization, and I struggled to keep track of the many different civilizations and cultures that occupied the region at one time or another. I had to find a youtube video to help me sort it out.

There was a very nice exhibit on Troia (Troy), which apparently really existed; it's ruins were unearthed in a farm field not too far from here. It was settled, destroyed, and resettled in 9 different epochs before being ultimately abandoned. Even back then, it seems that anything you dug up had a 1000-year history. Buildings were built on top of buildings. The reconstruction of the different settlements was interesting.

It was really hard for me to get my head around how small cities were in comparison to now. Istanbul currently has 13 Mpeople living in its greater metropolitan area. In 3000 BC, that was the human population of the world. The largest cities in antiquity were ~250 kpeople. It made me wonder if all of our advancements in technology and culture in the last couple hundred years could be attributed strictly to 1) more people to do the work and 2) longer tails on the normal distribution of people with various abilities.

So just how many people were there as a function of time? The log-log plot above from wikipedia shows current best estimates. Apparently, some 70 kyears ago, possibly as a result of a major volcano eruption, the human population was reduced to something on the order of 1000 to 10,000 "breeding pairs." Since then, the population rapidly recovered to several million, where it remained stable until agriculture was developed. This is all in a nice video tracing genetic migration via mDNA.


Since then, there has been exponential growth (a line on log-log plots) with a transition to a slower growth coefficient at ~400 BC. Occasional Black Plagues aside, the human population has increased dramatically. I remember hearing once that half the people who ever lived are alive right now. That's actually definitely false--it's closer to 6%. Also, everyone seems to think that population growth is accelerating (remember this video from the 80's ?). The graph above definitely shows that's not true, either.

But what is true is that this growth cannot continue unchecked without hitting its head on something, be it food supply, global warming, danger of pandemics, warfare, declining birth rates, or whathaveyou. It's estimated that in October of this year, 2011, there will be 7 Gpeople on the planet. This map shows where the population currently is, but it's estimated that much of the growth in the next century will happen in poverty-stricken Africa. Things pretty much have to plateau around 10 Gpeople, though.

So what to do? The most effective ways to reduce birth rates, which is key to controlling population growth, global warming, saving the environment, and many of the rest of our problems are:

1. contraception
2. improving the standard of living (ending poverty)
   
3. education (and education about contraception)
   
4. and reducing infant/child mortality

That last item is counter-intuitive. The reason it is important is that when survival rates are low, couples have more children to compensate, including a buffer for uncertainty. Having a predictable path from birth to adulthood allows for more precision in family planning.

What are the chances?

I cringe every time that I hear this phrase. I heard it most recently when my friend had her car stolen from San Juan. It was recovered in a semi-drivable state in Bayamon. She invested a couple thousand dollars to get rid of the "semi", only to have the car re-stolen a couple of months later. This time, when the car was recovered in Dorado, there was no "semi" to be had, so she's currently trying to sell it for pieces. While the police were fairly understanding (though less than helpful) the first time her car got stolen, the second time was occasion for all sorts of raised eyebrows and skepticism. And in exasperation my friend uttered the phrase in question.

"What are the chances" is a Pandora's box of bad statistics. Statistics is about hedging your bets given incomplete information, but this phrase is always uttered after the fact, when we have (relatively) complete information: it happened. So unless you plan on repeating the experiment, the chances are one. It happened.

As an example, let's take the famous Goat/Car Puzzle. There are 3 doors; one has a car behind it and the other two have goats. After you pick a door, the game-show host opens one of the other doors and reveals a goat. You are then offered the option of switching your choice to the other door. If you play this game repeatedly, you'll win more often if you switch your choice. But the instance just played out, the car was behind one of the doors, and if that was the door you picked, your chances of getting the car were 1. If you didn't, your chances were 0.

You might object: "What were the chances beforehand, when I didn't know where the goat and car were?". But to do that, you need to make some assumptions. You need to assume that at each playing of the game, the cars and goats are randomly assigned and/or you randomly pick doors. Otherwise, it might be the case that the car is always behind door #1, and you always pick door #2. Your chances of success wouldn't be so good in this case. You might have decent prior knowledge of how cars, goats, and doors are picked in this example, but for everyday occurrences, we usually have much more limited prior knowledge. Are cars randomly stolen, or are certain brands targeted? Are certain areas targeted? People often assume that these processes are random, but they rarely are. With limited priors on these events, the question "what are the chances" can't be answered with any certainty and any answers given should be taken with a great big shaker of salt.

Furthermore, people have selective attention. We ignore whole heaps of ordinary outcomes and only pay attention to ones that strike us as interesting. As a friend of mine once said: "Low probability stuff happens pretty regularly because stuff is happening all the time." Even if the processes involved are random, unlikely outcomes are to be expected if the processes are repeated often enough. People tend to ignore the ordinary outcomes, exclaim at the extraordinary ones, and then assume that something deeper is afoot. In my friend's case, the police started wondering if she was being personally targeted or if she was really bad at locking her car. But even if we assume a random model of car thefts, some number unlikely outcomes doesn't automatically imply that our random model is wrong.

Finally, we also need to keep in mind that in complex systems like real life, there may be a huge number of possible outcomes. But something has to happen. When you roll a die, each number only has a 1/6 chance of coming up. Would you roll a die once and then exclaim: "Wow, it came up six! What are the chances?" In real life, there might be millions of outcomes, each with one-in-a-million chance of coming true, but the fact that one of them happens shouldn't be surprising.

Fighting against all of the pitfalls inherent in asking "What are the chances?", I've developed a reflexive response: "What are the chances?" One.

Attiyah and His Theories

I guess when you're an astronomer, you have to expect to be the target of the occasional crackpot with their personal theory of the universe. My antagonist is Attiyah Zahdeh. I don't know where he's from (although devious research indicates he's on central time, so my current theory is Chicago), or how he got my email, but for a couple of years now I have been getting emails of which the following is the most recent example:

Attiyah's Planetary Motion I introduce this hypothesis in order to be discussed by scientists. I do not claim that I now have any mathematical proof or practical model to support Attiyah's Planetary Motion. I consider that the Kepler's second and third laws themselves support my hypothesis. It seems to me that Kepler failed to conclude that, relative to the Sun, the motion of the planets is the same as of the pendulum.Thus, he coined his second and third laws as alternative statements to express the laws of the simple harmonic motion of the planets. I'm inclined to say that Kepler (1571-1630 A.D.) was not aware of the work of Galileo (1564.1642 A.D.) on the pendulum and the laws of its motion he discovered. The hypothesis of Attiyah's Planetary Motion is four propositions: 1. The planets move not around the Sun but in front of it. 2. The planetary motion in front of the Sun is of the simple harmonic type. 3. The planet (the bob), gravitational force (the length, the line between the Earth's gravity center and the solar gravity center) and the Sun (the solar gravity center as the pivot point), altogether form a pendulum. 4. The planet oscillates in front of the Sun in a hemiellipse. Notes: 1. This hypothesis is an alternative of Kepler's first law only. 2. This hypothesis does not apply to the motion of the satellites.

I have also been spammed with Attiyah's Sun Theory, which I think says that daylight is caused by charged particles (or X-rays, or whatever) hitting our atmosphere--much the same as the mechanism causing the northern and southern lights, and with Attiyah's Hologeomagnetosphere, which asserts that the northern and southern lights are generated by electrical currents in the earth's molten core turning our ionosphere into a giant CRT monitor.

I once thought that these were created as jokes--that "Attiyah" was just the psuedonym of a humorist. Dozens of emails (and several years) later, I'm convinced that Attiyah is real and in earnest. In fact, I've discovered that he visits his theories upon astronomy message boards with some regularity, where he has revealed complete ignorance about how the scientific process works by demanding that others attempt to disprove his theories (the burden of evidence is on the newcoming theory) and by flatly ignoring the evidence that was provided against them. Two years ago, I myself was duped into providing a detailed refutation of Attiyah's Sun Theory, only to have my response disappear into the abyss of cyberspace.

But I'm not bitter. In some ways, Attiyah's doing a lot for science education by getting amateur scientists to review how we know what we know--reminding everyone that the reason we have such a widely adopted set of theories is that they are testably confirmed and mutually consistent. If only intelligent design, creationism, and young-earth hypotheses met with half the ridicule that Attiyah's theories meet on the message boards. Attiyah's only mistake, really, was failing to incorporate a little theology into the mix.

Hidden Variables

I've been having a few conversations about hidden variables lately, so I thought I would post about it. First a little background:

Quantum mechanics (QM), as we know it, is weird. It is a classic example of science as a selection process, as I talked about in the previous post. It set about to solve the problem of predicting the locations, energies, and other microscopic attributes of fundamental particles. When the dust settled, we had one of the most accurate theories ever made (it predicts the mass of the electron to 14 decimal places), but the model used to make these predictions countermanded a lot of things we'd thought were true but never actually got around to testing--intuitive things like "a particle can only be one place at a time", well-established things like "no particle may carry information faster than the speed of light" (which is true, but can be violated over short distances), and most importantly for this post "if you had enough information, you could determine the outcome of any experiment." Nature's rejection of this last idea comes dangerously close to undermining the pillar of scientific philosophy that the universe is predictable insofar as it can be modeled and tested, and it offended a lot of scientists (including Einstein).

What QM says is that there are certain pieces of information that are not simultaneously knowable. If you know a particle's position perfectly accurately, then it is impossible to know its momentum. If you know a particle's orientation along one axis, you can't know it along any other axis. For a long time, many people (including Einstein) thought that this was a shortcoming of QM--that these particles have "actual, hidden values" that QM just didn't know how to predict, and eventually there would be a better theory that could tell us what these values are. Those hopes were shattered in 1964 when John S. Bell proved that there can exist no hidden variables in a way that is compatible with QM. His predictions have been validated by experiment, showing that the reason we don't know the state of a particle is because the universe hasn't made up its mind (excuse the anthropomorphification) until you measure the particle. Crazy.

I like to think of QM like a black curtain at a magic show that allows the universe (the magician) to perform all sorts of sleight-of-hand shielded from the eyes of the audience. On our side of the curtain, there are rules you have to follow--conservation of energy, speed of light, definity of location and state, etc. On the other side of the curtain, anything can happen, so long as when you pull it back out (when we make a measurement), the rules have been obeyed. The "curtain" idea isn't so far-fetched; it's an analogy to Feynman's well-tested theory that the outcome of an interaction is the sum over all possible interaction pathways. The universe takes advantage of this curtain to do things that we think should be impossible, like transmitting information about a measurement instantaneously between two particles that share a quantum state. Furthermore, the universe relies on the fact that we can never see behind the curtain (this is an interpretation of Bell's theorem) because if we could, we could use that machinery to transmit our own information faster than the speed of light, and that violates causality. Causality, by the way, is another principle that we cling to because it seems self-evident, but may in fact be wrong. It will take a unification of the theories of QM and general relativity to sort that out.

Shifting gears into philosophy, I was talking with my uncle, who came to visit last week, about how people look for meaning in their lives. His argument was that back in human history, when the universe seemed a jumble of arbitrary events, a physical, all-powerful deity with direct control over all that happened was a powerful metaphor for finding meaning in the events of ones life. However, as scientific knowledge has gradually encroached on the idea that a god can take direct physical action in the universe, religion has had to respond to the sense that science is pushing away meaning in life. My uncle's thoughts were that a physical deity is becoming an outdated way of looking for meaning in life, and that we need to think about a more spiritual, humanistic God. I agree with this philosophy, but I wonder if the rejection of the hidden variable hypothesis (the magician's curtain) provides a home for religions that require a physical deity.

Philosophy of Science (a Rant)

I read an article today that got my back up a little. Let me give a little background to explain why.

I grew up in the rural, conservatively religious town of Rangely, CO. The first real experience I remember having that set me apart from the majority of the town came in 7th grade science class when we where discussing (you guessed it) evolution. Presented with another in the series of assertions that seems to constitute science education, I blithely bought in. My peers, who had been privately informed that evolution was not to be "believed in", discovered by waywardness, they dubbed me Monkey Boy. Yes, I know. Hilarious.

This was certainly not the last time that I butted heads with conservatives in my town, and it stands at the base of a growing sense of disconcert that I have felt towards organized religion. In the meantime, I went on to study physics in college, and am now a graduate student in astronomy (I do experimental cosmology). It has been surprising to me, now that I have started being introduced as an astronomer, to suddenly to have became an "Interpreter of the Voice of Science" (preacher) for people who want to know how our universe came to be.

The reason the above article got my back up was that I've always been careful, in these situations where I find myself describing the history (as we know it) of the universe, to stress the differences between science and religion. It's confusing terrain because cosmology has only recently come into the realm of science. My "what is science" speech usually ends up something like the following: science isn't a body of knowledge (despite what constitutes science education), or a belief system, or a religion. It is a methodology. Its groundings are philosophical, but that doesn't make its results philosophical. Science started from the philosophy that the universe is predictable: that one can predict the outcome of an experiment if one knows the initial conditions to sufficient accuracy.

Out of this philosophy (which the microscopic, quantum universe has helped us to understand is not strictly correct), a method was devised for arriving at an understanding of the predictability of the universe. Hypothesize, Predict, Experiment, Analyze, Conclude. Elementary school science fair stuff (except that "conclude" now means "peer review"), but still confusing. Science is a level playing field where anyone can make up any theory they want, in the face of all current knowledge if they want, using any strange force or being or Flying Spaghetti Monster, and science has nothing to say about it until you make predictions, devise an experiment to test them, and peer review to make sure it's reproducible. Science works like infants learning shapes--pick a block, try to jam it through the hole, and repeat until you succeed.

The framework that seems to work best for predicting the outcomes of experiments involves math. I'll save a discussion of why this might be for another blog, but it's important to realize that it didn't have to be this way. The universe could have chosen to play by different rules, or perhaps there are even models that can predict the outcomes of all the various experiments we've tried without using math. Math is just a model we have that works. Once you have two models that have equivalent predictive power, science has nothing to say again. Yes, I know about "Occam's Razor", but that's philosophy again, despite its popular portrayal as a pillar of science.

I get frustrated when people (even scientists and cosmologists) misunderstand science to be a body of knowledge, or a set of "transcendental laws", because (it seems to me) it's putting the cart before the horse. Whatever laws and rules we have are only as good as the degree of testing they have undergone, and are subject to revision and replacement as new experiments reveal their flaws. And we know they're flawed. The two most accurate physical models we have--gravity and quantum mechanics--are mutually inconsistent, and neither of them are able to account for an accelerating expansion of the universe (the "Dark Energy" problem) or for motions on galactic scales (the "Dark Matter" problem). So how can a self-respecting scientist hold up a "transcendental law" and claim it is more than our current best model?

My personal opinion is that referring to science as a body of knowledge makes it akin to religion--something transcendental and immutable (and inaccurate) handed down from above. What makes science science are the error bars: little reminders that our models are only as good as the extent to which they have been tested.