Blog Action Day 2009: Holimictic Lakes and Their Current Issues

So, in case you don’t know by now, it’s Blog Action Day 2009… ( or at least, it will be for another half hour. I’m a bit behind the times.)

Blog Action Day is an annual event held every October 15 that unites the world’s bloggers in posting about the same issue on the same day with the aim of sparking discussion around an issue of global importance. Blog Action Day 2009 will be one of the largest-ever social change events on the web.

The topic of choice for this year is: Climate Change. Yes, that scary thing.

I puzzled a while trying to think of something physicsy to tell you about climate change. I could tell you that same story about how CO2 in the atmosphere traps heat causing an increase in average global temperatures. I could tell you that this is exactly the reason why the planet Venus (with a CO2 rich atmosphere), although it is further than the sun from Mercury, is hotter by a long shot. But I decided against repeating those same old stories, because I figure you’ve probably heard them many times and are probably getting numb. Instead I’m going to go outside my comfort zone and plunge into the depths of Limnology and tell you about some current issues involving climate change in the convective currents of holimictic lakes.

…what’s a holimictic lake, you ask?

Good question. I’m not much for fancy names; I prefer concepts. So, let’s start with the basics. Firstly, you must have heard that hot air rises. But why does it do that? Well, air that is hotter than the air surrounding it is also less dense than that air. This means that a volume of hot air weighs less than the same volume of colder air. The colder air will be pulled towards the earth more than hot air and so hotter air will be pushed out of the way (upwards) by colder air.

The same is true for water, but only to a certain degree; 4°C to be exact. Water, unlike air, is densest at 4°C, so in a tub of 5°C water, a 7°C blob of water will tend to rise to the top. On the other hand, in a tub of 1°C water, a 3°C blob of water will tend to sink because even though it’s warmer it is more dense.

Now, consider a lake in the four seasons. During the Summer the lake water is generally above 4°C, so the sun will warm the top layers of the lake and that water (being warmer and less dense) will stay on top and the cooler water will stay deeper down.

When Fall comes around the top part of the lake will be cooled. Eventually that top part of the lake will cool to the same temperature as the bottom part. Winds can cause some turbulence and the bottom parts and top parts of the lake will get mixed up.

When Winter comes along the top part of the lake will be colder than the bottom part which can happen when the lake is lower than 4°C. The top layer of the lake may freeze over and the lake will again get separated into layers of different temperature — this is called stratification.

The lake gets mixed up again when Spring comes around. The top of the lake will be heated again and when the lake water at the top reaches 4°C it will sink to the bottom and mix up the lake.A lake that undergoes this kind of mixing is called a holimictic lake and if it does it twice a year (as described above) it’s called a dimictic lake.

…what does this have to do with climate change, you ask?

Well, nutrients from the lakebed seep into the lower parts of the lake while it’s stratified (Summer and Winter for a dimictic lake). When the lake mixes, these nutrients get mixed into the whole lake. If you are aquatic life which has adapted to depend on those nutrients, this mixing is a very good thing. Without it, many species of fish would not be able to survive in that lake.

Climate change threatens to put a damper on that mixing process for some lakes. As average global temperatures increase, unusually warm Winters become more likely. What would happen to a dimictic lake during one of these unusually warm Winters? Well, the lake won’t cool very much during the Fall, and might even stay above that 4°C mark. This would cause less mixing during the Fall. To make matters worse, because of the warm Winter, there will be less mixing during the Spring as well. To make matters worse still, those salts that are dissolved in the deep parts of the lake make those deep layers more dense. Less mixing during a certain Fall or Spring means more salts stay built up in the deep layers of the lake making it even more difficult to mix the upper and lower layers in future seasons. This is a runaway process and it can lead to a nutrient deficient lake, and very unhappy fish.

The take away message? Climate change isn’t just about things getting warmer and sweating more during the summer. Climate change is a direct threat to whole ecosystems. By tipping ecosystems out of balance it endangers many species of animals, including the animals causing the tipping (us). It’s high time that you start sweating over this situation. Please think about ways to cut your greenhouse gas emissions. If you need some suggestions, here are two good ones.

Eternal life – Dyson vs. Krauss

I’ve been meaning to post this for a while, but kept putting it off because I anticipated it being a rather long post. Several months ago I attended a lecture given by Lawrence Krauss at the CUPC. He gave us an overview of a “debate” he had with Freeman Dyson about whether or not life could exist forever. Keep in mind, this is not an argument for the likeliness of eternal life, it’s just simply addressing the possibility of it. In physics, the questions about whether or not something is even remotely physically possible are, many times, the most fun! And the ideas Krauss shared with us that originated from his back-and-forth with Dyson were so fun and interesting that I thought I’d take a stab at reproducing an overview of it all here. Keep in mind, I will be glazing over all of the mathematics and so if you want a more in depth look at the derivations of these results you should probably check out the original papers (here is Dyson’s; here is Krauss’s). They are enjoyable to read if you have a physics background (and maybe even if you don’t). So here it goes. Dyson vs. Krauss. But before we begin this faceoff, we need to buckle down and tend to a question that is begging to be answered:

…what do we mean by “life”?

Firstly, I must mention that we are not talking about eternal life for a single being. This debate was focused on eternal life for, say, a civilization albeit one that may evolve. Secondly, living things come in many shapes and forms, some of which we may not yet be aware of. It seems unreasonable to make the assumption that all forms of life are like those on earth; carbon based, dependent on water to survive, etc. In any case, Dyson and Krauss are both physicists and so for the purposes of their debate they were more concerned with the physics of “life” than its biology. Let me put it like this: we are not really concerned with the biological processes that lead to the thought “I think therefore I am”, we are simply concerned with the existence of the thought itself to define “life”. In other words, by “life” we really mean consciousness, or more simply, computation. Consciousness seems to have a lot to do with the firing of neurons which go about processing information much like a computer (or perhaps a quantum computer). Whether or not consciousness is really akin to some kind of computer program is a whole new debate in itself (perhaps some neuroscientist readers can comment on this). Despite this, computation must at least have a lot to do with consciousness and so surely by investigating the eternal existence of computation we won’t be doing too badly.

So, what restricts us from running a computer program for all time? Well, the first barrier is: energy. Hopefully you are familiar with the fact that the universe is expanding. Not only is it expanding, it is expanding at an accelerated rate. It turns out that this puts a constraint on the amount of energy any civilization can harvest to keep them alive (computing). With a finite amount of energy available one might give up at this point and declare that life, which requires energy to sustain itself, can’t exist for an infinite amount of time. Dyson, however, was still optimistic. He realized that living things are less concerned with physical time and are more concerned with, what he calls, subjective time. Living things measure time by the number of thoughts they have, so if a civilization can have an infinite number of thoughts using only a finite amount of energy, one could say that they have achieved eternal life. This subjective time depends on the temperature at which the entity operates. So if we assume that the civilization has the ability to change its temperature at whim, at first glance it seems like the civilization can have an infinite number of thoughts (live for an infinite subjective time) if it keeps decreasing its temperature for all time (getting closer and closer to absolute zero, but never exactly zero). That strategy (again, at first glance) will allow an infinite number of thoughts using only a finite amount of energy.

So, is this strategy really possible? Well, in answering this question we come to the next roadblock: heat dissipation. Computation generates heat (there’s a reason your computer gets warm when you turn it on). Living things will also generate heat. Even if we ignore all of the heat generated from familiar biological functions and only focus on the heat generated from thinking, we still have a minimum rate for heat production of a living entity. This heat has to be radiated away at a rate greater or equal to the rate at which the heat is produced, or the entity will “die” (there’s a reason your computer’s CPU needs a fan). Dyson considered this and deduced that the best way to get rid of waste heat would be through electromagnetic radiation. However, going through the math he deduced that the rate of radiation of waste heat this way would depend on the temperature and the number of electrons of which the entity was made. And if the life form kept reducing its temperature in this way, there would eventually be a time when it could not radiate its heat fast enough with only a finite number of electrons. So, this couldn’t work. Did Dyson give up?

Nope.

Think about this: what if you really really wanted to go about running a computation on your laptop but your fan couldn’t cool it off quickly enough. What would you do? What Dyson would probably do, is run the computation for a while, put the computer into sleep mode, let it cool off, wake it up, continue the computation and then repeat this until the computation was done! That’s exactly what he suggested a civilization might try to do to live forever; namely periodically hibernate in order to get rid of the excess waste heat! The civilization could continually lower its temperature (decrease its metabolism) and periodically hibernate for longer and longer in order to have an infinite number of thoughts using a finite amount of energy.

A nice strategy… but this is where Krauss stepped in and poked a lot of holes in this argument. The first caveat comes from the necessity for some kind of alarm clock to wake up the civilization from its hibernation. Any alarm clock is inevitably going to be performing some kind of computation in order to calculate when it should “ring” and tell the life forms to wake up and smell the coffee. This alarm clock is subject to the same laws of physics as the life forms themselves and, as such, will eventually use up all energy reserves by the same arguments as above (since a hibernating alarm clock would defeat the purpose).

The second caveat comes from the fact that we are living in a universe which is expanding at an accelerated rate. It turns out that a universe with that property will be permeated by background thermal radiation (analogous to Hawking radiation) which means a lower cutoff for temperature. In short, in a universe undergoing accelerated expansion there is a minimum temperature, which means that Dyson’s strategy of continually reducing a civilization’s temperature won’t work.

Now, you may have heard a bit about quantum computers and be thinking: “… but quantum computation doesn’t necessarily require any energy. You can, in principal, do as many computations as you like without generating heat as long as you don’t measure the result”. If you did think of that, great! However, as Krauss pointed out, you’ll necessarily have to radiate heat if you want to do any erasing in order to prepare for a new computation. If you had an infinite amount of memory storage available you could ignore that point, but any civilization’s memory storage is limited by the number of particles it has access to, which is (as with the case of energy) limited in supply. Krauss sums up this point well.

Thus any civilization can have only a finite total memory available, and resetting registers is therefore essential for any organism interacting with its environment, or initiating new calculations. While an existence, even nirvana, might be possible without this, we do not believe it is sensible to define this as life.

So right now it looks as though life (as some form of computation), by its very nature, must end. Mortality is a necessity of life. I am actually fond of this wistful result. I find it gives life more meaning and makes it more precious… but that’s just me. What do you think?

Physics explained through a Drinking (Dippy) Bird

As illustrated by the image to the right, physics is a serious subject.

It is a schematic diagram of a Drinking Bird toy (with hat). I didn’t make it. I just decided one day that I was curious about the physics of this timeless toy. Looking around on the Internet, I found many qualitative explanations for the Drinking Bird. I wanted something with more equations. Fortunately, I stumbled onto the article, “Experiments with the drinking bird”, by J. Güémez et al. Unfortunately, now I need a new Ph.D. thesis topic… Seriously though, it’s a fun paper to read.

If you aren’t familiar with the Drinking Bird, for shame! It is a toy that is remarkable in its simplicity. Given a glass of water in which to dip its beak, it will bob up and down with no batteries required! Surely a few dollars is a worthy price to pay for this perpetual entertainment machine.

…hey, wait a minute. Perpetual motion machines don’t exist!, you say?

You’re right. I’m just being provocative to keep you on your toes. It’s just that many people hint (or worse, even blatantly assert) that this is a perpetual motion machine. They are, of course, wrong. If you ever observe some contraption that seems to exhibit perpetual motion (that is, without an energy source), you are probably certainly overlooking the source of energy.

If you haven’t thought about it before, take a second now and try to make a rough deduction as to where the bird gets its energy (no googling!). To help you out, here’s a video of a drinking bird.

Ok, so you must have realized that the glass of water has something to do with it. But what’s up with the colored liquid inside the bird? And why do they all wear the same kind of hat? Well, I’ll just mention right now that, despite its inclusion in the “serious diagram”, the hat has more to do with the bird’s dignity and self-image than its functionality.

First, let me give you a rough sketch of what’s going on, then I’ll elaborate on a few specific phenomena. The colored liquid inside the bird is not water, it is Methylene Chloride (CH₂Cl₂). The gas inside the bird is not air, it’s (surprise!) Methylene Chloride vapor! The Methylene Chloride is called a volatile liquid. This means that it has a boiling point very close to room temperature. As a result, the Methylene Chloride inside the bird is in, what we call, thermal equilibrium resulting in a coexistence of its gas phase and its liquid phase. Next, you need to know that the bird’s head is a glass bulb (like the bottom) but the head is covered in fabric that absorbs a bit of water.

So, to start the drinking process the bird’s head must be covered in water. Once this happens, the water on the head begins to evaporate and cools the head a little bit. This decrease in temperature causes some of the Methylene Chloride vapor in the head to condense into a liquid and fill up the neck a little bit. Since the liquid phase takes up much less space than the vapor phase, there is less vapor in the head to fill up practically the same volume. This means that the pressure in the head will decrease, causing a difference in pressure between the head and the base of the bird. As we saw in my earlier post, a difference in pressure results in a net force from the higher pressure area to the lower pressure area. This means that the little bit of vapor in the base of the bird forces the liquid up the neck and into the head. This gives the bird a heavy head, and forces it to dip. Once it dips, the liquid moves out of the way, letting the warmer vapor in the bottom move to the top warming the head a bit and starting the cycle all over again.

Let’s look a bit closer at the water evaporating from the head. For the readers who are less experienced with physics, you might not have really thought about the reason water evaporates even at room temperature. Shouldn’t liquid water only turn into a gas at 100 degrees C (at standard pressure)? Well, water of course does become a gas at less than its boiling point (look at the steam from your coffee cup for evidence). To see why this is you need to remember that a liquid is really just a collection of molecules undergoing random collisions with each other. The molecules are going to have an overall average velocity that increases with the liquid’s temperature, but overall, the molecules will have different velocities. Near the surface of the liquid (the liquid-air boundary), some of the molecules will have a high enough velocity to “escape” the liquid and, instead, mix with the air. The reverse is also true; some water molecules already in the air will have low enough velocities to “stick” to the liquid water. The reverse process, however, is much less likely if the concentration of water in the surrounding air is low enough. When the air is saturated with water then that means there is enough water in the air that the rate of evaporation and rate of condensation are equal. So the frequency of the Drinking Bird’s sips will depend on the humidity of the surrounding air (here’s a video showing that).

But I still haven’t answered my original question; where does the bird get its energy? As you may have guessed, it gets it from the surrounding air. Even though higher energy water molecules are being lost to the atmosphere from the head, this creates a temperature difference which ultimately drives the motion. The base of the bird is continually being warmed by the air, so when the bird dips, the warm Methylene Chloride in the base carries the thermal energy originally absorbed from the surroundings to the head. That’s what keeps it drinking.

What do you think would happen if instead of giving the bird a glass of water, you gave it a glass of alcohol? Would it be more, or less enthusiastic about drinking the alcohol? Why?

An inverse glass of water

I have another neat Do-It-Yourself physics experiment for you to try.

Here’s what you need:

• Uniform drinking glass (in other words, not a funky shaped glass).
• Piece of sturdy, flat, smooth cardboard (that won’t curl up if wet). Big enough to completely cover the opening of the glass.
• Water.

The process is easy but it’s best to do it over a sink, just in case. Fill the glass with some water then place the piece of cardboard on top of the glass so that it covers it completely. Using your hand to keep the cardboard in place, quickly flip the glass and the cardboard upside down. Hopefully at this point you are not covered in water and no water is leaking out. Make sure the glass is completely upturned so that the cardboard is parallel to the ground. At this point, if all goes well, you should be able to remove your hand from the cardboard and the water should stay in!

Some of you have probably figured out that air pressure has something to do with this, and you are entirely correct. But there are a few subtle things I would like to point out. The rest of you who aren’t familiar with this kind of air pressure acrobatics are probably thinking…

…but why doesn’t the water fall out of the glass?

Well, first you need to realize that the water is not the only fluid substance in the glass, there is also air (which actually reminds me of a shirt I have). If the water were to fall out, then air would have to take its place, otherwise the same amount of air currently in the glass would occupy a larger volume than it did before, causing a huge pressure difference between the room and the glass.

Realistically, there must be a pressure difference between the room and the inside of the glass because something needs to cancel out the downward force of gravity of the water. A difference in pressure will create a net force upwards which cancels out the weight of the water. So the water is supported by the cardboard, and the cardboard is supported by thin air!

…but wait a second. Where did this pressure difference come from, you ask?

What’s going on here is that gravity is pulling the water down slightly, which increases the volume of the air inside the glass. If you increase the volume of a gas (without changing the temperature or number of molecules) you will decrease the pressure of the gas. So that means: lower pressure inside, higher pressure outside, giving a net force inwards which means a force upwards on the cardboard.

…but if gravity pulls the water down slightly then there must be a gap between the cardboard and the rim of the cup, so why doesn’t the water spill out from the gap?

Well, that’s an excellent question. The answer to this is: surface tension. Have you ever tried to float a paperclip on water? Despite the fact that the paperclip is denser than water, it is still possible. This is because the interface (boundary) between the water and the air can very loosely be thought of as an elastic band. It will resist distortion up to a certain point. This happens because nature likes to minimize energy, and in this case, that corresponds to minimizing the surface area of the interface between the air and the water. If you push it, that will put it into a  higher energy configuration, so the surface will push back. (For more, see wikipedia).

The gap between the glass and the cardboard is tiny (less than a millimeter). This is too small a gap for the air to break the surface tension. The air can’t bubble up through the gap into the glass while the water flows out so the water and the card just stay there, suspended. Not just suspended in mid air… but by mid air.

Edit: For another post about air pressure that really sucks, check out the “Everyday Physics: suction cups” post on Shores of the Dirac Sea. (…I just had to make that joke…)

Conservation of money and the distributions of wealth

Well, it’s Blog Action Day and the topic this year is poverty. Of course, I’m going to put a physics spin on this (spin 1/2 to be exact… the other half will be economics).

Bee at Backreaction wrote a nice post in which she related capital gain in economies to the reward response in the human brain. In the human brain, ways to cheat the reward circuit can be used, like drugs, which directly stimulate the reward response and as a consequence defeat the original purpose; namely survival. She argues that the same is true in economics.

One can cheat on these reward mechanisms as well, which leads to the emergence of tactics that run contrary to the original intention of being beneficial for the society. We therefore have means to constrain damaging behavior like proper product information, property rights, ethical codes for scientific conduct, trade laws, or marketplace regulations. Again, the question of what needs attention is a discussion constantly in flux. The aim is in all cases to ensure that the pursuit of individual interests within a given system results in desirable long-term and large-scale trends.

We develop regulations to reduce the amount of abuse. But on what are these regulations based? She argues that most of these regulations are developed by a process of trial and error. And experiments are conducted with the well-being of billions of people depending on the results. The scientific revolution has spawned fields of study (such as physics), which give precise and specific predictions of nature, from imprecise fields of study (such as philosophy). Why hasn’t the same been done for social sciences? Let’s consider the possibility of doing that. Until recently we haven’t had the means of dealing with the huge amounts of data needed to track people’s trends. We are now beginning to get this kind of data, and in fact, some are beginning to apply scientific methods to social problems.

One such field is called econothermodynamics. It tries to apply methods used in thermodynamics to describe large distributions of people, just as thermodynamics describes macroscopic distributions of particles. A simple model begins with a conservation law, just like in physics. Instead of conservation of energy between particles, it is conservation of money between people. When two people interact, one person will “loose” a certain amount of money to the other person. Obviously on the person-to-person level there are reasons for this money exchange, but if you look at a huge group of people, the money exchange is essentially random, like the random exchange of energy in an ideal gas [1]. The result is a distribution of wealth that looks very much like the classical Maxwell-Boltzmann distribution. When the researchers compare this to real data, they find it fits remarkably well [2].

Actually this gas model only fits for 97% of the population. The other 3%, are the super rich, who seem to fit another distribution called Pareto’s law, which is a power law. Essentially the majority of the wealth distribution is hogged by a minority of the population. To make things worse, one prediction of the gas model distribution of wealth is that it is very resistant to change. The economic state will always want to be in equilibrium (like a gas) and return to the same distribution in which it began [3].

…but people are too complex to model, you say? I disagree. History is filled with people saying that certain things are too hard to model, and yet we’ve modeled them. The point is not to model individual people, it is to model large groups by simplifying the data and making reasonable assumptions to make it easier to work with.

…but people aren’t like particles, they have free thought, you say? I’ll agree with that. But that’s no reason not to try to model them. Particles aren’t like particles! The ideal gas law has its limits even in thermodynamics. The goal of scientific models is not to apply it blindly to every situation. One must know the limits of the model, the sources of error, the assumptions made. Good science is honest about its own limitations. This does not make it less useful, it makes it more useful. ZapperZ at Physics and Physicists illustrates this:

It certainly is ironic that fields in “hard” sciences are more concerned about uncertainty and “error bars” in our work and experimental data, while “soft” science such as politics, economics, and social sciences that deal with less-verified principles are presented with such definite certainty.

One of the best criticisms of models of people that I’ve come across is that people are aware of the models describing them. In other words, there is a feedback mechanism to the very act of modeling a social system. Some see this as a dead end. I think that’s overly pessimistic. It makes it more difficult, surely. But there is a possibility of dealing with such a feedback. If it can’t be included in the model there’s at least a chance it can be used to put additional limitations on the model.

The scientific method has taken us astoundingly far. One hundred years ago, people would have called you crazy if you said that by measuring little vibrations of electrons in a metal rod, you could hear and see exactly what someone was saying and doing half way around the world (television). Maybe modeling people isn’t possible. But throwing up our hands and giving up seems like a very silly attitude. Even a little bit of precision is better than guesswork.

[1] A.M. Tishin, O.B. Baklitskaya (2008) EconoThermodynamics, or the world economy “thermal death” paradox.
[2] Dr Dragulescu AA, Yakovenko VM (2003) Statistical mechanics of money, income, and wealth: a short survey.
[3] Jenny Hogan, “Why it is hard to share the wealth”. New Scientist, 2005.