Monthly Archives: January 2013

Geek Feminism links

Both Jessamyn and I have written posts for the website Geek Feminism in the past weeks – go check them out!

Erin: How can I tell if my outreach to women is effective?

Jessamyn: Being visible – minority representation in a technical field.

how to talk about what you do in an easy to understand way

A new blog has sprung up recently, inspired by xkcd’s ‘Up-Goer Five’ comic and the list of the ‘ten hundred’ most used words in the English language.

The blog is called Ten Hundred Words of Science and it challenges scientists to describe what they do using only the 1000 most commonly used words, though there are a few work-arounds for less common but still crucial words (like ‘Mr Hydrogen and Ms Oxygen’). What you’ll see when scrolling through the posts are the many creative, interesting ways various people describe the science they do – most impressive considering ‘science’ isn’t even one of the thousand words you can use!

The Ten Hundred Words of Science blog just goes to show that with a little bit of creativity and effort almost anything can be explained (to a certain degree) in easy-to-understand language. My only critique is how long some of the explanations are – I’d love to force people to get *really* creative by imposing a word limit, but maybe that’s just cruel.

Here is Jessamyn’s attempt to explain nanoscience and electronics – no easy feat!

“My work is about studying really small things. It turns out that if you take a big thing and make it small, it does something different than what you’d expect. We understand some parts of why this happens, but there is a lot left to learn. So what I do is build something made of lots of tiny things, and look at what they do together. I can make things that respond to light, or put out light, or respond to air! And I figure out what’s happening by putting power in and looking at how it comes out. So I could build something that turns light into power, or power into light, or that moves power around like a computer does, but works more like the brain than computers do. And all this comes from the fact that small things are very different from large things.”

#OverlyHonestMethods

If you have spent much time on twitter this week, you have probably seen the hashtag #overlyhonestmethods, in which scientists volunteer some of the messy bits about science that don’t usually make it into published papers. There are some nice lists of tweets here and here, and the whole thing reminded me of PhD comicsmethodology translator explaining how science actually gets done.

The hashtag is funny if you have spent much time in science, but the thing I really like about it is how clearly it shows that our ideal of how science operates—craft a hypothesis, run simulations, perform carefully controlled experiments, learn something new about nature—is just that, an ideal. Very often things shake out differently than you were expecting when you started, or you’re constrained by resources or lab availability that’s unrelated to the project, or you get a big surprise and have to check your premises. And of course, the way that science is published, disseminated in popular press, and used practically (or not) often depends not only on the science itself, but on the lives of the researchers involved, and what their aims and constraints are. Which is another way of saying that the study of science is a part of life, and is affected by people’s agency and random chance in all the ways you’d expect.

In many ways this mirrors the difference between experiment and theory. We can have a theoretical idea of what the scientific method is, just as we can have a theoretical explanation of some observed phenomenon. But in the end, we are working and living in the real world, and as much as we want to understand the laws beneath everything, we also have to be adaptable to the unexpected! As Isaac Asimov said, “The most exciting phrase to hear in science, the one that heralds new discoveries, is not Eureka! (I found it!) but rather, ‘hmm… that’s funny…'”

What is Entropy?

Last time we talked about information-entropy, which is a way of quantifying the information in a given string of symbols. Each symbol has a certain uncertainty associated with it, which may be low if the symbol can be one of two things, or high if the symbol can be one of a hundred things. Summing all the possible outcomes gives the entropy, which is larger for more uncertain situations and smaller for more certain situations. So the more you stand to learn from the string, the higher its uncertainty and entropy, and the larger its information content.

But let’s get less abstract and think about examples. Say that we flip a coin and see if it lands with the head or tail side up. An evenly weighted coin will have an equal probability of being heads or tails. But perhaps an uneven coin is more likely to be heads, or maybe gnomes have swapped in a coin that’s heads on both sides. The results of the heads-only coin toss have very low entropy because there is only one possible result, and minimal information is gained by examining the result. Whereas the weighted coin will have higher entropy due to the larger number of results possible. And the evenly weighted coin not only has more results possible than the heads-only coin, those results are also maximally unpredictable, so the entropy is the highest. And if we do a series of coin tosses, we get a string of coin toss results. A longer string will have more entropy than a shorter string, except in the case where the coin is heads-only. Now if we replace the binary coin toss with choosing a letter from the alphabet, which has 26 possibilities instead of two, we have significantly increased the information-entropy!

Of course, sometimes it is useful to impose some rules on a string of symbols, for example the rules associated with a specific language. Doing so will reduce the uncertainty, and thus the entropy and information content, of the string. This is another way of saying that a string of letters that spells out words in English has a lower entropy than a string of random letters, because in English you know that not all the letters are equally probable, one letter affects the probability of letters following it, and other things like that. It’s the equivalent of weighting the coin! In fact, the trick of data compression is to reduce the number of symbols used in a string without reducing the entropy (and thus the information content) of the message. Data compression is not possible when each symbol in a message is maximally surprising, which explains the difficulty of compressing things like white noise.

Now, what if instead of a sequence of coin tosses or a string of letters, you instead had a collection of atoms that could be in different states? Consider a box filled with a gas, where each atom of the gas can be described by its position in the box and its momentum. The entropy of any given configuration of atoms would then be the sum of all the possible states for each atom, the same way the entropy of a string was the sum of possible symbols in the string (weighted for probability). Entropy is still a measure of uncertainty, but in this physical example the question is how many arrangements of atoms in specific states can make a configuration that has the same measurable properties, such as pressure, temperature, and volume. For example, if the gas is evenly distributed throughout the box, we can make a wide variety of changes to the individual atom positions and velocities without changing the measurable properties of the gas. Thus the entropy is high because of the large number of atomic arrangements that could yield the same result, which means there is a high uncertainty in what any individual atom is doing. In contrast, if the gas atoms are confined to a very small region of the box, there are fewer positions and momenta available to the atoms, and thus a smaller number of indistinguishable arrangements. So the entropy is lower, because there are fewer ways to have the same number of atoms all in a corner of the box.

The technical way to describe this formulation of entropy is that each atom has a number of microstates available to it, and all the atoms together have measurable properties (pressure, volume, temperature, etc.) that define the macrostate. The entropy of any given macrostate is equal to the number of microstate configurations that could produce that macrostate, which means it’s still about uncertainty. But you can also see that entropy is a form of state-counting: higher entropy macrostates can be attained in a larger number of ways than lower entropy macrostates. This means that in general, higher entropy states are more probable. If there is one way to pack all the atoms into the corner of a box, but there are a million ways to evenly distribute the atoms in the box, then the chances of just finding the atoms in the corner are one in a million. And since those atoms are constantly moving and exploring new microstates, over time they will tend to the highest entropy macrostates. This is where the Second Law of Thermodynamics comes from, which says that in any isolated system, total entropy increases over time toward a maximum value.

The idea of entropy as state-counting came from Ludwig Boltzmann, more than fifty years before information theory was developed. Shannon called his measure information-entropy because of the resemblance to entropy as defined in collections of atoms, which is the basis of statistical mechanics. Entropy is a measure of information and uncertainty, but also a way to count the number of states, and a measure of the relative ordering of a system.