What I Learned Today

The NRAO (National Radio Astronomy Observatory) offers online what just may be the coolest try-this-at-home project ever. How often do you get to do your own cosmology, with no equipment and no training? Well, now you can, by going through the measure the age of the universe tutorial.

Given the observation that all other galaxies are moving away from us (which is observable due to the Doppler effect, which manifests itself as a redshift in the light they emit), and assuming that other spiral galaxies are about the same size as ours (yes, quite an assumption), then using our current estimate of the size of our galaxy, we can convert the apparent size of another galaxy into its distance from us.

Then, we record the distribution of redshifts coming from the galaxy (different parts will shift by different amounts since some may be spinning towards us and some away) and convert those shifts into a velocity. For precision, we look at one particular wavelength (the radio spectral line of hydrogen, here).

Finally, we plot distance versus velocity to get the relationship between those two variables. Edwin Hubble‘s great discovery, after going through this same process, was that more distant galaxies are more red-shifted, and therefore moving faster — thus, there is some sort of acceleration going on. The slope of a line fit to these data points gives us that acceleration, which is referred to as the Hubble constant, H₀. Since this constant (slope) is velocity divided by distance, it has units of 1/time. Therefore, if you take its reciprocal, you get time itself: the age of the universe.

I downloaded the 10 example galaxies provided in the tutorial (and you can, too) and calculated distance and velocity values for each one. I felt more confident in my ability to estimate the velocity (average of the observed values) than for the distance, which is very sensitive to the angular size, which is extremely hard to be precise about with a paper ruler. :) I’m assuming that whoever prepared these examples already adjusted the images so that they all have the same scale. Since not all galaxies are perpendicular to us (some are tilted away), I used the largest diameter I could find. My observations are shown below, plotted against the line obtained using the current best estimate of Hubble’s constant (derived from thousands of observations, not just 10!). While I didn’t get a perfect linear relationship, apparently this isn’t expected due to relativity and other confounding factors. Hubble himself used 46 galaxies and ended up much, much further off (apparently due to “peculiar velocities” and poor calibration on distances).

Each galaxy provides an estimate of the age of the universe. Using these 10 galaxies, my estimates ranged from 10.0 to 39.8 billion years old. Excluding the crazy outlier (NGC 4214, which is the only one with an estimate outside the standard deviation), my estimate of the age of the universe is 14.2 billion years old. Not too far off the latest best estimate of 13.8 billion years!

And what of NGC 4214? It turns out that it isn’t a spiral galaxy at all, which could explain why it didn’t fit with the others. Its redshift indicates that it isn’t going very fast, so shouldn’t be very far away, but it appears to be very small given its proximity. I’m guessing that it’s much smaller than the 10 kpc that was used as the assumed size for all galaxies in this study. In fact, I found that its diameter has been determined to be only 6.7 kpc. So it’s a true outlier, not just due to measurement error.

Science is awesome.

An xkcd comic led me to the Simple English Wikipedia. This wikipedia aims to provide simplified versions of articles from the Ordinary English Wikipedia by limiting the vocabulary used, grammar complexity, and sentence length. I admire the motivation behind this resource: to make general knowledge accessible to non-native speakers, youthful readers, or those with disabilities. Yet to an adult native English speaker, the language of these articles can be gratingly unaesthetic (and imprecise). For example, consider this excerpt from the page on Mars:

The planet Mars is made of rock. The ground there is red because of iron oxide (rust) in the rocks and dust. The planet has a small carbon dioxide atmosphere. The temperatures on Mars are colder than on Earth, because it is farther away from the Sun. There is some ice at the north and south poles of Mars, and also frozen carbon dioxide.

This is all factually accurate, but achingly simplistic (especially the “because it is farther away from the Sun” statement — the atmospheric composition is also a critical player). On the other hand, if I had to read wikipedia in, say, French, I would no doubt appreciate the simplicity!

But I experienced even more wincing when reading pages about topics from Computer Science, such as the neural network page, half of which consists of:

What is important in the idea of neural networks is that they are able to learn by themselves, an ability which makes them remarkably distinctive in comparison to normal computers, which cannot do anything for which they are not programmed.

(Technically, they don’t learn by themselves — they require supervision in the form of labeled examples — and any machine learning method exhibits the learning property, not just neural networks, and what is a “normal computer” anyway? A neural network is an algorithm for learning a model, not a special-purpose computer. Finally, even neural networks cannot do anything for which they are not programmed! More accurate: “Neural networks can learn from examples, allowing them to make predictions about objects they may never have seen before (generalize).”)

Or consider this part of the page on Computer Science itself:

A computer is a device which takes orders as fast as you can give them to it and works as fast as it can to solve the orders.

(makes a computer sound like an active agent (e.g., waiter), which it isn’t) or from Computer programming:

The instructions in “machine form” are usually in a .EXE file (which is called an executable, because it can be executed). These machine-instructions will by default open a black “command-prompt” window, but can open games as well as other things.

(Well, am I really surprised that “simple” computer programming has such a strong Windows bias? ;) )

There’s an interesting issue at the heart of this project: how do you talk simply without talking down? (Or worse, misleading the reader!) Clear, simple language has real value even outside of this venue. However, translating all value judgments into the simple words “good” or “bad” not only gives the text a childlike sound but also gives its meaning a childlike interpretation, and important distinctions may be lost.

I actually find this wikipedia harder to read, not easier; the stilted sequences of simple sentences dominate my attention with their awkward rhythms and unanticipated gaps (likewise, you may have found my alliteration distracting :) ). Good writing blends its details in to the background and leaves you room to think about the ideas being presented. But yes, I know: I’m not the target audience for this product. I expect that many people are benefiting from much of the information in the Simple English Wikipedia. Hopefully they also get a chance to dig deeper for the real details on their subjects of most interest or need.