Amazing as Eureqa is, its application may go far beyond science. It may even extend into the realm of news reporting. The first news story to fall to a Eureqa reporter might be climate change. Imagine feeding all the data we have about the Earth’s climate over the past 600,000 years into Eureqa. It could very well create an equation that relates all those variables into a planetary temperature model. All the issues skeptics complain about: sunspots, methane concentrations, increased albedo from deforestation, decreased albedo from polar ice melting, urban heat islands, etc, could be analyzed by Eureqa. Being a computer program we’d expect it would analyze the data without any bias or prejudice. And like the biology example above, it will produce an answer, perhaps one we won’t understand, but one that we can still use for predictive capabilities. We could feed it data indicating how we’d like to change our behavior to mitigate or even reverse global warming* and Eureqa would tell us if our hypothetical new behavior would help or not.

In the old days of news reporting some reporters were valued for their honesty and ethical integrity. If such a reporter said something was true the public would largely believe it. No reporter today understands climate change, they are all reporting what the scientists say and some are relying on old investigative reporting techniques to dig up dirt that appears significant but is essentially meaningless**. In other words instead of fact checking they’re merely questioning the motivation of the scientists and not digging into the science. However, if a result came from Eureqa it would be impossible to question its motives. The only thing to question would be the science.

Climate change with the data collected on that topic may be a field that’s within Eureqa’s grasp to analyze. However, future versions of Eureqa or programs like it may be able to answer other types of questions:

• How do taxes affect economic growth?
• Do generous social welfare programs decrease national productivity?
• Do gun control laws reduce gun deaths?
• If we legalized certain drugs how many more drug addicts would we have?

These questions may not seem like they easily lend themselves to numerical analysis, but we are a nation of fifty states, a world of many nations and we’ve been collecting data for a long time. Across our nation, across the globe and for the last several decades we have taken many different stances on these issues with many different results. A program like Eureqa one day may very well be able to analyze this information and determine the ideal tax rate for a country or what drugs can be safely decriminalized, or what level of social welfare minimizes the number of the poor while maximizing productivity.

The benefit of having a computer program report these results is that it’s immune to the motivational inquisition that passes for investigative journalism these days. You can’t question a computer’s motivation, but you can question the underlying data and the assumptions that go into its analysis. Somewhere along the line we’ve lost the ability to trust someone who doesn’t share our world view. Skepticism has devolved into merely ascertaining whether someone shares our world view and if not we stop listening. When computers are able to give answers to meaningful questions ascertaining whether the computer shares our world view will be a meaningless exercise. We’ll have to resort to verifying its conclusions the old fashioned way, questioning the data or verifying the results on a small scale. That’s the sort of reporting we’re aiming for here at News With Numbers. I’ve downloaded my copy of Eureqa, have you got yours?

The blog/news site Good.is is running a series of articles on transportation. Recently they posted an infographic showing where the energy in your car is wasted. I was planning on running a similar article, but they beat me to the punch. Notice the large amount of loss coming from the engine. This, while true, is a bit misleading as the efficiency of an internal combustion engine (ICE) varies with RPM. Also the drive train losses vary depending on the type of drive train. All Wheel Drive is probably much more wasteful than the 5.6% shown below. So GOOD.IS’s infographic is nice, but it doesn’t quite give you enough information to make a decision.

I’m focusing on the engine and drive train losses because these are the things you can control when you decide on the type of car you want to buy. It would be great to see this same sort of infographic reproduced for several different types of cars. First up would be a hybrid like a Prius. This is sometimes called a Parallel-Hybrid because both the electric motor and the ICE can simultaneously supply power to the drive train. Of course, if you do that you incur some fraction of the engine losses and the drive train losses just to have the ICE hooked up in parallel.

What’s surprising is that the series hybrid is as efficient (if not more so) than a parallel hybrid. In a series hybrid there’s an ICE, but it powers a generator that is connected to electric motors that run the car. Part of the reason why this type achieves its efficiency is that it can run the ICE at the optimal RPM all the time and because it can dispense with much of the drive train that accompanies an ICE when it is connected to the wheels (there’s no gear box for example).

A fuel cell car would just replace the ICE and Generator in the above picture and provide power that way. Up until the BloomBox started getting attention the primary type of Fuel Cell that was being considered was a hydrogen fuel cell. It’s clean, producing only H2O as a waste product and relatively cool, but getting the hydrogen fuel is a big problem. Bloom’s fuel cell in contrast can run off of hydrocarbons which have a ready-made infrastructure, but they do run hot, about 2x hotter than a normal ICE. So it’s not clear if it’s feasible, but it would be way cool to have one.

I like Good.is’s website. They do good stuff. But this article set me back a bit. All it says is “Urmmmm, cars baaaaad”, they don’t give me enough information to decide what’s better or even… ahem good. Hopefully they’ll address this in the remaining 6 parts.

On January 28, 1986, the space shuttle Challenger exploded and seven astronauts died because two rubber O-rings leaked. These rings had lost their resiliency because the shuttle was launched on a very cold day. Ambient temperatures were in the low 30s and the O-rings themselves were much colder, less than 20°F.

One day before the flight, the predicted temperature for the launch was 26° to 29°. Concerned that the rings would not seal at such a cold temperature, the engineers who designed the rocket opposed launching Challenger the next day. Their misgivings derived from several sources: a history of O-ring damage during previous cool-weather
launches of the shuttle, the physics of resiliency (which declines exponentially with cooling), and experimental data. Presented in 13 charts, this evidence was faxed to NASA, the government agency responsible for the flight. A high-level NASA official responded that he was “appalled” by the recommendation not to launch and indicated that the rocket-maker, Morton Thiokol, should reconsider, even though this was Thiokol’s only no-launch recommendation in 12 years. Other NASA officials pointed out serious weaknesses in the charts. Reassessing the situation after these skeptical responses, the Thiokol managers changed their minds and decided that they now favored launching the next day.They said the evidence presented by the engineers was inconclusive, that cool temperatures were not linked to O-ring problems.

Thus the exact cause of the accident was intensely debated during the evening before the launch. That is, for hours, the rocket engineers and managers considered the question” Will the rubber O-rings fail catastrophically tomorrow because of the cold weather?” These discussions concluded at midnight with the decision to go ahead. That morning, the Challenger blew up 73 seconds after its rockets were ignited.

Since the engineers could not convince their management to scrub the launch it seems reasonable to conclude that the science and data were so esoteric as to make it impossible to come to a conclusive no-go decision before the launch. This is rocket science after all. But is this what happened? Was the science so esoteric as to be inscrutable to managers and non-scientists? The science is esoteric, but as we will see in a moment that doesn’t mean that a successful argument couldn’t have been made to management  convincing them to scrub the launch.

Before we proceed, I should point out there is a big difference between the setting that the engineers found themselves in and the sort of setting Julian Sanchez imagined in his post. Sanchez posited that the lay public is reasonably open minded but easily swayed by FUD especially when the counter arguments are detailed and complicated. The NASA engineers, on the other hand faced a very skeptical set of managers who, due to various political reasons, were strongly against further delaying the already delayed shuttle flight. With such a bias from the beginning, it is entirely possible that no argument could have convinced the managers to scrub the launch. However, given a more open minded audience and a more compelling argument, history could have been different.

As mentioned above the engineers hurriedly created a slide show to present to the NASA  managers. Tufte reproduces many of the charts from that slide show in his book and they are also available online. One thing is clear from these slides, the engineers were trying to give the managers a crash course in “rocket science”. The slides discussed the theory of how the booster rocket seals should work at various temperatures and presented information on how actual seals had failed under a variety of real-world circumstances, both from actual launches and from test firings. This sort of presentation is exactly the complicated, boring, experts only, losing side of the asymmetric one-way hash argument Sanchez discusses. Below are some slides to showcase this point.

However, even here the managers used FUD to counter these points. They asked if there were any successful launches in the 50° range. There were. They also pointed out there were launches with damage as warm as 75 degrees. These 2 points are examples of what Tufte calls “dueling anecdotes”. We could all train ourselves to watch out for this sort of fallacy or, as Tufte prefers, we could force one or the other arguer to present all the data. In this case the outlier nature of the single cited anecdote becomes clear for all to see. (Whenever I think of this approach to dueling anecdotes a poker image pops into my mind. One player says “I raise you one anecdote” to which the other poker player replies “I see your one anecdote. I’m going ‘all-in’ with every bit of data I have”.)

Tufte took the data the NASA engineers presented and put it into a single chart. But before doing that he boiled the issue down to the simplest question. Specifically how are cold temperatures and O-Ring damage correlated? He showed this in a chart that plotted all the shuttle launches with temperature at launch on one axis and a “damage index” on the other axis. This chart is reproduced below.

There were a few instances of damage occurring at warm temperatures, but every launch colder than 65° had some damage. Furthermore the chart shows that damage increased as the temperature got colder. The coldest launch before Challenger was at 52° and Challenger was launched when the temperature was in the mid to high 20s!

While not strictly accurate to do so, the eye wants to connect the dots for the launches colder than 65° and furthermore extrapolate to the 26° to 29° temperature range forecast for the launch time and arrive at a damage index of more than double the previous maximum damage.

This is a simple yet powerful diagram. The compelling points about it are:

• every launch colder than 65° had some damage
• damage got worse as it got colder
• expected launch temperatures were significantly colder than any other launch
• all the data is shown
• the gap between the previous coldest launch of 52 degrees and this launch succinctly captures gap in knowledge and the severity of the cold on the launch date

Notice that we neatly sidestep scientific issues of “shore hardness” and technical identifiers like SRM-15. All that we care about is shown above. Temperature at launch and (an albeit subjective) measure of damage. Additionally note that the phrase “A temperature lower than current database” gives no idea how much lower or what the implication of that lower temperature implies. However representing this temperature graphically gives a much more useful and comprehensive view.

This technique of arguing points through graphical data is a solution to the one-way hash argument, at least for arguments that are amenable to this sort of treatment. What more could one want? Being graphical it’s simple, comprehensive and, if done right, interesting. On the negative side it is graphical and for that segment of the public who is strongly verbally aligned (or at least non-visually aligned) such a presentation may not be that compelling. But imagine for a moment 2 experts on opposite sides of an argument debating the merits of an argument framed in such a way. These experts would be forced to argue the merits and interpretation of the data and not be detoured into off-topic FUD topics such as whether the opposing expert had a financial stake in the conclusion.

To be sure, not all issues are amenable to this sort of analysis. Many issues aren’t quantifiable at all. Some issues are purely judgment calls, situations where reasonable people can disagree; there is no single right or best answer. And some issues, even if they are quantifiable don’t show as clear cut an answer as the Challenger example. But there are many more issues that can be examined in this light; issues that are not being so examined. Finding and examining these issues is one of the goals of this blog.

References

Ed Tufte’s treatment of the Challenger disaster in his book Visual Explanations pages 38 – 53.

Background information came from the testimony given in the “Report of the Presidential Commission on the Space Shuttle Challenger Accident”.

The slides came from this same testimony. A direct link to the slides is available here.

Unlike our normal articles, this one is not focused on a recent news item. We’re publishing it because it’s an excellent example of the power of graphs to show why something is without resorting to techno-jargon or a lengthy verbal explanation. – Ed.

There is so much evidence for dark matter that hardly any physicist doubts its existence. What dark matter is, is still under some debate but that dark matter is, enjoys wide acceptance. Something unusual is happening in galaxies, something that we can’t explain with current physics. Something new is needed to explain it. The best evidence that something new was needed came from measurements of the Andromeda galaxy back in the late 1960s.

Background

Astronomers determine the relative masses of objects by observing how fast they move in relation to other objects. Most such systems of objects are like our solar system, with a big heavy object at the center (our sun) and smaller lighter objects orbiting it further out (plants, asteroids, comets, etc.) If gravity is the only thing holding these objects together then they must observe a certain speed limit. If they move faster than this speed limit gravity can’t hold them together and they fly apart. If they move slower than this speed limit they’ll crash into each other and become just one big object. Because gravity gets weaker with distance, the further an object is from the center the slower it will move. Pluto orbits the sun much more slowly than Mercury does, and it is not just because Pluto has further to travel, but because it is moving slower too. Currently Pluto takes about 250 years to orbit the sun once, but if Pluto were moving as fast as Mercury then it would only take about 25 years to orbit the sun.

The Study of Andromeda

Stars within galaxies behave similarly. In the 1960s no one had charted the speed that stars revolve around a galaxy before. This was the data the astronomers were collecting on Andromeda, the speed that various stars were moving around the galaxy. They sorted this data based on distance from the center of the galaxy and plotted a curve they call the galactic rotation curve. It is the shape of this curve that was the first most compelling evidence for the existence of dark matter.

The data revealed that objects far from the center of the Andromeda galaxy were moving faster than they should be. It is interesting to note that by the 1980s (some 15 years later) evidence was beginning to emerge that most galaxies and indeed the Andromeda galaxy harbored super massive black holes at their center. While, in the 1960s, this was a previously unknown source of mass, even this could not explain the surprising shape of the galactic rotation curve.

The Data

What astronomers had expected was a curve like the one shown at right. This curve shows that objects move slower the further away they are from the center of mass. This is how gravity works and represents graphically what was discussed above. Namely the further away an object is from the center the slower is must move. If it were moving faster, it would fly away from the center; if it were moving slower it would crash into the center.

When a super massive black hole is added, the curve would look like this. The heavier object at the center allows objects to move just a little faster because the gravity is just a little stronger. This curve is the same as the previous curve, but with everything shifted up, everything moves just a little faster. Indeed, objects far from the center of the galaxy are moving faster in the presence of a super massive black hold than they would be without. However, like the graph above, everything also slows down the further it is from the center of the galaxy. The addition of a super massive black hole doesn’t change the shape of the curve, just how big it is.

The curve that emerged from the study of Andromeda looked like this. Not merely shifted a little, but a different shape entirely. Indeed, distance from the center didn’t appear to affect velocity at all.

Other astronomers were skeptical; this result was too unexpected to be correct. The simplest explanation would have been an error in the data. But eventually similar measurements were made on other galaxies and all of them had similar curves, all of them vastly different from the expected one.

Something different was needed to explain this, either a new theory of gravity or a new form of matter. Initially astronomers didn’t know what, but it was impossible to tweak the existing theories to obtain a result consistent with the data. A new theory was needed.

Conclusion

Nearly all media reports on dark matter state the evidence for it is that galaxies are rotating faster than can be explained by gravity alone. While this is true, it’s a gross simplification, so simplified as to be misleading. Now that you’ve seen these galactic rotation curves it should be easy to imagine hypothetical curves that simultaneously fit the criteria of a) stars moving faster than expected while b) fitting the profile of moving under the influence of gravity. Indeed the theoretical curve of a galaxy with a black hole shown above when viewed by someone ignorant of a black hole at the galactic core could be said to have stars orbiting it faster than expected yet still be explainable by gravity. Very few articles in the popular media push the experts to explain why they say that gravity alone can’t explain the rotation curves. The media seems to be content to report that “experts say” and not bother with any sort of follow-up as to why “experts say”. Yet as we’ve seen such an explanation is not that complicated, all it requires is a few pictures.

References

Vera Rubin and Kent Ford did the original work on galactic rotation curves. Their paper is: Rubin, Vera C.; Ford, W. Kent Jr., “Rotation of the Andromeda Nebula from a Spectroscopic Survey of Emission Regions” Astrophysical Journal vol 159 p379 Feb 1970.

It is available online here:

http://adsabs.harvard.edu/abs/1970ApJ…159..379R

The image of rotation curves for multiple galaxies comes from page 4 of astronomy class notes from the University of Colorado. Available here:

http://rocinante.colorado.edu/~pja/astr3830/lecture17.pdf

Information about our solar system and relative masses of the planets is available here:

Pasachoff, Jay M. “Solar system” World Book Online Reference Center. 2004. World Book, Inc. http://www.worldbookonline.com/wb/Article?id=ar518960.

http://www.nasa.gov/worldbook/solarsystem_worldbook.html

http://solarsystem.nasa.gov/planets/index.cfm

The leading theory to explain these rotation curves is a sphere of dark matter encompassing most or all of the visible matter a galaxy, called dark matter halos. There are simulators online which allow you to tweak certain parameters of a galaxy and its halo. One of which is available here: http://burro.cwru.edu/JavaLab/RotcurveWeb/controls_MAIN.html and click on the “applet” button.

Finally, part of this website wants to be about compelling visual images. The rotation curves presented earlier are a little austere. The image below shows the Andromeda galaxy with the rotation curve superimposed on top of it. Hopefully this gives a better sense of what these curves mean.

This image is available online here:

http://cosmicvariance.com/2005/08/30/painting-pictures-of-astronomical-objects/