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Perceptions of wealth are often more complicated than just net worth, a new study indicates. Photo courtesy of flickr user AMagill

A recent thread on the urban parenting site Urbanbaby.com asked a simple pair of questions: What is your household income, and how rich do you feel? The resulting contradictions of income and perceived wealth drew widespread remark—and some scorn. One commenter, from New York City’s Upper East Side, makes $350,000 per year and feels “so, so, so poor.” Another earns $1.2 million and feels upper-middle class, while a third, with an income in the $180,000 range in the D.C. suburbs, feels rich.

How is this all possible? Everyone knows the old platitude “beauty is in the eye of the beholder.” A recent psychological study indicates that wealth is just the same. A new paper, published in the January issue of Psychological Science by Princeton researcher Abigail Sussman, demonstrates that total net worth is not the only thing that influences perceptions of wealth, whether for ourselves or others.

If you were asked to consider two individuals—Mr. Blue, who has $120,200 in assets and $40,200 in debt, and Ms. Green, who has $80,200 in assets and just $200 in debt—who do you think is better off? Of participants in the study, 79% said Ms. Green, although net worth is the same for both. When assessing those with positive net worth, having a lower degree of both assets and debt was seen as better than having more of each.

On the other hand, when considering a pair of individuals with equal negative net worth—say, Mr. Red, with $42,400 in assets and $82,400 in debt, and Ms. Gray, with just $400 in assets and $42,000 in debt—77% of respondents more often said that Mr. Red was wealthier. Having more assets, as well as more debt, was generally perceived as better.

What’s going on? Why do the trends move in opposite directions depending on whether the individuals were in the black or red? Sussman explains:

People generally like assets and dislike debt, but they tend to focus more on one or the other depending on their net worth. We find that if you have positive net worth, your attention is more likely to be drawn to debt, which stands out against the positive background. On the other hand, when things are bad, people find comfort in their assets, which get more attention.

These findings are more than just interesting—they seem likely to affect real lending and borrowing patterns. A second part of the study asked participants to imagine themselves in each of the scenarios, and then say how willing they would be to borrow money for purchases like a bathroom renovation or television. Again, people with positive net worth saw themselves as wealthier—and more willing to take on a loan—if they had fewer assets and debt to start with, and the reverse held true for those with negative net worth.

The study’s conclusions challenge traditional assumptions of classical economics—and, Sussman says, can be crucial in understanding otherwise puzzling economical choices we see in the real world.

The first Death Star from Star Wars (via Wookieepedia)

Obi-Wan: That’s no moon. It’s a space station.

That space station was the Empire’s first Death Star in Star Wars: A New Hope. Obi-Wan and company had just bounced through a debris field, the remnants of the planet Alderaan. Such an act of destruction would seem impossible to us–it seemed so to many of the movie’s characters until it happened. But perhaps not, say three students at the University of Leicester in England who last year published a study on the subject in their university’s undergraduate physics and astronomy journal.

The study’s authors start off by making some simple assumptions: The planet being fired upon doesn’t have some sort of protection, like a shield generator. And it’s about the size of Earth but solid through and through (Earth isn’t solid, but the planet’s layers would have significantly complicated the math here). They then calculate the planet’s gravitational binding energy, which is the amount of energy required to pull apart an object. Using the mass and radius of the planet, they calculate that destruction of the object would require 2.25 x 10³² joules. (One joule is equal to the amount of energy required to lift an apple one meter. 10³² joules is a lot of apples.)

The energy output of the Death Star isn’t given directly in the movie, but the space station was said to have had a “hypermatter” reactor that had the energy output of several main-sequence stars. For an example of a main-sequence star, the authors look to the Sun, which puts out 3 x 10²⁶ joules per second, and they conclude that the Death Star could “easily afford to output [the energy required for an Earth-like planet's destruction] due to to its tremendous power source.”

It would be a different story, though, if the planet scheduled for destruction had been more like Jupiter than Earth. The gravitational binding energy of Jupiter is 1,000 times that of the Earth-like planet in the study. “To destroy a planet like Jupiter [the space station] would probably have to divert all remaining power from all essential systems and life support, which is not necessarily possible.”

Of course, that assumes that the Emperor wouldn’t be willing to sacrifice a space station full of people to wipe out his enemies. And considering that he was just fine with wiping out whole planets, I’m not sure I’d take that bet.

A sample of highly enriched uranium (via wikimedia commons)

Enriched uranium is back in the news with a report that Iran has begun creating the stuff at a heavily fortified site in the north of that country. But what is enriched uranium?

Uranium is element 92 on the periodic table–every molecule has 92 protons in its nucleus. The number of neutrons can vary, and that’s the difference between the three isotopes of uranium that we find here on Earth. Uranium-238 (92 protons plus 146 neutrons) is the most abundant form, and about 99.3 percent of all uranium is U-238. The rest is U-235 (0.7 percent), with a trace amount of U-234.

Uranium has a bad reputation (it is radioactive, after all), but U-238 has a very long half-life, meaning that it can be handled fairly safely as long as precautions are taken (as seen in the video below). More importantly here, though, U-238 isn’t fissile–it can’t start a nuclear reaction and sustain it.

U-235, however, is fissile; it can start a nuclear reaction and sustain it. But that 0.7 percent in naturally occurring uranium isn’t enough to make a bomb or even a nuclear reactor for a power plant. A power plant requires uranium with three to four percent U-235 (this is known as low-enriched or reactor-grade uranium), and a bomb needs uranium with a whopping 90 percent U-235 (highly enriched uranium).

Uranium enrichment, then, is the process by which a sample of uranium has its proportion of U-235 increased.

The first people to figure out how to do this were the scientists of the Manhattan Project during World War II. They came up with four methods to separate the U-235 from uranium ore: gaseous diffusion, electromagnetic separation, liquid thermal diffusion and centrifugation, though at the time they deemed centrifugation not practical for large-scale enrichment.

The most common methods for enriching uranium today are centrifugation (decades of development have made this method more efficient than it was during WWII) and gaseous diffusion. And other methods are being developed, including several based on laser techniques.

Highly enriched uranium, the type used in bombs, is expensive and difficult to create, which is why it remains a barrier, though not an insurmountable one, for countries wishing to develop nuclear weapons. And once a nation develops the capability for enriching uranium beyond reactor grade (Iran has reportedly begun to produce uranium enriched up to 20 percent), the path to weapons-grade uranium is significantly sped up.

Find out more about nuclear concerns in Iran from Arms Control Wonk, the Carnegie Endowment for International Peace and ISIS NuclearIran, from the Institute for Science and International Security.

And learn more about the element uranium, including depleted uranium, in this selection from the Periodic Table of Videos:

Mauna Loa (as seen from nearby Mauna Kea) is tall enough to have snow, at least when the volcano isn't erupting (courtesy of flickr user superfluity)

If asked to name the tallest mountain on Earth, most people would answer Mount Everest. They’d be wrong–Everest is the highest peak on the planet, but mountains are measured from their base to their peak, and Everest’s base sits far above sea level on the Tibetan Plateau. And when you start looking at the tallest (known) mountains in the solar system, Mount Everest, at only 2.3 to 2.9 miles tall (depending on where you decide the mountain’s base is located), doesn’t even make the list:

(1) Olympus Mons - 15.5 miles
The largest volcano on Mars is also the solar system’s tallest mountain. Measuring 374 miles in diameter, it covers about the same amount of land as the state of Arizona. Olympus Mons is located near three other volcanoes known as the Tharsis Montes. The volcanoes in this area are all 10 to 100 times bigger than Earth’s largest volcanoes. They can get this big because, unlike on Earth, there are no plate tectonics on Mars that can drag a volcano away from its hotspot–they just sit in one volcanically active place and grow bigger and bigger.

(2) Rheasilvea Mons – 13.2 miles
Rheasilvea, on the asteroid Vesta, sits at the center of a 300-mile wide crater. The asteroid is currently the subject of a close study by the spacecraft Dawn, which will continue to circle it through the first half of 2012 before moving on for a rendezvous with the asteroid Ceres in 2015. Rheasilvea Mons sometimes gets named the tallest peak in the solar system, but even with satellites and spacecraft monitoring faraway planets, moons and asteroids, measuring these things is rather difficult (which should explain why the numbers for heights given here may differ from what you’ve seen elsewhere–sources often disagree).

(3) Equatorial Ridge of Iapetus – 12.4 miles
Saturn’s moon of Iapetus has a couple of weird features. The first is a huge crater that gives the moon the appearance of the Death Star from Star Wars. The second is an equatorial ridge, with some peaks reaching over 12 miles high, that makes Iapetus look like a walnut. Scientists aren’t quite sure how the ridge formed, but they have hypothesized that it was either the remnant of the moon’s earlier oblate shape, icy material pushed up from beneath the moon’s surface or even the remainder of a collapsed ring.

(4) Ascreaus Mons – 11.3 miles
This volcano on Mars is the tallest of the three volcanoes known as the Tharsis Montes, which appear in a straight line near Olympus Mons. Ascreaus Mons has a central caldera that is 2.1 miles deep. It was first spotted by the Mariner 9 spacecraft in 1971 and then named the North Spot, as it appeared as a spot in a dust storm photographed by the spacecraft. Later images revealed it was a volcano and the spot was remaned.

(5) Boösaule Montes – 10.9 miles
Boösaule Montes is a collection of three mountains on Io, a moon of Jupiter, all connected by a raised plain. The mountain termed “South” is the tallest of the three. One side of the mountain has such a steep slope, 40 degrees, that scientists think that it was the site of a huge landslide.

(6) Arsia Mons – 9.9 miles
This is second tallest volcano from the Tharsis Montes on Mars. Based on the discovery of certain geological features on the volcano, scientists think that Arsia Mons may be home to glaciers.

(7) Pavonis Mons – 8.7 miles
Pavonis Mons is the shortest of the three volcanoes that make up the Tharsis Montes, and it has also been suggested to be home to glaciers.

(8) Elysium Mons - 7.8 miles
This Martian volcano is a big fish in a little pond, metaphorically speaking. It is the tallest volcano in the Elysium Planitia, a region in Mars’ Eastern Hemisphere that is the second largest volcanic system on the planet.

(9) Maxwell Montes - 6.8 miles
This mountain range on Venus stretches for 530 miles. Scientists aren’t sure how the mountains formed, but they think they are home to large amounts of fool’s gold (iron pyrite).

(10) Mauna Loa – 5.7 miles
Earth just squeaks into this top ten list with this active volcano on the island of Hawaii (remember, mountains are measured from their base to their peak, and Mauna Loa’s base is far beneath the ocean surface). Mauna Loa is one of many active and dormant volcanoes created by a hotspot beneath the Pacific Ocean plate. As the plate moves over the hotspot, which has been active for at least 30 million years, new islands begin to form and old ones, no longer being built up through volcanic activity, whither wither away.

A good eye will spot the black-marble jawfish next to the mimic octopus's arm (Credit: Godehard Kopp)

The mimic octopus (Thaumoctopus mimicus) has the uncanny ability to make itself look like more dangerous creatures, such as lionfish, sea snakes and soles. The octopus does this with its distinctive color pattern and ability to adjust its shape and behavior (see this earlier blog post on the octopus for a video in which it mimics a flatfish). But now the mimic has a mimicker of its own, scientists report in the journal Coral Reefs.

Godehard Kopp  of the University of Gottingen in Germany was filming a mimic octopus during a diving trip to Indonesia last July when he spotted a companion–a small fish that followed the octopus for several minutes, always sticking close to the octopus’s arms. Kopp has some good observational skills, because the fish’s color and banding looks incredibly similar to that of the octopus.

Kopp sent his video (see below) to two marine scientists at the California Academy of Sciences who identified the fish as a black-marble jawfish (Stalix cf. histrio). The three write:

Jawfish are poor swimmers and usually spend their entire adult lives very close to burrows in the sand, to where they quickly retreat, tail first, upon sight of any potential predator….[In Kopp's video and photos], the Black-Marble Jawfish seems to have found a safe way to move around in the open. The Mimic Octopus looks so much like its poisonous models that it is relatively safe from predation, even when swimming in the open, and by mimicking the octopus’ arms, the Jawfish seems to also gain protection.

This might at first glance appear to be a case in which the fish evolved its coloring to gain protection by associating with the octopus, but the scientists don’t think that’s likely. The jawfish can be found from Japan to Australia, but the octopus lives only in the region around Indonesia and Malaysia. They contend that this is a case of “opportunistic mimicry,” in which the fish is taking advantage of a happy coincidence.