In western music, certain arrangements of chords and melodies sound “right” and others don’t. Musical theorists have long employed mathematics to try to understand harmony and melody, and particularly why only some sequences of notes lead from one specific chord to another in an aesthetically acceptable manner.

An advanced mathematical analysis uses a theoretical space in which all chords are points and sequences of notes connecting chords are lines between the points. The analysis shows that western music — even dissonant avant-garde compositions — use one of only three geometrical symmetries in the notes leading from one chord to another. This geometry of chords also provides a better understanding of consonance and dissonance, differences among musical genres and strategies of particular composers.

One of the few silver linings is fading as the ominous cloud of global warming comes into clearer view. Previous research involving greenhouse experiments suggested that the damaging effects of higher temperature and lower soil moisture on agriculture from global warming could be offset by the fertilizing effect of increases in carbon dioxide. A study based on open-field experiments shows that the carbon dioxide benefit is only half as great, leaving the world with a net loss in the global warming-agriculture equation.

A study of tropical mountain glaciers in the Andes and Himalayas shows that nothing like the global-warming-driven melting of the glaciers has happened for at least 2,000 years, and temperatures in those regions have not been as high for 5,000 years. The study found that Peru’s Qori Kalis glacier retreated 10 times faster — 60 meters per year — in the last 14 years than it did during the 15 years from 1963 to 1978. The study also found that precipitation in the glacial regions has increased over the last century, proving that rising temperatures are the cause of the glacial retreat. Glacier melt is contributing to rising sea levels and threatens the water supplies of many high-altitude communities.

The study also showed an abrupt global cooling about 5,200 years ago. Because tropical climates are relatively uniform, the abrupt cooling and today’s abrupt warming demonstrate the sensitivity of the global climate.

Separately, a study of sea surface temperatures in the tropical North Atlantic proves that about half of the record temperature increase last year was due to global warming, which is 1.5 times as much as natural variation and the effects of El Niño combined. The temperature increase was a major cause of last year’s deadly hurricane activity. Several previous studies had attributed the increased warming to a 60-to-80-year natural cycle.

The way isolated populations of a species change over time can become synchronized when they are under pressure from some external force like predators or climate, and threatened species whose populations are synchronized quickly become extinct. A mathematical analysis of the phenomenon shows that synchronization followed by extinction can happen even if some of the isolated populations are not affected by the external force. This could help explain why 99 percent of all species have gone extinct, and why conservationists have such a difficult task.

The climate of the early Pliocene, from 3 to 5 million years ago, could hold clues about the future of our climate in the era of global warming. In those days, two key factors in global warming — the amount of sunlight hitting the Earth and the concentration of carbon dioxide — were about the same as they are today, but the average global temperature was warmer by about 3 degrees Celsius and sea levels were about 25 meters higher.

According to a review study, the difference appears to be the permanence of El Niño during the early Pliocene, which led to a higher amount of moisture in the atmosphere. Water vapor is a major greenhouse gas, and the increased levels of water vapor also reduced the type of clouds that reflect sunlight back into space.

Another difference between the early Pliocene and the current long-term climate was the lack of ice ages in the Pliocene. The 100,000-year icy periods separated by 10,000-year interglacial periods, one of which we enjoy at the moment, are a feature of our cooler climate.

If today’s global warming boosts temperatures and precipitation near the poles, it could push the temperature boundary in the tropical oceans to lower depths. This could dramatically reduce the sensitivity of the climate to changes in the planet’s orbit, and usher in a Pliocene-like climate free of ice ages.

A study about the way medical studies are reported in the media doesn’t engender confidence in the press’s ability to convey scientific information to the public. The analysis of 187 news stories from newspapers, television and radio about studies reported at scientific conferences found that many relevant details were not reported. Only 6 percent of stories about animal studies mentioned that the results were not necessarily relevant to humans, 21 percent of stories about studies involving fewer than 30 subjects mentioned the studies’ imprecision, 29 percent of the 142 stories about treatments mentioned any potential downside, and just two out of 175 stories about unpublished results mentioned that the studies were unpublished, had not undergone peer review or were preliminary.

Humans are good at making decisions in the face of incomplete or shaky information. We’re able to work toward a goal without knowing every step of the way ahead of time because we can update and reevaluate our beliefs about our knowledge of the situation as we go. A brain imaging study reveals the neural circuitry involved, and shows that the two aspects of changing our minds about what we know — updating and reevaluating — are handled by two different parts of the cerebral cortex.

Despite the incredible complexity of weather, one aspect — tropical downpours — follows the relatively simple physics of critical phenomena, or natural systems that change abruptly at phase transitions. Critical phenomena are common throughout nature. The research could improve the climate models used by meteorologists and climate scientists.

We think differently about people like us and people not like us — literally.

A brain imaging study shows that when people think about someone they consider similar to themselves they use a part of the brain associated with thinking about the self, but use a different part of the brain when thinking about someone they consider to be different. The research highlights the social and political dangers of stressing differences between people.