Infinite in All Directions: New Math Magazine, Climatic Arrogance, Covenant of the Rainbow

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Credit: r8O0/Flickr, CC BY 2.0

Credit: r8O0/Flickr, CC BY 2.0

Where did chance come from?

Steven Weinberg has been more vocal and more articulate than many of his peers in the last few years about the philosophy of quantum mechanics, even if his latest book – To Explain the World (2015) – was a dud. In the January 19 issue of the New York Review of Books, Weinberg has a long essay on the slow descent to probabilistic chaos that the study of quantum mechanics has led physicists into. I’ve always found that scientists who also write are much better at writing about quantum mechanical problems than are writers who write, no matter how good the latter otherwise are. Weinberg is no exception. This is the central thesis:

The introduction of probability into the principles of physics was disturbing to past physicists, but the trouble with quantum mechanics is not that it involves probabilities. We can live with that. The trouble is that in quantum mechanics the way that wave functions change with time is governed by an equation, the Schrödinger equation, that does not involve probabilities. It is just as deterministic as Newton’s equations of motion and gravitation. That is, given the wave function at any moment, the Schrödinger equation will tell you precisely what the wave function will be at any future time. There is not even the possibility of chaos, the extreme sensitivity to initial conditions that is possible in Newtonian mechanics. So if we regard the whole process of measurement as being governed by the equations of quantum mechanics, and these equations are perfectly deterministic, how do probabilities get into quantum mechanics?


An India mathematics magazine

The Indian Mathematical Consortium has just published the inaugural edition of Bhavana – what it calls “India’s first mathematics publication for a general audience”. It is a laudable effort foremost. I haven’t read the magazine myself yet, though I found on a cursory skim that the first edition focuses on Ramanujan to a large extent, and perhaps underestimates a lay audience’s aversion to mathematical equations. If you would like to get in touch with anyone behind the magazine: their email IDs are on page 2.


Frankly, climate change is real… right?

I met someone over the weekend who wasn’t sure:

  1. That there is scientific consensus on the magnitude of anthropogenic global warming (AGW), and
  2. What the level of human contribution is to rising temperatures (or, how much natural variations could/couldn’t account for)

I believe that AGW is valid and that, if we don’t do something about the way we’re using Earth’s natural resources, AGW will be extremely damaging to the environment as soon as a century from now (to be even more proper about it: that AGW will force nature to adapt in ways that will no longer preserve characteristics that we have been able to attribute to it for thousands of years). This said: I’m not here to describe how the conversation with my friend went but to highlight one specific source of information that was in play last night and which I think is worth discussing because of its attempts at coming off as trustworthy.

In May 2013, John Cook et al published a paper titled ‘Quantifying the consensus on anthropogenic global warming in the scientific literature’. It was a literature review of 11,944 papers published in 1,980 journals, all papers dealing with climate change. Using a large team of volunteers, the authors then classified each paper into one of five groups depending on what its abstract said about the paper’s position on climate change. These were the results:

At the time of publication, the paper received a lot of play in the media – largely because of the numbers in the first row, columns two and four. According to it, 97.1% of all papers that have a position on AGW endorse AGW and 98.% of all authors that have a position on AGW endorse AGW. However, both the giant numbers don’t correspond to the 11,944 abstracts surveyed but the 3,893 (32.6%) that the authors qualified as having a position on AGW.

Clearly, the way to interpret John Cook et al would’ve been to say it like Der Spiegel did: ‘Von knapp 4000 Studien, die die Ursachen der Klimaerwärmung thematisierten, stützen 97 Prozent die Annahme vom menschgemachten Klimawandel’ (“Of nearly 4,000 studies dealing with the causes of climate warming, 97 percent support the assumption of human-driven climate change”). However, my friend – during the course of his arguments – often lingered on the 66.7% (7,966) of all papers that were uncertain about or refused to take a position on AGW. Specifically, he took the exclusion of these papers from the calculation that arrived at a number like “97.1%” to be misguided. After all, he reasoned, ~8,000 papers out of ~12,000 had seen it fit to not explicitly endorse AGW.

Dana Nuccitelli and John Cook, two of the paper’s authors, tried to explain these numbers thus on the Skeptical Science blog:

We found that about two-thirds of papers didn’t express a position on the subject in the abstract, which confirms that we were conservative in our initial abstract ratings. This result isn’t surprising for two reasons: 1) most journals have strict word limits for their abstracts, and 2) frankly, every scientist doing climate research knows humans are causing global warming. There’s no longer a need to state something so obvious. For example, would you expect every geological paper to note in its abstract that the Earth is a spherical body that orbits the sun?

I don’t buy it. The first sentence – “We found that about two-thirds of papers didn’t express a position on the subject in the abstract, which confirms that we were conservative in our initial abstract ratings” – is more of a self-fulfilling prophecy than anything else. The first part of the second sentence requires even more analysis to verify, considering the 11,944 papers they parsed appeared in 1,980 journals, and the fraction of journals that set a word-limit for the abstract might just be non-trivial. The second part is, to me, the display of off-putting arrogance. Doesn’t saying “frankly, every scientist doing climate research knows humans are causing global warming” imply the authors are being dismissive of their own conclusions? And finally, that Earth orbits the Sun is far more obvious than a thesis the defence of which rests on the presumption that the thesis is right – a circularity that renders all facts moot.

While none of this makes me question the validity of AGW, which I still endorse for various reasons, Nuccitelli-Cook’s pseudo-defence doesn’t help me trust them in particular. In fact, their position makes me more suspicious of why they arrived at a number like 32.6% when they were assuming at the outset that it would really be 100%.


Covenant of the Rainbow

On a related note: a deep-sea biologist named Andrew David Thaler recently wrote about why it’s no longer meaningful to talk about the science of climate change when talking about climate change because that’s been settled. Instead, Thaler focuses on the politics of it because that’s what’s keeping it unsettled wherever that is the case. I’m not sure I agree because I think politics ought also to be science’s business, and convincing someone across the aisle (a phrase I’ve become fond of) that there exists a motivation to do something – no matter what it is that we end up doing – should come out of science as much as it does out of realpolitik or policy.

However, what I want to really highlight from Thaler’s piece is how he translates the consequences of climate change to make sense to religious leaders:

But there are concrete reasons religious leaders need to take a stand, and that is the inundation and desecration of their history. Religions of every stripe have edicts against the desecration of graves. Across the world, cemeteries and grave sites are experiencing the creeping approach of sea level rise. Around the Chesapeake Bay, it has become such a problem that one historian noted that “the water is evicting the dead“. Arctic communities are hit even harder, as both rising seas and the thawing of the permafrost due to warming act in concert to inundate and uplift traditional grave sites, some thousands of years old, putting communities and their heritage at risk. Cemeteries by the Sea is a project to document these graves, once high and dry, about to be lost forever.


A man between Kepler and Newton

… much of the scientific investigations that took place in the Early Modern Period, and which led to the creation of modern science, did so in the midst of the many bitter and very destructive religious wars that raged throughout Europe during this period. The scholars who carried out those investigations did not remain unscathed by these disturbances and careers were often deeply affected by them. The most notable example being, of course Johannes Kepler, who was tossed around by the Reformation and Counter-Reformation like a leaf in a storm. Anyone attempting to write a history of the science of this period has to, in my opinion, take these external vicissitudes into account; a history that does not do so is only a half history.

This is the end of Thony Christie’s wonderfully insightful preface to his discussion of the work of Seth Ward, the Bishop of Salisbury and a noted astronomer of the 17th century. Christie uses Ward as an example of someone who made important, but what we perceive from our vantage point in the future to be incremental, contributions to planetary astronomy – and whose name relatively few of us remember because we think it was just Copernicus, Kepler, Galileo and Newton, with no one in between. Ward in particular was responsible for popularising Kepler’s work by extending it through his own calculations. While these calculations were wrong, they were less wrong than many of his peers’ at the time, and with whom he engaged in many bitter arguments. That Kepler’s ideas were so contested but never discarded could only have been good for Kepler himself. 🙂


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  • Nalawade

    Feel happy to see an article on science so regularly on your publication. Keep it up.