It was an absolute delight to read about percolation theory in “The Math of Making Connections,” by Kelsey Houston-Edwards. Please feature more articles by this author and about mathematics as applied to science. I’m not a mathematician, yet I enjoy learning about theory and application. I love the expanse of disciplines you cover.

I am an African-American woman with a biology degree. I used to work as a research assistant in cancer research. That was until the racism that I consistently encountered wore me down, and I just didn’t want to ever work with scientists again. Although I am in another line of work, I haven’t lost my love of the sciences and mathematics. Your magazine provides me with the joy I used to feel but without the heartache.

TRACIE S. JOHNSON via e-mail

One approach to developing a theory of quantum gravity is called loop quantum gravity (LQG). It treats space as a discrete substance composed of individual spatial atoms, or nodes, at the Planck distance scale of 10−35 meter. They are connected to one another in a way that would seem to lend itself very well to percolation theory, which is precisely geared toward modeling the connections among discrete nodes. Has percolation been applied to advancing LQG and quantum gravity?


HOUSTON-EDWARDS REPLIES: In response to Rosenblatt: In percolation theory, a “dial” controls the local connectivity of a network. When its needle lands on a critical point, a phase transition occurs, and the global connectivity of the network changes dramatically. To apply the theory to LQG, one needs to describe how and why this dial moves to the critical point. But as theoretical physicist Lee Smolin explained in an e-mail to Scientific American, nature exhibits several instances of “self-organized critical phenomena,” in which the dial tunes itself toward the critical threshold. Smolin hypothesizes that such a self-organized phase transition might explain “the emergence of classical spacetime in a quantum theory of gravity,” including loop quantum gravity. He and physicist Mohammad Ansari explored these ideas in the 2008 paper “Self-Organized Criticality in Quantum Gravity.” It is unclear how extensively a “self-tuning” version of percolation could be used for understanding a self-organized phase transition in the case of LQG.


I was troubled by “What to Do about Natural Gas,” Michael E. Webber’s article about ways to decarbonize the natural gas system. Pointing out that the primary alternative, electrification, will be challenging is fair enough. But electrification does not have barriers that are greater than, or even equal to, a zero-carbon gas system, which faces structural limitations. To his credit, Webber names some of these limitations. But his presentation of them as solvable with some tweaks is disingenuous. Even by the gas industry’s own estimates, two decades of scaling up all low-carbon gases would displace only about 13 percent of the U.S.’s existing gas demand. Also, it would squander any genuinely sustainable gases that could be used where we might actually need them, such as chemical feedstocks, shipping and aviation.

Keeping warming within the 1.5 degrees Celsius limit necessary to avoid catastrophic climate destabilization requires us to reach net-zero emissions, meaning we must leave the majority of the world’s existing gas reserves unburned. And whether methane is synthetic, biogenic or fracked, if it’s pumped through the existing distribution network, it will face leakage, adding to atmospheric warming.

Perhaps the most important omission is that decarbonizing gas does not solve the health impacts of combustion. With low-carbon gases, we only get more expensive ways of polluting our homes.

SASAN SAADAT Research and policy analyst, Earthjustice

WEBBER REPLIES: It seems that we agree that addressing climate change is the most urgent and important challenge of the 21st century. That realization led me to the conclusion that we need every solution possible to get us to carbon neutrality (and carbon negativity!) as quickly, safely and affordably as possible. As I write in the article, I think the first two priorities for decarbonizing the economy are (1) conservation and efficiency and (2) electrification. Because low-carbon fuels play an important role for sectors that are difficult to electrify, we need to make progress on decarbonizing gases as the third step.

As someone who invented sensors to measure the emissions from combustion, I’m well aware of its pollution. And as someone who quantitatively analyzes different forms of energy, I’m also aware of the significant ecosystem impacts of some utility-scale renewables. The energy system is all about trade-offs, and there is no one fuel or technology option that is purely villainous or virtuous. Rather we must design a suite of solutions that meets society’s complex needs.


In “Prediction Predicament” [Advances], Hannah Seo notes that making predictions impairs people’s ability to remember predictive events. I see this a lot in the martial arts. Often when an instructor demonstrates a technique, the students will be busy imagining what comes next and how they think the technique should be performed while failing to see the variation that the instructor is demonstrating. It’s like the students are watching to confirm their predictions instead of observing to learn something new.

IAN MCINTYRE via e-mail


Hope for Meth Addiction,” by Claudia Wallis [Science of Health], encouragingly describes the growing evidence base for contingency management as an effective treatment for stimulant use disorder, particularly in conjunction with bupropion and naltrexone. It notes that one trial of the two drugs found that they helped a significant number of treated users test methamphetamine-free “at least three quarters of the time.”

Wallis’s piece is to be applauded for its apparent recognition that complete abstinence is not the only recovery pathway. Harm reduction is effective, and reoccurrence of substance use is not unusual for most people as they seek recovery. While abstinence-based approaches may be ideal for some, they don’t work for everyone. Contingency management and harm reduction are both important strategies that can lead to improved health and wellness for those who are still struggling with harmful substance use.

Ann Herbst Interim CEO, Young People in Recovery


In “The Math of Making Connections,” by Kelsey Houston-Edwards, the bottom illustration in the box “Square Lattice” should have depicted the white pipe at the top left of the lattice filling with water.

In “Scientists: Admit You Have Values,” by Naomi Oreskes [Observatory], the end of the quote attributed to Francis Bacon should have read: “... man prefers to believe what he wants to be true.”