The turn against shale gas rests on three beliefs that have calcified into conventional wisdom among many environmental advocates. The first is that shale gas development causes massive damage to communities and the local environment—regardless of what regulations are put in place. This sets a daunting bar for any climate strategy that includes shale gas production. The second is that gas is no better than coal when it comes to climate change—at least not without big changes to the way gas is produced—and might even increase greenhouse gas emissions. This undercuts any imperative to wrestle with trade-offs between local risks and climate benefits from gas. The third is that renewable energy has made such rapid progress that a shift to a zero-carbon energy future is imminent. This makes natural gas unnecessary, and potentially a threat to a complete and speedy transition away from fossil fuels.
But each of these is a myth or half-truth. Strict rules and smart planning can safeguard communities. If policy drives natural gas to displace coal, the result can be much lower emissions. And, while renewables have made big strides, the biggest beneficiary of a setback to natural gas would, for now, still be coal.
People are colossally underestimating the Internet of Things. It’s not about alarm clocks that start your coffee maker, or about making more “things” talk to each other on a global network. The IoT will fundamentally alter how humans interact with the physical world, and will ultimately register as more significant than the Internet itself.
One can roughly divide mathematical education into three stages:
- The “pre-rigorous” stage, in which mathematics is taught in an informal, intuitive manner, based on examples, fuzzy notions, and hand-waving. (For instance, calculus is usually first introduced in terms of slopes, areas, rates of change, and so forth.) The emphasis is more on computation than on theory. This stage generally lasts until the early undergraduate years.
- The “rigorous” stage, in which one is now taught that in order to do maths “properly”, one needs to work and think in a much more precise and formal manner (e.g. re-doing calculus by using epsilons and deltas all over the place). The emphasis is now primarily on theory; and one is expected to be able to comfortably manipulate abstract mathematical objects without focusing too much on what such objects actually “mean”. This stage usually occupies the later undergraduate and early graduate years.
- The “post-rigorous” stage, in which one has grown comfortable with all the rigorous foundations of one’s chosen field, and is now ready to revisit and refine one’s pre-rigorous intuition on the subject, but this time with the intuition solidly buttressed by rigorous theory. (For instance, in this stage one would be able to quickly and accurately perform computations in vector calculus by using analogies with scalar calculus, or informal and semi-rigorous use of infinitesimals, big-O notation, and so forth, and be able to convert all such calculations into a rigorous argument whenever required.) The emphasis is now on applications, intuition, and the “big picture”. This stage usually occupies the late graduate years and beyond.
The popular image of the lone (and possibly slightly mad) genius – who ignores the literature and other conventional wisdom and manages by some inexplicable inspiration (enhanced, perhaps, with a liberal dash of suffering) to come up with a breathtakingly original solution to a problem that confounded all the experts – is a charming and romantic image, but also a wildly inaccurate one, at least in the world of modern mathematics. We do have spectacular, deep and remarkable results and insights in this subject, of course, but they are the hard-won and cumulative achievement of years, decades, or even centuries of steady work and progress of many good and great mathematicians; the advance from one stage of understanding to the next can be highly non-trivial, and sometimes rather unexpected, but still builds upon the foundation of earlier work rather than starting totally anew.
And under a parallel amendment to New Zealand’s Crimes Act, a person who tells another to kill themselves faces up to three years in prison.
The law will help mitigate the harm caused by cyber-bulling and give victims a quick and effective means of redress, supporters said.
But critics said the law harms free speech and its fine print could threaten public interest journalism in the country.