Not for the faint of art. |
Complex Numbers A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number. The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi. Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary. Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty. |
Another article that didn't get the memo that the only ones who can fight climate change are us individuals. This article is from about a year ago, so I'm going to go out on a limb and guess that they didn't pay the price. Via an unprecedented wave of lawsuits, America’s petroleum giants face a reckoning for the devastation caused by fossil fuels And they have an unprecedented army of lawyers, rivaling only that of Disney, to keep them from facing said reckoning. Coastal cities struggling to keep rising sea levels at bay, midwestern states watching “mega-rains” destroy crops and homes, and fishing communities losing catches to warming waters, are now demanding the oil conglomerates pay damages and take urgent action to reduce further harm from burning fossil fuels. But I thought the solution was organic, locally-sourced reusable cotton bags. But, even more strikingly, the nearly two dozen lawsuits are underpinned by accusations that the industry severely aggravated the environmental crisis with a decades-long campaign of lies and deceit to suppress warnings from their own scientists about the impact of fossil fuels on the climate and dupe the American public. Scientists? Meh. What do they know? Have they built a giant company to slake the public's thirst for energy? No? Then what good are they? “Things have to get worse for the oil companies,” he added. “Even if they’ve got a pretty good chance of winning the litigation in places, the discovery of pretty clearcut wrong doing – that they knew their product was bad and they were lying to the public – really weakens the industry’s ability to resist legislation and settlements.” Not going to happen. Corporations, by definition, can do no wrong. In 1979, an Exxon study said that burning fossil fuels “will cause dramatic environmental effects” in the coming decades. “The potential problem is great and urgent,” it concluded. And yet, here we still are, Cassandra. The urgency of the crisis is not in doubt. A draft United Nations report, leaked last week, warns that the consequences of the climate crisis, including rising seas, intense heat and ecosystem collapse, will fundamentally reshape life on Earth in the coming decades even if fossil fuel emissions are curbed. But the climate changes all the time. Who are we to think we have the power to change the entire climate? No, better to just let the coastal cities drown like nature intended. So what if a lot of people are displaced? It's their fault for living in places like Miami. Municipalities such as Imperial Beach, California – the poorest city in San Diego county with a budget less than Exxon chief executive’s annual pay – faces rising waters on three sides without the necessary funding to build protective barriers. Eh, they're just going to slide into the Pacific come the next big earthquake, anyway. Farber said cases rooted in claims that the petroleum industry lied have the most promising chance of success. The only time lying is bad is when a Democrat does it. Exxon worked alongside Chevron, Shell, BP and smaller oil firms to shift attention away from the growing climate crisis. They funded the industry’s trade body, API, as it drew up a multimillion-dollar plan to ensure that “climate change becomes a non- issue” through disinformation. The plan said “victory will be achieved” when “recognition of uncertainties become part of the ‘conventional wisdom’”. Conventional wisdom says we should drive and fly more. Gotta keep the economy running. The legal process is likely to oblige the oil conglomerates to turn over years of internal communications revealing what they knew about climate change, when and how they responded. Hm. I should have bought stock in shredder manufacturers. Oh well. Really, there's no need to worry about climate change. Pretty soon the global average temperature will decrease again. Nuclear winter will have that effect. Anyway, if it's not obvious, at least from that last bit, my comments here are intended as satire. Still, the time to do something about climate change was 30 years ago. Now, it's too late. I know they keep trying to get us to hope, but it's not working on me. Like I've said before, I'm riding this sucker down with the hot wind in my hair and a big grin on my face. |