Complex Numbers (Book)

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Complex Numbers

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.

http://www.ddewey.net/mandelbrot/

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February 5, 2022 at 12:02am

#1026065

The Yeast You Can Do

Today, in Booze News...

A newly discovered cryosphere-dwelling yeast stays alive by making ethanol
Rhodotorula frigidialcoholis was isolated from 150,000-year-old permafrost in the McMurdo Dry Valleys of Antarctica

I need to take a moment to point out that this is the best binomial I have seen in a long time: Rhodotorula frigidialcoholis.

Most of the Earth’s biosphere is permanently cold and contains environments below 0° C, known as the cryosphere.

Not for very much longer.

Microorganisms like bacteria and fungi call the cryosphere home, despite the seemingly inhospitable conditions. Some can even stick around in the ice for thousands of years.

This is why a lot of people think we could find life in otherwise inhospitable extraterrestrial locations, such as Mars. Not cogitating aliens, but microorganisms.

One example of cryosphere adapted fungi are a genus of single celled, pink pigmented yeast called Rhodotorula, which have been isolated and characterized from a range of cold ecosystems.

Hm, pink, much like all these elephants I'm seeing.

The researchers found it has two novel responses to extreme cold temperatures: it can switch its metabolism from respiration to ethanol fermentation as its main pathway, and can overexpress molecules called small non-coding RNAs (sRNAs) that help regulate which genes are expressed after transcription.

That last bit is above my pay grade, but I understood "ethanol fermentation as its main pathway."

...the metabolic switch from respiration to ethanol fermentation by R. frigidialcoholis may help the novel yeast – and potentially others like it – save energy, slowing down the freezing point in their cells as a long-term survival strategy.

Not mentioned in the article: new ways to make booze. Too bad.

One of my favorite stories concerning drunk history involves how Russian Imperial Stout, one of my favorite beer styles, was created. This is the way I like to tell it (and yeah, I may have mentioned it in here before, but it's been a while):

Long ago, during the reign of, I forget, Catherine or Peter (one of the Greats anyway), the British ambassador to Russia introduced the Russian imperial court to the concept of stout: that dark, roasty beer of which Guinness is probably the best-known example worldwide. The Russians loved the stuff, so the ambassador arranged for several casks to be sent to St. Petersburg.

In the winter.

Naturally, the casks froze and burst during the trip through the frigid waters, disappointing everyone involved.

The British, in a fit of genius not seen since Newton invented gravity, found a way to brew the stout with a higher alcohol content, while balancing the flavors of all the other ingredients. Alcohol has a lower freezing point than water, making it an effective antifreeze, so those casks made it to the Tsar, and Russians being Russians, no one complained about the higher alcohol content. And thus was born Russian Imperial Stout -- not a Russian brew at all, but originally British, much as India Pale Ale was invented by the British for parallel reasons -- but that's a story for another time.

The point being that these yeast presumably survive extreme cold by creating their own antifreeze in the form of ethanol. Obviously other yeast produce ethanol too, which is what makes some of the greatest beverages on Earth possible, but apparently this is a different mechanism? Or something; the article is a bit short on details where that's concerned.

But since it involves ethanol, well, here it is.

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