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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July 11, 2022 at 7:06am

#1035020

Speakers for the Dead

Here's another one from Atlas Obscura, shedding some light on our wonderful American history.

The Quest to Honor Disabled Patients Buried in Anonymous Graves
Historically, institutions often interred their dead with simple markers. In Massachusetts, researchers are learning about the patients’ lives and the facilities’ fraught legacies.

It's fairly long and involved, but worth it for a glimpse of how attitudes have changed (and not).

Between 1947 and 1979, these institutions buried 296 of their patients in simple, anonymous graves on a plot of former marshland now called the MetFern Cemetery, a portmanteau of the two institutions’ names. The grave markers are sunken and toppled, and have only two things etched onto their concrete slabs: “C” or “P,” for Catholic and Protestant (though records indicate that a Muslim man and two Jewish patients may have been buried there as well), and a number that denotes the order in which the patient was interred.

It's hard to say who was less valued to them: the differently abled, or the differently religious.

The Walter E. Fernald Developmental Center, also referred to as the Fernald School, was originally called the Massachusetts School for Idiotic and Feeble-Minded Youth.

But doesn't that describe all youth?

Founded in South Boston in 1848 by Samuel Gridley Howe, it opened as a small experimental school to teach children and teens with intellectual disabilities life skills so they could live independently. Due to the popular perception that children with disabilities couldn’t learn, it proved to be the most progressive and radical institution of its era, says Green.

I suppose they had to start somewhere.

As conditions declined, an increasing number of patients suffered premature deaths, leading the institutions to open a shared cemetery, says Green.

Easier than hiring more people.

The unnamed gravestones were likely a measure taken to protect a family’s reputation in an era of overwhelming social stigma surrounding disabilities.

I guess it doesn't much matter to someone who's dead, but what about protecting their reputation?

Rosenblatt says there’s now “a lot of energy” around unearthing information and restoring dignity to deceased people who have long been overlooked.

Again, it's a start.

I'm just hitting some lowlights here. There's much more to the article. As maddening as it is to hear about how some people were dehumanized, it's also rather gratifying to see that the trend is now toward some restoration.

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