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 16, 2022 at 9:17am

#1026805

Putting the Product in Productivity

I'm still in NYC, so another short one (this post, not the article) today -- one I don't quite know what to say about, but I'm going to try anyway.

the diminishing returns of productivity culture

Article is from last year, but I doubt there's much contextual difference now.

Like most of these kinds of articles, it opens with an anecdote of sorts. Which isn't bad in itself; I think it's a great way to hook a reader. It just doesn't have a lot that I can quote here, so I'm skipping it even though it's kind of important.

I thought about this passage this week, while working on the chapter in the new book on the history office tech that promised to make workers’ lives easier, but usually just created the compulsion to do more work. Much like the digital technologies of today, these technologies — from “24 hour computer lieutenants” in a GE dishwashing factory to word processors — were sold to workers as a means of making their work simpler, more predictable, safer.

You know what I remember from the 70s, maybe on into the early 80s? Someone promised we would have a three-day work week, or something to that effect, because computers and automation would help us get our jobs -- for various definitions of "our" -- done faster, leaving us more time for fishing. Imagine my shock and dismay when not only did that not happen, but employers started demanding more time out of us than during B.C. (Before Computers). In other words, not only were we compressing what used to take a week into a day; not only were we then expected to do five weeks' worth of B.C. work in a week, but we had to push it to add overtime and weekends.

Of course, we were also promised flying cars, so I suppose I should have known better.

Anyway, the article doesn't address that directly, I think, but it has a lot more to say than I'm going to relate here because, as I implied, I have a lot of other stuff to do today.

This is the dystopian reality of productivity culture. Its mandate is never “You figured out how to do my tasks more efficiently, so you get to spend less time working.” It is always: “You figured out how to do your tasks more efficiency, so you must now do more tasks.” Sometimes, if you’re a Wall Street investment banker, you can complete infinitely more tasks until you have so much money that you don’t even need it anymore — you’re productive for the thrill of it, but also because you don’t know how else to gauge your own self-worth.

My motivation was never productivity, though I did derive some satisfaction from completing a project. No, I only worked for one reason: to accumulate enough money such that I wouldn't have to participate in the productivity hamster wheel.

Obviously, different people are motivated by other things, and I'm not ragging on them here. Just on the culture that tries to squeeze more and more out of its workers until, like an empty tube of toothpaste, they just have nothing left.

The vast majority of people are not paid enough for the productivity that is demanded of them. More money can be stabilizing — and quiet the financial stress that interferes with productivity. But it doesn’t solve the fundamental problem: human productivity has a ceiling. Technology attempts to modify that reality, but it can only do so much. The body, and the mind, begins to falter.

And now, I'm off to be unproductive some more.

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