Not for the faint of art.
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.
How the internet was invented
In 40 years, the internet has morphed from a military communication network into a vast global cyberspace. And it all started in a California beer garden
You will note the prominent feature of the subhead is the phrase "in a California beer garden." Remember a while back I posted on the link between bars and invention?
In the kingdom of apps and unicorns, Rossotti’s is a rarity. This beer garden in the heart of Silicon Valley has been standing on the same spot since 1852. It isn’t disruptive; it doesn’t scale. But for more than 150 years, it has done one thing and done it well: it has given Californians a good place to get drunk.
And it hasn't achieved National Historic Monument status because...?
It doesn’t seem a likely spot for a major act of innovation. But 40 years ago this August, a small team of scientists set up a computer terminal at one of its picnic tables and conducted an extraordinary experiment. Over plastic cups of beer, they proved that a strange idea called the internet could work.
As far as proof of concept demonstrations go, I've seen worse.
If you had walked into Rossotti’s beer garden on 27 August 1976, you would have seen the following: seven men and one woman at a table, hovering around a computer terminal, the woman typing.
Typical 1970s scenario. It's always the woman typing. That's what they're for, don't you know?
The fact that we think of the internet as a world of its own, as a place we can be “in” or “on” – this too is the legacy of Don Nielson and his fellow scientists. By binding different networks together so seamlessly, they made the internet feel like a single space. Strictly speaking, this is an illusion. The internet is composed of many, many networks: when I go to Google’s website, my data must traverse 11 different routers before it arrives. But the internet is a master weaver: it conceals its stitches extremely well. We’re left with the sensation of a boundless, borderless digital universe – cyberspace, as we used to call it. Forty years ago, this universe first flickered into existence in the foothills outside of Palo Alto, and has been expanding ever since.
And so the internet, like civilization itself, owes its existence to beer.
Okay, so I had to do a search on Rossotti's. Turns out it was recently restyled.
Zott's may have new floors, clean bathrooms, free WiFi and artisan wood-fired pizza, but the spirit of the place largely lives on.
Heh. Free WiFi. And so we come full circle.