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Rated: 18+ · Book · Personal · #1196512
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.




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September 13, 2024 at 11:21am
September 13, 2024 at 11:21am
#1076742
Ran across this road-tripping article from Condé Nast Traveler, and, being no stranger to road trips, I couldn't resist snarking on it.

    The Golden Rules of Road Tripping  Open in new Window.
Veteran road trippers (including a gas station food evangelist) share their savviest tips and tricks.


Maybe I'm just sour because they didn't bother asking me.

Ahhhh, the great American road trip. A chance to put rubber to pavement along our millions of miles of roads and see the nooks and crannies of the country we’d never otherwise see.

Translation: "I wonder what's really in flyover country?"

Yes, this article is US-centric. It's called the great American road trip for a reason.

Along with all that good stuff, road trips have the potential for some big pitfalls, too, and in order to make sure your road trip is more life-changing than life-ruining, there are some basic guidelines first-time and veteran road trippers should follow.

Because you never know when you're going to be driving some empty stretch of country road and total your car into a deer.

Book your hotels ahead of time

There are certainly times you should do this, like if you know you're going to spend a couple of days in, like, Kansas City, and you care about location. Or if you're traveling during peak times to popular destinations like, I don't know, the Grand Canyon. But I've never once found a hotel that didn't have any vacancy. I suppose it helps if you decide to schedule your stops so that you find a hotel right after check-in starts.

It also helps not to be picky. I've stayed in 5-star hotels, and I've spent nights in sketchy roadside motels. Doesn't much matter to me, as long as there aren't bedbugs, which don't really care how fancy the hotel is, either.

Search out your roadside meals

It might be tempting to make a highway exit franchise row your lunch stop. But settling for processed tacos or sub sandwiches can mean missing out on some fantastic regional food.


You know what's good for that? Google Maps. I can read a paper map as well as anyone, and better than most, but GPS is the best thing that ever happened to road trips.

“Some of the best expressions of regional food flavors and unique culinary styles can be found in gas stations,” says Frank Beard, a traveling sales rep who’s become an evangelist for the convenience store industry, and once spent an entire month eating at only gas stations.

So this is the "gas station food evangelist" from the subhead. I have a challenge for him:

Go to Salt Lake City. Head west on U.S. Route 50, through the Utah and Nevada desert, destination: Reno. Once you pass Ely, Nevada, the road becomes signed as "The Loneliest Road in America," which it really isn't (that would be some roads in Alaska, or, if you want to limit your scope to the contiguous states, Route 6 south from Ely to Tonopah), because you can actually find gas stations along it occasionally.

The challenge is: drive this route, stop at one of the aforementioned US50 gas stations, buy one of their corn dogs, and eat it in the car as you drive off.

You will quickly lament the state of gas station food, and the lack of restrooms on US50.

Why, yes, I am speaking from personal experience. Why do you ask?

Make sure your tires are filled and your fluids are topped off

I mean, that's way more basic advice than some of the other stuff. It won't guarantee you won't get stuck somewhere, but it does improve your odds.

Don’t depend entirely on your phone’s maps

While I agree with this (I always carry a road atlas as a backup), there's no need to fear technology, either. GPS can only lead you into a lake if you let it. People act like no one ever got lost or turned around using paper maps, but they absolutely did, and way more often, I'd bet. And like I said above, it's great for finding nearby places of interest, not all of which can afford to advertise on the main roads.

Anyway, lots of the advice here is aimed at people taking road trips in groups. Since it's a documented fact that no one can put up with me for more than two hours at a time, I tend to do road trips alone.

But there's one piece of advice I feel should have been added:

Stay off the interstates.

Look, interstates are great. They're an everyday masterwork of civil engineering. Sure, there are some issues with them, especially in urban areas, but, overall, if your goal is to drive from Point A in the US to Point B elsewhere in the US, you can't beat an interstate for efficiency, speed, and convenience.

But road trips, in my view, shouldn't be about those things. If you have limited time, and you care more about the destination than the journey, I'm not going to knock you for taking the fast route. I've certainly done it, else I couldn't make the comparison. But, with a few exceptions, you can't see the US from interstates.

Taking secondary roads, also known sarcastically as "the scenic route," really gives you a better experience seeing the country. It's a bit harder to find services, but that's what GPS is for. I think of it like playing a video game in hard mode: somewhat trickier and more challenging, but more satisfying, too.

To quote from a Brandon Sanderson novel: "Journey Before Destination."


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