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Monday, Oct. 28, 2024

6:22am EDT

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Complex Numbers

by Spirit HalloWaltz

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.

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

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

Elisa: Stik or Treat

about 20 hours ago
In response to "Revisited: "Stylish""

I admit I don't even hear the "like/comment subscribe" verbiage anymore, although it helps that I follow several channels that don't include it. That said, having heard directly from some YouTubers, they say that because it works much better than we like to admit. I'll be touching on this a bit in today's Watch This Space entry (which I'm trying to write in a way that soesn't require watching the video to understand without being too full of spoilers for those who want to watch it).

As for drama, I think there is an overlooked middle ground: interacting with people in a meaningful context and having conflict stemming from a drive to achieve a common goal. I get this from my job and my PAC work, and it helps me maintain conflict resolution skills,

1 Like

tj: Tenebrous Jekyll

a day ago
In response to "Moon Illusion"

I've witnessed this as the moon, and sun have risen and set. I've also heard many of the wrong explanations.

1 Like

Spirit HalloWaltz

a day ago
In response to "But What I Want Is Cheesecake"

Good points, Elisa: Stik or Treat

. I hadn't known about the influenza thing, because I don't follow that sort of content.

Elisa: Stik or Treat

a day ago
In response to "But What I Want Is Cheesecake"

I've been mulling over this for a bit, and I've come to the conclusion that I think both the original post and you miss a few points on this concept. The term "intuitive eating" is being both actively and passively pushed as a way to try to counterbalance influencers that are straight up promoting disordered eating. (Yes, I would consider long term adherence to some protein-heavy diets to be disordered eating, as it promotes an incomplete picture of nutrition and contributes to forms of body dysmorphia that emphasize muscle size and visibility.) The discussion of intuitive eating is done the way it is to try to get a lot of bullshit out of algorithms, and I can appreciate that kind of move.

There are also a few things I'd like to offer comment on from the entry.

Given how emotional this work can be, experts recommend working with a professional when possible.

Again... this kind of nullifies the "intuitive" part.

Not necessarily. I've talked with my counselor about intuition. Honestly, I'm starting to believe that intuition is different from instinct (i.e. a behavior programmed prior to birth/hatching). Intuition is more of an unconscious expression of past experience. Since experience is different from person to person, how one experiences hunger on an intuitive level is actually externally learned first THEN internally programmed. Since intuitive eating is essentially a reprogramming exercise, working with a professional is useful. It's especially needed for those recovering from disordered eating.

Recently, there has been renewed interest in an approach called “intuitive eating”, based on the idea that your body already knows exactly what it needs.

Yes, it absolutely does, and apparently, it "needs" to be overweight.

Going back to the intuition development principle I mentioned earlier, if you are introduced to and eat vegetables regularly, it's definitely possible to come to crave them. And this can happen for those on assistance programs, but again there are a lot of cultural factors involved. I remember reading an article years ago where for a lot of low income people vegetables needed to be introduced to them in a somewhat structured way in order for them to more actively take donated produce of any kind. And yes, there is more active work being done to get fresh produce being donated to food banks. The point is, it takes time and practice, but a person can come around to picking produce or prepared veggies over a baked good. I'm not sure how I managed to reach this point as a toddler, but let's just say after I threw a fit to get an orange over a donut my mom stopped complaining about peeling oranges.

Giving yourself permission to eat what you want may involve wrestling with how your culture’s foods might have been villainized by mainstream, white American culture, Johnson explains.

Oh, give me a fucking break. I get that it's fashionable to turn mainstream white American culture into the Bad Guy, but how about doing it by ragging on deep-fried butter with mayonnaise, or whatever culinary abomination came out of some Midwestern state fair this year?

Because the worst food demonization isn't coming out of the Midwest? I mean, at least with those food-like things we all kind of know it's meant to be a joke. Unfortunately, I think the worst of this demonization is coming from the coasts. Feel free to fight me on that one.

1 Like

Fearlycia Lee ☮

Oct 25, 2024 at 12:24pm
In response to "Pass da Pasta"

Eh? No. I don't put it in the boiling water. I drizzle them on the pasta itself.

1 Like

Spirit HalloWaltz

Oct 25, 2024 at 11:00am
In response to "Pass da Pasta"

Fearlycia Lee ☮

- maybe it is true. At worst, you just waste olive oil; I don't think oil in the water can do any real harm to anything but your wallet.

1 Like

Fearlycia Lee ☮

Oct 25, 2024 at 10:57am
In response to "Pass da Pasta"

I think #2 is true though. I had only started drizzling olive oil on my pasta two attempts ago and it's true. I never put olive oil on pasta and they stick all the time. Also, it doesn't help that I forgetful and forget to try this method until two attempts ago. Took me years to remember. Yup.

1 Like

Elisa: Stik or Treat

Oct 24, 2024 at 10:57am
In response to "A Winner's Tale"

I'm just glad to see reporting showing young adults can exercise responsibility and restraint.

2 Like

🌕 HuntersMoon

Oct 24, 2024 at 10:43am
In response to "A Winner's Tale"

No, Lilli Munster 🧿 ☕ 🎃, WINNING is the first step.

2 Like

Lilli Munster 🧿 ☕ 🎃

Oct 24, 2024 at 9:59am
In response to "A Winner's Tale"

Remaining anonymous is the first step.

4 Like

October 25, 2024 at 9:56am

#1078904

Pass da Pasta

Today in You're Doing It Wrong...

No, Salted Water Doesn't Boil Faster and 7 Other Pasta Myths
We asked an Italian chef about the eight biggest myths and misnomers linked to making pasta at home.

Most likely they asked "an Italian chef" because if they'd asked 10 Italian chefs, they'd have gotten a hundred different opinions.

If you think salting your pasta water is going to get dinner on the table faster, think again.

I have to wonder how that bit got started. Adding salt to water increases its boiling point, making it take longer to come to a boil. The higher-temperature salt water would then, presumably, cook the noodles faster. It would be pretty simple to do an experiment to see which effect takes precedence... and then you probably find that the amount of salt used in cooking makes no meaningful difference to boiling temperature.

To separate pasta protocol from the false and fabricated, we asked an expert about the biggest pasta myths, mistakes and misnomers that could be ruining your rotini and putting your pappardelle in peril.

Really, I'm just quoting this bit to illustrate how proud the author is of his alliteration.

Filippo de Marchi, is chef de cuisine at De Majo Restaurant & Terrace.

Stealth ad!

We grilled Marchi on nine of the top-circulated pasta cooking myths.

Tough to grill pasta.

"Cooking pasta isn't difficult at all. It's all about timing and the right water-to-pasta ratio," he says.

So, let me tell you what I remember of my mom's pasta-cooking technique. First, fill a small pot halfway with water. Then throw in the pasta (breaking the hell out of it if it's spaghetti). Then put it on the stove over high heat. Wait 45 minutes. Drain and serve.

My mom had no Italian heritage.

1. Throwing pasta against a wall to see if it sticks proves it's done

Chef's take: FALSE

Of course this is false. I've always known it to be false. And yet, the false information persists, as it usually does.

2. Adding olive oil to pasta water keeps noodles from sticking

Chef's take: FALSE

"The oil just floats on top of the water and doesn't coat the pasta effectively," says de Marchi.

Pretty sure there's more to it than that. Once the water boils, the oil gets stirred in more, though it's still going to be gloppy and not stick to the noodles.

3. Fresh pasta is always better than dry pasta

Chef's take: FALSE

Pretty sure that's a question of individual taste and opinion, not fact or fiction.

It's all about personal preference. Fresh, dry or frozen; chefs aren't here to dictate what your taste buds like and don't like.

Like I said.

4. Leave the pot covered while the pasta is cooking

Chef's take: FALSE

Of all the "myths" on the list, this is the only one I'd never even heard of. All pasta-making recipes I've seen demand open-top pots.

On the flip side, everyone's other favorite cooked starch, rice, requires a covered pot. Unless you cheat and get instant rice or whatever.

5. Adding salt helps water boil faster

Chef's take: FALSE

As I noted above, middle-school chemistry disproves this one.

"If you're cooking without enough salt, the pasta can end up tasting a bit bland," warns de Marchi, whose signature dish at NHC Murano Villa is a spaghetti alle vongole.

The stealth ad continues!

6. Drain pasta until it's completely dry

Chef's take: FALSE

Besides, "completely" is misleading, here. Presumably, the pasta started out dry; that's why you stick it in boiling water.

7. You should run cooked pasta under water before serving

Answer: FALSE

Yeah, I'm pretty sure there are situations where you do want to do that (creating pasta salad, e.g.), but for your hot spaghetti dishes? Never.

8. You should precook sheets of lasagna

Answer: FALSE

I have to admit, this one confused me for a long time. Most store-bought lasagna has pre-cooking on the box instructions, as I recall (I haven't made it in a very long time). It wasn't until I met my second wife, who also had zero Italian ancestry, who introduced me to the lazy wonders of cook-it-in-the-baking-pan lasagna.

Left out of the article: the other two cooking tips mentioned above (they said nine total), which presumably aren't myths. I guess we'll all have to go to this guy's restaurant and ask him ourselves.

5 Like • Comment • View 3 comments

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