Complex Numbers (Book)

Blog Calendar

◄ January ► 2023
S	M	T	W	T	F	S
1	2	3	4	5	6	7
8	9	10	11	12	13	14
15	16	17	18	19	20	21
22	23	24	25	26	27	28
29	30	31
Archive				RSS

About This Author

Contact Me

Come closer.

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/

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:

Write_Mikey_Write!

about 2 hours ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

about 4 hours ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

January 11, 2023 at 1:47am

#1042949

Revisited: "Eruv L'olam"

I am fatigued from my journey, though at least my good fortune held out. The trip home was entirely uneventful apart from, again, some minor delays for construction. There's a reason why I use the phrase "as sure as construction on the Capital Beltway" to describe a thing that is absolutely certain to happen.

I even found street parking in Manhattan, which has never happened before. More, the spot was right across the street from my cousin's apartment building. I triple-checked; it was a legal parking space, though only until 9:30 am yesterday. Fortunately, I'd planned on leaving before then, anyway. I'm still waiting for the universe to throw me a curve ball to compensate. Watch this space; I'm sure it'll happen soon.

So it'll be tomorrow before things get back to what passes for normal here in the blog. Since the trip was so ordinary, I had little to write about today, so I decided to use the Wayback Machine, and behold, the entry it landed on was "Eruv L'olam"

from early August, 2020.

That month was an off-month for 30DBC, with the theme of travel, which, going in, I thought would be a good fit for me. Couldn't have been more wrong, as it started off in Antarctica. I can only reiterate what I said about it at the time: Nope.

So instead of participating in that, I did my usual article-linking. In yet another example of cosmic serendipity, the article (which still exists

as of today) concerned... Manhattan.

More specifically, it concerns the Jewish population of Manhattan, which, if memory serves, is higher than the Jewish population of Jerusalem.

Now, a bit of a personal aside: I make no secret of my heritage, as anyone who reads here regularly knows. But to me, that's all it is, a heritage. My life is almost entirely secular. I'm aware of Jewish holidays, but I don't observe any of them. Well, I have been known to make latkes on Hanukkah, but as I've said before, everyone's Jewish for latkes.

What makes a person Jewish can be complicated. Essentially, by tradition, a person is Jewish if their mother is Jewish. This matrilineal descent is rare in the West. I think other groups practice it, but there's a strong focus on paternal inheritance. This is most obvious when you consider how many WASP men have Jr or III after their name, signifying a continuation of one's father's line.

Reality is messy, however, and I think it was the absurdist playwright Bertolt Brecht (not a Jew, but fled Nazi Germany anyway) who pointed out that a father can never be completely sure that a child is his, while the mother usually is (I say "usually" because there have been recorded instances of inadvertent baby-switching at hospitals, including at the one I use, which implies that there were probably unrecorded instances as well).

This is not meant as a slight against women in general, incidentally. Lots of people raise children that aren't biologically theirs. My parents were two of them. Which leads me to the Talmudic question of whether I'm "really" Jewish or not.

The matrilineal descent thing doesn't help me there. My mother was Jewish, but she wasn't my biological mother. I don't know, and don't care to know, anything about my birth mother, but as she lived in the Midwest, I find it highly unlikely that she was Jewish. But I was adopted shortly after birth, and raised Jewish in a Jewish household and even went through a Bar Mitzvah. On the other hand, my religious life ended many years ago, so it's more like a fourth-generation American tracing their ancestry to, say, Scotland, calling themselves Scottish.

I even asked a rabbi about this conundrum once. He thought about it, shrugged, and said "I don't know."

I'm sure other rabbis would have different opinions. Being able to say "I don't know" is, however, the beginning of, if not the very soul of, wisdom, so I will always accept that answer. It's very scientific.

Just to be clear, while I still find the subject of that 2020 blog entry interesting (and still believe that my solution to it would change the world, or at least the tiny percentage of it which is Jewish), it's mostly an academic thing to me, like learning about quantum physics: it makes no difference whatsoever to my life. Even when I was a kid, we weren't the kind of Jews who were careful about doing / not doing certain things on Shabbat. Hell, we lived out in the country; the only way to get to Shabbat services was to drive, which is a big no-no for the Orthodox. Which is why so many Orthodox Jews in the US live in cities like New York, and preferably within walking distance of a shul.

Me, I only care about living within walking distance of a bar. Which I do. Several, in fact. Not as close as if I were living in New York, but at least I can afford to live where I do. Manhattan is bloody expensive.

If that sounds irreligious to you, well, I am irreligious. But even if I weren't, keep in mind that the Jews have a holiday where the whole purpose is to get so completely danchu that you can't tell the good guys from the bad guys. Even if that's a bit of an exaggeration, I wasn't raised with the whole Puritan anti-drinking ethos. I may take it a bit too far sometimes, but consider that a compensation for living in a country that's still reeling from the aftershocks of Prohibition, 100 years after.

As for that referenced blog entry, I even found a way to relate it to the Antarctica theme of the 30DBC prompt. Damn, I'm good.

Oh, and one more thing: I never did explain that entry's title. "Eruv" is explained in the text and in the linked article. The rest of the story is that "L'olam" is the transliteration of a Hebrew word meaning "of the world." Or, in modern usage, it can also mean "of the universe."

2 Like • Comment

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.