Complex Numbers (Book)

Blog Calendar

◄ August ► 2020
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 6 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 8 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.

August 4, 2020 at 12:02am

#989830

Decisions, Decisions

Today, I'm going to actually talk about religion.

Well, sort of. Not really. Well, you'll see.

As a bonus, though, it's time for another Merit Badge Mini-Contest! Details below.

https://theconversation.com/what-a-16th-century-mystic-can-teach-us-about-making...

What a 16th-century mystic can teach us about making good decisions

Decision-making is a complex process.

Well, it can be. When I pick an article to highlight in the blog, I use a random number generator. So it's not always. But I'm sure they're talking about big decisions here, like where to go to college, whether or not to break up with your boyfriend, what kind of house to buy, or where to go get beer tonight.

As individuals, working through our daily lives, we often take a number of shortcuts that may not always serve us well.

To be fair, if one is faced with a slew of decisions while going about one's daily business, it might be good to take a few shortcuts. The process described here can get fairly long and involved.

Among the many decision-making methods for life’s big decisions, one that stands out is from an early 16th-century soldier-turned-mystic, St. Ignatius of Loyola.

Anyone who's been following along knows that I'm not a big fan of religion. And yet, I have a lot of respect for the Jesuits, which this guy helped to create, with their focus on science and education.

Ignatius uses the language of faith, but, I believe, anyone can apply his method to make more informed decisions.

I'm also not going to reject something just because it comes from a religious person. That would be silly and self-destructive.

The article goes into a brief bio of Ignatius before getting into the "process."

1. Rely on reason and feelings

Ignatius advises creating a list, but also takes it a step further by urging people to listen to their feelings as they consider the pros and cons for each option.

What I think a lot of people miss, probably because of Spock from Star Trek, is that "logic" (or reason) doesn't stand alone. That is, one must consider emotions as part of the logic of human existence, because we have emotions. And so does everyone else, which should be taken into account when making decisions. Those who don't are known as sociopaths.

Ignatius teaches that freedom from attachment to a particular choice or outcome is essential.

That's kind of Buddhist, isn't it?

Ignatius also advises that individuals share their deliberations with a confidant, advice that he followed when making his own decisions. Modern psychological science too has found that the process of sharing emotions with others helps make sense of our thoughts and feelings.

I mean, I do that. Doesn't everyone do that? Well, probably not "everyone," but I think it's rather common.

He also urged people to make decisions for the “greater glory of God.” How can non-religious people use this advice? I argue they can consider how their decisions will affect the vulnerable, the poorest and the most marginalized.

This is probably good advice for even the most mundane decisions. For instance, buying cheap shoes from Wal-Mart or more expensive ones from elsewhere? The former might have been made in a sweatshop by people who get like $1 a week for their labor or whatever. On the other hand, I've argued before that if we all boycotted sweatshop clothing, they might go from $1 a week to $0 a week, and how is that helping? And you also have to take your own circumstances into account; not everyone can afford the more expensive items.

Point is, though, I agree that we should give these things some thought, and I like the non-religious alternative this author proposes.

2. Imaginative reflection

Ignatius offers three imaginative exercises if no clear choice emerges:

I won't copy them here; the link is there above. To summarize, though: 1) Imagine that a friend comes to you with the same situation; 2) Imagine you're on your deathbed reflecting on this choice; and 3) Imagine a conversation with the Divine.

The author provides an alternative to that last one:

Those who do not believe in a God could have an imaginary conversation with someone they loved and trusted and who has passed away.

Hey, little secret about atheists: if we're going to hold imaginary conversations, they might as well be with God, because the conversation is imaginary anyway. I mean, you can do what the author suggests, but it's not like you're breaking the Atheist Code by pretending for the sake of this exercise that you're talking to a god or goddess. (There is no Atheist Code -- though many, like me, have ethical standards.)

3. Seek confirmation

Ignatius advises individuals to act on reason, feeling confident that they have invested their time and energy to make a good choice. But he also says that people should seek out additional information to see if reason confirms the choice.

Here, I'm a little lost. Was one of those "reason" instances supposed to be "emotion?" Because otherwise I'm not sure that this bit makes a lot of sense.

The emotions they feel following a decision, such as peace, freedom, joy, love or compassion, might give an indication if it is the right choice.

Sometimes it's just relief that you've finally made a decision after going through all that.

Anyway, I thought this would be helpful. I think I've been using a process much like this already; I rarely act on reason alone (even if I do act on emotion alone far too often). At the same time, there are decisions I've been putting off because there's no clear "better" outcome. So this will lead us into today's...

Merit Badge Mini-Contest!

In the comments below, tell me: What process do you use to come to big decisions? Do you do something like Ignatius suggests, or something else entirely? Logic, meditation, prayer, a ritual circle, "what would *insert deity here* do," hard exercise to distract the mind? Maybe getting insight into others' process can help someone make their own decisions.

As usual, the deadline will be midnight WDC tonight, and the comment I like best will get its author an appropriate Merit Badge tomorrow.

(Additional disclaimer: I spent part of the evening giving out a bunch of MBs for the Quills, and I recognized a few of the names as people who comment here from time to time. If one of those authors wins, I'll delay the MB for two weeks for CR eligibility.)

4 Like • Comment • View 7 comments

© 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.