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Friday, Nov. 1, 2024

2:37am EDT

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Complex Numbers

by Robert Waltz

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:

tj: Tenebrous Jekyll

about 9 hours ago
In response to "Phases"

Perhaps, if the full moon drives one to madness, the half moon will only make one half-crazy.

1 Like

Battywyn🎶

Oct 29, 2024 at 12:18pm
In response to "The Numbers Don't Lie"

I hear ya. I like to think I'm discerning enough to detect fakes, but that might just be my ego talking. When it comes to local businesses, I also go to social media and request recommendations. With both reviews from strangers and recommendations from friends, I give more credence when more (anecdotal, heh) details are provided. It's more an art than science, but liars either have such flawless details that their story sounds fabricated, or they get embarrassed when they trip themselves up. Truthtellers make errors, because memories are fallible, but they get more confused than embarrassed. Ultimately, the only way to really know is to try the product/service yourself. Which is why you'll hear about my Cancun vacation next month, but you don't have to believe me.

1 Like

Robert Waltz

Oct 29, 2024 at 11:07am
In response to "The Numbers Don't Lie"

Battywyn🎶

- I, too, look at the 1-star reviews, though again, reviews aren't my sole criteria. But sometimes it's blatant fake reviewing from the competition: "Don't stay here! It has rats, bedbugs, and roaches! Stay at this other place instead!" where "this other place" is clearly owned by the reviewer.

On the other paw, five-star reviews are often salted by the establishment in question.

Used to be, you could look at the four- and two- star reviews to get more honest, nuanced opinions, but the establishments, and their competition, have figured out that trick.

Which is one reason why reviews aren't my sole criteria.

(None of this applies to WDC reviews, or to the artificially inflated Uber rating system)

Battywyn🎶

Oct 29, 2024 at 11:00am
In response to "The Numbers Don't Lie"

And I was going to conclude by saying, when evaluating Caribbean vacation destinations, even if 5,000 people gave it a 4.8 rating, if the one star reviews were from seven people who encountered rats in their rooms, I'm very likely to not choose this destination.

2 Like

Battywyn🎶

Oct 29, 2024 at 10:58am
In response to "The Numbers Don't Lie"

Well, that was annoying. I was still in the process of editing, so please excuse the multitude of errors. I also intended to italicize the quotes from your post. Stupid f****** Parkinson's.

1 Like

Battywyn🎶

Oct 29, 2024 at 10:56am
In response to "The Numbers Don't Lie"

You know what sometimes lies? Anecdotes.

Also, dogs, I've heard.

Oh, hell no.

🤣 I love a good inside joke, but my marketing guru would tell you to cross link here

The fallacy is named after Robert McNamara, the U.S. Secretary of Defense during the Vietnam War, where his over-reliance on measurable data led to several misguided strategies

Bet he's proud of his claim to fame.

What's the point in data, then?

The point in data is a decimal separator, unless here in non-english speaking countries, in which case it's more likely a thousands separator.

So, whenever I'm evaluating online reviews for pretty much anything, and for the record I check them for almost everything - I always consider three things: 1. The average rating (eg, number of stars); 2. The The number of contributors to the rating; and three. What the one star ratings say.

1 Like

Annette

Oct 28, 2024 at 2:47pm
In response to "Waste Not"

In Southern California, every single family residence has a green bin. Every trash day, three different trucks make the rounds.

1 for composting
1 for recycling
1 for garbage

Trader Joe's sells almost exclusively packaged foods, even perishables. They have contracts with college food pantries. In many colleges, there are now pantries that are open to the students 4 or 5 days a week plus 1 day when people from the community can drive up and receive a bag with a mix of fresh fruits and vegetables along with non-perishable foods and donated sundries.

Churches are huge food redistribution centers also.

The "too hard to set up" systems have created good jobs here. Instead of seeing food donations as a liability, they have created a supervised and refrigerated second market.

The cost for employees is small because, of course, many of the positions are volunteers. But the supervisors and some of the staff are full time employees with benefits.

The article has thrown up obstacles that are easy to overcome.

3 Like

AnotherDreamer

Oct 28, 2024 at 11:33am
In response to "Waste Not"

https://cdn.prod.website-files.com/6156cebc4c605e281289a232/6156cebc4c605eb8bc89... e%20for%20beginners%2024%2009%2018.pdf

1 Like

Robert Waltz

Oct 28, 2024 at 11:33am
In response to "Waste Not"

AnotherDreamer

- Hey, it's a replicator from Star Trek!

Now let's invent the holodeck.

2 Like

AnotherDreamer

Oct 28, 2024 at 11:27am
In response to "Waste Not"

We the people of the world could use those products before they are compost as free sources for 3D printed foods that could be used for emergency food, or if tasty enough, re sold.https://builtin.com/articles/3d-printed-food

2 Like

February 4, 2020 at 12:09am

#974835

Life, The Universe, and Everything

It's an Internet truism that the answer to any headline that asks a yes/no question is, at least 95% of the time, "no."

http://nautil.us/issue/42/fakes/is-physical-law-an-alien-intelligence

Is Physical Law an Alien Intelligence?
Alien life could be so advanced it becomes indistinguishable from physics.

Terrestrial life is indistinguishable from physics. That is to say, drill down deep enough and life is a complex chemical reaction that's been going on for about 4 billion years, give or take, and the underpinning of chemistry is physics.

But, okay, I know that's not what the author meant.

After all, if the cosmos holds other life, and if some of that life has evolved beyond our own waypoints of complexity and technology, we should be considering some very extreme possibilities.

Considering, sure. Taking our speculations at face value? Not so much. Just because we can think something, that doesn't make it true.

...it would neatly explain why we have yet to see advanced intelligence in the cosmos around us, despite the sheer number of planets it could have arisen on—the so-called Fermi Paradox.

So would my ruminations about the Fermi "Paradox" in here, what, two entries ago? I'm under no illusion that I'm any more right than this speculation is, but at least my speculation passes the parsimony test.

Indeed, perhaps our universe is one of the new forms into which some other civilization transcribed its world.

Ah, it's the old "maybe the universe is a simulation" canard again. No, I can't prove that it is or isn't. But that's one problem with this hypothesis: it's not falsifiable. The other problem with it can be summed up as: So what? Assume that the universe is a sophisticated simulation. What changes? We're still obligated to act ethically. We're still curious about the universe. We've still got science to search for answers and understanding. Unless you think The Matrix was a documentary (spoiler alert: it was not), all it does is kick the Consciousness Question can down the road.

Let me explain further. Assume, again, that this universe in which we live is, indeed, someone's sophisticated simulation. Where, then, does this "someone" live and what are the laws governing their existence? It seems likely that, as technology advances, we will at some point be able to create our own simulations, of ever-increasing complexity. But there's a hard limit - not one born of technology, but woven into the very fabric of reality, and that is that no simulation can approach the complexity of the universe in which it was born. So we create a simulation, and the simula-tees evolve and make their own simulations of lower complexity, and so on until it becomes painfully obvious that a certain iteration is a simulation. Now, which explanation is more parsimonious: that we just happen to be at an intermediate stage of simulation complexity, one that seems incredibly complex indeed, rather than a "daughter" simulation that is, necessarily, less complex? Or that we're in an actual, real, physical universe?

Given all the available evidence, my money's on the actual, real, physical universe. Nothing else makes statistical sense. Sure, you can say "but maybe that hard limit was programmed in to just our simulation." This smacks of special pleading, and you end up bleeding out from a cut from Occam's Razor.

These possibilities might seem wholly untestable, because part of the conceit is that sufficiently advanced life will not just be unrecognizable as such, but will blend completely into the fabric of what we’ve thought of as nature. But viewed through the warped bottom of a beer glass, we can pick out a few cosmic phenomena that—at crazy as it sounds—might fit the requirements.

"warped bottom of a beer glass?" More like "warped haze of weed smoke."

In that case, dark matter could contain real complexity, and perhaps it is where all technologically advanced life ends up or where most life has always been.

Sure, and Halle Berry could show up at my door tomorrow, wearing a Catwoman suit and carrying a couple of growlers of craft beer. That is, technically, a possibility. Do you want to bet on it?

Or to take this a step further, perhaps the behavior of normal cosmic matter that we attribute to dark matter is brought on by something else altogether: a living state that manipulates luminous matter for its own purposes.

Considering that the evidence we have for dark matter, whatever it ends up being, extends to clusters of galaxies that existed billions of years ago, what this is implying is that intelligence sprang, like Athena from the head of Zeus, fully formed at or near the birth of the universe. Might as well try to turn God into a scientific hypothesis.

Consider that at present we have neither identified the dark-matter particles nor come up with a compelling alternative to our laws of physics that would account for the behavior of galaxies and clusters of galaxies. Would an explanation in terms of life be any less plausible than a failure of established laws?

Um. Yes. Unequivocally less plausible. "Established laws" are refined all the time. And the author, an astrophysicist, should already be aware that science hasn't called its theories "laws" since, like, Newton's time.

Once we start proposing that life could be part of the solution to cosmic mysteries, there’s no end to the fun possibilities.

Sure, and I'm a big fan of science fiction. That doesn't mean I think it reflects reality. Okay, so you've made a hypothesis. How do we test it? What solid predictions can it make?

Again, I'm not saying it's definitely wrong. Just that it's probably the least parsimonious alternative.

Okay, I'm not going to get into more of the article here. Read it for yourself; draw your own conclusions. If you want to argue from authority, well, that author is an authority, and I'm just another putz with a blog and a diminishing supply of neurons. Could be I'm wrong. But I maintain that just because we don't understand something, that's no reason to go multiplying entities endlessly.

On the other hand, speculation like this is a good thing, because at the very least, it provides hypotheses that could potentially be ruled out.

2 Like • Comment

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