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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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October 5, 2019 at 12:04am
October 5, 2019 at 12:04am
I swear not all of the links in my blog fodder queue are from a certain British rag.

But this one is.


My patient swapped chemotherapy for essential oils. Arguing is a fool’s errand

These days whenever I see "essential oils" my mind replaces that phrase with "snake oil."

Oh, sure, essential oils have their uses. For example, some of them smell nice.

“Tell me why I should have your chemotherapy when I can be healed naturally!”

Shall I reiterate my various rants about the word "natural" (and its adverbial declension)? No? Okay.

I used to think that these second opinions were illuminating for patients and nudged them towards change. But what I have learnt in the last few years is that cancer patients in search of alternative cures are more deeply entrenched than ever in their beliefs. Thanks to the rise of social media, the ability to filter out conflicting viewpoints and a bevy of supporters for every outrageous idea, these people arrive convinced about their theories.

If I could change one thing about our language, it would be to stop using the word "theory" (and its various declensions) to mean "crackpot propaganda."

A survey commissioned by the American Society of Clinical Oncology spoke to more than 4,000 American adults, a quarter of whom were current or former cancer patients. Nearly 40% of those surveyed “somewhat” or “strongly” agreed that cancer can be cured via oxygen, diet and herbs alone.

Again, this article is from a UK source, and it's clear from the discussion of "taxes paying for healthcare" that the anecdote does not take place in the US. But I would be surprised if the level of idiocy in the UK was much different than in that survey. After all, 50% of them or so voted against their own interests on the Brexit referendum (I'm leaving that deliberately ambiguous).

Enzymes, waves and magnets do not cure cancer, and they cost the patient every step of the way. Small bottles of unknown and frequently adulterated or plainly toxic substances cost hundreds of dollars, not to mention every consultation that pretends to read the eyes and sense the energy to cure cancer, even as the patient worsens. How do I know? Because dying patients relate these stories in a last attempt to prevent their fellow patients being duped.

"Dollars?" *checks author bio* Oh, she's from Oz. My comment above about the level of idiocy remains; just ignore the jibe about Brexit.

It has been received wisdom that oncologists can see off quackery through good communication but I’m afraid that isn’t so.

That's because of cognitive bias, something that this author doesn't seem to be affected by; good on her.

Oncologists have been properly entangled in a web of fake news. Their authority has been undermined and their expertise ridiculed by a determined, global and hard-to-track battalion of quacks and their acolytes. Greater vigilance, stronger regulation and improved health literacy might help, but the pull of alternative cures is strong.

The two greatest forces in the universe are compound interest and marketing. Marketing can convince anyone of anything. Hell, it convinced people that Budweiser is beer, Smart Cars are cute, and bottled water should be a thing. I'm not immune, though I'd like to think I have some inoculation against it - but that might be wishful thinking.

Philosophical question: Consider a purveyor of quackery. Either they actually believe in their product, or they don't. In the former case, they are deluded. In the latter, they are committing fraud. The philosophical question is: which is worse?

I'm not sure either is worse. Both are bad. I sometimes wish I had fewer scruples so I could market my cats' shit as a healing balm.

Thing is, though, I have a different perspective than this author. She's an oncologist, who presumably went to medical school and had medical ethics drilled into her. Also presumably, she got into medicine out of a desire to help people - that's reflected in the writing. So her perspective is, "I want to help these patients see the truth so they don't die."

My take is, "fuck them." The more people die from stupidity, the less stupidity there is in the world.

I know that makes me a terrible person, but at least I'm not selling extract of belladonna as a cancer cure.

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