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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. ![Merit Badge in Quill Award
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| From The Guardian, an article that I'm going to try to be skeptical about, because I already agree with it. The big idea: why it’s great to be an only child  The notion that it’s bad to be brought up without siblings should be banished for good It won't be banished for good, though. People cling to their preconceptions. Hell, I know someone who was absolutely convinced that their cat would "steal the baby's breath." This was someone otherwise fairly rational. When I was growing up, only children were generally regarded as unfortunate souls; lonely, socially clumsy and often bullied. Well, being bullied can happen to anyone, but I imagine it would help to have a sibling on your side for defense and/or painful retribution. I'm not convinced, however, that it can make up for the bullying and/or annoyance of having said sibling in the first place. One can avoid bullies, much of the time; one cannot avoid one's sibling. But the stereotype has proved to be tenacious – so much so that many people still feel anxiety about the issue: parents over whether they have deprived their child of the experience of having siblings, only children that they may have missed out on a crucial part of their development. Such experience and development could, I will reiterate, go both ways. It can be positive. It can also be strongly negative. I'd imagine it would be worse to have a shitty sibling than none at all. And from my own experience, having none instilled in me a powerful sense of individuality, of not having to lean on anyone else. Based on current data, it’s estimated that by 2031 half of all UK families will be raising just one child. Obviously, this article focuses on the UK, and I don't know what the stats are for other countries. I'm not sure the exact details matter; such predictions are like weather forecasts, and shouldn't be taken as absolute truth. The author's point seems to be that being an "only" used to have stigma because the situation was rare; the situation isn't rare anymore, but the stigma remains, so she throws the numbers around to support the "not rare anymore" point. As a clinical psychologist with more than 40 years’ experience working with families and children, I’d like to reassure parents that having one child is now an excellent decision – and here are some of the reasons. As someone who lacks all sorts of credentials, I'd like to reassure people that having no children right now is an excellent decision. Have you seen the world? Can you honestly say they'd have a better life than you did? Can you really afford the luxury? First, a lot of the stigma, the source of so many difficult developmental experiences, has melted away because of the numbers game. It’s simply much less unusual to have no siblings, and less likely to draw unkind attention. I think the point here is that kids are mean to anyone who's different, but being an only isn't all that different anymore, so the hammers don't go after that particular nail. Second, the data that gave the stereotype of an ill-adjusted, unhappy only child a veneer of scientific credibility has been thoroughly debunked. Much of it was the result of a questionnaire that American psychologist EW Bohannon gave to 200 adults in the late 19th century. This is the bit I'd pay most attention to. Old study, single researcher, small and demographically narrow sample size. From this “study” – based on secondhand opinions, biased language, and without a control group – Bohannon concluded that only children were generally spoiled, selfish, intolerant and self-obsessed. I'm not intolerant, goddammit. More recent, better-designed investigations have, unsurprisingly, utterly failed to uphold these claims. Go figure. That isn’t to say that there aren’t any differences at all between single children and others. For example, recent research in China found that they are often more competitive and less tolerant of others; but they also tend to be better at lateral thinking and are more content spending time alone. Again, I contend that being able to be alone is a positive personality trait. It's good to not cling to others for validation or emotional support. Often people’s anxieties about single-child families are projected into the future. Isn’t it better to have siblings to share memories with in adulthood and who can lighten the load of caring for elderly parents should that become necessary? I'm always seeing instances where one of the parents' many kids is the primary caregiver in those situations. Hell, it happened to the friend of mine that I had to convince about the cat thing up there. I still maintain that having kids so you'll have someone to take care of you in old age is one of the biggest acts of selfishness. It’s true that I’ve worked with a number of only children who complain of exhaustion as they care for their parents in later life. But I would counter that by noting that the worst relationship issues I’ve had to deal with in my clinics are not those between couples, but among adult siblings when it comes to sharing out responsibility for the care of their parents, and who’s entitled to what once they die. When parents are even moderately rich, all the lessons they supposedly taught their kids about sharing and cooperating apparently go right out the window. The common metaphor is that of vultures circling a dying animal, but that doesn't really happen and it's not fair to the noble vulture to compare them to selfish brat offspring. Finally, are parents who have large families happier than those who have just one child? Apparently not. Ugh. "Happier." I've ragged on this concept before, I know, but I don't think it should be relevant. Part of this is because people are, believe it or not, different. It could be that a couple wants a large number of offspring, and they might be happier. It could be that a couple wants none, and they'd be unhappy with even one, let alone more. Happiness is notoriously subjective, and someone might convince themselves they're happy just because otherwise, they'd have to change something, and change is painful. Or maybe they can't change, so they do the self-convincing. When it comes down to it, there are advantages and disadvantages, and any disadvantages for the child can be compensated for by skilful parenting. This is perhaps the key message for mothers or fathers worried about the issue: nothing is set in stone. In the case of only children, helping them learn to share, and prioritising flexibility – even allowing for some disorder – in day-to-day scheduling is extremely helpful, as these are some of the skills children with siblings acquire as a matter of course. And then you get stuff like this, which is clearly geared toward the neurotypical. So, this is an example of how I handle confirmation bias: don't just agree with the article; find things to criticize about it. Remember what I just said about happiness? I can't change having been an only child. I couldn't make siblings appear out of thin air (multiverse theory notwithstanding) even if I wanted to, which I don't. My unique situation is the hand I've been dealt; fortunately, it's full of aces. |
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At my job, we only sold a cheap house wine for white zin, and when people ordered it I had to try to restrain my facial muscles from giving stank face. 
