I've known about the Mandelbrot set and have been familiar with its general shape for years, but have hitherto thought the maths behind it would too hard for the likes of me. Until I started following the Youtube channel mathologer and this video in particular:
Armed with Burkard Polster's simple explanation I wrote a program in VB6. It runs painfully slowly but at least it proves that the concept was not beyond a simple mind like mine. Here are a few screen-shots from my program. Each one took a minute or so to draw.
If you were presented with images like these without any notion of how they were formed you might conclude that, like the existence of a watch begs a watch-maker, there must have been a designer, and a pretty good one at that because you can zoom into the patterns indefinitely - in short it is a fractal. And yet the Mandelbrot set (which incidentally properly is the black region: the frilly halo is an indication of how close you are to being in the set, and the colours are somewhat arbitrary) comes about because of the simple iterative formula below in which z is a complex number. If after repeated iterations the modulus of z exceeds 2, then c is not in the set. And then you plot the set in the complex plane (aka Argand diagram) and that's it. Easy.
I'm reading a book "Homo Lapsus". Whilst I have not yet finished it, the author, who largely accepts the theory of evolution, mentions the evolution of language. Hitherto I had never considered that evolutionists would get their dirty hands on language. Next they'll be onto music which puzzles them because it does not appear to have any evolutionary advantage. She points out that there are many theories as to how language (the skills of which, along with music, sets humans radically apart from all other animals) evolved. Basically no-one knows. But one guy Nome Chomsky believes that language arose instantaneously in humans through a single mutation. That the area in the brain that has been identified as being responsible for language suddenly came about by that mutation. How whacky is that? Niamh's reticence about the evolution of language does not appear to extend to other marvels such as the oft quoted evolution of the human eye. On this subject one site says according to one scientist’s calculations, if the eye improved just 0.005 percent each generation, it would take 364,000 years from eyes to evolve from a patch of light sensitive cells to the complex eyes we have today. But what a facile and nonsensical statement! The only meaning I can thing he attributes to 0.005% is that he wants us to think it is a very small amount. So now we have: if the eye improved a small amount every 30 years or so it would take... which is totally meaningless. And having got this far in the book, my author shows herself to be well versed in evolutionary theory but her arguments have so far had the opposite effect to endearing me to that theory. Not that I go along necessarily with the fundamentalist Christian views of a literal six day creation, either.
I hate the fighting that goes on between evolutionists and the rest of us: apparently the retina is "wired backwards" so that the photo-sensitive rods and cones are behind all the wiring of nerves and I suppose blood vessels. Evolutionists like Dawkins have made fun of intelligent design advocates pointing out that no designer in their right mind would make a retina like that. But more recently scientists are finding out that there is a reason. There are many websites dealing with this for example here.
I hear you asking - so what do I think happened? Well, to be honest, the older I grow the more I realise that I don't know much about anything. I wasn't there, I don't know anybody that was, and even if I did I couldn't trust their word or my memory. You may recall that, as a child, I saw an angel standing tall, wings and all, on a chimney opposite my bedroom window. Was it real, a vision, a dream? I suspect a dream but I don't know. My memory of the angel is vivid enough but of the circumstances I now have no idea. And, other than the experience sticking in my memory, I am not aware of any other benefit it has conferred.
So much I do not know, but I do know when I smell something wacky. Mind, I don't dismiss an idea just because it is whacky - just that I treat it with the caution it deserves. I don't know about evolution with its millions of years, or about young-earth creation, except that I have noted numerous whackies in both camps, like the Nome Chomsky one above. And should Christians celebrate pagan Christmas? I'm not convinced either way, I don't know. There is so much fake news on the internet, so many theories about this and that. I don't know what to make of so many, except when I smell a rat. I was brought up in a Christian family and gladly accepted what I was taught about salvation but now, frankly, I am even wobbly about the existence of God himself. I cry constantly for revelation on that one. Sure, I see the arguments (on both sides) but I think a little more is required than consent.
I passed the access point (trail head) on my way back from Keadeen and, after checking the map, this sparked enough interest to do it. My cycle route was similar, and I parked the bike at Ballinabarney Gap and set off. It was Sunday afternoon and I met several other hikers including a couple possibly older that 1, which was kind of encouraging.
Kelsha Bridge over Slaney
A cool place to swim (literally)
On the way there, and again on the way home, I stopped for a swim in the Slaney River. Why not, I asked myself? After all I'm here to enjoy myself.
My photos follow, or if you prefer a Google Album go here.
