May the Mandelbrot be with you!

Whether you understand them or not, the visuals of the Mandelbrot set, and most other fractals, are bloody amazing to watch! But what makes them tick? What makes those shapes and colours happen? Depending on your math literacy, this can be anywhere from difficult to impossible to understand, but regardless of that, the images are still there to be enjoyed.

Mandelbrot detail (Wikipedia)

I flatter myself by saying to anyone who is interested (which is usually just me) that I feel I’m somewhere halfway between not getting it, and having something of a feeble grasp of the apparent magic. I’ve absorbed enough to, back in the early Nineties, make a working — if, to be honest, rather unimpressive — Mandelbrot renderer on my computer (a Commodore Amiga 1200) in some obscure version of the programming language Pascal. My breakthrough came when reading the appendix to Arthur C. Clarke’s 1990 novel “The Ghost From The Grand Banks”, in which fractals play an appreciable part, where he details the interplay between real and imaginary numbers to the point where I managed to break it down to a working algorithm for my Mandelbrot renderer.

But having the algorithm worked out, I still find it pretty darn hard to visualize in my mind what the heck is happening when you start crunching the numbers. It’s fascinating, but almost incomprehensible, and I’ll take any explanation that will make it easier to wrap my head around it.

Fortunately the Internet is full of helpful people with ideas for explaining seemingly inexplicable things to people like myself. Such as this highly inspiring and entertaining visual walk-through by Mathologer of how the maths of the Mandelbrot set works. Put on your science goggles and press Play!

Incidentally, if you’d like a cute (and bloody clever) redhead to explain the basics of the Mandelbrot set for you, then look no further, because Numberphile‘s Dr Holly Krieger delivers.

Thanks For Boldly Going


Congratulations, and great thanks,
to NASA for boldly going and
expanding our horizons!

If you took a baby grand piano, scrunched it up a bit, shook out all the noisy stuff, filled it with cameras, radio transmitters and all sorts of electronics, and then hurled it three billion miles into space, aimed at a tiny, distant, barely visible speck of light that is not even a planet anymore, then you'd be wasting your time, because it looks very much as if NASA has already done it.


“If you took a baby grand piano, scrunched it up a bit, shook out all the noisy stuff, filled it with cameras, radio transmitters and all sorts of electronics, and then hurled it three billion miles into space, aimed at a tiny, distant, barely visible speck of light that is not even a planet anymore, then you’d be wasting your time, because it looks very much as if NASA has already done it.”

Oh, and before anyone “catches” me: noble and observant readers of Douglas Adams’ “Last Chance to See” may notice a certain similarity to his memorable description of New Zealand, which is intentional 😉

“If you took the whole of Norway, scrunched it up a bit, shook out all the moose and reindeer, hurled it ten thousand miles around the world and filled it with birds then you’d be wasting your time, because it looks very much as if someone has already done it.”

— Douglas Adams, “Last Chance to See”

Growing Up in the Universe — Five Lectures by Richard Dawkins

Growing Up in the Universe

“Oxford professor Richard Dawkins presents a series of lectures on life, the universe, and our place in it. With brilliance and clarity, Dawkins unravels an educational gem that will mesmerize young and old alike. Illuminating demonstrations, wildlife, virtual reality, and special guests (including Douglas Adams) all combine to make this collection a timeless classic.”

These five videos should be mandatory viewing for anyone, young or old, with an interest in evolution. Richard Dawkins gives a light-hearted and entertaining, yet highly informative and educational presentation about the broader and subtler workings of the science, aimed first and foremost at children, which is evident from the lecture audience, but is equally suitable for kids of all ages.

You may click each video’s image to play it on this page, or click the heading above it to open in a new browser tab or window.

~ • ~

Episode 1: Waking Up in the Universe

Episode 2: Designed and Designoid Objects

Episode 3: Climbing Mount Improbable

Episode 4: The Ultraviolet Garden

Episode 5: The Genesis of Purpose

Links borrowed from The Richard Dawkins Foundation for Reason and Science

Easter Blood Moon: Moon of Doom?

I was urged by a concerned friend to watch this InfoWars YouTube video posted by The Alex Jones Channel, featuring Lee Ann McAdoo, which allegedly “uncovers the potentially prophetic blood moon taking place this Saturday”.

It goes on to say, “A total lunar eclipse is rare, yet this is the third time we’ve seen a blood moon in less than a year. Does this signal a world changing event that’s soon to take place? Is this a prophecy of WWIII on the horizon?”

I know I’m probably wasting my time here, but what the hell. To those of you who are wondering if there’s actually something to this video, here’s a few pointers that I hope may help:

    The statements put forth in this InfoWars video are pure pseudo-science, mumbo-jumbo, superstition, fairy tale and utter crap.
    The moon’s apparent “blood” red colour during totality is caused by the same physics that make the sky look blue; scattering of sunlight. Blue light scatters most, green light less and red least, so the sky appears to be plain blue to slightly greenish blue depending on the angle from the sun. Likewise, when the moon is in the Earth’s full shadow, some light filters through the Earth’s atmosphere and falls on the moon. Since most of the blue is scattered away, it gets mostly red light. Just how bright and how red depends on Earth atmospheric conditions such as cloud cover. The only reason to use the word “blood” in this context is that it is intimidating.
    The Earth’s shadow forms a large circle, compared to the moon. The moon may pass through the shadow (totality) anywhere from top to bottom. It’s widest at the middle, i.e. along the equator, so if the moon goes through there it will take the longest. This time it was right at the top, almost touching the edge of shadow, where it’s at its narrowest, and consequently that took far less time, mere minutes compared to hours.

  4. Graphic taken from, showing the moon’s
    position within the Earth’s shadow at time of maximum.

    The Easter holiday (and thus Easter vigil) is timed by the full moon, as are many other religious holidays in various religions. All lunar eclipses take place at full moon. Sooner or later, and repeatedly on a larger time scale, these two events WILL coincide. Easter Sunday (or whatever your particular religious designation may be) is the first Sunday after the first full moon after March 21st. Thus there is about a 1/7 chance that Easter Vigil falls on a full moon. Calculate that against the occurrences of lunar eclipses, and there you have the odds. It won’t be extremely frequent, but sooner or later it is bound to happen.
    They point out that there is a “tetrad” of lunar eclipses, four in a row over an unusually short time span. Uncommon as it might seem, there is nothing abnormal about it. Many astronomical events are cyclic, meaning they repeat themselves at certain regular intervals. The Moon orbits the Earth once every 30 days (actually 29.53 days). The Earth orbits the Sun every 365 days (actually 365.24 days). These two cycles overlap but aren’t in tune. Also, those orbits aren’t precisely aligned, so that to us, the Sun and the Moon will appear to bob slightly up and down relative to each other. The bobbing is also cyclic, but not quite in tune with the Earth’s 365.24 day orbit or the Moon’s 30 day orbit. This creates something akin to a seemingly irregular, chaotic pattern of repetition when seen on a shorter time scale. On a larger time scale it will smooth out and look like regular occurrences, much like the motions of the pendulums in this video:
    If anything happens at all connected to the lunar eclipses, it’s because the makers of these doomsday predictions are scaring people so much that things are going to shits anyway. Tell people the economy will fail, they will stop spending money, and consequently the economy will fail. Tell them that war is coming, they will prepare for war, and a bunch of scared people with weapons (considering the volatility of the situation in the Middle-East this could easily happen, no, wait, there’s actually war there already) is enough to start one (or they can claim that tons of praying helped prevent it). Furthermore, bad things happen all the time, and it’s all to easy to look at some disaster which happens after an eclipse and say, “yeah, the eclipse caused that”. The eclipse doesn’t do this, it is people like these and people who believe them who do this.
    Obviously a word they’re only barely familiar with, or which they choose to ignore or twist beyond recognition to serve their own agenda. The best antidote to bullshit pseudoscience is to read up on science yourself. Keep in mind that you don’t need to be an actual scientist in order to grasp the basics, which is all you need to protect yourself against this sort of thing.

So rest assured that if anything bad happens, it would have happened regardless of the eclipse. If nothing bad happens, it wouldn’t have happened anyway. Don’t let these people frighten you or mislead you with their quasi-religious quackery. There are natural explanations for everything. If I can ease the mind of just one person here, my time spent writing this will have been well invested.

Also posted on the YouTube video comment thread, was directed to the video via their Facebook post.

Relevant links:

From Big Bang To Black Hole: The Mind Trip

Inspired by the article “Goodbye Big Bang, Hello Black Hole? A New Theory Of The Universe’s Creation” at, by Elizabeth Howell, on September 18, 2013.

I just read an article at Universe Today which, though it was published over a year ago, had so far evaded my attention. It speaks of the possibility that our universe did not come about by way of a Big Bang, but rather that it is something like the inside of a black hole resulting from the collapse of a dying star in a four-dimensional universe (presumably one dimension is lost in the process), and perhaps what we conceive as a Big Bang is the inside-out version that collapse, at least as far as I can understand.

Illustration borrowed from the above mentioned article. With apologies to those involved.

It’s a dashingly interesting and mindboggling concept, but it would seem that it merely pushes the problem of the great coming-into-being of everything (I generally avoid the word “creation” as it implies that someone is doing the creating, which is a whole ‘nother bag of wossname) one more generation backwards. What came before the hypothetical four-dimensional star which hypothetically collapsed into our tree-dimensional universe? Was its universe, too, born out of a collapsing five-dimensional star in a previous universe? And before that?

Illustration borrowed from the above mentioned article. With apologies to those involved.

It smacks slightly of “turtles all the way down”, but I am not one to say that that’d be an incorrect conclusion. Turtles, after all, are known for impressive longevity, if left to to their own devices under favourable circumstances, and as far as turtles go, universes are long-lived indeed.

Lonesome George 1.jpg
Example of particularly long-lived turtle (Wikipedia)

But wait. Aren’t black holes supposed to steadily consume all available matter around them? Would not that cause a steady stream of further matter to be injected into the universe born of that black hole? Our universe? Would that not make the sum total matter in that universe anything but unchanging? Doesn’t that run against the rule that the sum of mass and energy is constant? Or is the content of the resulting universe limited to the matter present at the moment of collapse? If the latter, where does the later consumed matter go? And how the heck do we define matter on that scale anyway? A previous universe with a higher number of dimensions (I’ve barely been able to wrap my mind around four dimensions, I dare not think what five would be like, not to mention six) would be unlike anything we know from our three-dimensional one. And black holes in our universe, do they lead to two-dimensional universes? What happens when you run out of dimensions? Will the next generation be one of Flatlanders, or are the dimensions themselves simply rearranged and redefined so that there is no real beginning or end to a long, continuous line of stars dying and universes being born?

Carl Sagan on Flatland and Flatlanders (Youtube)

I wish that I could say that questions like these do not keep me awake at night, and indeed I can, but during my waking hours they tend to buzz around my cerebrum like infuriatingly annoying house flies, and there tends to be rather a lot of them. Though before you start questioning my personal hygiene, I am quite sure that those aren’t actual house flies, as their buzzing takes place inside my head, and at least so far no-one else has actually reported seeing them.

My point, if there is one, is that every new discovery, every new theory, even if it should happen to provide answers and explanations to existing questions, tends to present anywhere from a single one to a whopping multitude of new ones. But that’s the astonishing beauty of science: We will never run out of things to find out, questions to ask, amazing stuff big and small to drop our jaws at, as well as little things, at a more manageable magnitude, to keep us occupied in our everyday lives. It’s bloody marvellous!

Welcome to the Universe. It’s the biggest thing you will ever know.

Related links:

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