Very Short Introductions

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Fractals

Are fractals simple or complicated objects? Or perhaps both?  The beauty and attraction of many fractals stems from their complex and intricate form, with ever more detail becoming apparent under increasing magnification. Yet many fractals depend on a very simple rule, applied over and over again, a process called iteration.

The Mandelbrot set is perhaps the best known example. It is completely determined by the very simple formula  z2 + c, where z and c code points in the plane or on a computer screen in terms of ‘complex numbers’.  If, starting at 0 and repeatedly applying the formula to move from one point to the next, the sequence of points stay ‘close to home’, then c belongs to the Mandelbrot set and is coloured black in the pictures. If, on the other hand, the itinerary rapidly shoots off or ‘escapes’ into the distance, then c lies outside the Mandelbrot set and is coloured according to the rate of escape.

This simple rule is very easily programmed on a computer. Yet the Mandelbrot set is an extraordinarily complex object. It has a prominent cardioid, or heart shape, surrounded by near circular buds, which in turn have smaller buds attached to them. On closer inspection, stars, spirals and sea horses become apparent. Joined to these are many fine hairs on which lie miniature copies of the Mandelbrot set itself, and increased magnification reveals an endless gallery of ever more exotic features.

For its appearance alone, the Mandelbrot set would merely be a fascinating curiosity. But in recent years its remarkable mathematical properties have become enormously significant. Naturally associated with each point c of the Mandelbrot set is another fractal, called a Julia set. If c is in the main cardioid, then the Julia set is a closed loop, if c is in the largest bud, then it is formed by infinitely many loops, meeting systematically in pairs, and so on.  Moreover, the Mandelbrot set is ‘universal’ in that it codes the behaviour of iteration by many formulae other than just z2 + c.

Kenneth Falconer is a mathematician who specializes in Fractal Geometry and related topics. He is author of Fractals: A Very Short Introduction.

Images courtesy of Kenneth Falconer.

The West won the world not by the superiority of its ideas or values or religion but rather by its superiority in applying organized violence. Westerners often forget this fact, non-Westerners never do.
— 

Samuel P. Huntington, cited on the ‘Where is Raed?’ website, a day-to-day journal of everyday life in Baghdad under bombardment.

Extract in Robert J. C. Young, Postcolonialism, A Very Short Introduction (UK: Oxford University Press, 2003), p. 32.

“So who were the Druids? … Given the range of attributes, it is probably best to regard them as a caste of intellectuals. Caesar’s famous generalization, that in Gaul there are only two classes of men who are of any account or importance – the Druids and the Knights – puts them on a par with the tribal elite.”

It’s the Vernal (or Spring) Equinox today, and many people will be coming together to celebrate the Druid ceremony. But who actually were the druids?

Image: Historical Druid Temple, public domain via Public Domain Pictures.

External image

Hey, guys! So here’s a book I borrowed and am currently reading:

If you’re like me, and you have an interest in Forensic Psychology or any other Psychology fields, get a book like this. Oxford has books for Forensic Psychology, Child Psychology and Psychology.

I’ve been watching crime shows all my life and still do. Psychology has always been of great interest to me, especially when it’s to do with the world of crime. I’m currently pursuing a diploma in Information Technology instead of Applied Drama and Psychology because I didn’t get enough points in my National Exams.

But it didn’t mean I had to let go of my interest. I still want to do Psychology when it’s time to go to university (I’m torn between fields, haha!). So in the meantime, I’m gonna read the book, watch the crime shows, hang out at psych2go.tumblr.com, pretty much anything. :D 

I’m gonna keep the dream alive! :D 

Morning Cake

Yum.

   In other news, I finished that Very Short Introduction on The Computer by Darrel Ince. It was a strange book, incredibly dense in places and then really condescending. For instance, did you know that you can use a computer to send and receive messages? And sometimes these messages contain viruses that can fuck your computer up? Meanwhile, here are some formulas that contain more letters than numbers. You know the basics of quantum mechanics, right?

  There wasn’t much on other forms of computing, like DNA or chemical which would have been more interesting to read about, though I understand binary (kinda…) now. Or at least I sort of get out it works.

  Ince name dropped a few of his favourite websites and while I guess this says something about his likes and dislikes, perhaps his personality, I didn’t really care. One that did stand out simply because of I can do this?! factor was the Human Genome Project. You can apparently help them decipher DNA, or at least download some software that uses your unused memory to analyze data. The ability to say you helped unravel the mysteries of the human genome gets a thumbs up in my book, and mark my words, I’ll be looking into this when I’m not having to sit on the floor in the hallway.

  And here’s an interesting factoid; ever wonder where the term ‘bug’ came from? Back in ye olde days, when a single computer took up an entire room and consisted of ticker tape and levers, a moth got stuck between relay points in the Harvard computer.

  So in conclusion, would I recommend it? Possibly not. The author obviously knows his stuff, but he doesn’t seem quite sure of who he is writting for. The Amish or undergraduate engineering students? He does helpfully direct you to other books on various issues in computing and technology in an index at the end, so if you’re intrigued, try giving that a scan instead.

  Next up: Cosmology!

Apologies in advance because I just realised that this is probably a really, really pretentious photo (look at me with my METAPHYSICS and my PLATO) but I was taking pictures to motivate me as part of my desk-tidying process and I love how these look together.

The internet can decide which to get most excited about here: the washi tape or the Very Short Introductions. I know there are niche communities for both.

The ancients did not define themselves in terms of their sexual identities. The idea of classifying people according to sexual partner would have seemed bizarre to them. Sexual culture wasn’t homogeneous across the ancient world. There was substantial variation across regions and time.
—  Veronique Mottier, in “Before sexuality,” from Sexuality: A Very Short Introduction via Very Short Introductions.
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The Laudatio Tauriae is an inscription by a Roman husband about his wife, ‘So great was her sense of duty that, when the marriage proved childless, she offered divorce to allow her husband to seek a more fertile partner. His response speaks volumes: “…What desire, what need to have children could I have had that was so great that I should have broken faith for that reason and changed certainty for uncertainty”’ - Gwynn, David M. The Roman Republic A Very Short Introduction (Oxford: OUP, 2012)

Yeah, Doctor Who has parallels with Ancient Rome

Many human efforts, particularly those in the service of serious ambitions rather than just comfort and survival, get some of their energy from a sense of importance—a sense that what you are doing is not just important to you, but important in some larger sense: important, period. If we have to give this up, it may threaten to take the wind out of our sails. If life is not real, life is not earnest, and the grave is its goal, perhaps it’s ridiculous to take ourselves so seriously. On the other hand, if we can’t help taking ourselves so seriously, perhaps we just have to put up with being ridiculous. Life may be not only meaningless  but absurd.
—  What Does It All Mean?: A Very Short Introduction to Philosophy  
By Thomas Nagel
Top ten facts about knowledge

Jennifer Nagel, author of Knowledge: A Very Short Introduction, has created a list of ten facts about knowledge. How much do you know about knowledge?

1.       Groups of people can together know things that aren’t known by any individual member of the group.

2.       If John Locke’s theory of knowledge is right, no person alive today can actually know that John Locke ever lived.

3.       It’s possible to gain knowledge of a fact even when some of your relevant evidence is misleading.

4.       The deepest objection to Alvin Goldman’s causal theory of knowledge was formulated by Alvin Goldman.

5.       In 1963, an American philosopher became famous for discovering a way to prove that knowledge is not the same as justified true belief, but what he discovered had been found over a thousand years earlier in Eastern epistemology.

6.       Contextualists think that the verb “to know”, like the adverbs “tomorrow” and “here”, picks out different targets depending on when and where it is used.

7.       There is a brain region near your right ear that is specialized in adults for tracking what people think, want, and know.

8.       According to the American philosopher Jennifer Lackey, you can sometimes gain knowledge of a fact by hearing it from someone who doesn’t even believe it to be true.

9.       Ancient Academic Sceptics concluded that knowledge was humanly unattainable; ancient Pyrrhonian Sceptics went one step further and doubted all conclusions, even the Academic one about knowledge being unattainable.

10.    “Know” is one of the top ten most common verbs in English, and there’s a word meaning “know” in all of the 6000+ languages spoken on Earth.

Gif via giphy.com.

The ancient Greek philosophers recognized just four elements, earth, water, air, and fire, all of which survive in the astrological subdivision of the twelve signs of the zodiac. Some of these philosophers believed that these different elements consisted of microscopic components with differing shapes, and that this explained the various properties of the elements.
—  “The elements,” from, The Periodic Table: A Very Short Introduction via Very Short Introductions.
The 150th Anniversary of the Periodic Table

oupacademic:

Over the years, many scientists contributed to the creation of our contemporary periodic table of elements. On 20 August 1864, John Reina Newlands published one such contribution — a way to organize elements with similar chemical properties as you move from left to right across the periodic table. These days, periodic tables present groups of similar elements in vertical columns, but that’s just a cosmetic difference. In honor of Newlands’ discovery, we have compiled a list of books on the periodic table.

Image: Chemistry by macaroni1945. CC BY 2.0 via Flickr.

Submitted by srikard

Edited by Jessica F.