human in search

In Islamic culture, geometry is everywhere.You can find it in mosques, madrasas, palaces and private homes.This tradition began in the 8th century CE during the early history of Islam, when craftsman took preexisting motifs from Roman and Persian cultures and developed them into new forms of visual expression.

Masjid Nasir al-Mulk (Persia / Iran)

This period of history was a golden age of Islamic culture, during which many achievements of previous civilizations were preserved and further developed, resulting in fundamental advancements in scientific study and mathematics. Accompanying this was an increasingly sophisticated use of abstraction and complex geometry in Islamic art, from intricate floral motifs adorning carpets and textiles, to patterns of tilework that seemed to repeat infinitely, inspiring wonder and contemplation of eternal order.

illustration islamic golden ages

Despite the remarkable complexity of these designs, they can be created  with just a compass to draw circles and a ruler to make lines within them, and from these simple tools emerges a kaleidoscope multiplicity of patterns.

So how does that work?

Well, everything starts with a circle. The first major decision is how will you divide it up? Most patterns split the circle into four, five or six equal sections. And each division gives rise to distinctive patterns. There's an easy way to determine whether any pattern is based on fourfold, fivefold, or sixfold symmetry. Most contain stars surrounded by petal shapes. Counting the number of rays on a starburst, or the number of petals around it, tells us what category the pattern falls into. A star with six rays, or surrounded by six petals, belongs in the sixfold category. One with eight petals is part of the fourfold category, and so on. There's another secret ingredient in these designs: an underlying grid. Invisible, but essential to every pattern, the grid helps determine the scale of the composition before work begins, keeps the pattern accurate, and facilitates the invention of incredible new patterns.



Let's look at an example of how these elements come together.

We'll start with a circle within a square, and divide it into eight equal parts. We can then draw a pair of criss-crossing lines and overlay them with another two. These lines are called construction lines, and by choosing a set of their segments, we'll form the basis of our repeating pattern. Many different designs are possible from the same construction lines just by picking different segments. And the full pattern finally emerges when we create a grid with many repetitions of this one tile in a process called tessellation.

basic tessellation

The possibilities are virtually endless. We can follow the same steps to create sixfold patterns by drawing construction lines over a circle divided into six parts, and then tessellating it, we can make something like this.

sixfold patterns tessellation

Here's another sixfold pattern that has appeared across the centuries and all over the Islamic world, including Marrakesh, Agra, Konya and the Alhambra. Fourfold patterns fit in a square grid, and sixfold patterns in a hexagonal grid.

one of  the popular sixfold pattern tessellation

Fivefold patterns, however, are more challenging to tessellate because pentagons  don't neatly fill a surface, so instead of just creating
a pattern in a pentagon, other shapes have to be added to make something that is repeatable, resulting in patterns that may seem confoundingly complex, but are still relatively simple to create.

Also, tessellation is not constrained to simple geometric shapes, as M.C. Escher's work demonstrates.
And while the Islamic geometric design tradition doesn't tend to employ elements like fish and faces,
it does sometimes make use of multiple shapes to craft complex patterns. This more than 1,000-year-old tradition has wielded basic geometry to produce works that are intricate, decorative and pleasing to the eye. And these craftsman prove just how much is possiblewith some artistic intuition, creativity, dedication and a great compass and ruler.

transcript video ted ed : ed.ted.com

Myths and misconceptions about evolution. Let's talk about evolution. You've probably heard that some people consider it controversial, even though most scientists don't. But even if you aren't one of those people and you think you have a pretty good understanding of evolution, chances are you still believe some things about it that aren't entirely right, things like,

"Evolution is organisms adapting to their environment."

This was an earlier, now discredited, theory of evolution. Almost 60 years before Darwin published his book, Jean-Baptiste Lamarck proposed that creatures evolve by developing certain traits over their lifetimes and then passing those on to their offspring.

Jean-Baptiste Lamarck

For example, he thought that because giraffes spent their lives stretching to reach leaves on higher branches, their children would be born with longer necks. But we know now that's not how genetic inheritance works. In fact, individual organisms don't evolve at all. Instead, random genetic mutations cause some giraffes to be born with longer necks, and that gives them a better chance to survive than the ones who weren't so lucky,
which brings us to

"survival of the fittest".

This makes it sound like evolution always favors the biggest, strongest, or fastest creatures, which is not really the case. For one thing, evolutionary fitness is just a matter of how well-suited they are to their current environment. If all the tall trees suddenly died out and only short grass was left, all those long-necked giraffes would be at a disadvantage. Secondly, survival is not how evolution occurs,
reproduction is. And the world if full of creatures like the male anglerfish, which is so small and ill-suited for survival at birth that it has to quickly find a mate before it dies. But at least we can say
that if an organism dies without reproducing, it's evolutionarily useless, right?

Wrong!

Remember, natural selection happens not at the organism level, but at the genetic level, and the same gene that exists in one organism will also exist in its relatives. So, a gene that makes an animal altruistically sacrifice itself to help the survival and future reproduction of its siblings or cousins, can become more widespread than one that is solely concerned with self-preservation. Anything that lets more copies of the gene pass on to the next generation will serve its purpose, except :

"Evolutionary Purpose."

One of the most difficult things to keep in mind about evolution is that when we say things like, "Genes want to make more copies of themselves," or even, "natural selection," we're actually using metaphors. A gene doesn't want anything, and there's no outside mechanism that selects which genes are best to preserve. All that happens is that random genetic mutations cause the organisms carrying them to behave or develop in different ways. Some of those ways result in more copies of the mutated gene being passed on, and so forth. Nor is there any predetermined plan progressing towards an ideal form. It's not ideal for the human eye to have a blind spot where the optic nerve exits the retina, but that's how it developed, starting from a simple photoreceptor cell.

In retrospect, it would have been much more advantageous for humans to crave nutrients and vitamins rather than just calories. But over the millenia, during which our ancestors evolved, calories were scarce, and there was nothing to anticipate that this would later change so quickly.

So, evolution proceeds blindly, step, by step, by step, creating all of the diversity we see in the natural world.

transcript from video ted ed : ed.ted.com