The Operating System

zoom

Image: Issey Miyake

Christopher Forte: { Japan — An Ascetic Aesthetic }

There is a notion of modesty and subtlety, a respect for ceremony and procedure, an approach to duty and honor – that is unique to Japan. To the western eye these values are construed as anything from hopelessly anachronistic to downright obsessive – yet they contribute to a reverence for aesthetics that is utterly unique and exquisitely complex. This distinctive approach to all that appeals to the senses has, over centuries, imbued the Japanese with a veritable omnibus of terms that define everything from the simplest idea of placement (shibui: austerity of taste – not concealing the true nature of an object – a vase is a vase, a toaster is a toaster…) to the most esoteric concepts of shaping space (aji: where the incongruity of the object speaks of the congruity of the whole – the idea of sleeves filled with nothing, of space filled only with color…)

11 months ago on June 27, 2012

Comments · 43 notes

a short introduction to complex numbers ›

yasmoose:

Because I wanted to help out with this but couldn’t include my entire answer in an ask submission.

Complex numbers are of the form a+bi where a is the real component and bi is the imaginary component.

i is like a placeholder that indicates that the number it’s next to is imaginary; it’s easiest to think of it as the square root of -1. So i² = -1, and is therefore a real number (or maybe just the real component of a complex number, which we’ll get to).

Visualizing a complex number isn’t too hard if you don’t take the idea of imaginary numbers too seriously (and by that, I mean, don’t get stuck on the idea that it’s called imaginary, or that it’s the square root of a negative number—not that imaginary numbers are frivolous).

Picture a plane where you have a real axis and an imaginary axis, as follows:

You can also do the above in 3D! Just like the movies.

So instead of having a real axis and imaginary axis, you’d have a real plane and an imaginary plane, like below:

where the x-y plane is real.

Now say I have a complex number z = 2 + 3i.

[side note: z is the conventional letter picked for complex numbers]

I would draw it like this on my plane:

where my real component has a magnitude of 2 and my imaginary component has a magnitude of 3. The resulting vector of these magnitudes:

is my complex number z.

So a real number is basically a complex number with no imaginary component (and vice versa).

Using the example above, Re{z} = 2 and Im{z} = 3i.

#math #mathematics #infinity #infinities #imaginary #numbers #complex

1 year ago on May 17, 2012 via yasmoose

Comments · 9 notes

One of the great challenges of contemporary science is to trace the mix of simplicity and complexity, regularity and randomness, order and disorder up the ladder from elementary particle physics and cosmology to the realm of complex adaptive systems.

Murray Gell-Mann, The Quark and the Jaguar, 119-120

••••••

{ How do “yin” & “yang” conditions across levels of science produce life as we know it? }

1 year ago on May 07, 2012 via olena

Comments · 2 notes

What is really meant by the opposing terms simplicity and complexity? In what sense is Einsteinian gravitation simple while a goldfish is complex?

Murray Gell-Mann, The Quark and the Jaguar

#simple #simplify #complex #braid #Murray Gell-Mann #Gell-Mann #Einstein #physics #science #quantum #design

1 year ago on February 12, 2012

Comments · 3 notes

zoom

How Computational Complexity Will Revolutionize Philosophy

The theory of computation has had a profound influence on philosophical thinking. But computational complexity theory is about to have an even bigger effect, argues one computer scientist.

KFC 08/10/2011
{ Technology Review }

Read the short paper by Scott Aaronson (who has proposed these ideas):
{ Cornell University Library }