Saturday, June 27, 2009

The Pythagorean theorem

The Pythagorean theorem is named after the Greek mathematician Pythagoras, who by tradition is credited with its discovery and proof, although it is often argued that knowledge of the theory predates him. (There is much evidence that Babylonian mathematicians understood the principle, if not the mathematical significance.)


An elegant proof of Pythagorean theorem can be found in Roger Penrose's popular science classic "The Road to Reality - A Complete Guide to the Laws of the Universe". His proof suits perfectly to the central theme of this blog; "Negative Matter", in other words the ability to see and transform negative spaces in order to convey further "meaning" into positive spaces.


First consider the pattern illustrated below. It is composed entirely of squares of two different sizes. It is 'obvious' that this pattern can be continued indefinitely, and the entire Euclidean plane can be covered in this repeating way with no gaps or overlaps by squares of these two sizes.



If we mark the centres of the larger squares, they form the vertices of another system of squares, at somewhat greater size than either, but tilted at an angle to the original ones.


Instead of taking the centres of the two large squares of the original pattern, we may choose any other point, together with its set of corresponding points throughout the pattern. The new pattern of tilted squares is just the same as before but moved along across either vertices without rotation (i.e. by means of motion referred as translation). For simplicity lets choose our starting point to be one of the corners in the original pattern.


It should be clear that the area of the tilted square must be equal to the sum of the areas of the two smaller squares. The small square at the top-left has a small triangular portion outside the tilted square, which is identical to the one inside, if we move along the vertex of tilted square. A similar observation can be made about larger triangles, proving our assertion.

Moreover it is evident that the edge-length of the large tilted square is the hypotenuse of a right-angled triangle whose two other sides have lengths equal to those of the smaller squares. We have thus established the Pythagorean theorem:: the square on the hypotenuse is equal to the sum of the squares on the other two sides.

Friday, June 26, 2009

Ockham's Razor


Pluralitas non est ponenda sine necessitate
Plurality is not to be posited without necessity
William of Ockham (c. 1288 - c. 1348)
I like simple designs. Simplicity makes us humans happy, often unknowingly. But what does 'simple' mean anyway?

Simple is less, and less is more. If you can do with less why waste your energy and resources. Simple is elegant, and elegant is desirable.


Less is more. Why so? A bird's egg is simply round, smooth and slippery, no awkward angles. Difficult to capture intact and transport by predators. Optimised for smooth delivery, comfortable resting, and even temperature distribution. Space efficient for internal layout and external storage at the same time. i.e. 'do more with less'. A good example of natural selection favoring minimalism.

Tuesday, June 23, 2009

WaveDeck

My nephew Aksel Çoruh, who works as an architect in Rotterdam recently mentioned me;
" a book by Dutch urban planner Adrian Geuze (West 8 Landscape Architects), in which he writes about the notion of the ' void' as a sea of potential in spatial planning strategies. His designs and interventions in the city are known to take the viewpoint of trying to elicit public interaction with spaces, and form beds of potential where people, dwellers, and visitors alike become momentary participants in an urban (mini-) drama."
Then Aksel kindly provided their web site:


West8 designed a dramatic urban deck that they call WaveDeck. This is interesting because a wave shaped deck automatically creates a wave shaped space as well. One fills the other one and vice versa. Neither side of the wave is more important than the other side.

Waves possess spatial and reassuring harmony and continuity. So I would imagine people observing, standing or walking on the WaveDeck must be experiencing a certain sense of visual music. Music is by definition harmonic combinations of sound waves. There is no real reason why music can not be played visually. WaveDeck I guess works around this principle.

What about Edvard Munch's The Scream. In this painting we can't help but see the sound of scream:

Sunday, June 21, 2009

Software Entropy

One of the common reasons why software bugs are not fixed is:
"The developers often don't have time or it is not economical to fix all non-severe bugs."
Bugs scattered across software systems cause "software entropy" to increase (a term that I coined.) Therefore disorderedness of any isolated software system increases over time, similar to physical systems.

On the other hand what makes a software company survive is selling "orderly behaving" products. But competitive market forces and aggressive Sales pressures may increase organizational tendency not to fix bugs. This behavior in turn may lead to software entropy to increase in an exponential rate.

Therefore the size of the backlog of Support department may start to increase exponentially rather than logarithmically. In those circumstances increase in software entropy may result in "customer dissatisfaction" which may eventually lead to sales to decrease.

Therefore there must be a balancing act between Sales and Support. Development resources must be shared and utilized in a way to keep software entropy increase in a logarithmic but controllable and stable fashion if not decrease.

This is similar to "clean house" analogy. If you don't clean up, air and maintain your house regularly, say once every two weeks, it would become more difficult to keep up with entropy. Dust and mold will cumulate. Certain mechanical devices will rust away, or start to malfunction, more dust-mite colonies will flourish, the air will become stuffy and unhealthy. If you leave your house for 20 years, the chances are you may need to rebuild the interiors, i.e. start from scratch.

Software business is no different, negligence of balancing out software entropy may bring catastrophic consequences. And at some "no return" point the business may fail all together if not acted early enough.

Bugs

A software bug is the common term used to describe an error, flaw, mistake, failure, or fault in a computer program that prevents it from behaving as intended (e.g., producing an incorrect or unexpected result). Most bugs arise from mistakes and errors made by people in either a program's source code or its design.
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There are various reasons for not fixing bugs:
  • The developers often don't have time or it is not economical to fix all non-severe bugs.
  • The bug could be fixed in a new version or patch that is not yet released.
  • The changes to the code required to fix the bug would be large, and would bring with them the chance of introducing other bugs into the system.
  • Users may be relying on the undocumented, buggy behavior; it may introduce a breaking change.
  • It's "not a bug". A misunderstanding has arisen between expected and provided behavior
Given the above, it is often considered impossible to write completely bug-free software of any real complexity. So bugs are categorized by severity, and low-severity non-critical bugs are tolerated, as they do not affect the proper operation of the system for most users.
Wikipedia Software Bug



Second Law of Thermodynamics

Since energy is conserved, why does energy have to be fed to a car to keep it from stopping? Since energy is conserved, why does hot soup cool and ice-cream melt? Why does smoke fill up a room rather than crowding into one corner? Why do re-chargeable batteries eventually die? Why do machines eventually fail?
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There are many equivalent statements of the second law of thermodynamics: Isolated systems inevitably become less organised; the usable energy in an isolated system is constantly decreasing; a system naturally attempts to distribute its energy equally among all of its parts; mechanical energy, on average, degrades into heat; heat naturally flows from hot places to cold, equalizing temperatures; isolated machines cannot remain in perpetual motion; entropy (disorder), on average, increases. These statements all express the second law of thermodynamics. Physicists believe that it is the second law of thermodynamics that defines the direction of time, that distinguishes the past from the future.
Great Ideas in Physics, Alan Lightman

Negative Matter

Years back I attended a drawing course. One day we were painting still life. There was a vase and a green bottle on a table top, in the corner of our class. Our instructor told something about seeing and drawing negative spaces, and he added that Degas drew and painted like that.

I listened to him and tried to focus on what "we are not supposed to see", the shape of the space between the wall and the vase, and the green bottle, and shapes of the shades reflected and competing with each other on the bottle and so forth. In the end what I ended up with was amazingly truthful, powerful and beautiful despite its simplicity.

There is something about seeing the "negative matter", the stuff that is seemingly uninteresting but without it we are unable to make connections and "make sense" of our "positive universe".

We are almost brainwashed to think positively. Whereas I feel like there is an ultimate sense of truthfulness and accompanying beauty about negativity .

In this blog I shall be pursuing the negative matter. I'll talk about engineering, philosophy, physics, software, marketing, evolution, design, consciousness, politics etc. At times I will attempt to see negative forgotten spaces in order to make sense of positive matter and other times to reshape it.