Geometry
Isometry
A Website by Nick TrombleyLittle Blank Riding Hood
As a student at Chouinard, Larry Bell also started as a painter. His early canvases features simple shapes rendered in gestural strokes...From there he started eliminating the texture of the strokes, applying opaque color (thin Liquitex paint) to unprimed canvas, masking off shapes to create straight-edged parallelograms. An example of these works is Little Blank Riding Hood, whose top left and bottom right corners are clipped, suggesting an isometric projection of a three-dimensional form.
A rhombic geometry
The logo consists of a rhombic geometry which was inspired by Morioka’s drawing which he brought to the first meeting with Takram. During the process of design development, the team explored many different shapes and motifs other than the rhombic, but in the end came back to the very origin. In fact, the rhombic shape embraces two meanings, “an open single book” and “a single small room”. The first message was the vision team shared through the design process, and the second message was later proposed by Takram in order to make the geometry more connected to the character of the space, which Morioka often emphasised unconsciously.
1/3 House
Rever & Drage Architects.
Pylons
Not all the towers along a transmission line are identical. Look closely at a tower where the line makes a sharp turn and you will likely find it is wider and beefier than other towers along the route. The added strength and weight are needed to resist the unbalanced pull of the conductors, which might overturn an ordinary tower. These special towers are called deviation or angle towers.
The transmission-line tower everybody knows is an Erector Set latticework of steel girders and diagonal braces. The techniques for designing and building these towers are the same ones used in constructing steel bridge trusses or crane booms. The individual pieces can be made cheaply from rolled steel and then bolted together on the site. This last point is more important than it might seem: transporting a fully assembled tower 100 feet tall is an awkward and expensive business.
Authentic architectural experiences
Authentic architectural experiences consist of approaching or confronting a building, rather than the formal apprehension of a facade; of the act of entering, and not simply the visual design of the door; of looking in or out through a window, rather than the window itself as a material object; or of occupying the sphere of warmth, rather than the fireplace as an object of visual design.
Architectural space is lived space rather than physical space, and lived space always transcends geometry and measurability.
A World Where Things Only Almost Meet
Recall that great line from Umberto Eco’s novel The Name of the Rose
How beautiful the world would be if there were a procedure for moving through labyrinths.
Only, here, it’s some lonely postal worker—or a geography Ph.D. driven mad by student debt—out mapping the frayed edges of the world, wearily noting every new dead-end and cul-de-sac in a gridded notebook, diagramming loops, sketching labyrinths and mazes, driving empty streets all day on a quest for something undefinable, some answer to why the world’s patterns have gone so wrong. A self-diverging world, where things only almost meet.
Rearranged
Put together with odd bits of the useless Clarice, a survivors’ Clarice was taking shape, all huts and hovels, festering sewers, rabbit cages. And yet, almost nothing was lost of Clarice’s former splendor; it was all there, merely arranged in a different order, no less appropriate to the inhabitants’ needs than it had been before.
Simple variations of the parts
Symmetry, indeed, has been grossly overemphasized in both art and science: its main value is in giving meaning to its absence, dissymmetry, without which there could be no hierarchy.
The eye is repulsed by complexity if no order is detected, but it can be delighted by repetition, translation, rotation, reflection, magnification, and other simple variations of the parts.
The Topography of Tears
A Book by Rose-Lynn FisherThe Topography of Tears is a visual investigation of tears photographed through an optical, standard light microscope, a vintage Zeiss from the late 1970's, mounted with a digital microscopy camera.
Tears are the medium of our most primal language in moments as unrelenting as death, as basic as hunger, and as complex as a rite of passage. They are the evidence of our inner life overflowing its boundaries, spilling over into consciousness. Wordless and spontaneous, they release us to the possibility of realignment, reunion, catharsis, intractable resistance short-circuited. Shedding tears, shedding old skin. It’s as though each one of our tears carries a microcosm of the collective human experience, like one drop of an ocean.
Plus Equals #4
An Article by Rob WeychertOne of the seeds for Plus Equals was planted a few years ago with Incomplete Open Cubes Revisited, my extension of a Sol LeWitt work. I learned a lot about isometric projection from that project, but my affection for the concept didn’t begin there. Whether I’m looking at a Chris Ware illustration or an exploded-view technical drawing of a complex machine, an isometric rendering always stirs something in me.
The joy of the humble brick
An Article by Tim HarfordThe brick is one of those old technologies, like the wheel or paper, that seem to be basically unimprovable. ‘The shapes and sizes of bricks do not differ greatly wherever they are made,’ writes Edward Dobson in the fourteenth edition of his Rudimentary Treatise on the Manufacture of Bricks and Tiles. There’s a simple reason for the size: it has to fit in a human hand. As for the shape, building is much more straightforward if the width is half the length.
Subtilitas
A BlogSUBTĪLITĀS (latin; noun f., 3rd):
fineness of texture, logic, detail; slenderness, exactness, acuteness; sharpness : precisionnarrowdesign.com
A Website by Nick JonesDesign
Prototype
CodeRafael Araujo's Golden Ratio
A GalleryBlue Morpho Double Helix & Icosahedron
Cityspace series
A Gallery by Emily GarfieldPrimary series for imaginary map drawings, spanning 2008-present and using various materials and techniques.
bees & bombs
A Blog
The Art of Doing Science and Engineering: Learning to Learn
The Art of Doing Science and Engineering is the full expression of what "You and Your Research" outlined. It's a book about thinking; more specifically, a style of thinking by which great ideas are conceived.
Gifts of knowledge to humanity
There are many commonalities we can admire in these endeavors: the dazzling leap of imagination, the broad scope of applicability, the founding of a new paradigm. But let’s focus here on their form of distribution. These are all things that are taught. To “use” them means to learn them, understand them, internalize them, perform them with one’s own hands. They are free to any open mind.
In Hamming’s world, great achievements are gifts of knowledge to humanity.
Hamming-greatness
Hamming-greatness is tied, inseparably, with the conception of science and engineering as public service. This school of thought is not extinct today, but it is rare, and doing such work is not impossible, but fights a nearly overwhelming current.
It cannot be taught in words
How to be a great painter cannot be taught in words; one learns by trying many different approaches that seem to surround the subject. Art teachers usually let the advanced student paint, and then make suggestions on how they would have done it, or what might also be tried, more or less as the points arise in the student’s head—which is where the learning is supposed to occur!
Preparing for problems
I firmly believe in Pasteur’s remark, “Luck favors the prepared mind.” In this way I can illustrate how the individual’s preparation before encountering the problem can often lead to recognition, formulation, and solution.
Student's future, not teacher's past
Teachers should prepare the student for the student’s future, not for the teacher’s past.
If you know what you are doing
In science, if you know what you are doing, you should not be doing it.
In engineering, if you do not know what you are doing, you should not be doing it.The homogeneity of knowledge
The standard process of organizing knowledge by departments, and sub-departments, and further breaking it up into separate courses, tends to conceal the homogeneity of knowledge, and at the same time to omit much which falls between the courses.
Another goal of the course is to show the essential unity of all knowledge rather than the fragments which appear as the individual topics are taught. In your future anything and everything you know might be useful, but if you believe the problem is in one area you are not apt to use information that is relevant but which occurred in another course.
An information service society
Society is steadily moving from a material goods society to an information service society. At the time of the American Revolution, say 1780 or so, over 90% of the people were essentially farmers—now farmers are a very small percentage of workers.
What will the situation be in 2020? As a guess I would say less than 25% of the people in the civilian workforce will be handling things; the rest will be handling information in some form or other. In making a movie or a tv program you are making not so much a thing, though of course it does have a material form, as you are organizing information.
From hands to machines
It has rarely proved practical to produce exactly the same product by machines as we produced by hand. Mechanization requires you produce an equivalent product, not identically the same one.
A matter of choice and balance
More than ever before, engineering is a matter of choice and balance rather than just doing what can be done. And more and more it is the human factors which will determine good design—a topic which needs your serious attention at all times.
Central planning gives poor results
Central planning has been repeatedly shown to give poor results (consider the Russian experiment, for example, or our own bureaucracy). The persons on the spot usually have better knowledge than can those at the top and hence can often (not always) make better decisions if things are not micromanaged.
"Real programmers"
At the time the Symbolic Assembly Program (SAP) first appeared I would guess about 1% of the older programmers were interested in it—using SAP was “sissy stuff,” and a real programmer would not stoop to wasting machine capacity to do the assembly.
Using your own expertise
Almost all professionals are slow to use their own expertise for their own work. The situation is nicely summarized by the old saying, “The shoemaker’s children go without shoes.”
History tends to be charitable
History tends to be charitable. It gives credit for understanding what something means when we first do it. But there is a wise saying, “Almost everyone who opens up a new field does not really understand it the way the followers do.”
The reason this happens so often is the creators have to fight through so many dark difficulties, and wade through so much misunderstanding and confusion, they cannot see the light as others can, now the door is open and the path made easy.
Mass production of variable products
Computers have opened the door much more generally to the mass production of a variable product, regardless of what it is: numbers, words, word processing, making furniture, weaving, or what have you. They enable us to deal with variety without excessive standardization, and hence we can evolve more rapidly to a desired future!
Thinking is a matter of degree
Perhaps “thinking” is not a yes/no thing, but maybe it is a matter of degree.
Making coal miners into programmers
Many humans at present are not equipped to compete with machines—they are unable to do much more than routine jobs. There is a widespread belief (hope?) that humans can compete, once they are given proper training. However, I have long publicly doubted you could take many coal miners and make them into useful programmers.
A minimum size to fish
There is the famous story by Eddington about some people who went fishing in the sea with a net. Upon examining the size of the fish they had caught, they decided there was a minimum size to the fish in the sea! Their conclusion arose from the tool used and not from reality.
Spelled with a lowercase letter
I used to tease John Tukey that you are famous only when your name was spelled with a lowercase letter such as watt, ampere, volt, fourier (sometimes), and such.
Why it can't be done
Moral: when you know something cannot be done, also remember the essential reason why, so later, when the circumstances have changed, you will not say, “It can’t be done.”
When you decide something is not possible, don’t say at a later date it is still impossible without first reviewing all the details of why you originally were right in saying it couldn’t be done.
Intellectual shelf life
Let lab equipment lie idle for some time, and suddenly it will not work properly! This is called “shelf life,” but it is sometimes the shelf life of the skills in using it rather than the shelf life of the equipment itself! I have seen it all too often in my direct experience. Intellectual shelf life is often more insidious than is physical shelf life.
Beware of jargon
Beware of jargon—learn to recognize it for what it is, a special language to facilitate communication over a restricted area of things or events. But it also blocks thinking outside the original area it was designed to cover. Jargon is both a necessity and a curse.
You cannot consume what is not produced
The only law of economics that I believe in is Hamming’s law: “You cannot consume what is not produced.” There is not another single reliable law in all of economics I know of which is not either a tautology in mathematics or else sometimes false.
I walked the crest of the dune
Thus piece by piece I walked the crest of the dune, and each time the solution slipped on one side or the other I knew what to do to get back on the track.
God loved sand
“God loved sand, He made so much of it.” I heard, inside myself, that we were already having to exploit lower-grade copper mines, and could only expect to have an increasing cost for good copper as the years went by, but the material for glass is widely available and is not likely to ever be in short supply.
The Hawthorne effect
At the Hawthorne plant of Western Electric, long, long ago, some psychologists were trying to improve productivity by making various changes in the environment. They painted the walls an attractive color, and productivity rose. They made the lighting softer, and productivity rose. Each change caused productivity to rise. One of the men got a bit suspicious and sneaked a change back to the original state, and productivity rose! Why? It appears that when you show you care, the person on the other end responds more favorably than if you appear not to care. The workers all thought the changes were being made for their benefit and they responded accordingly. In the field of education, if you tell the students you are using a new method of teaching, then they respond by better performance, and so, incidentally, does the professor. A new method may or may not be better, indeed it may be worse, but the Hawthorne effect, which is not small in the educational area, is likely to indicate that here is a new, important, improved teaching method. It hardly matters what the new method is; its trial will produce improvements if the students perceive it as being done for their benefit.
What you learn for yourself
What you learn from others you can use to follow;
What you learn for yourself you can use to lead.The unreasonable effectiveness of mathematics
We now see that all this “truth” which is supposed to reside in mathematics is a mirage. It is all arbitrary, human conventions.
But we then face the unreasonable effectiveness of mathematics. Having claimed there was neither “truth” nor “meaning” in the mathematical symbols, I am now stuck with explaining the simple fact that mathematics is used and is an increasingly central part of our society, especially in science and engineering. We have passed from absolute certain truth in mathematics to the state where we see there is no meaning at all in the symbols—but we still use them! We put the meaning into the symbols as we convert the assumptions of the problem into mathematical symbols, and again when we interpret the results. Hence we can use the same formula in many different situations—mathematics is sort of a universal mental tool for clear thinking.
What can be put into words
It is not evident, though many people, from the early Greeks on, implicitly act as if it were true, that all things, whatsoever they may be, can be put into words—you could talk about anything: the gods, truth, beauty, and justice. But if you consider what happens in a music concert, then it is obvious that what is transmitted to the audience cannot be put into words—if it could, then the composer and musicians would probably have used words. All the music critics to the contrary, what music communicates cannot (apparently) be put into words. Similarly, but to a lesser extent, for painting. Poetry is a curious field where words are used but the true content of the poem is not in the words!
Initial psychological distance
Creativity seems, among other things, to be “usefully” putting together things which were not perceived to be related before, and it may be the initial psychological distance between the things which counts most.
Tossing an idea around
Can we do anything to increase creativity? There are training courses, and books, as well as “brainstorming sessions” which are supposed to do this. Taking the brainstorming sessions first, while they were very fashionable at one time, they have generally been found to be not much good when formally done, when a brainstorming session is carefully scheduled. But we all have had the experience of “tossing an idea around” with a friend, or a few friends (but not a large group, generally), from which insight, creativity, or whatever you care to call it, arises and we make progress.
Prepare your mind for the future
Probably the most important tool in creativity is the use of an analogy. Something seems like something else which we knew in the past. Wide acquaintance with various fields of knowledge is thus a help—provided you have the knowledge filed away so it is available when needed, rather than to be found only when led directly to it. This flexible access to pieces of knowledge seems to come from looking at knowledge while you are acquiring it from many different angles, turning over any new idea to see its many sides before filing it away. This implies effort on your part not to take the easy, immediately useful “memorizing the material” path, but to prepare your mind for the future.
Stuck with a problem
If you cannot drop a wrong problem, then the first time you meet one you will be stuck with it for the rest of your career.
Experts and impossibility
If an expert says something can be done he is probably correct, but if he says it is impossible then consider getting another opinion.
Always time to fix it later
As the saying goes:
There is never time to do the job right, but there is always time to fix it later,
especially in computer software!
The average adult
Averages are meaningful for homogeneous groups (homogeneous with respect to the actions that may later be taken), but for diverse groups averages are often meaningless. As earlier remarked, the average adult has one breast and one testicle.
Solution to evaluation and back again
A second reason the systems engineer’s design is never completed is the solution offered to the original problem usually produces both deeper insight and dissatisfactions in the engineers themselves.
Furthermore, while the design phase continually goes from proposed solution to evaluation and back again and again, there comes a time when this process of redefinement must stop and the real problem be coped with—thus giving what they realize is, in the long run, a suboptimal solution.
The heart of systems engineering
While the client has some knowledge of his symptoms, he may not understand the real causes of them, and it is foolish to try to cure the symptoms only. Thus while the systems engineers must listen to the client, they should also try to extract from the client a deeper understanding of the phenomena. Therefore, part of the job of a systems engineer is to define, in a deeper sense, what the problem is and to pass from the symptoms to the causes.
Just as there is no definite system within which the solution is to be found, and the boundaries of the problem are elastic and tend to expand with each round of solution, so too there is often no final solution, yet each cycle of input and solution is worth the effort. A solution which does not prepare for the next round with some increased insight is hardly a solution at all.
I suppose the heart of systems engineering is the acceptance that there is neither a definite fixed problem nor a final solution, rather evolution is the natural state of affairs. This is, of course, not what you learn in school, where you are given definite problems which have definite solutions.