1. Science at Cal, October 2016 Vision + Light; Extending the Senses
Granada 2003
Science at Cal, October 2016
Vision + Light; Extending the Senses
Scientific Visualization, Mental Images, and Creativity
The official title of the symposium: “Vision + Light,” had quite different associations among the 3 panelists; they span the three topics expressed in the second title.
Carlo H. Séquin
EECS Computer Sciences
University of California, Berkeley

2. My Interpretation ( in the context of Science @ Cal )
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My Interpretation ( in the context of Cal )
“Vision”  A well-thought-out plan “Light”  Insight (as in “Fiat Lux”)
Personally, I am not an expert on our visual system – or any other human senses. So I have given the symposium title a broader interpretation:
I take the words “vision” and “light” beyond their physical definitions and look at their more abstract, metaphorical meanings. I understand “Vision” as in the planning of some specific research, and “Light” in the sense of “insight” – as in “Fiat Lux”.

3. The Scientific Process
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The Scientific Process
99 % Labor-intensive, repetitive tasks; observations, measurements, checking …
1 % “Heureka”-Moments, when suddenly all the data fall into place and a new concept emerges.
Science involves a lot of tedious, repetitive tasks of: observation, measurement, checking, and so on. But the exciting moments occur, when a new model is conceived that makes sense of all the data, and when suddenly all results fall into place in a wonderful “aha”-moment -- that is when a new light bulb goes on.
These wonderful events cannot be scheduled. They just happen when all the circumstances are right. But that step is the least controllable, the least understood …

4. Puzzling Questions Where do novel insights come from ?
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Puzzling Questions
Where do novel insights come from ?
Are there any truly novel ideas ? Or are they evolutionary developments, and just combinations of known ideas ?
What is creativity ?
How do we evaluate open-ended designs ?
What’s a good solution to such a problem ?
How do we know when we are done ?
So it raises some puzzling questions: . . .

5. First all-solid-state TV camera
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Bell Labs
I started my career 45 years ago at Bell Telephone Laboratories in NJ, -- working on Charge-Coupled Devices and developing the first solid-state TV camera.
Bell Labs was a great place. It offered many in-house courses; some of them given by Nobel-prize winners.
First all-solid-state TV camera

6. Granada 2003
Nobel Prize in Physics 1956
Thinking about “thinking” improves thinking!
I took three courses from Shockley on transistors and energy bands in semiconductors. In each of these courses Shockley pointed out at some point that
>>> “Thinking about thinking improves thinking!”
Discovery of the transistor

7. William Shockley’s Model of Creativity
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William Shockley’s Model of Creativity
Our mind has a pool of known ideas and models.
A “generator” randomly churns up some of these.
Multi-level filtering weeds out poor associations; only a small fraction percolate to consciousness.
We critically analyze those ideas with the left brain.
See diagram  (from inside front cover of “Mechanics”)
Shockley also liked to talk about creativity and has presented the following model of creativity: …
[LIST]
He also made a diagram of this process, which appears on the inside cover of his text-book on “Mechanics” (by W. Shockley and Walter A. Gong).

8. Shockley’s Model of Creativity
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Shockley’s Model of Creativity
“ACOR”:
Key Attributes
Comparison Operators
Orderly Relationships
= Quantum of conceptual ideas ?
This is what Shockley thinks is going on in your mind: Most of this happens at a subconscious level. Shockley defines these items that he calls ACORs – which may be seen as quanta of conceptual ideas …
There is a pump that randomly picks up such ACORS and then checks whether there is any association with the current problem under investigation. Perhaps you are contemplating a Light-bulb and an ACOR related to the Sun is picked up: round? – irrelevant; – yellow? – trivial – => So these connections get rejected at the subconscious level. => They both emit light? – perhaps this comes to the conscious level and you start pondering: how are the 2 light-generating processes might differ? === Or, if you are Sir Isaac Newton, and observe a falling apple – falling meteorite – falling planet: -- obey same force?? -- Heureka moment!
>>> The more ACORs this pump can churn up, the more likely a new innovative and useful link may be established. Shockley gives some suggestion of what might increase the productivity of this pump: Most importantly: Don’t just sit around and wait; DO Something! Go for a walk, doodle with paper and pencil, play with clay or with pipe-cleaners…
===
Also in:
The Public Need and the Role of the Inventor: Proceedings, Issue 388
edited by Florence Essers, Jacob Rabinow

9. Granada 2003
CREATIVITY
To this I would like to add, that you should do these activities in a relaxed state of mind. You should be in a mode of play.
When you are under attack by a ferocious creature, you might apply some judo move that you have learned years ago, -- but you will NOT invent a clever new karate move on the spot.
It is only when you are in a playful mood, with extra time at your disposal, that you can conceive new creations.
PLAY

10. Berkeley Faculty ... ? Math-Art Conference Bridges 1999
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Berkeley Faculty ... ?
Math-Art Conference Bridges 1999
In 1985 I started to teach a graduate course on “Creative Geometric Modeling” – which I then repeated every couple of years. Geometric Design Exercises are a good domain to train and to demonstrate creative thinking.
And as much as possible, I try to make this fun: On the left is a picture of the art-exhibit that we had at the end of the 1985 class.
>>>On the right is a picture from my favorite annual conference: … where we build bridges from Mathematics to Art, and music, and dance, and juggling, and origami, and macramé, and poetry, and many other cultural venues that make use of underlying mathematical structures. The conference is now in its 20th year.
1985: Creative Geometric Modeling

11. Class exercises to further this kind of thinking:
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Think Outside the Box !
Class exercises to further this kind of thinking:
Build analogies ...
Do this in 3D !
One approach to make the students think “outside the box” is to give them open-ended problems.
For instance, I show them the classical Yin-Yang symbol and then ask them to do this in 3D!

12. 3D Yin-Yang Solutions: Two congruent parts (Fall 1997)
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3D Yin-Yang Solutions: Two congruent parts (Fall 1997)
J. Smith: Computer Model
Most student will soon interpret this to mean that a sphere should be partitioned into two congruent parts. And I get several fine solutions.
A. Hsu: Clay Model
R. Hillaire: Acrylite Model

13. Korean Yin-Yang  Partition sphere into 3 parts?
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Korean Yin-Yang
But some students may decide that, as we go from 2 dimensions to 3 dimensions, we should also go from 2 parts to 3 parts; -- after all, there is a Korean Yin Yang symbol showing 3 colors.
Others may argue for 4 parts, because going up one dimension should double the number of components, just as the number of vertices doubles when you go from a square to a cube.
 Partition sphere into 3 parts?

14. 3D Yin-Yang : Two mirror parts
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3D Yin-Yang : Two mirror parts
My own favorite solution has only two parts, and they are mirror images of one another!
Stereolithography models (Séquin 1999)

15. A plane-filling Peano curve
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The 2D Hilbert Curve (1891)
A plane-filling Peano curve
Here is another example to exercise this analogy from 2D to 3D:
I show the students the famous space-filling curve named after Hilbert and ask them to “Do This In 3D!”
Do This In 3 D !

16. Artist’s Use of the Hilbert Curve
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Artist’s Use of the Hilbert Curve
And I don’t mean to just put this pattern on a 3D surface, as Helaman Ferguson has done so beautifully.
Helaman Ferguson: Umbilic Torus NC, silicon bronze, 27x27x9 in., SIGGRAPH’86

17. Construction of 3D Hilbert Curve
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Construction of 3D Hilbert Curve
Again the students understand quickly, that they are supposed to construct a space-filling curve that fills a cube, in a recursive manner, by breaking the whole cube into 8 smaller cubes that are properly interconnected.

18. Jane Yen: “Hilbert Radiator Pipe” (2000)
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Jane Yen: “Hilbert Radiator Pipe” (2000)
Flaws from a sculptor’s point of view:
4 coplanar segments
Not a closed loop
Broken symmetry
Some students introduce some extra design elements, such as color, to make their solutions artistically more pleasing.
But we always look for ways to improve on a design. We may discuss whether it would be better, and possible, to avoid more then 3 subsequent coplanar segments.
And perhaps it would be nice, if the pipes formed an overall closed loop (giving up strict recursion).
Also, maximizing symmetry may be another worthwhile goal.

19. Metal Sculpture at SIGGRAPH 2006
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Here is a solution that eliminates all these flaws.
It has been realized with a metal sintering process that builds this sculpture layer by layer on a 3D printer.

20. A Graph-Embedding Problem
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A Graph-Embedding Problem
Embed graph (K12) crossing-free in a symmetrical surface.
The surface needs to be of genus 6.
What is the maximal symmetry that can be obtained?
Here is a math problem that I grappled with for a while. The goal is to find a highly symmetrical surface with enough tunnels so that this graph completely connecting twelve vertices can be drawn on that surface without any crossings. What might such a surface look like.

21. My Model: 3D-Print, Over-Painted
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My Model: 3D-Print, Over-Painted
This is the solution that I eventually came up with – presented in the form of a model made on a 3D printer. The borders between the differently colored countries are the edges in the original graph. The black dots are the vertices.

22. Virtual Genus-6 Map (shiny metal / glass)
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Virtual Genus-6 Map (shiny metal / glass)
Here is the same basic solution displayed as a virtual model using shiny metal or colored glass
If it is made from glass, then we could place 4 light bulbs into the four tetrahedral corners and turn this into a Tiffany lamp ...

23. Light Field of Genus-6 Tiffany Lamp
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And this is the kind of light display that you would obtain from such a Tiffany lamp. -- Clearly, light and vision play an important role here.
In the last few years I have often started from a math problem and tried to make a good model that makes me understand the problem better and also helps to explain it to others.
Sometimes the models get nice enough, so that they become art pieces in their own right, and people might want to have them on their mantelpiece -- even if they don’t know the math-story underlying them.
Some examples can be seen in the exhibit.
Light Field of Genus-6 Tiffany Lamp

25. NOT USED . . .

26. MATH ART Part I: Math models become Art objects
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MATH ART
Part I: Math models become Art objects
Part II: Art captured with Math tools ...
Two ways to link math and art.

27. Brent Collins “Hyperbolic Hexagon II”
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Brent Collins
Since 1995 I have had a close collaboration with Brent Collins
whom you see holding here our first collaborative wood sculpture.
“Hyperbolic Hexagon II”

28. 9-story Intertwined Double Toroid
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9-story Intertwined Double Toroid
Bronze
investment
casting from wax original made on 3D Systems’ “Thermojet”
Over time our designs became gradually more elaborate.

29. Stepwise Expansion of Horizon
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Stepwise Expansion of Horizon
Playing with many different shapes and
experimenting at the limit of the domain of the sculpture generator,
stimulates new ideas for alternative shapes and generating paradigms.
This would not have been possible without the use of computers and a sophisticated parameterized modeling program.
Swiss Mountains

30. Sculpture Generator 1 as a Playground
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Sculpture Generator 1 as a Playground
The computer becomes an amplifier / accelerator for the creative process.
Yet another way to extend the senses.