Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5

The illusion of cosmic structure + Origami algorithm + Legislative bill algorithm

#1
C C Offline
Chaos Makes the Multiverse Unnecessary
http://m.nautil.us/issue/49/the-absurd/c...nnecessary

EXCERPT: [...] How does one explain all this structure? Why do the laws seem so perfect for producing life and why are they expressed in such exact mathematical language? Is the universe really as structured as it seems? One answer to some of these questions is Platonism (or its cousin Realism). This is the belief that the laws of nature are objective and have always existed. They possess an exact ideal form that exists in Plato’s realm. These laws are in perfect condition and they have formed the universe that we see around us. Not only do the laws of nature exist in this realm, but they live alongside all perfectly formed mathematics. This is supposed to help explain why the laws are written in the language of mathematics.

Platonism leaves a lot to be desired. The main problem is that Platonism is metaphysics, not science. [...] The multiverse is another answer that has recently become quite fashionable. This theory is an attempt to explain why our universe has the life-giving laws that it does. One who believes in a multiverse maintains that our universe is just one of many universes. Each universe has its own set of rules and its own possible structures that come along with those rules. Physicists who push the multiverse theory believe that the laws in each universe are somewhat arbitrary. [...]

There is another, more interesting, explanation for the structure of the laws of nature. Rather than saying that the universe is very structured, say that the universe is mostly chaotic and for the most part lacks structure. The reason why we see the structure we do is that scientists act like a sieve and focus only on those phenomena that have structure and are predictable. They do not take into account all phenomena; rather, they select those phenomena they can deal with.

[...] As physics progresses and we become aware of more and more physical phenomena, larger and larger classes of mathematical structures are needed and we get them by looking at fewer and fewer axioms. Dirac calls these mathematical structures with fewer axioms “increasing abstraction” and “generalisations of the axioms.” There is no doubt that if Dirac lived now, he would talk about the rise of octonions and even the sedenions within the needed number systems.

In order to describe more phenomena, we will need larger and larger classes of mathematical structures and hence fewer and fewer axioms. What is the logical conclusion to this trend? How far can this go? Physics wants to describe more and more phenomena in our universe. Let us say we were interested in describing all phenomena in our universe. What type of mathematics would we need? How many axioms would be needed for mathematical structure to describe all the phenomena? Of course, it is hard to predict, but it is even harder not to speculate. One possible conclusion would be that if we look at the universe in totality and not bracket any subset of phenomena, the mathematics we would need would have no axioms at all. That is, the universe in totality is devoid of structure and needs no axioms to describe it. Total lawlessness! The mathematics are just plain sets without structure. This would finally eliminate all metaphysics when dealing with the laws of nature and mathematical structure. It is only the way we look at the universe that gives us the illusion of structure.

With this view of physics we come to even more profound questions. These are the future projects of science. If the structure that we see is illusory and comes about from the way we look at certain phenomena, then why do we see this illusion? Instead of looking at the laws of nature that are formulated by scientists, we have to look at scientists and the way they pick out (subsets of phenomena and their concomitant) laws of nature. What is it about human beings that renders us so good at being sieves? Rather than looking at the universe, we should look at the way we look at the universe....



Artificial intelligence can predict which congressional bills will pass
http://www.sciencemag.org/news/2017/06/a...-will-pass

EXCERPT: The health care bill winding its way through the U.S. Senate is just one of thousands of pieces of legislation Congress will consider this year, most doomed to failure. Indeed, only about 4% of these bills become law. So which ones are worth paying attention to? A new artificial intelligence (AI) algorithm could help. Using just the text of a bill plus about a dozen other variables, it can determine the chance that a bill will become law with great precision.[...] Nay says he is surprised that a bill’s text alone has predictive power. “At first I viewed the process as just very partisan and not as connected to the underlying policy that’s contained within the legislation,” he says. Nay’s use of language analysis is “innovative” and “promising,” says John Wilkerson, a political scientist at the University of Washington in Seattle. But he adds that without prior predictions relating certain words to success—the word “impact,” for example—the project doesn’t do much to illuminate how the minds of Congress members work. “We don’t really learn anything about process, or strategy, or politics.” But it still seems to be the best method out there....



Algorithm generates origami folding patterns for any shape
https://www.eurekalert.org/pub_releases/...062317.php

RELEASE: In a 1999 paper, Erik Demaine -- now an MIT professor of electrical engineering and computer science, but then an 18-year-old PhD student at the University of Waterloo, in Canada -- described an algorithm that could determine how to fold a piece of paper into any conceivable 3-D shape.

It was a milestone paper in the field of computational origami, but the algorithm didn't yield very practical folding patterns. Essentially, it took a very long strip of paper and wound it into the desired shape. The resulting structures tended to have lots of seams where the strip doubled back on itself, so they weren't very sturdy.

At the Symposium on Computational Geometry in July, Demaine and Tomohiro Tachi of the University of Tokyo will announce the completion of a quest that began with that 1999 paper: a universal algorithm for folding origami shapes that guarantees a minimum number of seams.

"In 1999, we proved that you could fold any polyhedron, but the way that we showed how to do it was very inefficient," Demaine says. "It's efficient if your initial piece of paper is super-long and skinny. But if you were going to start with a square piece of paper, then that old method would basically fold the square paper down to a thin strip, wasting almost all the material. The new result promises to be much more efficient. It's a totally different strategy for thinking about how to make a polyhedron."

Demaine and Tachi are also working to implement the algorithm in a new version of Origamizer, the free software for generating origami crease patterns whose first version Tachi released in 2008.

Maintaining boundaries

The researchers' algorithm designs crease patterns for producing any polyhedron -- that is, a 3-D surface made up of many flat facets. Computer graphics software, for instance, models 3-D objects as polyhedra consisting of many tiny triangles. "Any curved shape you could approximate with lots of little flat sides," Demaine explains.

Technically speaking, the guarantee that the folding will involve the minimum number of seams means that it preserves the "boundaries" of the original piece of paper. Suppose, for instance, that you have a circular piece of paper and want to fold it into a cup. Leaving a smaller circle at the center of the piece of paper flat, you could bunch the sides together in a pleated pattern; in fact, some water-cooler cups are manufactured on this exact design.

In this case, the boundary of the cup -- its rim -- is the same as that of the unfolded circle -- its outer edge. The same would not be true with the folding produced by Demaine and his colleagues' earlier algorithm. There, the cup would consist of a thin strip of paper wrapped round and round in a coil -- and it probably wouldn't hold water.

"The new algorithm is supposed to give you much better, more practical foldings," Demaine says. "We don't know how to quantify that mathematically, exactly, other than it seems to work much better in practice. But we do have one mathematical property that nicely distinguishes the two methods. The new method keeps the boundary of the original piece of paper on the boundary of the surface you're trying to make. We call this watertightness."

A closed surface -- such as a sphere -- doesn't have a boundary, so an origami approximation of it will require a seam where boundaries meet. But "the user gets to choose where to put that boundary," Demaine says. "You can't get an entire closed surface to be watertight, because the boundary has to be somewhere, but you get to choose where that is."

Lighting fires

The algorithm begins by mapping the facets of the target polyhedron onto a flat surface. But whereas the facets will be touching when the folding is complete, they can be quite far apart from each other on the flat surface. "You fold away all the extra material and bring together the faces of the polyhedron," Demaine says.

Folding away the extra material can be a very complex process. Folds that draw together multiple faces could involve dozens or even hundreds of separate creases.

Developing a method for automatically calculating those crease patterns involved a number of different insights, but a central one was that they could be approximated by something called a Voronoi diagram. To understand this concept, imagine a grassy plain. A number of fires are set on it simultaneously, and they all spread in all directions at the same rate. The Voronoi diagram -- named after the 19th-century Ukrainian mathematician Gyorgy Voronoi -- describes both the location at which the fires are set and the boundaries at which adjacent fires meet. In Demaine and Tachi's algorithm, the boundaries of a Voronoi diagram define the creases in the paper.

"We have to tweak it a little bit in our setting," Demaine says. "We also imagine simultaneously lighting a fire on the entire polygon of the polyhedron and growing out from there. But that concept was really useful. The challenge is to set up where to light the fires, essentially, so that the Voronoi diagram has all the properties we need."

###

Additional background

Paper: "Origamizer: A Practical Algorithm for Folding Any Polyhedron http://erikdemaine.org/papers/Origamizer.../paper.pdf

ARCHIVE: "Super Mario Brothers" is hard http://news.mit.edu/2016/mario-brothers-...space-0601

ARCHIVE: Origami robot folds itself up, crawls away http://news.mit.edu/2014/mobile-folding-robots-0807

ARCHIVE: Bake your own robot http://news.mit.edu/2014/bake-your-own-robot-0530

ARCHIVE: The math of the Rubik's cube http://news.mit.edu/2011/rubiks-cube-0629

- - -
Reply


Possibly Related Threads…
Thread Author Replies Views Last Post
  Research 'Dark force' theory could solve 2 open cosmic mysteries C C 0 72 Dec 10, 2023 10:55 PM
Last Post: C C
  A peculiar protected structure links Viking knots with quantum vortices C C 0 147 Dec 13, 2022 09:08 AM
Last Post: C C
  Using optical data to reveal basic structure of spacetime in rotating frames C C 0 137 May 11, 2021 07:57 PM
Last Post: C C
  Cosmic global warming C C 0 172 Nov 11, 2020 01:04 AM
Last Post: C C
  Why is glass rigid? Signs of its secret structure emerge. C C 0 137 Jul 10, 2020 07:47 PM
Last Post: C C
  Has reductionism run its course? + 'Quantum foam' may explain away huge cosmic energy C C 1 278 Oct 7, 2019 09:15 PM
Last Post: Magical Realist
  Space: The final illusion C C 1 348 Apr 9, 2019 11:09 PM
Last Post: Syne
  Mathematicians have disproved the strong cosmic censorship conjecture + Skyrmions C C 1 682 May 19, 2018 07:28 PM
Last Post: Ostronomos
  Chemists argue end of RNA hypothesis + Cosmic shape (maths) + Euro quantum future C C 0 459 Dec 20, 2017 07:41 PM
Last Post: C C
  Converting music to topology + Is gravity an illusion? C C 0 327 Oct 6, 2017 09:33 PM
Last Post: C C



Users browsing this thread: 1 Guest(s)