Photos of popped balloon
Locked
 
|
============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives back to 2003: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove |
|
|
For two summers while I was an undergrad I worked on a crack propagation project that was using high speed photography to image crack propagation on thin seamless 18” copper cylinders. During the first summer, I made the cylinders by first making solid wax molds that I lathed to the right shape. I then electroplated copper on them before melting the wax away. The second summer I worked on the photography side which was right out of Muybridge. The film was in a 6 foot in diameter ring. In the middle was a spinning prism at the end of a turbine which sent the light around the ring of film. The whole thing was triggered by the crack breaking a small wire. We all had to hide behind a barrier during each run as the whole assembly
was pretty delicately balanced. Ed ____________ Ed Angel Founding Director, Art, Research, Technology and Science Laboratory (ARTS Lab) Professor Emeritus of Computer Science, University of New Mexico 1017 Sierra Pinon
============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives back to 2003: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove |
|
|
How did the melting wax exit the sphere? Probably a hole. So how did you patch the hole to retain perfect symmetry T? On Fri, Feb 1, 2019, 10:03 PM Edward Angel <[hidden email] wrote:
============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives back to 2003: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove |
|
|
I think they were cylinders, not spheres, so there were two holes. This is where we start talking about homology groups. --Barry On 2 Feb 2019, at 12:56, Tom Johnson wrote:
============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives back to 2003: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove |
|
|
Yes. Cylinders not Spheres. Once I had lathed the wax and electroplated the copper shell, I put the heat back up in my vat and the wax melted and the cylinder slid off, They then crushed my precious cylinders I had worked so hard to make.
Ed ____________ Ed Angel Founding Director, Art, Research, Technology and Science Laboratory (ARTS Lab) Professor Emeritus of Computer Science, University of New Mexico 1017 Sierra Pinon
============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives back to 2003: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove |
|
|
In reply to this post by Barry MacKichan
> I think they were cylinders, not spheres, so there were two holes. This
> is where we start talking about homology groups. We don't absolutely *have* to. The theories of Riemann surfaces and algebraic functions got pretty far just having the (proto-homological, but very ungroupy) notions of "simple connectivity" vs. "multiple connectivity". [For those readers, possibly consisting of Nick alone, here's what that means. Suppose you produce a thin sheet of copper by electroplating onto some or all of the surface of a solid piece of wax that you then melt away. For instance, you get a cylindrical surface if you start with a solid wax cylinder and only electroplate onto its lateral surface, leaving the round disks at its two ends unplated; and it will be possible to melt the wax away without cutting a hole in the copper. On the other hand, you get a spherical surface if you start with a solid round ball of wax and electroplate onto its entire surface (let's not worry about how you do that...); in that case, you'll have to puncture the sphere (maybe cutting out a little disk around the south pole) to let the melted wax escape. Just make one hole! (And don't worry about possible difficulties draining out all the wax, okay?) For a third example, start with a piece of wax in the shape of a donut (a so-called "solid torus" or, in a charmingly antique idiom, an "anchor ring"); the resulting copper surface is a "torus" plain and simple. Again, a single hole will suffice to drain the (idealized) wax; again, don't make any others. Now take your pair of metal shears and start cutting somewhere on an edge of the copper sheet. In the cylinder example, you have two edges, each of them a circle at one end of the cylinder. In the sphere and torus examples, you have a single (circular) edge, around the hole you drained the wax through. It is a fact (which I hope you can imagine visually with no trouble, because all this electroplating would be expensive and difficult) that no matter how you the sphere-with-one-hole with your shears, starting and ending at edge points, you will cut the copper into two pieces. It is also a fact that on both the cylinder and the once-punctured (i.e., drained) torus, there are *some* ways to cut from an edge point to another edge point that do *not* cut the copper into two pieces. (On the cylinder, you have to start somewhere on one of the two circular edges and end somewhere on the other: when you've done that you can unroll the cylinder flat onto a table. On the once-punctured torus, there are many very different ways to make such a "non-separating" cut.) Riemann and Co. described this qualitative distinction between the surface of a sphere and the (lateral) surface of a cylinder (and torus, etc., etc.) by calling a sphere "simply connected" and the others "multiply connected". "Simple" here is like 0, and "multiple" like "a strictly positive integer", which began the process of refining the qualitative distinction into a quantitative distinction. Very soon the quantitative distinction was refined much more by making the various positive integers distinct (so the "cut number" of the sphere is 0, the cut number of the cylinder is 1, and--as it turns out--the cut number of the torus is 2). Rather later, this quantitative distinction became more refined. Eventually it became *so* refined that "homology groups" appeared as the best way to describe the refinements. It is quite possible that the mathematical physicist John Baez, Joan's younger cousin, wrote all this stuff up very clearly 15 or 20 years ago. If so, it would be findable with Google.] ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives back to 2003: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove |
|
|
When I brought up homology I (for real) thought that in this case there are so many alternatives I could have used. A short start of a list: homology and cohomology homotopy triangulating the surface and counting vertices, edges, triangles, … with signs looking a functions on the surface and counting its critical points with signs based on the types of critical points (max, min, saddle, etc) — Morse theory summing (with signs) the dimensionality of solutions of certain partial differential equations on the surface properties of open coverings of the surface (Čech cohomology) a bunch of physics stuff once you accept the space-time, or wherever your interest lies, might be more complicated. I tend to think of all these things as the petals of a daisy which all intersect at the center — an indication that the ideas here are fundamental. --Barry On 4 Feb 2019, at 11:32, [hidden email] wrote:
============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives back to 2003: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove |
|
|
In reply to this post by lrudolph
Holy Moly, Lee. With text books like that, I coulda beena mathematician
after all! Nick Nicholas S. Thompson Emeritus Professor of Psychology and Biology Clark University http://home.earthlink.net/~nickthompson/naturaldesigns/ -----Original Message----- From: Friam [mailto:[hidden email]] On Behalf Of [hidden email] Sent: Monday, February 04, 2019 9:33 AM To: The Friday Morning Applied Complexity Coffee Group <[hidden email]> Subject: Re: [FRIAM] Photos of popped balloon > I think they were cylinders, not spheres, so there were two holes. > This is where we start talking about homology groups. We don't absolutely *have* to. The theories of Riemann surfaces and algebraic functions got pretty far just having the (proto-homological, but very ungroupy) notions of "simple connectivity" vs. "multiple connectivity". [For those readers, possibly consisting of Nick alone, here's what that means. Suppose you produce a thin sheet of copper by electroplating onto some or all of the surface of a solid piece of wax that you then melt away. For instance, you get a cylindrical surface if you start with a solid wax cylinder and only electroplate onto its lateral surface, leaving the round disks at its two ends unplated; and it will be possible to melt the wax away without cutting a hole in the copper. On the other hand, you get a spherical surface if you start with a solid round ball of wax and electroplate onto its entire surface (let's not worry about how you do that...); in that case, you'll have to puncture the sphere (maybe cutting out a little disk around the south pole) to let the melted wax escape. Just make one hole! (And don't worry about possible difficulties draining out all the wax, okay?) For a third example, start with a piece of wax in the shape of a donut (a so-called "solid torus" or, in a charmingly antique idiom, an "anchor ring"); the resulting copper surface is a "torus" plain and simple. Again, a single hole will suffice to drain the (idealized) wax; again, don't make any others. Now take your pair of metal shears and start cutting somewhere on an edge of the copper sheet. In the cylinder example, you have two edges, each of them a circle at one end of the cylinder. In the sphere and torus examples, you have a single (circular) edge, around the hole you drained the wax through. It is a fact (which I hope you can imagine visually with no trouble, because all this electroplating would be expensive and difficult) that no matter how you the sphere-with-one-hole with your shears, starting and ending at edge points, you will cut the copper into two pieces. It is also a fact that on both the cylinder and the once-punctured (i.e., drained) torus, there are *some* ways to cut from an edge point to another edge point that do *not* cut the copper into two pieces. (On the cylinder, you have to start somewhere on one of the two circular edges and end somewhere on the other: when you've done that you can unroll the cylinder flat onto a table. On the once-punctured torus, there are many very different ways to make such a "non-separating" cut.) Riemann and Co. described this qualitative distinction between the surface of a sphere and the (lateral) surface of a cylinder (and torus, etc., etc.) by calling a sphere "simply connected" and the others "multiply connected". "Simple" here is like 0, and "multiple" like "a strictly positive integer", which began the process of refining the qualitative distinction into a quantitative distinction. Very soon the quantitative distinction was refined much more by making the various positive integers distinct (so the "cut number" of the sphere is 0, the cut number of the cylinder is 1, and--as it turns out--the cut number of the torus is 2). Rather later, this quantitative distinction became more refined. Eventually it became *so* refined that "homology groups" appeared as the best way to describe the refinements. It is quite possible that the mathematical physicist John Baez, Joan's younger cousin, wrote all this stuff up very clearly 15 or 20 years ago. If so, it would be findable with Google.] ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives back to 2003: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives back to 2003: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove |
| Free forum by Nabble | Edit this page |