Department of Mathematics

La Jolla, CA 92093

United States of America

Email: dp-rideout at pm.me

My publications according to Google scholar

Math 20B Calculus for Science and Engineering II

Math 102 Applied Linear Algebra

Math 103A Modern Algebra I

A good introduction for 'laypersons' can be found at the Albert Einstein Institute's "Einstein online" site.

Below is a demonstration of the Lorentz invariant character of causal sets. The top left image is a square region of 1+1 Minkowski space, into which has been sprinkled 4096 points. To the right is a blow up of a small region of the original region. The bottom left image shows the same points as viewed by an observer moving at v=-4/5. The same region (by the v=0 observer's coordinates) is blown up on the right. The arrangement of points is not literally the same, of course, but it is also a random Poisson sprinkling, of the same density.

The growth process is depicted by the *poset of finite causal sets*, sometimes called *poscau*, in which two causets are related (in the poset's order) if one can reach the other by a sequence of sequential growth. (Equivalently, a causet *A* comes before, or precedes, *B*, if *B* contains a past-closed subcauset which is isomorphic to *A*.) I have generated diagrams of poscau for all causets up to four elements, and five. The green or blue arrows indicate gregarious children (those which arise when the new element appears unrelated to any others), and red arrows timid children (the child which occurs when the new element appears above the entire parent causet). The numbers attached to the edges give the "number of ways to transition from the parent to the child". All these are explained in detail in my paper with Rafael Sorkin on the subject, or in my Ph.D. thesis, both of which are available on arXiv.org.
[These diagrams are available in a variety of file formats, colors schemes, and licenses. Please write me at the above email address to inquire on details. I grant permission to use the images in presentation slides, provided the attribution and copyright notice remain intact. Please also write if you detect an error!]

Below are some Hasse diagrams of random causal sets generated by the transitive percolation dynamics. The colors of the links do not play an essential role. (The purple links connect elements on neighboring 'layers', where the layer of an element is the length of the longest past directed chain which ends at that element. The green links span multiple layers.)

The following movies depict sequential growth of a region of 2+1 Minkowski space:

slow
and
fast
and
fast, and larger

Link to Rafael Sorkin's Sixtieth Birthday Celebration.

David Meyer's thesis on the dimension of causal sets is available from MIT. If you have trouble obtaining it feel free to drop me a note. I also have paper copies of Luca Bombelli's and Alan Daughton's theses.

A topical school on causal sets held at Imperial College London from 18-22 September 2006.

`Slides' from the last day of the Causal Set mini-conference held December 2000.

Some VRML images of causal sets embedded into three dimensions that I made in 1997.

"The fear of the LORD is the beginning of wisdom..."

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