Hanson born is an American theoretical physicist and computer scientist. Hanson is best known in theoretical physics as the co-discoverer of the Eguchi-Hanson Metric , [2] the first Gravitational instanton. This Einstein metric is asymptotically locally Euclidean and self-dual, closely parallel to the Yang-Mills instanton. He is also known as the co-author of Constrained Hamiltonian Systems [3] and of Gravitation, Gauge Theories, and Differential Geometry, [4] which attempted to bridge the gap between theoretical physicists and mathematicians at a time when concepts relevant to the two disciplines were rapidly unifying. His subsequent work in computer science focused on computer graphics and visualization of exotic mathematical objects, including widely used images of the Calabi-Yau quintic cross-sections used to represent the hidden dimensions of dimensional string theory. He is the author of Visualizing Quaternions.

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My participation in the history of computing began in high-school when I was a programmer for the PLATO computer-based teaching project, for which I implemented one of the first functional simultaneous multiuser operating system kernels. A basic chart of my personal academic genealogy can be found here , and a more detailed graphical representation, including my Ph. My family also has connections with the history of physics through the Manhattan Project. On July , , our family survived the sinking of the ocean liner Andrea Doria.

Some musings along with graphics of the Doria sinking that I wrote to accompany a talk I gave on July 26, the 57th anniversary can be found here. In May , I contributed an oral history on my childhood Andrea Doria experience similar to the written memoir to the StoryCorps archive. An excerpt is at the very end after of this WFIU public media broadcast. My mother not only survived the Doria, but was one of the oldest among those survivors upon her death at age 98 in the 60th anniversary ; in , she published a unique environment-oriented book, "East-Central Illinois: Exploring the Beginnings" on the geological, ecological, and cultural history of the plains of central Illinois website and hardcopy orders here.

The family has now released the eBook for free download here. My Google Scholar Profile gives a nice picture of the various fields I have worked in. This was an OpenGL-based course introducing the mathematical foundations and practical programming methods of modern interactive computer graphics.

The course emphasized creating interactive interfaces to help understand the graphics objects and techniques being studied.

Lighting and simple material modeling were covered as an introduction to the creation of realistic images. Public B syllabus: Overview of B This course focused on Mathematica-based methods of producing rapid prototypes solving complex software modeling problems.

This class introduced the Mathematica programming environment, and incorporated Mathematica prototyping methods implicitly into a broad survey of mathematical modeling methods, techniques, and folklore used widely throughout computer science, computer graphics, scientific visualization, mathematics, and physics. Interactive Mathematics Interfaces: Quaternion Rotations This WebGL App implemented by Leif Christiansen from a corresponding OpenGL desktop application uses the left-mouse or 1-finger drag to apply a 3D rotation to a triad of axes, each corresponding to a column of a 3D rotation matrix.

As the rotations accumulate, the left-hand bar shows the corresponding quaternion q0 component, and the thick tube emanating from the origin shows the qx,qy,qz 3-vector component. The entire viewpoint can be rotated without changing the matrix or its quaternion components using mouse-right, and alt-left-mouse restricts the rotation to the z-axis for pedagogical study.

The application is here: The QuatRot App. On a touch-screen device, check the boxes for fixed z-axis and xw-plane and yw-plane rotation to change from 1-finger 3D rotation to the above 4D operations. More details below. Images of Mathematical Physics: Images of the Calabi-Yau Quintic: Hidden dimensions of string theory Shown below are my graphical representations of the Calabi-Yau quintic representing the hidden dimensions of string theory, based on my paper.

These were made available on the Wiki Commons domain in , and clicking on the images takes you to the source material. The first is a 2-dimensional cross-section of the quintic in CP2, and the second is a complete 6-dimensional representation of the local C4 quintic embedded in CP4 using 4D discrete samples in a C2 subspace to produce a hypercubic array of the corresponding varying 2D cross-sections.

We review the problem of transforming matching collections of data points into optimal correspondence. The classic RMSD root-mean-square deviation method sometimes referred to as the "Orthogonal Procrustes Problem," calculates a 3D rotation that minimizes the RMSD of a set of test data points relative to a reference set of corresponding points.

Similar literature threads in aeronautics, photogrammetry, and proteomics employ an approach based on the maximal eigenvalue of a particular 4x4 quaternion-based matrix, thus specifying the quaternion eigenvector corresponding to the optimal 3D rotation.

Much of the literature uses numerical methods to solve this eigenvalue problem; we also explore the features of algebraic solutions based on the 16th century solutions of the quartic equation. In addition, we show how these methods can be extended to include orientation frame matching using quaternion frame representations.

Further extensions of the quaternion method are given for 4D spatial coordinate and 4D orientation frame data sets. DOI: We present a mathematical framework based on quantum interval-valued probability measures to study the effect of experimental imperfections and finite precision mesasurements on defining aspects of quantum mechanics such as contextuality and the Born rule.

This work continues our systematic investigation into finite precision, limited resources, and errorful processes in quantum mechanics. Hanson and Ji-Ping Sha, pp. Phua, H. Xiong, World Scientific Pub. A local copy can be found here. Memories of Kerson Huang, by Andrew J.

Hanson, pp. Frisch, A. Berdyugin, V. Piirola, A. Magalhaes, D. Seriacopi, S. Wiktorowicz, B-G Andersson, H. Funsten, D. McComas, N. Schwadron, J. Slavin, A. Hanson, and C. Fu, appearing in Astrophysical Journal, November, A: Math.

This work continues a systematic investigation of the formulation of discrete quantum computing using finite fields, and introduces that concept of Cardinal Probability as a way of dealing with probabilistic concepts in the absence of ordered numbers for finite fields. The DOI link is doi Tullis, Robert L. Goldstone, and Andrew J. Andrew J.

A local copy is here. Hanson, and Pheng-Ann Heng. Multitouching the Fourth Dimension. The IEEE site for the article is here , and a local copy can be found here. Popodi, Andrew J. Hanson, and Patricia L. June Accepted manuscript posted online 22 June DOI link is here doi Mutational Topology of the Bacterial Genome.

By Patricia L. Foster, Andrew J. Hanson and S. The paper PDF site is here , and a local copy can be found here. Presentations and Talks: Talk. The 4D Room, Andrew J. Discrete Quantum Computing, Andrew J. The Bugcatcher. Quaternion Applications. New application topics included optimal, smoothly controllable tubing and tube texturing, quaternion protein maps, and how dual quaternions solve the century-old conundrum of how a quaternion acts on a vector.

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## Andrew J. Hanson

Search Menu Abstract The existing thermodynamics of the cosmological horizon in de Sitter spacetime is established in the micro-canonical ensemble, while the thermodynamics of black hole horizons is established in the canonical ensemble. Generally in the ordinary thermodynamics and statistical mechanics, both of the micro-canonical and canonical ensembles yield the same equation of state for any thermodynamic system. This implies the existence of a formulation of de Sitter thermodynamics based on the canonical ensemble. This paper reproduces the de Sitter thermodynamics in the canonical ensemble. The procedure is as follows: We put a spherical wall at the center of de Sitter spacetime, which has negligible mass and perfectly reflects the Hawking radiation coming from the cosmological horizon. Then the region enclosed by the wall and horizon settles down to a thermal equilibrium state, for which the Euclidean action is evaluated and the partition function is obtained.

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## Andrew J. Hanson's Home Page

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