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**1 - 5**of**5**### THE NATURE OF CONTEMPORARY CORE MATHEMATICS

, 2010

"... Abstract. The goal of this essay is a description of modern mathematical practice, with emphasis on differences between this and practices in the nineteenth century. I explain how and why these differences greatly increased the effectiveness of mathematical methods and enabled sweeping developments ..."

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Abstract. The goal of this essay is a description of modern mathematical practice, with emphasis on differences between this and practices in the nineteenth century. I explain how and why these differences greatly increased the effectiveness of mathematical methods and enabled sweeping developments in the twentieth century. A particular concern is the significance for mathematics education: elementary education remains modeled on the mathematics of the nineteenth century and before, and use of modern methodologies might give advantages similar to those seen in mathematics. This draft is about 90 % complete, and comments are welcome. 1.

### Self-Replicating Space-Cells and the Cosmological Constant

, 706

"... We consider what the implications would be if there were a discrete fundamental model of physics based on locally-finite self-interacting information, in which there is no presumption of the familiar space and laws of physics, but from which such space and laws can nevertheless be shown to be able t ..."

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We consider what the implications would be if there were a discrete fundamental model of physics based on locally-finite self-interacting information, in which there is no presumption of the familiar space and laws of physics, but from which such space and laws can nevertheless be shown to be able to emerge stably from such a fundamental model. We argue that if there is such a model, then the familiar laws of physics, including Standard Model constants, etc., must be encodable by a finite quantity C, called the complexity, of self-interacting information I, called a Space-Cell. Copies of Space-Cell I must be distributed throughout space, at a roughly constant and near-Planck density, and copies must be created or destroyed as space expands or contracts. We then argue that each Space-Cell is a self-replicator that can duplicate in times ranging from as fast as near-Planck-times to as slow as Cosmological-Constant-time which is 10 61 Planck-times. From standard considerations of computation, we argue this slowest duplication rate just requires that 10 61 is less than about 2 C, the number of length-C binary strings, hence requiring only the modest complexity C at least 203, and at most a few thousand. We claim this provides a reasonable explanation for a dimensionless constant being as large as 10 61, and hence for the Cosmological Constant being a tiny positive 10 −122. We also discuss a separate conjecture on entropy flow in Hole-Bang Transitions. We then present Cosmological Natural Selection II. 1

### Quiver Gauge Theory and Conformality at the Large Hadron Collider

, 706

"... This review describes the conformality approach to extending the standard model of particle phenomenology using an assumption of no conformal anomaly at high energy. Topics include quiver gauge theory, the conformality approach to phenomenology, strong-electroweak unification at 4 TeV, cancellation ..."

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This review describes the conformality approach to extending the standard model of particle phenomenology using an assumption of no conformal anomaly at high energy. Topics include quiver gauge theory, the conformality approach to phenomenology, strong-electroweak unification at 4 TeV, cancellation of quadratic divergences, cancellation of U(1) anomalies, and a dark matter candidate. Table of Contents 1.

### Quiver Gauge Theory and Conformality at the TeV Scale

, 706

"... This review describes the conformality approach to extending the standard model of particle phenomenology using an assumption of no conformal anomaly at high energy. Topics include quiver gauge theory, the conformality approach to phenomenology, strong-electroweak unification at 4 TeV, cancellation ..."

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This review describes the conformality approach to extending the standard model of particle phenomenology using an assumption of no conformal anomaly at high energy. Topics include quiver gauge theory, the conformality approach to phenomenology, strong-electroweak unification at 4 TeV, cancellation of quadratic divergences, cancellation of U(1) anomalies, and a dark matter candidate. Table of Contents 1.

### Particle phenomenology and Maldacena

, 804

"... Abstract. A brief review is offered of employing Maldacena’s AdS/CFT correspondence in attempting to identify a model which extends to higher energy the standard model of particle phenomenology. ..."

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Abstract. A brief review is offered of employing Maldacena’s AdS/CFT correspondence in attempting to identify a model which extends to higher energy the standard model of particle phenomenology.