Euler Characteristic in Odd Dimensions

It is well known that the Euler characteristic of an odd dimensional compact manifold is zero. An Euler complex is a combinatorial analogue of a compact manifold. We present here an elementary proof of the corresponding result for Euler complexes

Clarifying spatial distance measurement

We examine length measurement in curved spacetime, based on the 1+3-splitting of a local observer frame. This situates extended objects within spacetime, in terms of a given coordinate which serves as an external reference. The radar metric is shown to coincide with the spatial projector, but these only give meaningful results on the observer's 3-space, where they reduce to the metric. Examples from Schwarzschild spacetime are given.Comment: 6 pages, 0 figures, submitted to the proceedings of the 2018 Marcel Grossmann conference, Rome. v2 has minor rewording and typo correction

Cosmic cable

I investigate the relativistic mechanics of an extended "cable" in an arbitrary static, spherically symmetric spacetime. Such hypothetical bodies have been proposed as tests of energy and thermodynamics: by lowering objects toward a black hole, scooping up Hawking radiation, or mining energy from the expansion of the universe. I review existing work on stationary cables, which demonstrates an interesting "redshift" of tension, and extend to a case of rigid motion. By using a partly restrained cable to turn a turbine, the energy harvested is up to the equivalent of the cable's rest mass, concurring with the quasistatic case. Still, the total Killing energy of the system is conserved.Comment: 6 pages, 0 figures, submitted to the proceedings of the 2018 Marcel Grossmann conference in Rom

The impact of artificial intelligence on jobs and work in New Zealand

Artificial Intelligence (AI) is a diverse technology. It is already having significant effects on many jobs and sectors of the economy and over the next ten to twenty years it will drive profound changes in the way New Zealanders live and work. Within the workplace AI will have three dominant effects. This report (funded by the New Zealand Law Foundation) addresses: Chapter 1 Defining the Technology of Interest; Chapter 2 The changing nature and value of work; Chapter 3 AI and the employment relationship; Chapter 4 Consumers, professions and society. The report includes recommendations to the New Zealand Government

On the alleged simplicity of impure proof

Roughly, a proof of a theorem, is “pure” if it draws only on what is “close” or “intrinsic” to that theorem. Mathematicians employ a variety of terms to identify pure proofs, saying that a pure proof is one that avoids what is “extrinsic,” “extraneous,” “distant,” “remote,” “alien,” or “foreign” to the problem or theorem under investigation. In the background of these attributions is the view that there is a distance measure (or a variety of such measures) between mathematical statements and proofs. Mathematicians have paid little attention to specifying such distance measures precisely because in practice certain methods of proof have seemed self- evidently impure by design: think for instance of analytic geometry and analytic number theory. By contrast, mathematicians have paid considerable attention to whether such impurities are a good thing or to be avoided, and some have claimed that they are valuable because generally impure proofs are simpler than pure proofs. This article is an investigation of this claim, formulated more precisely by proof- theoretic means. After assembling evidence from proof theory that may be thought to support this claim, we will argue that on the contrary this evidence does not support the claim

Algorithmic Decision-Making and the Control Problem

Abstract: The danger of human operators devolving responsibility to machines and failing to detect cases where they fail has been recognised for many years by industrial psychologists and engineers studying the human operators of complex machines. We call it “the control problem”, understood as the tendency of the human within a human–machine control loop to become complacent, over-reliant or unduly diffident when faced with the outputs of a reliable autonomous system. While the control problem has been investigated for some time, up to this point its manifestation in machine learning contexts has not received serious attention. This paper aims to fill that gap. We argue that, except in certain special circumstances, algorithmic decision tools should not be used in high-stakes or safety-critical decisions unless the systems concerned are significantly “better than human” in the relevant domain or subdomain of decision-making. More concretely, we recommend three strategies to address the control problem, the most promising of which involves a complementary (and potentially dynamic) coupling between highly proficient algorithmic tools and human agents working alongside one another. We also identify six key principles which all such human–machine systems should reflect in their design. These can serve as a framework both for assessing the viability of any such human–machine system as well as guiding the design and implementation of such systems generally