Persistence of Homology

I recently started reading Topology for Computing by Afra J. Zomorodian, and before it launched into its admirably lucid explanation of topology, group theory and the like, it featured a clever illustration by the author:

Bookmarks for August 20th through August 23rd

These are my links for August 20th through August 23rd:

  • Fallacies of Risk (application/pdf Object) – In addition to traditional fallacies such as ad hominem, discussions of risk contain logical and argumentative fallacies that are specific to the subject-matter. Ten such fallacies are identified, that can commonly be found in public debates on risk. They are named as follows: the sheer size fallacy, the converse sheer size fallacy, the fallacy of naturalness, the ostrich's fallacy, the proof-seeking fallacy, the delay fallacy, the technocratic fallacy, the consensus fallacy, the fallacy of pricing, and the infallibility fallacy.
  • NIST/SEMATECH e-Handbook of Statistical Methods – The e-Handbook provides a comprehensive overview of statistical methods, including experiment design, data analysis and quality control. It is tailored to the needs of engineers and scientists for rapid understanding and quick solution of statistical problems so that they can get back to their primary work. The approach is problem-oriented and includes detailed case studies from the semiconductor industry and from NIST laboratories to illustrate statistical approaches to solving engineering and scientific problems. The Web site also includes links to integrated software packages.
  • Itamar Pitowsky, From logic to physics: How the meaning of computation changed over time | PhilPapers – The intuition guiding the definition of computation has shifted over time, a process that is reflected in the changing formulations of the Church-Turing thesis. The theory of computation began with logic and gradually moved to the capacity of finite automata. Consequently, modern computer models rely on general physical principles, with quantum computers representing the extreme case. The paper discusses this development, and the challenges to the Church-Turing thesis in its physical form, in particular, Kieu’s quantum computer and relativistic hyper-computation. Finally, the robustness of the boundary between polynomial and exponential time complexity is considered in connection with quantum computers and quantum information theory.
  • 30 Classic Games for Simple Outdoor Play | GeekDad | Wired.com – When I was a kid, we played outside with the other kids in the neighborhood with most of our free time. We also made the most of recess at school. We kept ourselves quite occupied without any of today’s modern technologies. Listed below are some no-tech games that you may have enjoyed as a kid. I sure did. Some can be done indoors. Some can be done by yourself or with just one friend. But most of them are best when done outside with a group of people. Also, most of these games can be changed or improved by making up your own rules. Use your imagination!
  • Mark Colyvan, A topological sorites | PhilPapers – This paper considers a generalisation of the sorites paradox, in which only topological notions are employed. We argue that by increasing the level of abstraction in this way, we see the sorites paradox in a new, more revealing light—a light that forces attention on cut-off points of vague predicates. The generalised sorites paradox presented here also gives rise to a new, more tractable definition of vagueness.

Bookmarks for August 17th through August 20th

These are my links for August 17th through August 20th:

  • Mark Colyvan, A topological sorites | PhilPapers – This paper considers a generalisation of the sorites paradox, in which only topological notions are employed. We argue that by increasing the level of abstraction in this way, we see the sorites paradox in a new, more revealing light—a light that forces attention on cut-off points of vague predicates. The generalised sorites paradox presented here also gives rise to a new, more tractable definition of vagueness.
  • Vincent F. Hendricks, The Bain of two truths | PhilPapers – A view among methodologists is that truth and convergence are related in such a way that scientific theories in their historical order of appearance contribute to the convergence to an ultimate ideal theory. It is not a fact that science develops accordingly but rather a hypothetical thought experiment to explain why science develops at all. Here, a simple formal model is presented for scrutinizing the relations between two truths and convergence.
  • Risk (Stanford Encyclopedia of Philosophy) – Since the 1970s, studies of risk have grown into a major interdisciplinary field of research. Although relatively few philosophers have focused their work on risk, there are important connections between risk studies and several philosophical subdisciplines. This entry summarizes the most well-developed of these connections and introduces some of the major topics in the philosophy of risk. It consists of five sections dealing with the definition of risk and with treatments of risk related to epistemology, the philosophy of science, ethics, and the philosophy of economics.
  • The Management Myth – The Atlantic (June 2006) – Most of management theory is inane, writes our correspondent, the founder of a consulting firm. If you want to succeed in business, don’t get an M.B.A. Study philosophy instead

Bookmarks for July 8th through July 29th

These are my links for July 8th through July 29th:

  • Should Copyright Of Academic Works Be Abolished? – The conventional rationale for copyright of written works, that copyright is needed to foster their creation, is seemingly of limited applicability to the academic domain. For in
    a world without copyright of academic writing, academics would still benefit from publishing in the major way that they do now, namely, from gaining scholarly esteem.
    Yet publishers would presumably have to impose fees on authors, because publishers
    would not be able to profit from reader charges. If these publication fees would be borne
    by academics, their incentives to publish would be reduced. But if the publication fees
    would usually be paid by universities or grantors, the motive of academics to publish
    would be unlikely to decrease (and could actually increase) – suggesting that ending
    academic copyright would be socially desirable in view of the broad benefits of a
    copyright-free world…
  • BBC – Radio 4 In Our Time – Philosophy Archive – You can listen again to all the programmes online. The most recent programmes appear at the top of the page.
  • [0907.1579] The Computational Power of Minkowski Spacetime – The Lorentzian length of a timelike curve connecting both endpoints of a classical computation is a function of the path taken through Minkowski spacetime. The associated runtime difference is due to time-dilation: the phenomenon whereby an observer finds that another's physically identical ideal clock has ticked at a different rate than their own clock. Using ideas appearing in the framework of computational complexity theory, time-dilation is quantified as an algorithmic resource by relating relativistic energy to an $n$th order polynomial time reduction at the completion of an observer's journey. These results enable a comparison between the optimal quadratic \emph{Grover speedup} from quantum computing and an $n=2$ speedup using classical computers and relativistic effects. The goal is not to propose a practical model of computation, but to probe the ultimate limits physics places on computation.
  • How to choose a statistical test – This book has discussed many different statistical tests. To select the right test, ask yourself two questions: What kind of data have you collected? What is your goal? Then refer to Table 37.1.
  • NPWRC :: Statistical Significance Testing – Four basic steps constitute statistical hypothesis testing. First, one develops a null hypothesis about some phenomenon or parameter. This null hypothesis is generally the opposite of the research hypothesis, which is what the investigator truly believes and wants to demonstrate. Research hypotheses may be generated either inductively, from a study of observations already made, or deductively, deriving from theory. Next, data are collected that bear on the issue, typically by an experiment or by sampling. (Null hypotheses often are developed after the data are in hand and have been rummaged through, but that's another topic.)
  • Data Mining Techniques – Data Mining is an analytic process designed to explore data (usually large amounts of data – typically business or market related) in search of consistent patterns and/or systematic relationships between variables, and then to validate the findings by applying the detected patterns to new subsets of data. The ultimate goal of data mining is prediction – and predictive data mining is the most common type of data mining and one that has the most direct business applications.