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Iterations of the Words-To-Numbers Function
1 2 Journal of Integer Sequences, Vol. 21 (2018), 3 Article 18.9.2 47 6 23 11 Iterations of the Words-to-Numbers Function Matthew E. Coppenbarger School of Mathematical Sciences 85 Lomb Memorial Drive Rochester Institute of Technology Rochester, NY 14623-5603 USA [email protected] Abstract The Words-to-Numbers function takes a nonnegative integer and maps it to the number of characters required to spell the number in English. For each k = 0, 1,..., 8, we determine the minimal nonnegative integer n such that the iterates of n converge to the fixed point (through the Words-to-Numbers function) in exactly k iterations. Our travels take us from some simple answers, to an etymology of the names of large numbers, to Conway/Guy’s established system representing the name of any integer, and finally use generating functions to arrive at a very large number. 1 Introduction and initial definitions The idea for the problem originates in a 1965 book [3, p. 243] by recreational linguistics icon Dmitri Borgmann (1927–85) and in a 1966 article [16] by another icon, recreational mathematician Martin Gardner (1914–2010). Gardner’s article appears again in a book [17, pp. 71–72, 265–267] containing reprinted Gardner articles from Scientific American along with his comments on his reader’s responses. Both Borgmann and Gardner identify the only English number that requires exactly the same number of characters to spell the number as the number represents. Borgmann goes further by identifying numbers in 16 other languages with this property. Borgmann calling such numbers truthful and Gardner calling them honest. -
Cryonics Magazine, Q1 2001
SOURCE FEATURES PAGE Fred Chamberlain Glass Transitions: A Project Proposal 3 Mike Perry Interview with Dr. Jerry Lemler, M.D. 13 Austin Esfandiary A Tribute to FM-2030 16 Johnny Boston FM & I 18 Billy H. Seidel the ALCOR adventure 39 Natasha Vita-More Considering Aesthetics 45 Columns Book Review: Affective Computing..................................41 You Only Go Around Twice .................................................42 First Thoughts on Last Matters............................................48 TechNews.......................................................................51 Alcor update - 19 The Global Membership Challenge . 19 Letter from Steve Bridge . 26 President’s Report . 22 “Last-Minute” Calls . 27 Transitions and New Developments . 24 Alcor Membership Status . 37 1st Qtr. 2001 • Cryonics 1 Alcor: the need for a rescue team or even for ingly evident that the leadership of The Origin of Our Name cryonics itself. Symbolically then, Alcor CSC would not support or even would be a “test” of vision as regards life tolerate a rescue team concept. Less In September of 1970 Fred and extension. than one year after the 1970 dinner Linda Chamberlain (the founders of As an acronym, Alcor is a close if meeting, the Chamberlains severed all Alcor) were asked to come up with a not perfect fit with Allopathic Cryogenic ties with CSC and incorporated the name for a rescue team for the now- Rescue. The Chamberlains could have “Rocky Mountain Cryonics Society” defunct Cryonics Society of California forced a five-word string, but these three in the State of Washington. The articles (CSC). In view of our logical destiny seemed sufficient. Allopathy (as opposed and bylaws of this organization (the stars), they searched through star to Homeopathy) is a medical perspective specifically provided for “Alcor catalogs and books on astronomy, wherein any treatment that improves the Members,” who were to be the core of hoping to find a star that could serve as prognosis is valid. -
Mathematical Circus & 'Martin Gardner
MARTIN GARDNE MATHEMATICAL ;MATH EMATICAL ASSOCIATION J OF AMERICA MATHEMATICAL CIRCUS & 'MARTIN GARDNER THE MATHEMATICAL ASSOCIATION OF AMERICA Washington, DC 1992 MATHEMATICAL More Puzzles, Games, Paradoxes, and Other Mathematical Entertainments from Scientific American with a Preface by Donald Knuth, A Postscript, from the Author, and a new Bibliography by Mr. Gardner, Thoughts from Readers, and 105 Drawings and Published in the United States of America by The Mathematical Association of America Copyright O 1968,1969,1970,1971,1979,1981,1992by Martin Gardner. All riglhts reserved under International and Pan-American Copyright Conventions. An MAA Spectrum book This book was updated and revised from the 1981 edition published by Vantage Books, New York. Most of this book originally appeared in slightly different form in Scientific American. Library of Congress Catalog Card Number 92-060996 ISBN 0-88385-506-2 Manufactured in the United States of America For Donald E. Knuth, extraordinary mathematician, computer scientist, writer, musician, humorist, recreational math buff, and much more SPECTRUM SERIES Published by THE MATHEMATICAL ASSOCIATION OF AMERICA Committee on Publications ANDREW STERRETT, JR.,Chairman Spectrum Editorial Board ROGER HORN, Chairman SABRA ANDERSON BART BRADEN UNDERWOOD DUDLEY HUGH M. EDGAR JEANNE LADUKE LESTER H. LANGE MARY PARKER MPP.a (@ SPECTRUM Also by Martin Gardner from The Mathematical Association of America 1529 Eighteenth Street, N.W. Washington, D. C. 20036 (202) 387- 5200 Riddles of the Sphinx and Other Mathematical Puzzle Tales Mathematical Carnival Mathematical Magic Show Contents Preface xi .. Introduction Xlll 1. Optical Illusions 3 Answers on page 14 2. Matches 16 Answers on page 27 3. -
Etergen Whitepaper.Pages
ETERGEN WHITE PAPER Executive Summary I. Brief History II. The problem III. Solution – business model IV. Token offer V. Our Accountability with Your investments VI. Timeline VII. Our Team Disclamer The ETERGEN Foundation – Live longer. Executive Summary At Eternity foundation we believe that human life is precious. And we want you and your loved ones to live longer. In fact, we are doing everything we can for it, through supporting scientific research in the field of human life extension. With technology and knowledge our society has now, we all can live a longer, healthier life, only if the needed attention was paid to the financing of the research in the field of life extension. We support international medical and scientific research, aimed at human life extension, with system of grants and investments for the best projects. We believe that significant human life extension can be reached within our lifetime. To finance this research, we offer our own cryptocurrency, THE ETER. THE ETER is state of the art cryptocurrency giving you the lowest cost per transaction and true anonymous security . Not only will the ETER help the mankind to solve the most important question we face, but it will also create great value for all the currency holders, since every project, financed by us, will have a contract obligation to share the profits with all the holders. This will be guaranteed through use of smart contracts utilizing the blockchain technology. "1 ETERGEN WHITE PAPER We will build up the industry of human life extension through introducing cutting edge technology. Our key advantages are: A global project A growing multibillion industry with huge growth potential Real value behind the currency Experienced team with high qualifications Unique idea - there is no other project like this. -
Antioxidative Defense Mechanisms in the Aging Brain
Arch. Biol. Sci., Belgrade, 66 (1), 245-252, 2014 DOI:10.2298/ABS1401245J ANTIOXIDATIVE DEFENSE MECHANISMS IN THE AGING BRAIN ZORICA JOVANOVIĆ Department of Pathophysiology, Faculty of Medicine, 34000 Kragujevac, Serbia Abstract - Aging is an extremely complex, multifactorial process that is characterized by a gradual and continuous loss of physiological functions and responses, particularly marked in the brain. A common hallmark in aging and age-related diseases is an increase in oxidative stress and the failure of antioxidant defense systems. Current knowledge indicates that the level of glutathione progressively declines during aging. Because nerve cells are the longest-living cells that exhibit a high consumption rate of oxygen throughout an individual’s lifetime, the brain may be especially vulnerable to oxidative damage and this vulnerability increases during aging. In addition, the brain contains high concentrations of polyunsatu- rated fatty acids and transition metals and low antioxidative defense mechanisms. Although aging is an inevitable event, a growing volume of data confirms that antioxidant supplementation in combination with symptomatic drug treatments reduces oxidative stress and improves cognitive function in aging and age-related diseases. The present review discusses the neuroprotective effects of antioxidants in the aging brain. Key words: Aging, brain, oxidative stress, glutathione, polyphenols OXIDATIVE STRESS AND AGING cells and tissues with advancing age that increase the risk of disease and death”. Later, Harman added The aging process is associated with a progressive a slight modification to this theory to bring special decline in multiple aspects of cognitive perform- attention to the role of the mitochondria in the ag- ance, including reductions in mental speed, atten- ing process because these organelles are a major site tion, memory, hearing, vision and stamina, as well of reactive oxygen species (ROS) generation (Har- as decreases in brain structure size and white mat- man, 1972). -
Anti-Aging 2018
Anti-Aging 2018 Altern verstehen Altern messen Altern behandeln Prof. Dr. Bernd Kleine-Gunk Präsident der Deutschen Gesellschaft für Präventions- und Anti-Aging Medizin (GSAAM) www. kleine-gunk.de Metropol Medical Center Nürnberg Ist Altern eine Krankheit? www. kleine-gunk.de Metropol Medical Center Nürnberg Risikofaktor biologisches Lebensalter ESC Score – Kardiovaskuläre Erkrankungen ¹ DeBacker G et al. European guidelines on cardiovascular disease prevention in clinical practice. The Third Joint Task Force of European and other Societies on Cardiovascular Disease Prevention in Clinical Practice (constituted by representatives of eight societies and by invited experts) executive summary. Eur Heart J 2003; 24: 1601–10. www. kleine-gunk.de Metropol Medical Center Nürnberg Risikofaktor biologisches Lebensalter AGLA Score – Kardiovaskuläre Erkrankungen Eur J Clin Invest. 2007; 37:925-32 www. kleine-gunk.de Metropol Medical Center Nürnberg www. kleine-gunk.de www. Heft 39,2006: 2542-2548 Häusler,Gothe, Göl, Glaeske,Pientka, Felsenberg,Dtsch. Ärzteblatt 103, Jg [%] Anteil der Patienten mit Osteoporose Risikofaktor Lebensalter biologisches 7% 7% 7% 7% 1,3 Mio1,3 Männer 1,3 Mio1,3 Männer Osteoporose in Deutschland in Osteoporose > 75> Jahre 65–74Jahre 50–64Jahre > 75> Jahre 65–74Jahre 50–64Jahre 11% 11% 11% 11% 16% 16% 16% 16% 23% 23% 23% 23% 6,5 Mio Frauen 6,5 Mio Frauen 47% 47% 47% 47% 59% 59% 59% 59% Nürnberg Center Medical Metropol Risikofaktor biologisches Lebensalter Altersabhängige Häufigkeit der Demenz http://www.alzheimerinfo.de/alzheimer/zahlen/index.jsp www. kleine-gunk.de Metropol Medical Center Nürnberg Risikofaktor biologisches Lebensalter Bösartige Neuerkrankungen nach Alter 1989 bis 1998 im Saarland Frauen Quelle der Statistik: Arbeitsgemeinschaft Bevölkerungsbezogener Krebsregister in Deutschland. -
2 the Biology of Ageing
The biology of ageing 2 Aprimer JOAO˜ PEDRO DE MAGALHAES˜ OVERVIEW .......................................................... This chapter introduces key biological concepts of ageing. First, it defines ageing and presents the main features of human ageing, followed by a consideration of evolutionary models of ageing. Causes of variation in ageing (genetic and dietary) are reviewed, before examining biological theories of the causes of ageing. .......................................................... Introduction Thanks to technological progress in different areas, including biomed- ical breakthroughs in preventing and treating infectious diseases, longevity has been increasing dramatically for decades. The life expectancy at birth in the UK for boys and girls rose, respectively, from 45 and 49 years in 1901 to 75 and 80 in 1999 with similar fig- ures reported for other industrialized nations (see Chapter 1 for further discussion). A direct consequence is a steady increase in the propor- tion of people living to an age where their health and well-being are restricted by ageing. By the year 2050, it is estimated that the per- centage of people in the UK over the age of 65 will rise to over 25 per cent, compared to 14 per cent in 2004 (Smith, 2004). The greying of the population, discussed elsewhere (see Chapter 1), implies major medical and societal changes. Although ageing is no longer considered by health professionals as a direct cause of death (Hayflick, 1994), the major killers in industrialized nations are now age-related diseases like cancer, diseases of the heart and 22 Joao˜ Pedro de Magalhaes˜ neurodegenerative diseases. The study of the biological mechanisms of ageing is thus not merely a topic of scientific curiosity, but a crucial area of research throughout the twenty-first century. -
Controversy 2
Controversy 2 WHY DO OUR BODIES GROW OLD? liver Wendell Holmes (1858/1891), in his poem “The Wonderful One-Hoss Shay,” invokes a memorable image of longevity and mortality, the example of a wooden Ohorse cart or shay that was designed to be long-lasting: Have you heard of the wonderful one-hoss shay, That was built in such a logical way, It ran a hundred years to a day . ? This wonderful “one-hoss shay,” we learn, was carefully built so that every part of it “aged” at the same rate and didn’t wear out until the whole thing fell apart all at once. Exactly a century after the carriage was produced, the village parson was driving this marvelous machine down the street, when What do you think the parson found, When he got up and stared around? The poor old chaise in a heap or mound, As if it had been to the mill and ground! You see, of course, if you’re not a dunce, How it went to pieces all at once, All at once, and nothing first, Just as bubbles do when they burst. The wonderful one-horse shay is the perfect image of an optimistic hope about aging: a long, healthy existence followed by an abrupt end of life, with no decline. The one-horse shay image also suggests that life has a built-in “warranty expiration” date. But where does this limit on longevity come from? Is it possible to extend life beyond what we know? The living organism with the longest individual life span is the bristlecone pine tree found in California, more than 4,500 years old, with no end in sight. -
University of Copenhagen
Latest advances in aging research and drug discovery Bakula, Daniela; Ablasser, Andrea; Aguzzi, Adriano; Antebi, Adam; Barzilai, Nir; Bittner, Martin Immanuel; Jensen, Martin Borch; Calkhoven, Cornelis F.; Chen, Danica; de Grey, Aubrey D.N.J.; Feige, Jerome N.; Georgievskaya, Anastasia; Gladyshev, Vadim N.; Golato, Tyler; Gudkov, Andrei V.; Hoppe, Thorsten; Kaeberlein, Matt; Katajisto, Pekka; Kennedy, Brian K.; Lal, Unmesh; Martin-Villalba, Ana; Moskalev, Alexey A.; Ozerov, Ivan; Petr, Michael A.; Reason; Rubinsztein, David C.; Tyshkovskiy, Alexander; Vanhaelen, Quentin; Zhavoronkov, Alex; Scheibye-Knudsen, Morten Published in: Aging DOI: 10.18632/aging.102487 Publication date: 2019 Document version Publisher's PDF, also known as Version of record Document license: CC BY Citation for published version (APA): Bakula, D., Ablasser, A., Aguzzi, A., Antebi, A., Barzilai, N., Bittner, M. I., Jensen, M. B., Calkhoven, C. F., Chen, D., de Grey, A. D. N. J., Feige, J. N., Georgievskaya, A., Gladyshev, V. N., Golato, T., Gudkov, A. V., Hoppe, T., Kaeberlein, M., Katajisto, P., Kennedy, B. K., ... Scheibye-Knudsen, M. (2019). Latest advances in aging research and drug discovery. Aging, 11(22), 9971-9981. https://doi.org/10.18632/aging.102487 Download date: 28. Sep. 2021 www.aging-us.com AGING 2019, Vol. 11, No. 22 Meeting Report Latest advances in aging research and drug discovery Daniela Bakula1, Andrea Ablasser2, Adriano Aguzzi3, Adam Antebi4,5, Nir Barzilai6, Martin- Immanuel Bittner7, Martin Borch Jensen8, Cornelis F. Calkhoven9, Danica Chen10, Aubrey D.N.J. de Grey11, Jerome N. Feige12,13, Anastasia Georgievskaya14, Vadim N. Gladyshev15, Tyler Golato16, Andrei V. Gudkov17, Thorsten Hoppe18, Matt Kaeberlein19,20, Pekka Katajisto21,22, Brian K. -
Looking Back at the Early Times of Redox Biology Author: Leopold Flohé
Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 26 October 2020 doi:10.20944/preprints202010.0511.v1 1 Title: Looking back at the early times of redox biology Author: Leopold Flohé Affiliations: Dipartimento di Medicina Molecolare, Università degli Studi di Padova, v.le G. Colombo 3, 35121 Padova (Italy) and Departamento de Bioquímica, Universidad de la República, Avda. General Flores 2125, 11800 Montevideo (Uruguay) E-mail: [email protected] Abstract: The beginnings of redox biology are recalled with special emphasis on formation, metabolism and function of reactive oxygen and nitrogen species in mammalian systems. The review covers the early history of heme peroxidases and the metabolism of hydrogen peroxide, the discovery of selenium as integral part of glutathione peroxidases, which expanded the scope of the field to other hydroperoxides including lipid hydroperoxide, the discovery of superoxide dismutases and superoxide radicals in biological systems and their role in host defense, tissue damage, metabolic regulation and signaling, the identification of the endothelial-derived relaxing factor as the nitrogen monoxide radical and its physiological and pathological implications. The article highlights the perception of hydrogen peroxide and other hydroperoxides as signaling molecules, which marks the beginning of the flourishing fields of redox regulation and redox signaling. Final comments describe the development of the redox language. In the 18th and 19th century, it was highly individualized and hard to translate into modern terminology. In the 20th century, the redox language co-developed with the chemical terminology and became clearer. More recently, the introduction and inflationary use of poorly defined terms has unfortunately impaired the understanding of redox events in biological systems. -
The Unexpected Hanging and Other Mathematical Diversions
AND OTHER MATHEMATICAL nIVERSIONS OLLECTION OF GI ES FRON A ERIC" The Unexpected Hanging A Partial List of Books by Martin Gardner: The Annotated "Casey at the Bat" (ed.) The Annotated Innocence of Father Brown (ed.) Hexaflexagons and Other Mathematical Diversions Logic Machines and Diagrams The Magic Numbers of Dr. Matrix Martin Gardner's Whys and Wherefores New Ambidextrous Universe The No-sided Professor Order and Surprise Puzzles from Other Worlds The Sacred Beetle and Other Essays in Science (ed.) The Second Scientific American Book of Mathematical Puzzles and Diversions Wheels, Life, and Other Mathematical Entertainments The Whys of a Philosopher Scrivener MARTIN GARDNER The Unexpected Hanging And Other Mathematical Diversions With a new Afterword and expanded Bibliography The University of Chicago Press Chicago and London Material previously published in Scientific American is copyright 0 1961, 1962, 1963 by Scientific American, Inc. All rights reserved. The University of Chicago Press, Chicago 60637 The University of Chicago Press, Ltd., London O 1969, 1991 by Martin Gardner All rights reserved. Originally published 1969. University of Chicago Press edition 1991 Printed in the United States of America Library of Congress Cataloging-in-Publication Data Gardner, Martin, 1914- The unexpected hanging and other mathematical diversions : with a new afterword and expanded bibliography 1 Martin Gardner. - University of Chicago Press ed. p. cm. Includes bibliographical references. ISBN 0-226-28256-2 (pbk.) 1. Mathematical recreations. I. Title. QA95.G33 1991 793.7'4-dc20 91-17723 CIP @ The paper used in this publication meets the minimum requirements of the American National Standard for Information Sciences-Permanence of Paper for Printed Library Materials, ANSI 239.48-1984. -
Martin Gardner Papers SC0647
http://oac.cdlib.org/findaid/ark:/13030/kt6s20356s No online items Guide to the Martin Gardner Papers SC0647 Daniel Hartwig & Jenny Johnson Department of Special Collections and University Archives October 2008 Green Library 557 Escondido Mall Stanford 94305-6064 [email protected] URL: http://library.stanford.edu/spc Note This encoded finding aid is compliant with Stanford EAD Best Practice Guidelines, Version 1.0. Guide to the Martin Gardner SC064712473 1 Papers SC0647 Language of Material: English Contributing Institution: Department of Special Collections and University Archives Title: Martin Gardner papers Creator: Gardner, Martin Identifier/Call Number: SC0647 Identifier/Call Number: 12473 Physical Description: 63.5 Linear Feet Date (inclusive): 1957-1997 Abstract: These papers pertain to his interest in mathematics and consist of files relating to his SCIENTIFIC AMERICAN mathematical games column (1957-1986) and subject files on recreational mathematics. Papers include correspondence, notes, clippings, and articles, with some examples of puzzle toys. Correspondents include Dmitri A. Borgmann, John H. Conway, H. S. M Coxeter, Persi Diaconis, Solomon W Golomb, Richard K.Guy, David A. Klarner, Donald Ervin Knuth, Harry Lindgren, Doris Schattschneider, Jerry Slocum, Charles W.Trigg, Stanislaw M. Ulam, and Samuel Yates. Immediate Source of Acquisition note Gift of Martin Gardner, 2002. Information about Access This collection is open for research. Ownership & Copyright All requests to reproduce, publish, quote from, or otherwise use collection materials must be submitted in writing to the Head of Special Collections and University Archives, Stanford University Libraries, Stanford, California 94304-6064. Consent is given on behalf of Special Collections as the owner of the physical items and is not intended to include or imply permission from the copyright owner.