Free Essay

Entropy and Energy Density in a Finite and Infinite Universe

In:

Submitted By GlalieGail
Words 587
Pages 3
ENTROPY AND ENERGY DENSITY

From the beginning of the universe, during the big bang up to now, entropy has been steadily increasing while energy density is decreasing. Putting aside the steady state theory, wherein the universe is static, and utilizing the expanding universe theory, we arrive to this conclusion.

Entropy is the state of disarray and chaos in the universe. It has been increasing ever since the big bang. With the formula for entropy being Joules/Kelvin (energy over temperature), and as the universe expands it becomes colder and colder, the value for temperature goes down, resulting in a greater number as we go along the arrow of time. Using the CMBR (Cosmic Microwave Background Radiation), which is radiation left over from the Big Bang, scientists have measured the cosmic temperatures to be averaging at around 2.73 Kelvin [1], and it still decreasing.

On the other hand, energy density, which is the amount of energy in a given space, has been decreasing. Having the formula of Joules/meter3 (energy over cubic meter), and with the earlier assumption that the universe is expanding, the quotient becomes smaller and smaller. In a non-mathematical explanation, as the universe expands, energy does not have to be confined in a small space and has a bigger area to travel and spread itself to.

ENTROPY AND ENERGY DENSITY IN AN INFINITE UNIVERSE

Having said everything above, given an infinite length of time and an infinite amount of particles, in a universe that will keep on expanding without any boundaries, entropy will eventually reach its maximum at equilibrium, and the universe will eventually reach a state of equilibrium after x amount of interactions between the particles [2]. As we have discussed in class, once thermal, mechanical, and chemical equilibrium are established, the Heat Death of the universe will occur. In this case, entropy is increasing until it reaches equilibrium, and energy density will be decreasing, although it is unknown what will happen in the future as we cannot possibly know the end of infinity.

ENTROPY AND ENERGY DENSITY IN A FINITE UNIVERSE

In a finite universe, the universe will eventually reach a period in time wherein it cannot expand anymore because it has reached its borders, or its maximum. According to physics, if the rate at which the universe is expanding is not enough to overpass the escape velocity, which is the speed needed by an object to escape from a gravitational attraction by a huge body such as a star or a planet, it will begin to contract [3]. When the time comes that the universe has stopped expanding, and the rate of its expansion is 0, it will be unable to overpass the escape velocity, setting in motion the Big Crunch.

In which case, entropy, from the beginning until the point of maximum expansion, is increasing, afterwards it will start to decrease as everything condenses back into a black hole singularity or a point.

Energy density is in reverse. Decreasing from the big bang until the point of maximum expansion, and then increasing until everything is condensed in a point. References: [1] G. Lavender, "Is the universe cooling down?", Spaceanswers.com, 2016. [Online].
Available: http://www.spaceanswers.com/deep-space/is-the-universe-cooling-down/.
[Accessed: 11- May- 2016]. [2] K. Stanyukovich, "On Increasing Entropy in an Infinite Universe", The Abraham Zelmanov Journal, vol. 1, no. 1654-9163, pp. 111-117, 2016.
[3]"Escape velocity", Wikipedia, 2016. [Online]. Available: https://en.wikipedia.org/wiki/Escape_velocity. [Accessed: 11- May- 2016].

Similar Documents

Free Essay

Blace Hole

...through space are warped inwards towards the center of the volume, preventing all matter and radiation within it from escaping. While general relativity describes a black hole as a region of empty space with a point-like singularity at the center and an event horizon at the outer edge, the description changes when the effects of quantum mechanics are taken into account. [pic]Name The term black hole to describe this phenomenon dates from the mid-1960s, though its precise origins are unclear. According to Einstein’s general theory of relativity, as mass is added to a degenerate star a sudden collapse will take place and the intense gravitational field of the star will close in on itself. Such a star then forms a "black hole" in the universe. Popular accounts commonly try to explain the black hole phenomenon by using the concept of escape velocity, the speed needed for a vessel starting at the surface of a massive object to completely clear the object's gravitational field. It follows from Newton's law of gravity that...

Words: 2768 - Pages: 12

Free Essay

Paper

...g Easier! Making Everythin ™ heory tring T S Learn: • The basic concepts of this controversial theory • How string theory builds on physics concepts • The different viewpoints in the field • String theory’s physical implications Andrew Zimmerman Jones Physics Guide, About.com with Daniel Robbins, PhD in Physics Get More and Do More at Dummies.com® Start with FREE Cheat Sheets Cheat Sheets include • Checklists • Charts • Common Instructions • And Other Good Stuff! To access the Cheat Sheet created specifically for this book, go to www.dummies.com/cheatsheet/stringtheory Get Smart at Dummies.com Dummies.com makes your life easier with 1,000s of answers on everything from removing wallpaper to using the latest version of Windows. Check out our • Videos • Illustrated Articles • Step-by-Step Instructions Plus, each month you can win valuable prizes by entering our Dummies.com sweepstakes. * Want a weekly dose of Dummies? Sign up for Newsletters on • Digital Photography • Microsoft Windows & Office • Personal Finance & Investing • Health & Wellness • Computing, iPods & Cell Phones • eBay • Internet • Food, Home & Garden Find out “HOW” at Dummies.com *Sweepstakes not currently available in all countries; visit Dummies.com for official rules. String Theory FOR DUMmIES ‰ by Andrew Zimmerman Jones with Daniel Robbins, PhD in Physics String Theory For Dummies® Published by Wiley Publishing, Inc. 111 River St. Hoboken, NJ 07030-5774 www...

Words: 133965 - Pages: 536

Free Essay

The Logistic Map

...Chaotic Growth with the Logistic Model of P.-F. Verhulst Hugo Pastijn Department of Mathematics, Royal Military Academy B-1000 Brussels, Belgium Hugo.Pastijn@rma.ac.be Summary. Pierre-Fran¸ois Verhulst was born 200 years ago. After a short biograc phy of P.-F. Verhulst in which the link with the Royal Military Academy in Brussels is emphasized, the early history of the so-called “Logistic Model” is described. The relationship with older growth models is discussed, and the motivation of Verhulst to introduce different kinds of limited growth models is presented. The (re-)discovery of the chaotic behaviour of the discrete version of this logistic model in the late previous century is reminded. We conclude by referring to some generalizations of the logistic model, which were used to describe growth and diffusion processes in the context of technological innovation, and for which the author studied the chaotic behaviour by means of a series of computer experiments, performed in the eighties of last century by means of the then emerging “micro-computer” technology. 1 P.-F. Verhulst and the Royal Military Academy in Brussels In the year 1844, at the age of 40, when Pierre-Fran¸ois Verhulst on November c 30 presented his contribution to the “M´moires de l’Acad´mie” of the young e e Belgian nation, a paper which was published the next year in “tome XVIII” with the title: “Recherches math´matiques sur la loi d’accroissement de la e population” (mathematical investigations of the law of...

Words: 138629 - Pages: 555

Free Essay

La Singularidad

...NOTE: This PDF document has a handy set of “bookmarks” for it, which are accessible by pressing the Bookmarks tab on the left side of this window. ***************************************************** We are the last. The last generation to be unaugmented. The last generation to be intellectually alone. The last generation to be limited by our bodies. We are the first. The first generation to be augmented. The first generation to be intellectually together. The first generation to be limited only by our imaginations. We stand both before and after, balancing on the razor edge of the Event Horizon of the Singularity. That this sublime juxtapositional tautology has gone unnoticed until now is itself remarkable. We're so exquisitely privileged to be living in this time, to be born right on the precipice of the greatest paradigm shift in human history, the only thing that approaches the importance of that reality is finding like minds that realize the same, and being able to make some connection with them. If these books have influenced you the same way that they have us, we invite your contact at the email addresses listed below. Enjoy, Michael Beight, piman_314@yahoo.com Steven Reddell, cronyx@gmail.com Here are some new links that we’ve found interesting: KurzweilAI.net News articles, essays, and discussion on the latest topics in technology and accelerating intelligence. SingInst.org The Singularity Institute for Artificial Intelligence: think tank devoted to increasing...

Words: 237133 - Pages: 949

Free Essay

Global Warming

...Physical Chemistry Understanding our Chemical World Physical Chemistry Understanding our Chemical World Paul Monk Manchester Metropolitan University, UK Copyright  2004 John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England Telephone (+44) 1243 779777 Email (for orders and customer service enquiries): cs-books@wiley.co.uk Visit our Home Page on www.wileyeurope.com or www.wiley.com All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP, UK, without the permission in writing of the Publisher. Requests to the Publisher should be addressed to the Permissions Department, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England, or emailed to permreq@wiley.co.uk, or faxed to (+44) 1243 770620. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the Publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. Other Wiley...

Words: 233668 - Pages: 935

Free Essay

Psychology

...NATURE OF MAN HISTORY AND PHILOSOPHY OF SCIENCE IN 10 MODULES E. Kolawole Ogundowole, Ph.D., D.Sc. Professor & Head of Philosophy Department University of Lagos. Akoka, Lagos. Nigeria Correct Counsels Limited Research. Counselling. Publishing. Book Supply First published 2003 Correct Counsels Ltd. P. O. Box 53 Akoka, Lagos. C E. Kolawole Ogundowole, 2003 ISBN: 978 -37004 - 0 – 5 This book is copyright. All rights reserved under the Copyright La Enquiries should be addressed to the Publishers. Printed in Nigeria by: Mustard Press Enterprises 16, Ogundola Street Sungas-BAriga. PREFACE A few words about the overall objectives of the course is appropriate as a starting point. Historically, philosophy was the first form of theoretical knowledge. As a rational theoretical tool of comprehending the world, philosophy arose in ancient Greece in stiff battle with mythology and religious consciousness. It came out to lay the foundation for the evolvement of scientific consciousness and the emergence and development of the sciences - Mathematics, Astronomy, Physics, Chemistry, Biology, etc. In an environment rife with various and varying superstitions and myths, the study of the History of Science and Philosophy of Science becomes crucial, lest science itself falls within the ambit of mythology and superstition and becomes another form of myth even in the hands of the tutored. The study of the History of Science...

Words: 54229 - Pages: 217

Free Essay

Physics

...Introductory Physics I Elementary Mechanics by Robert G. Brown Duke University Physics Department Durham, NC 27708-0305 rgb@phy.duke.edu Copyright Notice Copyright Robert G. Brown 1993, 2007, 2013 Notice This physics textbook is designed to support my personal teaching activities at Duke University, in particular teaching its Physics 141/142, 151/152, or 161/162 series (Introductory Physics for life science majors, engineers, or potential physics majors, respectively). It is freely available in its entirety in a downloadable PDF form or to be read online at: http://www.phy.duke.edu/∼rgb/Class/intro physics 1.php It is also available in an inexpensive (really!) print version via Lulu press here: http://www.lulu.com/shop/product-21186588.html where readers/users can voluntarily help support or reward the author by purchasing either this paper copy or one of the even more inexpensive electronic copies. By making the book available in these various media at a cost ranging from free to cheap, I enable the text can be used by students all over the world where each student can pay (or not) according to their means. Nevertheless, I am hoping that students who truly find this work useful will purchase a copy through Lulu or a bookseller (when the latter option becomes available), if only to help subsidize me while I continue to write inexpensive textbooks in physics or other subjects. This textbook is organized for ease of presentation and ease of learning. In particular, they are...

Words: 224073 - Pages: 897

Free Essay

Physics

...SENIOR SECONDARY COURSE PHYSICS 1 (CORE MODULES) Coordinators Dr. Oum Prakash Sharma Sh. R.S. Dass NATIONAL INSTITUTE OF OPEN SCHOOLING A-25, INSTITUTIONAL AREA, SECTOR-62, NOIDA-201301 (UP) COURSE DESIGN COMMITTEE CHAIRMAN Prof. S.C. Garg Former Pro-Vice Chancellor IGNOU, Maidan Garhi, Delhi MEMBERS Prof. A.R. Verma Former Director, National Physical Laboratory, Delhi, 160, Deepali Enclave Pitampura, Delhi-34 Dr. Naresh Kumar Reader (Rtd.) Deptt. of Physics Hindu College, D.U. Dr. Oum Prakash Sharma Asstt. Director (Academic) NIOS, Delhi Prof. L.S. Kothari Prof. of Physics (Retd.) Delhi University 71, Vaishali, Delhi-11008 Dr. Vajayshree Prof. of Physics IGNOU, Maidan Garhi Delhi Sh. R.S. Dass Vice Principal (Rtd.) BRMVB, Sr. Sec. School Lajpat Nagar, New Delhi-110024 Dr. G.S. Singh Prof. of Physics IIT Roorkee Sh. K.S. Upadhyaya Principal Jawahar Navodaya Vidyalaya Rohilla Mohammadabad (U.P.) Dr. V.B. Bhatia Prof. of Physics (Retd.) Delhi University 215, Sector-21, Faridabad COURSE DEVELOPMENT TEAM CHAIRMAN Prof. S.C. Garg Former Pro-Vice Chancellor IGNOU, Delhi MEMBERS Prof. V.B. Bhatia 215, Sector-21, Faridabad Prof. B.B. Tripathi Prof. of Physics (Retd.), IIT Delhi 9-A, Awadhpuri, Sarvodaya Nagar Lucknow-226016 Sh. K.S. Upadhyaya Principal Navodaya Vidyalaya Rohilla Mohammadabad, (U.P.) Dr. V.P. Shrivastava Reader (Physics) D.E.S.M., NCERT, Delhi EDITORS TEAM CHAIRMAN Prof. S.C. Garg Former Pro-Vice Chancellor IGNOU, Delhi MEMBERS Prof. B.B. Tripathi Prof...

Words: 131353 - Pages: 526

Premium Essay

Hiiiiiiiiiiiiii

...PHYSIC AL CONSTANTS CONSTANT Speed of light Elementary charge Electron mass Proton mass Gravitational constant Permeability constant Permittivity constant Boltzmann’s constant Universal gas constant Stefan–Boltzmann constant Planck’s constant Avogadro’s number Bohr radius SYMBOL c e me mp G m0 P0 k R s h 15 2p"2 NA a0 THREE-FIGURE VALUE 3.003108 m/s 1.60310219 C 9.11310231 kg 1.67310227 kg 6.67310211 N # m2/kg 2 1.2631026 N/A2 1H/m2 8.85310212 C 2/N # m2 1F/m2 1.38310223 J/K 8.31 J/K # mol 5.6731028 W/m2 # K4 6.63310234 J # s 6.0231023 mol21 5.29310211 m BEST KNOWN VALUE* 299 792 458 m/s (exact) 1.602 176 4871402 310219 C 9.109 382 151452 310231 kg 1.672 621 6371832 310227 kg 6.674 281672 310211 N # m2/kg 2 4p31027 (exact) 1/m0c2 (exact) 1.380 65041242 310223 J/K 8.314 4721152 J/K # mol 5.670 4001402 31028 W/m2 # K4 6.626 068 961332 310234 J # s 6.022 141 791302 31023 mol21 5.291 772 08591362 310211 m *Parentheses indicate uncertainties in last decimal places. Source: U.S. National Institute of Standards and Technology, 2007 values SI PREFIXES POWER 1024 1021 1018 1015 1012 109 106 103 102 101 100 1021 1022 1023 1026 1029 10212 10215 10218 10221 10224 THE GREEK ALPHABET PREFIX yotta zetta exa peta tera giga mega kilo hecto deca — deci centi milli micro nano pico femto atto zepto yocto SYMBOL Y Z E P T G M k h da — d c m μ n p f a z y Alpha ...

Words: 201181 - Pages: 805

Free Essay

Magt

...i Computational Complexity: A Modern Approach Draft of a book: Dated January 2007 Comments welcome! Sanjeev Arora and Boaz Barak Princeton University complexitybook@gmail.com Not to be reproduced or distributed without the authors’ permission This is an Internet draft. Some chapters are more finished than others. References and attributions are very preliminary and we apologize in advance for any omissions (but hope you will nevertheless point them out to us). Please send us bugs, typos, missing references or general comments to complexitybook@gmail.com — Thank You!! DRAFT ii DRAFT About this book Computational complexity theory has developed rapidly in the past three decades. The list of surprising and fundamental results proved since 1990 alone could fill a book: these include new probabilistic definitions of classical complexity classes (IP = PSPACE and the PCP Theorems) and their implications for the field of approximation algorithms; Shor’s algorithm to factor integers using a quantum computer; an understanding of why current approaches to the famous P versus NP will not be successful; a theory of derandomization and pseudorandomness based upon computational hardness; and beautiful constructions of pseudorandom objects such as extractors and expanders. This book aims to describe such recent achievements of complexity theory in the context of the classical results. It is intended to both serve as a textbook as a reference for self-study. This means...

Words: 210134 - Pages: 841

Free Essay

Maglev

...*3963103* [3963] – 103 T.E. (Petroleum) (Semester – I) Examination, 2011 DRILLING & PRODUCTION OPERATIONS (2003 Course) Time : 3 Hours Max. Marks : 100 Instructions : 1) Question Nos. 1 and 5 are compulsory. Out of the remaining attempt 2 questions from Section I and 2 questions from Section II. 2) Answers to the two Sections should be written in separate books. 3) Neat diagrams must be drawn wherever necessary. 4) Black figures to the right indicate full marks. 5) Use of Logarithmic Tables, Slide Rule, Mollier Charts, Electronic Pocket Calculator and Steam Tables is allowed. 6) Assume suitable data, if necessary. SECTION – I 1. What are different systems on a drilling rig ? Explain any one in detail with suitable diagramme. 18 2. a) Calculate Bottom hole pressure if well depth is 2500 m and mud weight is 1.2 gm/cc. b) Calculate mud weight if mud gradient is 0.87 psi/ft. ′ c) Calculate volume bbl/meter for drill pipe O.D. = 5′ inch and I.D. = 4.276 inch. 2 2 2 10 8 8 16 d) Draw circulation system on a drilling rig. 3. a) Discuss IADC classification of a bit in details. b) Discuss different factors affecting rate of penetration in details. 4. Write short note on : i) Coring ii) Fishing tools iii) BOP iv) Directional well P.T.O. [3963] – 103 -2- *3963103* SECTION – II 5. a) Discuss different types of casings and function of the casings in brief. b) Discuss different types of well completion techniques. 6. a) Discuss primary cementation process with...

Words: 172166 - Pages: 689

Premium Essay

Dataminig

...Data Mining Third Edition This page intentionally left blank Data Mining Practical Machine Learning Tools and Techniques Third Edition Ian H. Witten Eibe Frank Mark A. Hall AMSTERDAM • BOSTON • HEIDELBERG • LONDON NEW YORK • OXFORD • PARIS • SAN DIEGO SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO Morgan Kaufmann Publishers is an imprint of Elsevier Morgan Kaufmann Publishers is an imprint of Elsevier 30 Corporate Drive, Suite 400, Burlington, MA 01803, USA This book is printed on acid-free paper. Copyright © 2011 Elsevier Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must...

Words: 194698 - Pages: 779

Free Essay

Jon Von Nomann

...John von Neumann From Wikipedia, the free encyclopedia "Von Neumann" redirects here. For other uses, see Von Neumann (disambiguation). The native form of this personal name is Neumann János Lajos. This article uses the Western name order. John von Neumann | Von Neumann in the 1940s | Born | Neumann János Lajos December 28, 1903 Budapest, Austria-Hungary | Died | February 8, 1957 (aged 53) Walter Reed General Hospital Washington, D.C. | Residence | United States | Nationality | Hungarian and American | Fields | Mathematics, physics, statistics, economics | Institutions | University of Berlin Princeton University Institute for Advanced Study Site Y, Los Alamos | Alma mater | University of Pázmány Péter ETH Zürich | Doctoral advisor | Lipót Fejér | Other academic advisors | László Rátz | Doctoral students | Donald B. Gillies Israel Halperin | Other notable students | Paul Halmos Clifford Hugh Dowker Benoit Mandelbrot[1] | Known for |  [show] | Notable awards | Bôcher Memorial Prize (1938) Enrico Fermi Award (1956) | Signature | John von Neumann (/vɒn ˈnɔɪmən/; December 28, 1903 – February 8, 1957) was a Hungarian and American pure and applied mathematician, physicist, inventor and polymath. He made major contributions to a number of fields,[2] including mathematics (foundations of mathematics, functional analysis, ergodic theory, geometry, topology, and numerical analysis), physics (quantum mechanics, hydrodynamics, and fluid dynamics)...

Words: 9454 - Pages: 38

Premium Essay

Data Mining Practical Machine Learning Tools and Techniques - Weka

...Data Mining Practical Machine Learning Tools and Techniques The Morgan Kaufmann Series in Data Management Systems Series Editor: Jim Gray, Microsoft Research Data Mining: Practical Machine Learning Tools and Techniques, Second Edition Ian H. Witten and Eibe Frank Fuzzy Modeling and Genetic Algorithms for Data Mining and Exploration Earl Cox Data Modeling Essentials, Third Edition Graeme C. Simsion and Graham C. Witt Location-Based Services Jochen Schiller and Agnès Voisard Database Modeling with Microsoft® Visio for Enterprise Architects Terry Halpin, Ken Evans, Patrick Hallock, and Bill Maclean Designing Data-Intensive Web Applications Stefano Ceri, Piero Fraternali, Aldo Bongio, Marco Brambilla, Sara Comai, and Maristella Matera Mining the Web: Discovering Knowledge from Hypertext Data Soumen Chakrabarti Understanding SQL and Java Together: A Guide to SQLJ, JDBC, and Related Technologies Jim Melton and Andrew Eisenberg Database: Principles, Programming, and Performance, Second Edition Patrick O’Neil and Elizabeth O’Neil The Object Data Standard: ODMG 3.0 Edited by R. G. G. Cattell, Douglas K. Barry, Mark Berler, Jeff Eastman, David Jordan, Craig Russell, Olaf Schadow, Torsten Stanienda, and Fernando Velez Data on the Web: From Relations to Semistructured Data and XML Serge Abiteboul, Peter Buneman, and Dan Suciu Data Mining: Practical Machine Learning Tools and Techniques with Java Implementations Ian H. Witten and Eibe Frank ...

Words: 191947 - Pages: 768

Free Essay

Deep Learning Wikipedia

...Deep Learning more at http://ml.memect.com Contents 1 Artificial neural network 1 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2.1 Improvements since 2006 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3.1 Network function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3.2 Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3.3 Learning paradigms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3.4 Learning algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Employing artificial neural networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.5 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5.1 Real-life applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5.2 Neural networks and neuroscience . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.6 Neural network software ...

Words: 55759 - Pages: 224