Quantum-like Networks: An Approach To Neural Behavior Through Their Mathematics And Logic

354 Pages·2022·14.853 MB·English

by  Stephen A. Selesnick

Quantum-like
Networks
An Approach to Neural
Behavior through their
Mathematics and Logic
1122997755 99778899881111226600669988 ttpp..iinndddd 11 1111//44//2222 88::4444 AAMM
Other World Scientific Titles by the Author
Quanta, Logic and Spacetime: Variations on Finkelstein’s
Quantum Relativity
ISBN: 978-981-02-3255-9
Quanta, Logic and Spacetime
Second Edition
ISBN: 978-981-238-691-5
SShhaauunn -- 1122997755 -- QQuuaannttuumm--lliikkee NNeettwwoorrkkss..iinndddd 11 2255//77//22002222 99::0077::5599 aamm
Quantum-like
Networks
An Approach to Neural
Behavior through their
Mathematics and Logic
| Stephen A Selesnick
University of Missouri-St Louis, USA
World Scientific
NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI • TOKYO
1122997755 99778899881111226600669988 ttpp..iinndddd 22 1111//44//2222 88::4444 AAMM
Published by
World Scientific Publishing Co. Pte. Ltd.
5 Toh Tuck Link, Singapore 596224
USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601
UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
Library of Congress Cataloging-in-Publication Data
Names: Selesnick, S. A. (Stephen Allan), author.
Title: Quantum-like networks : an approach to neural behavior through their
mathematics and logic / Stephen A Selesnick.
Description: 1st. | New Jersey : World Scientific, [2023] |
Includes bibliographical references and index.
Identifiers: LCCN 2022017522 | ISBN 9789811260698 (hardcover) |
ISBN 9789811260704 (ebook for institutions) | ISBN 9789811260711 (ebook for individuals)
Subjects: LCSH: Neural networks (Neurobiology)--Mathematical models. |
Quantum systems. | Quantum computing.
Classification: LCC QP363.3 .S35 2023 | DDC 612.8--dc23/eng/20220720
LC record available at https://lccn.loc.gov/2022017522
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
Copyright © 2023 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
electronic or mechanical, including photocopying, recording or any information storage and retrieval
system now known or to be invented, without written permission from the publisher.
For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance
Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy
is not required from the publisher.
For any available supplementary material, please visit
https://www.worldscientific.com/worldscibooks/10.1142/12975#t=suppl
Desk Editor: Shaun Tan Yi Jie
Typeset by Stallion Press
Email: [email protected]
Printed in Singapore
SShhaauunn -- 1122997755 -- QQuuaannttuumm--lliikkee NNeettwwoorrkkss..iinndddd 22 2255//77//22002222 99::0077::5599 aamm
July18,2022 15:9 Quantum-likeNetworks-9inx6in b4780-fm pagev
NETWORK: Any thing reticulated or decussated, at equal
distances, with interstices between the intersections.
Samuel Johnson (1709–1784)
A Dictionary of the English Language (1755)
Pay attention to the chatter we use to convince someone of
the truthof amathematical proposition.Itshedslight on the
function of these beliefs. I mean the chatter with which the
intuition is awakened. By which, that is to say, the machine
of a computing technique is set in motion.
Ludwig Wittgenstein (1889–1951)
Remarks on the Foundations of Mathematics
(From III,§27, 1942, translated by the author.)
Even if a minefield or the abyss should lie before me, I will
march straight ahead without looking back.
Zhu Rongji (1928–(cid:10)(cid:10)(cid:10)(cid:10))
Une simple largeur apparaˆıt comme profondeur pour ceux qui
sont allong´es.
(Mere width appears as depth to those who are supine.)
Simplicien de Forcenex du Resnell-Tr´emoille
(1758–1810)
(Translated by Haifa Nouaime.)
B1948 Governing Asia
TTTThhhhiiiissss ppppaaaaggggeeee iiiinnnntttteeeennnnttttiiiioooonnnnaaaallllllllyyyy lllleeeefffftttt bbbbllllaaaannnnkkkk
BB11994488__11--AAookkii..iinndddd 66 99//2222//22001144 44::2244::5577 PPMM
July18,2022 15:9 Quantum-likeNetworks-9inx6in b4780-fm pagevii
For
Robert A. Taylor
doctor mirabilis and savior of networks
and
Joe Z. Tsien
seeker and finder indomitable
B1948 Governing Asia
TTTThhhhiiiissss ppppaaaaggggeeee iiiinnnntttteeeennnnttttiiiioooonnnnaaaallllllllyyyy lllleeeefffftttt bbbbllllaaaannnnkkkk
BB11994488__11--AAookkii..iinndddd 66 99//2222//22001144 44::2244::5577 PPMM
July18,2022 15:9 Quantum-likeNetworks-9inx6in b4780-fm pageix
Introduction
This work was inspired essentially by the old question of whether or
notbrainscompute.Andiftheydo,whatisittheycomputeandhow
do they do it? On the way to this goal, whether or not it has been
reached — please see Chapter 4 in this connection — many other
issues arose.
It is aimed at: mathematicians, physicists, computer scientists,
andphilosopherswithaninterestinthetopicsdiscussed;mathemati-
cians with an interest in extensions of the range of applicability of
mathematical resources apparently not previously so exploited; and
neuroscientists andpsychologists with strongmathematical leanings.
This having been said, let me assure the potential reader that
almost no background in quantum physics, logic, network theory,
computation or neuroscience is required for a readingof this work. A
slight exposure to the basics of quantum mechanics and logic would
be an advantage but, apart from requiring a knowledge of linear
algebra, an effort has been made to render the work essentially
self-contained. Where it is not, full references to the literature are
supplied. Other than a knowledge of linear algebra, all that is
required is an appreciation of the power of formalisms such as those
to be found here.
We start from first principles, namely a logical take on very
complex systems such as those found in living organisms. Our
particular approach to the logic of such systems, while not entirely
without precedent in its general philosophy, seems in detail to be
ix