Trick or Truth?: The Mysterious Connection Between Physics and Mathematics

253 Pages·2016·4.34 MB·English

by  Anthony Aguirre, Brendan Foster, Zeeya Merali (eds.)

T H E F R O N T I E R S C O L L E C T I O N
Anthony Aguirre
Brendan Foster
Zeeya Merali
(Eds.)
Tr ic k or
Tr ut h?
The Mysterious Connection
Between Physics
and Mathematics
123
THE FRONTIERS COLLECTION
Series editors
Avshalom C. Elitzur
Iyar The Israel Institute for Advanced Research, Rehovot, Israel
e-mail: [email protected]
Laura Mersini-Houghton
Department of Physics, University of North Carolina, Chapel Hill,
NC 27599-3255, USA
e-mail: [email protected]
T. Padmanabhan
Inter University Centre for Astronomy and Astrophysics (IUCAA), Pune, India
Maximilian Schlosshauer
Department of Physics, University of Portland, Portland, OR 97203, USA
e-mail: [email protected]
Mark P. Silverman
Department of Physics, Trinity College, Hartford, CT 06106, USA
e-mail: [email protected]
Jack A. Tuszynski
Department of Physics, University of Alberta, Edmonton, AB T6G 1Z2, Canada
e-mail: [email protected]
Rüdiger Vaas
Center for Philosophy and Foundations of Science, University of Giessen,
35394, Giessen, Germany
e-mail: [email protected]
THE FRONTIERS COLLECTION
Series Editors
A.C. Elitzur L. Mersini-Houghton T. Padmanabhan M. Schlosshauer
M.P. Silverman J.A. Tuszynski R. Vaas
The books in this collection are devoted to challenging and open problems at the
forefront of modern science, including related philosophical debates.In contrast to
typical research monographs, however, they strive to present their topics in a
manner accessible also to scientifically literate non-specialists wishing to gain
insight into thedeeper implicationsandfascinating questions involved.Taken asa
whole,theseriesreflectstheneedforafundamentalandinterdisciplinaryapproach
to modern science. Furthermore, it is intended to encourage active scientists in all
areas to ponder over important and perhaps controversial issues beyond their own
speciality. Extending from quantum physics and relativity to entropy, conscious-
ness and complex systems—the Frontiers Collection will inspire readers to push
back the frontiers of their own knowledge.
More information about this series at http://www.springer.com/series/5342
Forafulllistofpublishedtitles,pleaseseebackofbookorspringer.com/series/5342
Anthony Aguirre Brendan Foster
(cid:129)
Zeeya Merali
Editors
Trick or Truth?
The Mysterious Connection
Between Physics and Mathematics
123
Editors
Anthony Aguirre Zeeya Merali
Department ofPhysics FoundationalQuestions Institute
University of California Decatur,GA
SantaCruz, CA USA
USA
Brendan Foster
FoundationalQuestions Institute
Decatur,GA
USA
ISSN 1612-3018 ISSN 2197-6619 (electronic)
THEFRONTIERS COLLECTION
ISBN978-3-319-27494-2 ISBN978-3-319-27495-9 (eBook)
DOI 10.1007/978-3-319-27495-9
LibraryofCongressControlNumber:2015958338
©SpringerInternationalPublishingSwitzerland2016
Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart
of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,
recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission
orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar
methodologynowknownorhereafterdeveloped.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this
publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom
therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.
The publisher, the authors and the editors are safe to assume that the advice and information in this
book are believed to be true and accurate at the date of publication. Neither the publisher nor the
authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor
foranyerrorsoromissionsthatmayhavebeenmade.
Printedonacid-freepaper
ThisSpringerimprintispublishedbySpringerNature
TheregisteredcompanyisSpringerInternationalPublishingAGSwitzerland
Preface
This book is a collaborative project between Springer and The Foundational
Questions Institute (FQXi). In keeping with both the tradition of Springer’s
FrontiersCollectionandthemissionofFQXi,itprovidesstimulatinginsightsintoa
frontier area of science, while remaining accessible enough to benefit a
non-specialist audience.
FQXi is an independent, nonprofit organization that was founded in 2006. It
aimstocatalyze,support,anddisseminateresearchonquestionsatthefoundations
of physics and cosmology.
The central aim of FQXi is to fund and inspire research and innovation that is
integraltoadeepunderstandingofreality,butwhichmaynotbereadilysupported
byconventionalfundingsources.Historically,physicsandcosmologyhaveoffered
a scientific framework for comprehending the core of reality. Many giants of
modernscience—suchasEinstein, Bohr,Schrödinger,andHeisenberg—werealso
passionately concerned with, and inspired by, deep philosophical nuances of the
novel notions of reality they were exploring. Yet, such questions are often over-
looked by traditional funding agencies.
Often, grant-making and research organizations institutionalize a pragmatic
approach,primarilyfundingincrementalinvestigationsthatuseknownmethodsand
familiar conceptual frameworks, rather than the uncertain and often interdisci-
plinary methods required to develop and comprehend prospective revolutions in
physics and cosmology. As a result, even eminent scientists can struggle to secure
fundingforsomeofthequestionstheyfindmostengaging,whileyoungerthinkers
findlittlesupport,freedom,orcareerpossibilitiesunlesstheyhewtosuchstrictures.
FQXi views foundational questions not as pointless speculation or misguided
effort, but as critical and essential inquiry of relevance to us all. The institute is
dedicated to redressing these shortcomings by creating a vibrant, worldwide
community of scientists, top thinkers, and outreach specialists who tackle deep
questions in physics, cosmology, and related fields. FQXi is also committed to
engaging with the public and communicating the implications of this foundational
research for the growth of human understanding.
v
vi Preface
Aspartofthisendeavor,FQXiorganizesanannualessaycontest,whichisopen
toeveryone,fromprofessionalresearcherstomembersofthepublic.Thesecontests
are designed to focus minds and efforts on deep questions that could have a pro-
found impact across multiple disciplines. The contest is judged by an expert panel
andupto20prizesareawarded.Eachyear,thecontestfeatureswelloverahundred
entries, stimulating ongoing online discussion long after the close of the contest.
Wearedelightedtosharethiscollection,inspiredbythe2015contest,“Trickor
Truth:TheMysteriousConnectionBetweenPhysicsandMathematics.”Inlinewith
our desire to bring foundational questions to the widest possible audience, the
entries, in their original form, were written in a style that was suitable for the
general public. In this book, which is aimed at an interdisciplinary scientific
audience, the authors have been invited to expand upon their original essays and
include technical details and discussion that may enhance their essays for a more
professionalreadership,whileremainingaccessibletonon-specialistsintheirfield.
FQXi wouldlike tothank our contestpartners: Nanotronics Imaging,The Peter
and Patricia Gruber Foundation, The John Templeton Foundation, and Scientific
American. The editors are indebted to FQXi’s scientific director, Max Tegmark,
andmanagingdirector,KavitaRajanna,whowereinstrumentalinthedevelopment
of the contest. We are also grateful to Angela Lahee at Springer for her guidance
and support in driving this project forward.
2015 Anthony Aguirre
Brendan Foster
Zeeya Merali
Contents
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Anthony Aguirre, Brendan Foster and Zeeya Merali
Children of the Cosmos. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Sylvia Wenmackers
Mathematics Is Physics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
M.S. Leifer
My God, It’s Full of Clones: Living in a Mathematical Universe. . . . . . 41
Marc Séguin
Let’s Consider Two Spherical Chickens. . . . . . . . . . . . . . . . . . . . . . . . 55
Tommaso Bolognesi
The Raven and the Writing Desk. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Ian T. Durham
The Deeper Roles of Mathematics in Physical Laws . . . . . . . . . . . . . . . 77
Kevin H. Knuth
How Mathematics Meets the World. . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Tim Maudlin
Mathematics: Intuition’s Consistency Check. . . . . . . . . . . . . . . . . . . . . 103
Ken Wharton
How Not to Factor a Miracle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
Derek K. Wise
The Language of Nature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
David Garfinkle
Demystifying the Applicability of Mathematics. . . . . . . . . . . . . . . . . . . 135
Nicolas Fillion
vii
viii Contents
Why Mathematics Works so Well . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Noson S. Yanofsky
Genesis of a Pythagorean Universe . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
Alexey Burov and Lev Burov
Beyond Math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
Sophía Magnúsdóttir
The Descent of Math. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
Sara Imari Walker
The Ultimate Tactics of Self-referential Systems. . . . . . . . . . . . . . . . . . 193
Christine C. Dantas
Cognitive Science and the Connection Between Physics
and Mathematics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
Anshu Gupta Mujumdar and Tejinder Singh
A Universe from Universality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
Philip Gibbs
And the Math Will Set You Free. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
Ovidiu Cristinel Stoica
Appendix: List of Winners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
Introduction
AnthonyAguirre,BrendanFosterandZeeyaMerali
Themiracleoftheappropriatenessofthelanguageof
mathematicsfortheformulationofthelawsofphysicsisa
wonderfulgiftwhichweneitherunderstandnordeserve.
EugeneWigner(1960)1
Modernmathematicsistheformalstudyofstructuresthatcan
bedefinedinapurelyabstractway,withoutanyhuman
baggage.Thinkofmathematicalsymbolsasmerelabelswithout
intrinsicmeaning.Itdoesn’tmatterwhetheryouwrite“twoplus
twoequalsfour”,“2+2=4”or“dosmasdosigualacuatro”.
Thenotationusedtodenotetheentitiesandtherelationsis
irrelevant;theonlypropertiesofintegersarethoseembodiedby
therelationsbetweenthem.Thatis,wedon’tinvent
mathematicalstructures–wediscoverthem,andinventonlythe
notationfordescribingthem.
MaxTegmark(2014)2
Theoreticalphysicshasdevelopedhand-in-handwithmathematics.Itseemsalmost
impossibletoimaginedescribingthefundamentallawsofrealitywithoutrecourseto
amathematicalframework;atthesametime,questionsinphysicshaveinspiredmany
1Wigner, E. in “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,”
CommunicationsinPureandAppliedMathematics(JohnWiley&Sons:1960).
2Tegmark,M.inOurMathematicalUniverse:MyQuestfortheUltimateNatureofReality
(RandomHouse:2014).
B
A.Aguirre( )
DepartmentofPhysics,UniversityofCalifornia,SantaCruz,CA,USA
e-mail:[email protected]
B.Foster·Z.Merali
FoundationalQuestionsInstitute,Decatur,GA,USA
e-mail:[email protected]
Z.Merali
e-mail:[email protected]
©SpringerInternationalPublishingSwitzerland2016 1
A.Aguirreetal.(eds.),TrickorTruth?,TheFrontiersCollection,
DOI10.1007/978-3-319-27495-9_1