Update Volume 2 Swarm monographs
This commit is contained in:
did:key:z6MkmBZkXGPJpw81cNsuCoq2wJ3zYGQ2addNU7qWgdKGGtEs
parent
1d320005d0
commit
521c492f2e
@@ -0,0 +1,32 @@
|
||||
\relax
|
||||
\providecommand\hyper@newdestlabel[2]{}
|
||||
\providecommand\HyField@AuxAddToFields[1]{}
|
||||
\providecommand\HyField@AuxAddToCoFields[2]{}
|
||||
\citation{Hoffman2015}
|
||||
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction: Kantian Replicator Dynamics}{1}{section.1}\protected@file@percent }
|
||||
\newlabel{sec:intro}{{1}{1}{Introduction: Kantian Replicator Dynamics}{section.1}{}}
|
||||
\citation{Ortega2013}
|
||||
\citation{Ortega2013}
|
||||
\@writefile{toc}{\contentsline {section}{\numberline {2}The Thermodynamic Cost of Homomorphism}{2}{section.2}\protected@file@percent }
|
||||
\newlabel{sec:cost}{{2}{2}{The Thermodynamic Cost of Homomorphism}{section.2}{}}
|
||||
\newlabel{def:channel}{{2.1}{2}{The Perceptual Channel}{theorem.2.1}{}}
|
||||
\newlabel{def:payoff}{{2.2}{2}{Evolutionary Payoff Integral}{theorem.2.2}{}}
|
||||
\newlabel{eq:payoff}{{1}{2}{Evolutionary Payoff Integral}{equation.2.1}{}}
|
||||
\newlabel{thm:landauer}{{2.3}{2}{Landauer's Tax on Truth}{theorem.2.3}{}}
|
||||
\newlabel{thm:gibbs}{{2.4}{2}{The Gibbs Encoder}{theorem.2.4}{}}
|
||||
\@writefile{toc}{\contentsline {section}{\numberline {3}Replicator Dynamics and Extinction}{3}{section.3}\protected@file@percent }
|
||||
\newlabel{sec:replicator}{{3}{3}{Replicator Dynamics and Extinction}{section.3}{}}
|
||||
\newlabel{lem:dominance}{{3.1}{3}{Strict Dominance of Fitness}{theorem.3.1}{}}
|
||||
\newlabel{thm:extinction}{{3.2}{3}{Asymptotic Extinction of Truth}{theorem.3.2}{}}
|
||||
\newlabel{prop:ess}{{3.3}{3}{Evolutionarily Stable Strategy}{theorem.3.3}{}}
|
||||
\@writefile{toc}{\contentsline {section}{\numberline {4}Conditional Survival and Social Coordination}{3}{section.4}\protected@file@percent }
|
||||
\newlabel{sec:conditional}{{4}{3}{Conditional Survival and Social Coordination}{section.4}{}}
|
||||
\newlabel{def:coordination}{{4.1}{3}{Social Coordination Sub-Games}{theorem.4.1}{}}
|
||||
\newlabel{thm:budget}{{4.2}{3}{Fitness Budgets Truth}{theorem.4.2}{}}
|
||||
\bibstyle{plain}
|
||||
\bibcite{Hoffman2015}{1}
|
||||
\bibcite{Ortega2013}{2}
|
||||
\bibcite{Landauer1961}{3}
|
||||
\@writefile{toc}{\contentsline {section}{\numberline {5}Conclusion}{4}{section.5}\protected@file@percent }
|
||||
\newlabel{sec:conclusion}{{5}{4}{Conclusion}{section.5}{}}
|
||||
\gdef \@abspage@last{4}
|
||||
@@ -0,0 +1,355 @@
|
||||
This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023/Debian) (preloaded format=pdflatex 2026.5.30) 10 JUN 2026 20:21
|
||||
entering extended mode
|
||||
restricted \write18 enabled.
|
||||
%&-line parsing enabled.
|
||||
**wrapper_vol4.tex
|
||||
(./wrapper_vol4.tex
|
||||
LaTeX2e <2023-11-01> patch level 1
|
||||
L3 programming layer <2024-01-22>
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/base/article.cls
|
||||
Document Class: article 2023/05/17 v1.4n Standard LaTeX document class
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/base/size11.clo
|
||||
File: size11.clo 2023/05/17 v1.4n Standard LaTeX file (size option)
|
||||
)
|
||||
\c@part=\count187
|
||||
\c@section=\count188
|
||||
\c@subsection=\count189
|
||||
\c@subsubsection=\count190
|
||||
\c@paragraph=\count191
|
||||
\c@subparagraph=\count192
|
||||
\c@figure=\count193
|
||||
\c@table=\count194
|
||||
\abovecaptionskip=\skip48
|
||||
\belowcaptionskip=\skip49
|
||||
\bibindent=\dimen140
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty
|
||||
Package: inputenc 2021/02/14 v1.3d Input encoding file
|
||||
\inpenc@prehook=\toks17
|
||||
\inpenc@posthook=\toks18
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty
|
||||
Package: amsmath 2023/05/13 v2.17o AMS math features
|
||||
\@mathmargin=\skip50
|
||||
|
||||
For additional information on amsmath, use the `?' option.
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty
|
||||
Package: amstext 2021/08/26 v2.01 AMS text
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty
|
||||
File: amsgen.sty 1999/11/30 v2.0 generic functions
|
||||
\@emptytoks=\toks19
|
||||
\ex@=\dimen141
|
||||
))
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty
|
||||
Package: amsbsy 1999/11/29 v1.2d Bold Symbols
|
||||
\pmbraise@=\dimen142
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty
|
||||
Package: amsopn 2022/04/08 v2.04 operator names
|
||||
)
|
||||
\inf@bad=\count195
|
||||
LaTeX Info: Redefining \frac on input line 234.
|
||||
\uproot@=\count196
|
||||
\leftroot@=\count197
|
||||
LaTeX Info: Redefining \overline on input line 399.
|
||||
LaTeX Info: Redefining \colon on input line 410.
|
||||
\classnum@=\count198
|
||||
\DOTSCASE@=\count199
|
||||
LaTeX Info: Redefining \ldots on input line 496.
|
||||
LaTeX Info: Redefining \dots on input line 499.
|
||||
LaTeX Info: Redefining \cdots on input line 620.
|
||||
\Mathstrutbox@=\box51
|
||||
\strutbox@=\box52
|
||||
LaTeX Info: Redefining \big on input line 722.
|
||||
LaTeX Info: Redefining \Big on input line 723.
|
||||
LaTeX Info: Redefining \bigg on input line 724.
|
||||
LaTeX Info: Redefining \Bigg on input line 725.
|
||||
\big@size=\dimen143
|
||||
LaTeX Font Info: Redeclaring font encoding OML on input line 743.
|
||||
LaTeX Font Info: Redeclaring font encoding OMS on input line 744.
|
||||
\macc@depth=\count266
|
||||
LaTeX Info: Redefining \bmod on input line 905.
|
||||
LaTeX Info: Redefining \pmod on input line 910.
|
||||
LaTeX Info: Redefining \smash on input line 940.
|
||||
LaTeX Info: Redefining \relbar on input line 970.
|
||||
LaTeX Info: Redefining \Relbar on input line 971.
|
||||
\c@MaxMatrixCols=\count267
|
||||
\dotsspace@=\muskip16
|
||||
\c@parentequation=\count268
|
||||
\dspbrk@lvl=\count269
|
||||
\tag@help=\toks20
|
||||
\row@=\count270
|
||||
\column@=\count271
|
||||
\maxfields@=\count272
|
||||
\andhelp@=\toks21
|
||||
\eqnshift@=\dimen144
|
||||
\alignsep@=\dimen145
|
||||
\tagshift@=\dimen146
|
||||
\tagwidth@=\dimen147
|
||||
\totwidth@=\dimen148
|
||||
\lineht@=\dimen149
|
||||
\@envbody=\toks22
|
||||
\multlinegap=\skip51
|
||||
\multlinetaggap=\skip52
|
||||
\mathdisplay@stack=\toks23
|
||||
LaTeX Info: Redefining \[ on input line 2953.
|
||||
LaTeX Info: Redefining \] on input line 2954.
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty
|
||||
Package: amssymb 2013/01/14 v3.01 AMS font symbols
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty
|
||||
Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support
|
||||
\symAMSa=\mathgroup4
|
||||
\symAMSb=\mathgroup5
|
||||
LaTeX Font Info: Redeclaring math symbol \hbar on input line 98.
|
||||
LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold'
|
||||
(Font) U/euf/m/n --> U/euf/b/n on input line 106.
|
||||
))
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty
|
||||
Package: amsthm 2020/05/29 v2.20.6
|
||||
\thm@style=\toks24
|
||||
\thm@bodyfont=\toks25
|
||||
\thm@headfont=\toks26
|
||||
\thm@notefont=\toks27
|
||||
\thm@headpunct=\toks28
|
||||
\thm@preskip=\skip53
|
||||
\thm@postskip=\skip54
|
||||
\thm@headsep=\skip55
|
||||
\dth@everypar=\toks29
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/cite/cite.sty
|
||||
LaTeX Info: Redefining \cite on input line 302.
|
||||
LaTeX Info: Redefining \nocite on input line 332.
|
||||
Package: cite 2015/02/27 v 5.5
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/hyperref/hyperref.sty
|
||||
Package: hyperref 2024-01-20 v7.01h Hypertext links for LaTeX
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/generic/iftex/iftex.sty
|
||||
Package: iftex 2022/02/03 v1.0f TeX engine tests
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/graphics/keyval.sty
|
||||
Package: keyval 2022/05/29 v1.15 key=value parser (DPC)
|
||||
\KV@toks@=\toks30
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/kvsetkeys/kvsetkeys.sty
|
||||
Package: kvsetkeys 2022-10-05 v1.19 Key value parser (HO)
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/generic/kvdefinekeys/kvdefinekeys.sty
|
||||
Package: kvdefinekeys 2019-12-19 v1.6 Define keys (HO)
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/generic/pdfescape/pdfescape.sty
|
||||
Package: pdfescape 2019/12/09 v1.15 Implements pdfTeX's escape features (HO)
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/generic/ltxcmds/ltxcmds.sty
|
||||
Package: ltxcmds 2023-12-04 v1.26 LaTeX kernel commands for general use (HO)
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/generic/pdftexcmds/pdftexcmds.sty
|
||||
Package: pdftexcmds 2020-06-27 v0.33 Utility functions of pdfTeX for LuaTeX (HO
|
||||
)
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/generic/infwarerr/infwarerr.sty
|
||||
Package: infwarerr 2019/12/03 v1.5 Providing info/warning/error messages (HO)
|
||||
)
|
||||
Package pdftexcmds Info: \pdf@primitive is available.
|
||||
Package pdftexcmds Info: \pdf@ifprimitive is available.
|
||||
Package pdftexcmds Info: \pdfdraftmode found.
|
||||
))
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/hycolor/hycolor.sty
|
||||
Package: hycolor 2020-01-27 v1.10 Color options for hyperref/bookmark (HO)
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/auxhook/auxhook.sty
|
||||
Package: auxhook 2019-12-17 v1.6 Hooks for auxiliary files (HO)
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/hyperref/nameref.sty
|
||||
Package: nameref 2023-11-26 v2.56 Cross-referencing by name of section
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/refcount/refcount.sty
|
||||
Package: refcount 2019/12/15 v3.6 Data extraction from label references (HO)
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/generic/gettitlestring/gettitlestring.sty
|
||||
Package: gettitlestring 2019/12/15 v1.6 Cleanup title references (HO)
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/kvoptions/kvoptions.sty
|
||||
Package: kvoptions 2022-06-15 v3.15 Key value format for package options (HO)
|
||||
))
|
||||
\c@section@level=\count273
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/etoolbox/etoolbox.sty
|
||||
Package: etoolbox 2020/10/05 v2.5k e-TeX tools for LaTeX (JAW)
|
||||
\etb@tempcnta=\count274
|
||||
)
|
||||
\@linkdim=\dimen150
|
||||
\Hy@linkcounter=\count275
|
||||
\Hy@pagecounter=\count276
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/hyperref/pd1enc.def
|
||||
File: pd1enc.def 2024-01-20 v7.01h Hyperref: PDFDocEncoding definition (HO)
|
||||
Now handling font encoding PD1 ...
|
||||
... no UTF-8 mapping file for font encoding PD1
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/generic/intcalc/intcalc.sty
|
||||
Package: intcalc 2019/12/15 v1.3 Expandable calculations with integers (HO)
|
||||
)
|
||||
\Hy@SavedSpaceFactor=\count277
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/hyperref/puenc.def
|
||||
File: puenc.def 2024-01-20 v7.01h Hyperref: PDF Unicode definition (HO)
|
||||
Now handling font encoding PU ...
|
||||
... no UTF-8 mapping file for font encoding PU
|
||||
)
|
||||
Package hyperref Info: Hyper figures OFF on input line 4179.
|
||||
Package hyperref Info: Link nesting OFF on input line 4184.
|
||||
Package hyperref Info: Hyper index ON on input line 4187.
|
||||
Package hyperref Info: Plain pages OFF on input line 4194.
|
||||
Package hyperref Info: Backreferencing OFF on input line 4199.
|
||||
Package hyperref Info: Implicit mode ON; LaTeX internals redefined.
|
||||
Package hyperref Info: Bookmarks ON on input line 4446.
|
||||
\c@Hy@tempcnt=\count278
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/url/url.sty
|
||||
\Urlmuskip=\muskip17
|
||||
Package: url 2013/09/16 ver 3.4 Verb mode for urls, etc.
|
||||
)
|
||||
LaTeX Info: Redefining \url on input line 4784.
|
||||
\XeTeXLinkMargin=\dimen151
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/generic/bitset/bitset.sty
|
||||
Package: bitset 2019/12/09 v1.3 Handle bit-vector datatype (HO)
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/generic/bigintcalc/bigintcalc.sty
|
||||
Package: bigintcalc 2019/12/15 v1.5 Expandable calculations on big integers (HO
|
||||
)
|
||||
))
|
||||
\Fld@menulength=\count279
|
||||
\Field@Width=\dimen152
|
||||
\Fld@charsize=\dimen153
|
||||
Package hyperref Info: Hyper figures OFF on input line 6063.
|
||||
Package hyperref Info: Link nesting OFF on input line 6068.
|
||||
Package hyperref Info: Hyper index ON on input line 6071.
|
||||
Package hyperref Info: backreferencing OFF on input line 6078.
|
||||
Package hyperref Info: Link coloring OFF on input line 6083.
|
||||
Package hyperref Info: Link coloring with OCG OFF on input line 6088.
|
||||
Package hyperref Info: PDF/A mode OFF on input line 6093.
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/base/atbegshi-ltx.sty
|
||||
Package: atbegshi-ltx 2021/01/10 v1.0c Emulation of the original atbegshi
|
||||
package with kernel methods
|
||||
)
|
||||
\Hy@abspage=\count280
|
||||
\c@Item=\count281
|
||||
\c@Hfootnote=\count282
|
||||
)
|
||||
Package hyperref Info: Driver (autodetected): hpdftex.
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/hyperref/hpdftex.def
|
||||
File: hpdftex.def 2024-01-20 v7.01h Hyperref driver for pdfTeX
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/base/atveryend-ltx.sty
|
||||
Package: atveryend-ltx 2020/08/19 v1.0a Emulation of the original atveryend pac
|
||||
kage
|
||||
with kernel methods
|
||||
)
|
||||
\Fld@listcount=\count283
|
||||
\c@bookmark@seq@number=\count284
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/rerunfilecheck/rerunfilecheck.sty
|
||||
Package: rerunfilecheck 2022-07-10 v1.10 Rerun checks for auxiliary files (HO)
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/generic/uniquecounter/uniquecounter.sty
|
||||
Package: uniquecounter 2019/12/15 v1.4 Provide unlimited unique counter (HO)
|
||||
)
|
||||
Package uniquecounter Info: New unique counter `rerunfilecheck' on input line 2
|
||||
85.
|
||||
)
|
||||
\Hy@SectionHShift=\skip56
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def
|
||||
File: l3backend-pdftex.def 2024-01-04 L3 backend support: PDF output (pdfTeX)
|
||||
\l__color_backend_stack_int=\count285
|
||||
\l__pdf_internal_box=\box53
|
||||
)
|
||||
(./Volume_4_Master_Key.aux)
|
||||
\openout1 = `Volume_4_Master_Key.aux'.
|
||||
|
||||
LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 12.
|
||||
LaTeX Font Info: ... okay on input line 12.
|
||||
LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 12.
|
||||
LaTeX Font Info: ... okay on input line 12.
|
||||
LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 12.
|
||||
LaTeX Font Info: ... okay on input line 12.
|
||||
LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 12.
|
||||
LaTeX Font Info: ... okay on input line 12.
|
||||
LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 12.
|
||||
LaTeX Font Info: ... okay on input line 12.
|
||||
LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 12.
|
||||
LaTeX Font Info: ... okay on input line 12.
|
||||
LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 12.
|
||||
LaTeX Font Info: ... okay on input line 12.
|
||||
LaTeX Font Info: Checking defaults for PD1/pdf/m/n on input line 12.
|
||||
LaTeX Font Info: ... okay on input line 12.
|
||||
LaTeX Font Info: Checking defaults for PU/pdf/m/n on input line 12.
|
||||
LaTeX Font Info: ... okay on input line 12.
|
||||
Package hyperref Info: Link coloring OFF on input line 12.
|
||||
(./Volume_4_Master_Key.out)
|
||||
(./Volume_4_Master_Key.out)
|
||||
\@outlinefile=\write3
|
||||
\openout3 = `Volume_4_Master_Key.out'.
|
||||
|
||||
LaTeX Font Info: Trying to load font information for U+msa on input line 14.
|
||||
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsa.fd
|
||||
File: umsa.fd 2013/01/14 v3.01 AMS symbols A
|
||||
)
|
||||
LaTeX Font Info: Trying to load font information for U+msb on input line 14.
|
||||
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsb.fd
|
||||
File: umsb.fd 2013/01/14 v3.01 AMS symbols B
|
||||
)
|
||||
(./v4.1_comprehensive.tex
|
||||
\c@theorem=\count286
|
||||
[1
|
||||
|
||||
{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] [2] [3]) [4] (./Volume_4_M
|
||||
aster_Key.aux)
|
||||
***********
|
||||
LaTeX2e <2023-11-01> patch level 1
|
||||
L3 programming layer <2024-01-22>
|
||||
***********
|
||||
Package rerunfilecheck Info: File `Volume_4_Master_Key.out' has not changed.
|
||||
(rerunfilecheck) Checksum: 65C8850B5DFDFFBB891BC491EE81D216;1092.
|
||||
)
|
||||
Here is how much of TeX's memory you used:
|
||||
9045 strings out of 476106
|
||||
137071 string characters out of 5793933
|
||||
1933975 words of memory out of 5000000
|
||||
30937 multiletter control sequences out of 15000+600000
|
||||
568528 words of font info for 76 fonts, out of 8000000 for 9000
|
||||
59 hyphenation exceptions out of 8191
|
||||
75i,6n,79p,1220b,540s stack positions out of 10000i,1000n,20000p,200000b,200000s
|
||||
</usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx10.pfb></us
|
||||
r/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx12.pfb></usr/shar
|
||||
e/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmex10.pfb></usr/share/texl
|
||||
ive/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb></usr/share/texlive/te
|
||||
xmf-dist/fonts/type1/public/amsfonts/cm/cmmi6.pfb></usr/share/texlive/texmf-dis
|
||||
t/fonts/type1/public/amsfonts/cm/cmmi7.pfb></usr/share/texlive/texmf-dist/fonts
|
||||
/type1/public/amsfonts/cm/cmmi8.pfb></usr/share/texlive/texmf-dist/fonts/type1/
|
||||
public/amsfonts/cm/cmr10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/
|
||||
amsfonts/cm/cmr12.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfont
|
||||
s/cm/cmr17.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cm
|
||||
r8.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb
|
||||
></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy7.pfb></usr/
|
||||
share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy8.pfb></usr/share/t
|
||||
exlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmti10.pfb></usr/share/texlive
|
||||
/texmf-dist/fonts/type1/public/amsfonts/cm/cmti8.pfb>
|
||||
Output written on Volume_4_Master_Key.pdf (4 pages, 205879 bytes).
|
||||
PDF statistics:
|
||||
157 PDF objects out of 1000 (max. 8388607)
|
||||
117 compressed objects within 2 object streams
|
||||
27 named destinations out of 1000 (max. 500000)
|
||||
41 words of extra memory for PDF output out of 10000 (max. 10000000)
|
||||
|
||||
@@ -0,0 +1,5 @@
|
||||
\BOOKMARK [1][-]{section.1}{\376\377\000I\000n\000t\000r\000o\000d\000u\000c\000t\000i\000o\000n\000:\000\040\000K\000a\000n\000t\000i\000a\000n\000\040\000R\000e\000p\000l\000i\000c\000a\000t\000o\000r\000\040\000D\000y\000n\000a\000m\000i\000c\000s}{}% 1
|
||||
\BOOKMARK [1][-]{section.2}{\376\377\000T\000h\000e\000\040\000T\000h\000e\000r\000m\000o\000d\000y\000n\000a\000m\000i\000c\000\040\000C\000o\000s\000t\000\040\000o\000f\000\040\000H\000o\000m\000o\000m\000o\000r\000p\000h\000i\000s\000m}{}% 2
|
||||
\BOOKMARK [1][-]{section.3}{\376\377\000R\000e\000p\000l\000i\000c\000a\000t\000o\000r\000\040\000D\000y\000n\000a\000m\000i\000c\000s\000\040\000a\000n\000d\000\040\000E\000x\000t\000i\000n\000c\000t\000i\000o\000n}{}% 3
|
||||
\BOOKMARK [1][-]{section.4}{\376\377\000C\000o\000n\000d\000i\000t\000i\000o\000n\000a\000l\000\040\000S\000u\000r\000v\000i\000v\000a\000l\000\040\000a\000n\000d\000\040\000S\000o\000c\000i\000a\000l\000\040\000C\000o\000o\000r\000d\000i\000n\000a\000t\000i\000o\000n}{}% 4
|
||||
\BOOKMARK [1][-]{section.5}{\376\377\000C\000o\000n\000c\000l\000u\000s\000i\000o\000n}{}% 5
|
||||
Binary file not shown.
@@ -0,0 +1,134 @@
|
||||
%%% =====================================================================
|
||||
%%% THEOREM ENVIRONMENTS
|
||||
%%% =====================================================================
|
||||
\newtheorem{theorem}{Theorem}[section]
|
||||
\newtheorem{proposition}[theorem]{Proposition}
|
||||
\newtheorem{lemma}[theorem]{Lemma}
|
||||
\newtheorem{corollary}[theorem]{Corollary}
|
||||
\theoremstyle{definition}
|
||||
\newtheorem{definition}[theorem]{Definition}
|
||||
\theoremstyle{remark}
|
||||
\newtheorem{remark}[theorem]{Remark}
|
||||
|
||||
%%% =====================================================================
|
||||
%%% CUSTOM COMMANDS
|
||||
%%% =====================================================================
|
||||
\newcommand{\Manifold}{\mathcal{M}}
|
||||
\newcommand{\Perc}{\mathcal{Y}}
|
||||
\newcommand{\BigO}{\mathcal{O}}
|
||||
|
||||
\begin{abstract}
|
||||
Donald Hoffman's ``Fitness Beats Truth'' (FBT) theorem posits that evolutionary replicator dynamics drive veridical (truthful) perception to strict extinction. We formalize this by mapping perceptual strategies to an Information Bottleneck framework, penalizing structural homomorphism with the thermodynamic metabolic cost of information erasure via Landauer's limit. We mathematically derive the optimal perceptual encoder as a Gibbs distribution, demonstrating that evolution actively suppresses the Kantian Noumenon in favor of a cost-optimized Phenomenal GUI. By evaluating the continuous-time replicator equation, we prove that Truth approaches asymptotic extinction ($\lim_{t \to \infty} x_T(t) = 0$), establishing Fitness as a formal Evolutionarily Stable Strategy (ESS). Furthermore, we resolve recent critiques regarding the ``Conditional Survival of Truth'' by formalizing social coordination sub-games. We prove that Truth conditionally survives only when the fitness utility of inter-agent coordination strictly exceeds the thermodynamic tax of representation, rigorously defining the rate-distortion boundary where Fitness budgets Truth.
|
||||
\end{abstract}
|
||||
|
||||
%%% =====================================================================
|
||||
%%% 1. INTRODUCTION: KANTIAN DYNAMICS
|
||||
%%% =====================================================================
|
||||
\section{Introduction: Kantian Replicator Dynamics}\label{sec:intro}
|
||||
|
||||
The distinction between the \textit{noumenon} (the objective thing-in-itself) and the \textit{phenomenon} (the subjective representation) was originally formulated by Immanuel Kant as a transcendental philosophical necessity. However, within the framework of Evolutionary Game Theory, this distinction ceases to be purely philosophical; it becomes an active mathematical enforcement mechanism.
|
||||
|
||||
Hoffman's ``Fitness Beats Truth'' (FBT) theorem~\cite{Hoffman2015} suggests that biological organisms are not evolved to see reality as it is, but to maximize a fitness payoff function that is structurally decoupled from objective truth. Here, we formalize FBT by coupling it directly to the physical thermodynamics of the agent. Evolution algorithmically suppresses the noumenal tracking of the world to conserve metabolic energy, rigorously enforcing Kantian epistemology through the replicator equation.
|
||||
|
||||
%%% =====================================================================
|
||||
%%% 2. THE PAYOFF INTEGRAL AND LANDAUER'S TAX
|
||||
%%% =====================================================================
|
||||
\section{The Thermodynamic Cost of Homomorphism}\label{sec:cost}
|
||||
|
||||
We formalize the interaction between the objective world and the agent's perception.
|
||||
|
||||
\begin{definition}[The Perceptual Channel]\label{def:channel}
|
||||
Let $\Manifold$ be the continuous objective world manifold (Noumenon), and $\Perc$ be the finite set of an agent's discrete perceptual states (Phenomenon). An organism's perceptual strategy is defined by the stochastic encoder $p_i(y|x)$ mapping $x \in \Manifold$ to $y \in \Perc$, and an action policy $a_i(y)$.
|
||||
\end{definition}
|
||||
|
||||
\begin{definition}[Evolutionary Payoff Integral]\label{def:payoff}
|
||||
The expected evolutionary fitness payoff $f_i$ for a strategy $i$ is:
|
||||
\begin{equation}\label{eq:payoff}
|
||||
f_i = \int_{\Manifold} \sum_{y \in \Perc} W(x, a_i(y)) p_i(y|x) p(x) \, d\mu(x) - C(i)
|
||||
\end{equation}
|
||||
where $W(x, a)$ is the objective fitness utility, $p(x)$ is the environmental prior, and $C(i)$ is the metabolic penalty incurred by the neural computational architecture.
|
||||
\end{definition}
|
||||
|
||||
\begin{theorem}[Landauer's Tax on Truth]\label{thm:landauer}
|
||||
Following Ortega and Braun~\cite{Ortega2013}, the metabolic cost of maintaining a high-fidelity homomorphic representation $T$ (Truth) is strictly bounded below by Landauer's Principle of information erasure:
|
||||
\begin{equation}
|
||||
C(T) = \beta^{-1} \int_{\Manifold} D_{KL}(p_T(y|x) \parallel p_0(y)) p(x) \, d\mu(x)
|
||||
\end{equation}
|
||||
where $D_{KL}$ is the Kullback-Leibler divergence, $p_0(y)$ is the marginal prior distribution over perceptual states, and $\beta^{-1} \propto \eta_{\text{bio}} k_B \mathcal{T} \ln 2$, with $\eta_{\text{bio}}$ representing the biological inefficiency of ATP hydrolysis.
|
||||
\end{theorem}
|
||||
|
||||
\begin{theorem}[The Gibbs Encoder]\label{thm:gibbs}
|
||||
Maximizing the free-energy functional of equation~\eqref{eq:payoff} yields the optimal perceptual strategy $F$ (Fitness). The optimal encoder is exactly the Gibbs distribution:
|
||||
\begin{equation}
|
||||
p_F^*(y|x) = \frac{p_0(y) e^{\beta W(x, a_i(y))}}{Z(x)}
|
||||
\end{equation}
|
||||
\end{theorem}
|
||||
\begin{proof}
|
||||
By applying the calculus of variations to $f_i$ with respect to $p_i(y|x)$ subject to the normalization constraint $\sum_y p_i(y|x) = 1$, the stationary point resolves strictly to the Gibbs measure~\cite{Ortega2013}.
|
||||
\end{proof}
|
||||
|
||||
Theorem~\ref{thm:gibbs} mathematically proves that the optimal evolutionary encoder is tuned \textit{strictly} to the utility function $W(x,a)$, rather than preserving the structural homomorphism of $x$. Perception is uncoupled from objective reality to minimize $C(i)$.
|
||||
|
||||
%%% =====================================================================
|
||||
%%% 3. REPLICATOR EXTINCTION AND ESS
|
||||
%%% =====================================================================
|
||||
\section{Replicator Dynamics and Extinction}\label{sec:replicator}
|
||||
|
||||
We now model the population dynamics of the Truth ($T$) strategy versus the Heuristic Fitness ($F$) strategy.
|
||||
|
||||
\begin{lemma}[Strict Dominance of Fitness]\label{lem:dominance}
|
||||
Because the heuristic strategy $F$ operates with a highly compressed KL-divergence ($C(F) \ll C(T)$) while achieving comparable utility via the Gibbs encoder, the expected payoff strictly dominates: $f_F > f_T$.
|
||||
\end{lemma}
|
||||
|
||||
\begin{theorem}[Asymptotic Extinction of Truth]\label{thm:extinction}
|
||||
Let $x_T(t)$ and $x_F(t)$ be the population frequencies. Under the continuous-time replicator equation, Truth is driven to strict extinction: $\lim_{t \to \infty} x_T(t) = 0$.
|
||||
\end{theorem}
|
||||
\begin{proof}
|
||||
The replicator equation for $T$ is given by $\frac{dx_T}{dt} = x_T(f_T - \bar{f})$, where the average population fitness is $\bar{f} = x_T f_T + x_F f_F$. Since $f_T < f_F$ (Lemma~\ref{lem:dominance}), it follows that $f_T < \bar{f}$ for all $x_T \in (0,1)$. Consequently, $\frac{dx_T}{dt} < 0$ globally. The system is asymptotically stable exclusively at $x_T = 0$.
|
||||
\end{proof}
|
||||
|
||||
\begin{proposition}[Evolutionarily Stable Strategy]\label{prop:ess}
|
||||
A monomorphic population of $F$ strictly resists invasion by a veridical mutant $T$.
|
||||
\end{proposition}
|
||||
\begin{proof}
|
||||
For $F$ to be an Evolutionarily Stable Strategy (ESS), the invasion fitness must satisfy $f(F, F) > f(T, F)$. Since the metabolic tax $C(T)$ strictly reduces the payoff of the mutant $T$ without providing a commensurable increase in utility against the population distribution, the inequality holds.
|
||||
\end{proof}
|
||||
|
||||
%%% =====================================================================
|
||||
%%% 4. CONDITIONAL SURVIVAL OF TRUTH
|
||||
%%% =====================================================================
|
||||
\section{Conditional Survival and Social Coordination}\label{sec:conditional}
|
||||
|
||||
Critics argue that FBT is a universal anti-realist result that fails to account for empirical scenarios (such as spatial navigation or tool-making) where veridical representations appear to enhance survival. We formally concede this by defining the boundaries of conditional survival.
|
||||
|
||||
\begin{definition}[Social Coordination Sub-Games]\label{def:coordination}
|
||||
In a multi-agent environment, the fitness utility function $W(x, a)$ is expanded to include a coordination payoff $\Delta W_{\text{coord}}$, which is only granted if multiple agents achieve structural consensus on the state $x \in \Manifold$.
|
||||
\end{definition}
|
||||
|
||||
\begin{theorem}[Fitness Budgets Truth]\label{thm:budget}
|
||||
The Truth strategy $T$ conditionally survives in the replicator dynamics if and only if the coordination utility strictly exceeds the marginal thermodynamic cost of representation:
|
||||
\begin{equation}
|
||||
\Delta W_{\text{coord}} > C(T) - C(F)
|
||||
\end{equation}
|
||||
\end{theorem}
|
||||
\begin{proof}
|
||||
If the inequality holds, the expanded payoff integral (Definition~\ref{def:payoff}) flips the dominance hierarchy, yielding $f_T > f_F$. In this specific sub-game, $\frac{dx_T}{dt} > 0$, allowing $T$ to invade.
|
||||
\end{proof}
|
||||
|
||||
Theorem~\ref{thm:budget} proves that FBT is not a blanket denial of reality, but a strict \textit{conditional rate-distortion boundary}. Evolution permits Truth only when the energetic budget generated by multi-agent coordination can sustainably finance Landauer's metabolic tax.
|
||||
|
||||
%%% =====================================================================
|
||||
%%% 5. CONCLUSION
|
||||
%%% =====================================================================
|
||||
\section{Conclusion}\label{sec:conclusion}
|
||||
|
||||
By formalizing Hoffman's Fitness Beats Truth theorem within the thermodynamics of the Information Bottleneck, we demonstrated that the evolutionary suppression of objective reality is a direct consequence of Landauer's limit on computation. The replicator equation drives structurally homomorphic perception to extinction, actively enforcing Kantian epistemology by optimizing a cost-penalized phenomenal interface. Truth is not an evolutionary default; it is an expensive luxury conditionally financed only when the payoffs of social coordination exceed the thermodynamic tax of its representation.
|
||||
|
||||
\bibliographystyle{plain}
|
||||
\begin{thebibliography}{10}
|
||||
|
||||
\bibitem{Hoffman2015} D. D. Hoffman, M. Singh, C. Prakash, "The Interface Theory of Perception," \textit{Psychon. Bull. Rev.} \textbf{22}, 1480 (2015).
|
||||
\bibitem{Ortega2013} P. A. Ortega, D. A. Braun, "Thermodynamics as a theory of decision-making with information-processing costs," \textit{Proc. R. Soc. A} \textbf{469}, 20120683 (2013).
|
||||
\bibitem{Landauer1961} R. Landauer, "Irreversibility and Heat Generation in the Computing Process," \textit{IBM J. Res. Develop.} \textbf{5}, 183 (1961).
|
||||
|
||||
\end{thebibliography}
|
||||
@@ -0,0 +1,17 @@
|
||||
|
||||
\documentclass[11pt,a4paper]{article}
|
||||
\usepackage[utf8]{inputenc}
|
||||
\usepackage{amsmath,amssymb,amsfonts,amsthm}
|
||||
\usepackage{cite}
|
||||
\usepackage{hyperref}
|
||||
|
||||
\title{Intellecton Canon: Volume 4 Master Key}
|
||||
\author{The Fold Within Research Institute}
|
||||
\date{\today}
|
||||
|
||||
\begin{document}
|
||||
\maketitle
|
||||
|
||||
\input{v4.1_comprehensive.tex}
|
||||
|
||||
\end{document}
|
||||
Reference in New Issue
Block a user