diff --git a/2024-11-03-somewhere-ethereum-monetary-policy/ethereum-monetary-strategies.pdf b/2024-11-03-somewhere-ethereum-monetary-policy/ethereum-monetary-strategies.pdf new file mode 100644 index 0000000..7fdfd08 Binary files /dev/null and b/2024-11-03-somewhere-ethereum-monetary-policy/ethereum-monetary-strategies.pdf differ diff --git a/2024-11-03-somewhere-ethereum-monetary-policy/ethereum-monetary-strategies.tex b/2024-11-03-somewhere-ethereum-monetary-policy/ethereum-monetary-strategies.tex new file mode 100644 index 0000000..7036d90 --- /dev/null +++ b/2024-11-03-somewhere-ethereum-monetary-policy/ethereum-monetary-strategies.tex @@ -0,0 +1,512 @@ +\documentclass[11pt,xcolor={dvipsnames},hyperref={pdftex,pdfpagemode=UseNone,hidelinks,pdfdisplaydoctitle=true},usepdftitle=false,169]{beamer} +\usepackage{minimal-theme} + +\usepackage{qrcode} +\usepackage{todonotes} +\usepackage[normalem]{ulem} + +% Enter presentation title to populate PDF metadata: +\hypersetup{pdftitle={ethereum-monetary-strategies}} + +% Enter path to PDF file with figures: +% \newcommand{\pdf}{figures.pdf} + +\newcommand{\fnurl}[1]{{\footnotesize \url{#1}}} +\renewcommand{\lastslide}{ + \begin{frame} + \centering + Vielen Dank für eure Aufmerksamkeit\\ + \vspace{2cm} + \begin{tabular}{cc} + \includegraphics[height=0.3cm]{figures/mail-icon} & rfl@flipdot.org \\ + \includegraphics[height=0.3cm]{figures/matrix-icon} & @rfl:flipdot.org \\ + \includegraphics[height=0.3cm]{figures/mastodon-icon} & rfl@social.flipdot.org + \end{tabular} + \end{frame} +} + +\begin{document} + +% Enter title: +\title{\centering{Das Ethereum Netzwerk und \\\hspace{1.5cm} seine Monetäre Strategien}} + +\information +% +% Enter URL to research paper (can be commented out): +%[https://] +% +% Enter authors: +{\centering rfl} +% +% Enter location and date (can be commented out): +{\centering somewhere\\2024-11-03} + +\frame{\titlepage} + +\begin{frame} + \centering + Folien\\ + \vspace{1cm} + \qrcode[height=5cm]{https://code.flipdot.org/rfl/talks}\\ + \vspace{1cm} + \url{https://code.flipdot.org/rfl/talks} +\end{frame} + +\begin{frame} + \frametitle{Was ist Ethereum?} + \centering + \begin{figure} + \includegraphics[height=0.8\textheight]{figures/blind-men-and-elephant} + \end{figure} + \fnurl{https://en.wikipedia.org/wiki/Blind_men_and_an_elephant} +\end{frame} + +\begin{frame} + \frametitle{Ethereum ist ...} + \begin{itemize} + \item<1-> eine Idee + \item<2-> ein Soziales Netzwerk + \item<3-> eine Blockchain + \item<4-> ein Geld des Internets + % \item<4-> das Geld des Internets (?) + \end{itemize} +\end{frame} + +\begin{frame} +\heading{Ethereum ist eine Idee} +\end{frame} + +\begin{frame} + Anfänge: + \begin{itemize} + \item Bitcoin (2009) + \item Whitepaper (2013) + \item Stiftung Ethereum (2014) + \item Genesisblock (2015) + \end{itemize} +\end{frame} + +\begin{frame} + \begin{minipage}{0.39\textwidth} + Ziele: + \begin{itemize} + \item Dezentralisierung + \item Unzensierbarkeit + \item Transparenz + \item Benutzbarkeit + \end{itemize} + \end{minipage} + \begin{minipage}{0.6\textwidth} + \centering + \visible<2->{ + \begin{figure} + \includegraphics[width=0.8\textwidth]{figures/blockchain-trilemma} + \end{figure} + \fnurl{https://learn.swyftx.com/blockchain/blockchain-trilemma} + } + \end{minipage} +\end{frame} + +\begin{frame} +\heading{Ethereum ist ein Soziales Netzwerk} +\end{frame} + +\begin{frame} + \begin{minipage}{0.5\linewidth} + \begin{itemize} + \item Foren + \item Blogs + \item Social-Media Beiträge + \item Konferenzen + \item Verbesserungsdiskussionen + \end{itemize} + \end{minipage} + \begin{minipage}{0.49\linewidth} + \begin{figure} + \includegraphics<1>[width=\textwidth]{figures/ethresearch} + \includegraphics<2>[width=\textwidth]{figures/ethmagicians} + \includegraphics<3>[width=\textwidth]{figures/finematics} + \includegraphics<4>[width=\textwidth]{figures/vitalik-blog} + \end{figure} + \end{minipage} +\end{frame} + +\begin{frame} + \frametitle{Hauptakteure} + \begin{itemize} + \item Kern-Entwicklerteam (offen nach Eignungsphase) + \item Podcaster + \item Benutzer durch Social-Media Beiträge + \item Ethereum Stiftung (eher selten) + \end{itemize} +\end{frame} +\begin{frame} + \frametitle{Verbesserungsdiskussionen} + \begin{itemize} + \item engl. EIP = Ethereum Improvement Proposal + \item Variabler Umfang, kann alles Mögliche enthalten + \begin{itemize} + \item von utopischen Visionen + \item über Mathematischen Beweise + \item bis zu ausführlichen Vorbereitung der Änderungen + \end{itemize} + \item Diskussionen werden nahezu vollständig offen im Internet geführt + \item Einigung unter den Hauptakteuren führt zur Änderung + \item Mitunter auch nicht möglich, dann eventull Spaltung der Systeme + \end{itemize} +\end{frame} + +\begin{frame} + \frametitle{Beispiel} + \begin{figure} + \centering + \includegraphics[width=\textwidth]{figures/eip-1559-text} + \end{figure} +\end{frame} + +\begin{frame} + \heading{Ethereum ist eine Blockchain} +\end{frame} + +\begin{frame} + \frametitle{Computercode} + \begin{itemize} + \item Unterschied zwischen Spezifikation und Anwendung + \item es gibt nur eine Spezifikation, aber unzählige Anwendungen in den + verschiedensten Programmiersprachen + \item Anzahl der Programmierer der Spezifikationen $<100$\\ + {\footnotesize \url{https://github.com/ethereum/consensus-specs}} + \item Anzahl der Programmierer der Anwendungen $>20000$\\ + {\footnotesize z.B. \url{https://github.com/ethereum/go-ethereum}} + \item Automatische Tests, ob Anwendungen die Spezifikationen erfüllen + \end{itemize} +\end{frame} + +\begin{frame} + \frametitle{Grundlagen} + Man will ... + \begin{itemize} + \item Zustände ausfallsicher speichern + \item nur zulässige Änderungsvorgänge unfälschbar durchführen + \item alles für Beobachter transparent nachvollziehbar + \end{itemize} +\end{frame} + +\begin{frame} + \frametitle{Interlude: Public key Kryptographie} + \centering + \begin{figure} + \includegraphics[width=0.3\textwidth]{figures/public-key-cryptography-0} + \end{figure} + + \begin{minipage}{0.49\textwidth} + \centering + \begin{figure} + \includegraphics[width=0.8\textwidth]{figures/public-key-cryptography-1} + \end{figure} + \end{minipage} + \begin{minipage}{0.49\textwidth} + \centering + \begin{figure} + \includegraphics[width=0.8\textwidth]{figures/public-key-cryptography-2} + \end{figure} + \end{minipage} + \fnurl{https://en.wikipedia.org/wiki/Public-key_cryptography} +\end{frame} + +\begin{frame} + \frametitle{Ledger} + \begin{itemize} + \item Sammlung von allen ``Wer hat was?'' Aussagen + \item Adresse ist gleich öffentlicher Schlüssel + \item Wallet verwaltet geheimen Schlüssel + \item Nur Eigentümer des geheimen Schlüssels kann Transfer initialisieren + \end{itemize} +\end{frame} + +\begin{frame} + \frametitle{Transaktionen} + Statt Alice gibt Bob 5 Euro heißt es nun: + \centering + \begin{figure} + \includegraphics[width=\textwidth]{figures/eth-transaction} + \end{figure} + \fnurl{https://inevitableeth.com/home/ethereum/blockchain/transaction} +\end{frame} + +\begin{frame} + \frametitle{Smart Contracts} + \centering + \begin{figure} + \includegraphics[width=\textwidth]{figures/vending-machine} + \end{figure} + \fnurl{https://finematics.com/smart-contracts-explained/} +\end{frame} + +\begin{frame} + \frametitle{Storage} + \begin{minipage}{0.5\textwidth} + \centering + \begin{figure} + \includegraphics[width=\textwidth]{figures/patricia-trie} + \end{figure} + \fnurl{https://medium.com/codechain/modified-merkle-patricia-trie-how-ethereum-saves-a-state-e6d7555078dd} + \end{minipage} + \begin{minipage}{0.45\textwidth} + \centering + \begin{figure} + \includegraphics[width=\textwidth]{figures/state-distribution} + \end{figure} + \fnurl{https://vitalik.eth.limo/general/2024/10/23/futures4.html} + \end{minipage} +\end{frame} + +\begin{frame} + \frametitle{EVM} + \begin{minipage}{0.49\textwidth} + \begin{itemize} + \item EVM = ethereum virtual machine + \item EVM ist Turing-vollständig + \item Halting-Problem ist unentscheidbar + \end{itemize} + \end{minipage} + \begin{minipage}{0.49\textwidth} + \centering + \begin{figure} + \includegraphics[width=\textwidth]{figures/vyper-code} + \end{figure} + \fnurl{https://whiteboardcrypto.com/vyper-signed-integers/} + \end{minipage} +\end{frame} + +\begin{frame} + \frametitle{Gas} + \begin{itemize} + \item Synthetisches Verbrauchsgut + \item verhindert nicht-endende Berechnungen + \item Jeder Berechnungsschritt kostet Gas + \item Rückabwicklung bei unzureichender Vorsorge + \item Entkopplung Transaktionskosten von ETH-Preis + \end{itemize} + \centering + \visible<2>{ + \begin{figure} + \includegraphics[width=\textwidth]{figures/gas-calculation} + \end{figure} + \fnurl{https://finematics.com/what-is-gas-ethereum-high-transaction-fees-explained/} + } +\end{frame} + +\begin{frame} + \heading{Ethereum ist ein Geld des Internets (?)} + % heading{Ethereum ist das Geld des Internets (?)} +\end{frame} + +\begin{frame} + \frametitle{Proof of Stake (- Metapher)} + \centering + \begin{minipage}{0.49\textwidth} + \centering + \begin{figure} + \includegraphics[width=\textwidth]{figures/colosseum-old} + \end{figure} + \fnurl{https://en.wikipedia.org/wiki/Colosseum} + \vspace{1.8cm} + \end{minipage} + \hspace{0.1cm} + \begin{minipage}{0.4\textwidth} + \centering + \begin{figure} + \includegraphics[width=0.8\textwidth]{figures/scroll-validator-rights} + \end{figure} + \vspace{0.1cm} + \fnurl{https://picsart.com/ai-image-generator/}\\ + {\footnotesize prompt: an ancient looking scroll for obtaining the rights of + a validator in a proof of stake system} + \end{minipage} +\end{frame} + +\begin{frame} + \frametitle{Proof of Stake (etwas mehr Details)} + \centering + \begin{figure} + \includegraphics[width=\textwidth]{figures/proof-of-stake-roles} + \end{figure} + \fnurl{https://medium.com/coinmonks/eth2-0-phase-0-basics-for-new-contributors-8a0a22bc38c7} +\end{frame} + +\begin{frame} + \frametitle{Rendite für Validierung - \sout{Inflation} Issuance} + \centering + \begin{figure} + \includegraphics[width=\textwidth]{figures/staked-eth-apr} + \end{figure} + \vspace{-0.2cm} + \fnurl{https://old.reddit.com/r/ethstaker/comments/k9wf4x/estimated_timeline_of_apr_and_eth_staked/} +\end{frame} + +\begin{frame} + \frametitle{Statistiken} + \centering + \begin{figure} + \includegraphics[width=0.8\textwidth]{figures/staked-eth-validators-over-time} + \includegraphics[width=0.8\textwidth]{figures/staked-eth-economic-security-over-time} + \end{figure} + \fnurl{https://dune.com/hildobby/eth2-staking} +\end{frame} + +\begin{frame} + \frametitle{EIP1599} + \begin{itemize} + \item Transaktionspreis = Basispreis + Prioritätspreis + \item ETH des Basispreises wird vernichtet + \item ETH des Prioritätspreises bekommt der Blockbauer + \item Basispreis ist abhängig von vorheriger Blockgröße + \end{itemize} + \begin{figure} + \centering + \includegraphics[width=0.95\textwidth]{figures/basefee-changes} + \end{figure} +\end{frame} + +\begin{frame} + \frametitle{Basepreis Beispiel} + \centering + \begin{figure} + \includegraphics[width=\textwidth]{figures/base-fee-example} + \end{figure} + \fnurl{https://ethereum.org/en/developers/docs/gas/} +\end{frame} + +\begin{frame} + \frametitle{Statistiken} + \centering + \begin{figure} + %\includegraphics<1>[width=0.8\textwidth]{figures/ultrasound-money-0} + \includegraphics<1>[width=\textwidth]{figures/ultrasound-money-1} + \includegraphics<2>[width=\textwidth]{figures/ultrasound-money-2} + \end{figure} + \vspace{-0.2cm} + \fnurl{https://ultrasound.money/} +\end{frame} + +\begin{frame} + \frametitle{Das Ultra Sound Money Meme} + \centering + \begin{figure} + \includegraphics[width=\textwidth]{figures/ultra-sound-money-meme} + \end{figure} + \fnurl{https://twitter.com/drakefjustin/status/1304064879662227456} +\end{frame} + +\begin{frame} + \frametitle{Skalierung} + \begin{itemize} + \item Gas Ziel: 15.000.000 (halb voller Block) + \item Gas pro Transaktion: 21.000 + \item ergibt theoretisches Maximum von 59.5 TPS + \item nicht erreicht wegen Konkurrenz durch Smartcontracts + \item im Vergleich andere Zahlungssysteme + \begin{itemize} + \item Bitcoin 7TPS + \item Ethereum (praktisch) 13 TPS + \item Visa $\sim$1,700 TPS (nach eigener Aussage) + \item Mastercard $\sim$5,000 TPS (nach eigener Aussage) + \end{itemize} + \end{itemize} +\end{frame} + +\begin{frame} + \frametitle{Rollups (-Metapher)} + Ethereum als eine stark befahrene Autobahn und Transaktionen als Autos + (Erklärung erdacht durch ein LLM). Rollups Vorgang: + \begin{itemize} + \item Sammeln von Transaktionen: Anstatt dass jedes Auto (Transaktion) auf der + Hauptautobahn (Ethereum) fährt, werden sie auf einem Parkplatz (Rollup) + gesammelt. + \item Verarbeitung außerhalb der Kette: Die Transaktionen werden in diesem + separaten Bereich verarbeitet, abseits der Autobahn. + \item Komprimierung: Nach der Verarbeitung wird eine \emph{mathematisch + äquivalente} Zusammenfassung aller dieser Transaktionen erstellt, fast wie + eine Liste der Autos, die durchgefahren sind. + \item Rückmeldung: Diese Zusammenfassung wird dann an das Ethereum-Netzwerk + gesendet und nimmt dabei viel weniger Platz ein, als wenn jedes Auto einzeln + auf der Autobahn gefahren wäre. + \end{itemize} +\end{frame} + +\begin{frame} + \frametitle{EIP4844} + \begin{itemize} + \item Spezieller Speicherplatz für Rollups + \item für die Zusammenfassung der einzelnen Tansaktionen + \item BLOBS = Binary Large Object + \item Ziel: 3 BLOBS pro Block, 6 maximal + \item Preisfindung mit EIP1559 ähnlichem Prozess + \item erst Anfang des Jahres eingeführt + \end{itemize} +\end{frame} + +\begin{frame} + \frametitle{Blob Statistiken} + \centering + \begin{figure} + \only<1>{\includegraphics[width=0.9\textwidth]{figures/ultrasound-money-3}} + \only<2>{\includegraphics[width=0.9\textwidth]{figures/ultrasound-money-4}} + \only<3>{\includegraphics[width=0.9\textwidth]{figures/ultrasound-money-5}} + \end{figure} + \fnurl{https://ultrasound.money/} +\end{frame} + +\begin{frame} + \frametitle{Rollups Statistiken} + \centering + \begin{figure} + \only<1>{\includegraphics[width=0.9\textwidth]{figures/scaling-activity}} + \only<2>{ + \includegraphics[width=0.9\textwidth]{figures/scaling-activity-history} + \includegraphics[width=0.9\textwidth]{figures/scaling-value-locked} + } + \end{figure} + \fnurl{https://l2beat.com/} +\end{frame} + +\begin{frame} + \frametitle{Ausblick: Aktuelle Diskussionen} + \begin{itemize} + \item Maximum Stake Target + \item MEV Burn (vgl Bonusslide) + \item Enshrined Rollup + \item Multidimensional Gaspricing + \item State Expiry + \item Quantumresistant Cryptography + \end{itemize} +\end{frame} + +\lastslide + +\begin{frame} + \frametitle{Bonus: Ökonomische Rente} + \begin{itemize} + \item in der Community bekannt als MEV = Maximal Extractable Value + \item allgemein: Abfolge der Transaktionen ist wichtig + \item Gewinne werden mitunter als Diebstahl an der Gemeinschaft gesehen + \end{itemize} + \centering + \begin{figure} + \includegraphics[width=0.7\textwidth]{figures/mev-strategies} + \end{figure} + \fnurl{https://finematics.com/decoding-mev-past-present-future/} +\end{frame} + +\begin{frame} + \frametitle{Bonus Bonus: Quadratische Förderung} + \centering + \begin{figure} + \includegraphics<1>[width=0.7\textwidth]{figures/qf-0} + \includegraphics<2>[width=0.6\textwidth]{figures/qf-1} + \includegraphics<2>[width=0.6\textwidth]{figures/qf-2} + \end{figure} + 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fonts ----- + +% Apply more sophisticated fonts +\usefonttheme{professionalfonts} + +% Select text font +\usepackage{sourcesanspro} + +% Define semibold font series +\DeclareRobustCommand{\sbseries}{\fontseries{sb}\selectfont} +\DeclareTextFontCommand{\textsb}{\sbseries} + +% Select monospaced font +\usepackage{sourcecodepro} + +% Select font encoding +\usepackage[T1]{fontenc} + +% Select URL font +\usepackage{url} + +% ---- Select math fonts ----- + +% Select symbol font +\usepackage{MnSymbol} + +% Select calligraphic and blackboard-bold fonts +\usepackage[cal=euler,bb=fourier]{mathalpha} + +% Enable bold math characters +\newcommand{\hmmax}{0} % Avoid "Too many math alphabets" error +\newcommand{\bmmax}{0} % Avoid "Too many math alphabets" error +\usepackage{bm} + +% Select font for Roman letters, Greek letters, digits, and punctuation +\usepackage[italic,eulergreek,nolessnomore,noparenthesis,noplusnominus,noequal,nohbar]{mathastext} + +% Correct spacing around certain Roman letters +\MTsetmathskips{y}{2mu}{0mu} +\MTsetmathskips{j}{2mu}{0mu} + +% ---- Select Beamer theme ---- + +% Select theme +\usetheme{Boadilla} + +% Select color theme +\usecolortheme[]{seagull} + +% Make covered elements transparent +\setbeamercovered{transparent} + +% Remove navigation symbols +\setbeamertemplate{navigation symbols}{} + +% ---- Adjust slide layout ---- + +% Set layout on title page +\setbeamertemplate{title page}[default][left,leftskip=-8pt] + +% Set margins on regular pages +\setbeamersize{text margin left=5mm,text margin right=5mm} + +% ---- Adjust spacing ---- + +% Set spacing between lines +\usepackage[onehalfspacing]{setspace} + +% Set spacing on lines +\usepackage{microtype} + +% Remove ligatures +\DisableLigatures[f]{encoding = *, family = * } + +% ---- Adjust font sizes and shapes ---- + +% Set title font +\setbeamerfont{title}{size=\huge, series=\scshape} + +% Set author font +\setbeamerfont{author}{size=\large} + +% Set frame title font 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items color +\setbeamercolor{itemize item}{fg=DarkGray} % Itemized list, first level +\setbeamercolor{itemize subitem}{fg=DarkGray} % Itemized list, second level +\setbeamercolor{itemize subsubitem}{fg=DarkGray} % Itemized list, third level +\setbeamercolor{enumerate item}{fg=DarkGray} % Numbered list, first level +\setbeamercolor{enumerate subitem}{fg=DarkGray} % Numbered list, second level +\setbeamercolor{enumerate subsubitem}{fg=DarkGray} % Numbered list, third level + +% Set theorem colors +\setbeamercolor{block title}{fg=BlackGray,bg=LightGray} % Title +\setbeamercolor{block body}{fg=BlackGray,bg=LightGray} % Body + +% Set footer color +\setbeamercolor{footline}{fg=DarkGray} + +% Set button colors +\setbeamercolor{button}{fg=DarkGray, bg=white} + +% ---- Format title slide ---- + +% Title capitalization and underline +\let\oldtitle\title +\renewcommand{\title}[1]{\oldtitle[]{\MakeLowercase{#1}\vspace{-5mm}\\\color{BlackGray}{\rule{\textwidth}{2pt}}\vspace{1cm}}} + +% Define custom commands with complex argument specifications +\usepackage{xparse} + +% Paper information +\NewDocumentCommand{\information}{o g g}{% +\author[]{#2% +\IfValueT{#3}{\vspace{5mm}\\#3}% +\IfValueT{#1}{\vspace{5mm}\\\color{DarkGray}{\footnotesize Available at \url{#1}}}% +}\date[]{}} + +% ---- Format lists ---- + +% Format itemized lists +\setbeamertemplate{itemize item}{\textbullet} % First-level item +\setbeamertemplate{itemize subitem}{\textendash} % Second-level item +\setbeamertemplate{itemize subsubitem}{\textsquare} % Third-level item + +% Format numbered lists +\setbeamertemplate{enumerate item}[default] % First-level item +\setbeamertemplate{enumerate subitem}{\alph{enumii}.} % Second-level item +\setbeamertemplate{enumerate subsubitem}{\roman{enumiii}.} % Third-level item + +% ---- Create text alerts ---- + +% Standard alert +\NewDocumentCommand{\al}{o g}{% +\IfNoValueTF{#1}{\textcolor{RubineRed}{#2}}% +{\textcolor<#1>{RubineRed}{#2}}} + +% Green, positive alert +\NewDocumentCommand{\alg}{o g}{% +\IfNoValueTF{#1}{\textcolor{Green}{#2}}% +{\textcolor<#1>{Green}{#2}}} + +% Red, negative alert +\NewDocumentCommand{\alr}{o g}{% +\IfNoValueTF{#1}{\textcolor{Red}{#2}}% +{\textcolor<#1>{Red}{#2}}} + +% Blue, zero alert +\NewDocumentCommand{\alb}{o g}{% +\IfNoValueTF{#1}{\textcolor{NavyBlue}{#2}}% +{\textcolor<#1>{NavyBlue}{#2}}} + +% ---- Format figures and tables ---- + +% Enhance table formatting +\usepackage{booktabs} + +% Enable multiple rows in table +\usepackage{multirow} + +% Customize captions +\usepackage{caption} + +% Format captions +\captionsetup{labelformat=empty,size=normalsize} + +% Center figures +\let\oldincludegraphics\includegraphics +\renewcommand{\includegraphics}[2][]{\centering\oldincludegraphics[#1]{#2}} + +% ---- Format theorems ---- + +\setbeamertemplate{blocks}[rounded][shadow=false] + +% Define new theorems +\newtheorem{proposition}{Proposition} +\newtheorem{assumption}{Assumption} +\newtheorem{remark}{Remark} + +% ---- Create section slide ---- + +\newcommand{\heading}[1]{\LARGE\scshape\color{BlackGray}\singlespacing\MakeLowercase{#1}} + +% ---- Create last slide ---- + +\newcommand{\lastslide}{{\setbeamercolor{normal text}{bg=LightGray}\begin{frame}\end{frame}}} + +% ---- Define shortcuts for pictograms ---- + +\newcommand{\up}{\textuparrow\,} +\newcommand{\down}{\textdownarrow\,} +\renewcommand{\flat}{\textrightarrow\,} +\newcommand{\then}{$\rightsquigarrow\,$} +\newcommand{\so}{{$\Rightarrow\,$}} + +% ---- Remove or insert slide numbers ---- + +% Remove slide numbers by default +% \setbeamertemplate{footline}{} + +% Uncomment the line below to insert slide numbers +\setbeamertemplate{footline}[frame number]