Mathematical Tools in a Digital World 7th September 2012 An investigation into their development and their impact on the wider world from the perspective of digital culture by Anthony Durity May 2012 Digital Culture / Department of Art and Culture Studies / University of Jyväskylä i Final year thesis, Jyväskylä 2011 – Cork 2012 From Anthony Durity At University of Jyväskylä, central Finland In the International Master’s Degree in Digital Culture Supervisors (senior) Raine Koskimaa (junior) Kristóf Fenyvesi ex-Supervisors Susanna Paasonen Kimmo Lehtonen Publishing, copyright and licensing information: Anthony Durity, copyright © 2012 Some rights reserved Typeset in Big Caslon (serif), Source Sans Pro (sans serif), Monaco (monospace) Published online via https://kirjasto.jyu.fi/publish-and-buy/publishing-your-thesis Mathematical Tools in a Digital World is copyrighted and licensed in accordance with the terms and policies laid out by the Jyväskylä Library Thesis Portal. Where there is no conflict of interest and without prejudice it relicensed under a Cre- ative Commons Attribution - NonCommercial - Sharealike 3.0 Unported License. Please see the Creative Commons website for more details. Acknowledgments: (in no particular order) Susanna Paasonen, Raine Koskimaa, Kristóf Fenyvesi: all of Jyväskylä university; Ronan Farrell friend and eagle-eyed editor; Gio- vanna di Rosario for showing me how and encouragement; Anne Durity and Leo Du- rity for unceasing support; Jonne Arjoranta for translating the abstract; Pamela Jones of Groklaw fame, Tony Wasserman of Carnegie Mellon university, Carlo Daffara of Conecta, Martin Michlmayr of Cyrius, Diana Harrelson of cyber-anthro.com: for help- ful pointers, advice and information; Darrel C. Ince, Leslie Hatton & John Graham- Cumming for their timely Nature article and correspondence; to all who responded to my questionnaires and follow-up questions. ii Abstract Humanistinen tiedekunta Athenaeum PL 35 40014 Jyväskylän yliopisto puh. 040 805 3412, 040 805 3404 [email protected].fi twitter: @jyuhum Käyntiosoite: Seminaarinkatu 15 A-rakennus Avoinna: ma klo 10-16 ti-to klo 9-16 pe klo 9-15 On monia näkökulmia, joista digitaalista kulttuuria voidaan tarkastella. Matematiikan ja matemaattisten työvälineiden yhteys kaikkeen digitaaliseen on yksi näistä näkökul- mista. Tämä viittaa matemaattisten ohjelmien tutkimukseen. Pääasialliset lähestymis- tavat, joita voidaan noudattaa, ovat matematiikan harjoittaminen, soveltaminen ja koulu- tus. Tämä tutkielma keskittyy harjoittamiseen ja soveltamiseen, jättäen huomiotta koulut- tamisen. Tässä tutkielmassa osoitetaan miten kasvavassa määrin tietokoneistettu maailmamme vaikuttaa matematiikan harjoittamiseen. Mikään matematiikan osa-alue kuvaamisesta teoreeman todistukseen ei ole jäänyt koskemattomaksi. Esimerkkinä tästä ohjelmoin fraktaaliuniversumin osajoukon, L-systeemin, osaksi tutkielmaa. Matematiikkaa soveltavien ihmisten työ on helpottunut heidän pystyessään automatisoimaan tehtäviään, ovat he sitten insinöörejä, tutkijoita tai taiteilijoita. Olen tuonut tätä esiin keskittymällä matemaat- tisen taiteen viimeaikaiseen kasvuun. Kulttuuri ja ideologia vaikuttavat kaikkiin elämän osa-alueisiin, eikä ohjelmistonke- hitys ole poikkeus. Keskeisiä kysymyksiä ovat hallinta ja vapaus, suljetut järjestelmät ja läpinäkyvyys. Sillä, miten ohjelmistoja kehitetään on eettisiä/pragmaattisia seurauksia, sillä voi olla lainopillisia seurauksia, tieteellisessä käytössä matemaattisilla ohjelmistoilla on epistemologisia seurauksia, ja sen lisäksi ovat taloudelliset seuraukset. Selvitin en- sin tekijänoikeuksien ja henkisen omaisuuden oikeuksien historiaa - sitten tarkastelin, miten nämä toimivat viitekehyksinä ohjelmistoalalla. Voidakseni vertailla ilmaisia ja avoimen lähdekoodin matemaattisia ohjelmistoja sul- jettuihin ohjelmistoihin laadin joukon kyselylomakkeita ja käytin niihin digitaalisen etno- grafian metodologiaa. Tämä tarkoitti avoimen lähdekoodin Sage-projektin käyttäjien ja kehittäjien ja suljetun lähdekoodin Mathematican käyttäjien ja kehittäjien kanssa puhu- mista. Annoin myös yksityiskohtaisen yleiskatsauksen molemmista järjestelmistä ennen kuin analysoin saamani vastaukset. There are many vantage points from which to gain a perspective on digital culture. The intersection of mathematics and mathematical tools with all things digital is one such vantage point. This implies an inspection of mathematical software. The broad lines that can be taken are the practice, education and application of mathematics. This the- sis focuses on practice and application, disregarding education. iii With regards the former it is shown how the practice of mathematics itself has been affected by the increasingly pervasive computational nature of our world. From visu- alisation to theorem proving no area has been untouched. I programmed a subset of the fractal universe, L-Systems, into the thesis to demonstrate this. In the latter case those who apply mathematics have been aided by the automation of their tasks: be they engineers or academics or artists. I have focused on the recent growth in mathematical art to highlight this. Culture and ideology affect all areas of life, and the development of software is no ex- ception. At heart are issues of control and freedom, lock-in and transparency. How one develops software can have ethical/pragmatic considerations, it can have legal ramifica- tions, when we get into how mathematics software is used in science there are increas- ing epistemological issues, finally there are economic ones. First I looked backward in time to survey the history of copyright and intellectual property rights – then I consid- ered how these frameworks operate in the software world. In order to compare and contrast free and open source mathematical software with proprietary software I composed a set of questionnaires and used the methodology of digital ethnography. In the end this meant talking to users and developers of the open- source Sage project and users and developers of the proprietary Mathematica package. I also gave a detailed overview of both systems prior to analysing the responses. iv Table of Contents 1 Prefatory remarks 1 1.1 These digital times ............................ 1 1.2 The topic of this thesis .......................... 3 1.3 Coda, what is meant by digital? ..................... 5 2 Research overview 9 2.1 Thesis outline ............................... 9 2.2 Overview of source material ....................... 9 2.2.1 Mathematical art, fractals, chaos, computer algebra systems .. 10 2.2.2 Free and open source software, hacker culture, software devel- opment .............................. 10 2.2.3 Various viewpoints: legal, economic, ethical, epistemological . 11 2.2.4 Other notable sources of material ................ 11 2.3 Methodological decisions ........................ 11 3 The impact of mathematics having gone digital 13 3.1 A bird’s-eye view of mathematical software ............... 13 3.2 Historical development and state of play ................. 15 3.3 An excursion into a fractal world ..................... 17 3.3.1 Koch curves (curves, islands and snowflakes) .......... 20 3.3.2 Sierpiski triangle ........................ 21 3.3.3 Fractal plant ........................... 22 3.3.4 Hilbert curve ........................... 22 3.4 The flight to abstraction: abstract expression and mathematical art .. 23 4 The culture and ideology of intangible media (data) and software development (code) 37 4.1 The origin of copyright .......................... 37 4.2 History and snapshot of FOSS ..................... 40 4.3 The tar pit: software programming is hard ............... 43 4.4 Legal, economic, ethical, epistemological angles ............ 45 4.4.1 Legal: no, all, or some rights reserved .............. 45 4.4.2 Economic: the new economy .................. 47 4.4.3 Ethical: pragmatism versus ethics ................ 49 4.4.4 Epistemological: the case for open computer programs .... 50 5 Specific comparison and questionnaires 52 5.1 Compare and contrast open versus proprietary tools .......... 52 5.2 Sage .................................... 52 5.2.1 Lead-up to open source questionnaire .............. 52 5.2.2 Feedback to open source questionnaire ............. 56 5.2.3 Follow-up questions to open source questionnaire ....... 61 5.3 The proprietary world .......................... 62 5.3.1 Lead-up to proprietary questionnaire .............. 62 v 5.3.2 Feedback to proprietary questionnaire ............. 65 5.3.3 Follow-up questions to proprietary questionnaire ....... 74 5.4 Results .................................. 75 5.5 What I learnt about posing surveys ................... 75 6 Summary of results and conclusion 76 6.1 Brief finishing remark .......................... 77 7 Endnotes and citations 78 8 Appendix 86 vi “Patterns are everywhere, Best not to read too much into that.” Pythagoras (to an acolyte), 3rd Book of the Apocrypha Geometrica 1 Prefatory remarks 1.1 These digital times Humanity is living in the digital age. In the span of a few generations the world has been transformed utterly by the microelectronic revolution. Most recently there has been the transition from wired to wireless – all within the space of a handful of decades – this means that the very atmosphere is suffused with digital information. Gadgets that were the fodder of the wildest pulp science fiction mere decades ago have now become ubiquitous, everyday, commonplace. Every era has a beat [Luhmann, 1982, cf.], [1] to which it thrums and hums. This characteristic