Title Page AbstractOutline of Presentation of Talk OutlineOutline of Presentation of Talk October 1st 2008 I will describe and illustrate my experiences 0. Early Chronology of a Company What’s New, What’s Possible, What’s Coming … What’s New, What’s Possible, What’s Coming over the past two-and-a-bit decades in Jonathan Borwein, FRSC www.cs.dal.ca/~jborwein using, designing and trying to sell Canada Research Chair in Collaborative Technology, Dalhousie I. The Changing Research Landscape Visiting Professor Laureate, University of Newcastle mathematical software “intuition comes to us much earlier and with much less outside influence than formal II. New Ways of Doing Mathematics arguments which we cannot really understand I will do this from the perspective(s) of a unless we have reached a relatively high level of researcher, an educator, a consultant, and logical experience and sophistication.” of a partner in a small but robust business III. New Ways of Seeing Mathematics George Polya 1887-1985 Revised 25/09/2008 IV. Amazing New Web Services 1998-2002 A 1985 Relational Silicon Database I. Changing Research Landscape: a new triangle How I Fell into a Company •Dot bubble burst We learned about •Burn rates Computational •Naming products (dry science) •Retail software •How schools decide •Bundling •Casio •… 2002-2008 •$2.5M from Gov’t for Interactive School Math •Dictionary in Maple •Reference books die Maple •Morph in part to contractor: Experimental (wet science) Theoretical inside MAA, NIST, NSF, IBM… (thought experiments) http://www.mathresources.com/ • MacWrite, 3 Apple+’s, a brain dead Lisa, and 5” floppies Research: A Changing Computing Landscape Math and CS often win Science Fairs 1 HPC Needs in Canada or Oz My Lab in Halifax Ddrive in Halifax Moore’s Law and its Implications 2008 “The complexity for minimum component costs has increased at a rate of roughly a factor of two per year ... • now taken as “every 18 months to 2 years” Certainly over the short term this rate can be expected to continue, if not to increase. Over the longer term, the rate of increase is a bit more uncertain, although there is no reason to believe it will not remain nearly constant for at 240 cpu Glooscap at Dal least 10 years. That means by 1975, the number of components per integrated circuit for minimum cost will be 65,000. I believe that such a large circuit can be built on a single wafer. 2008: a sustained Petaflop Gordon Moore (Intel) "Cramming more components onto Electronic Circuits", Electronics attained at LANL-- 2 years early Magazine 19 April 1965 The Changing Computing Landscape Tera becomes Peta becomes … Bigga Unprecedented and expected to continue for 10-20 years. Moore’s Law This picture is worth 100,000 ENIACs NERSC’s 6000 cpu Seaborg in 2004 (10Tflops/sec) - we need new software paradigms for `bigga-scale’ hardware (1965-2005) ENIAC (1947) NERSC’s Seaborg (2004) The number of ENIACS needed to store the 20Mb TIF the Smithsonian sold me Moore’s Law t he pas ar- 1965 to 2005 1947 T The ne Mathematical Immersive Reality sec) (5Kf/ present in Vancouver 2 IBM BlueGene/L at LANL System Things we can’t model here include: (64 cabinets, 64x32x32) Sick of Payroll… IBM Computer Achieves PetaflopCabinet Performance (32 Node boards, 8x8x16) 2005 Self assembling wires 2nm apart (HP Labs) 6/9/2008 A National Nuclear Security Administration Node Board (NNSA) supercomputer(32 chips, 4x4x2) has achieved an operational rate16 Compute of 1,000 Cards trillion calculations per second,Compute or 1Card petaflop, making the Roadrunner -- (2 chips, 2x1x1) 180/360 TF/s which the NNSA commissioned IBM Corp. to16 TB DDR Chip build(2 processors) in 2006 for around $130 million -- the 2.9/5.7 TF/s world's fastest computer, the agency256 GB DDR announced 90/180 GF/s today. 8 GB DDR 5.6/11.2 GF/s 2.8/5.6 GF/s 0.5 GB DDR 217 cpu’s: Oct 2007 ran Linpack 4 MB 2 cpu’s: benchmark at over 596 Tflop /sec re The futu (5 x Canada or 8 x Oz) -2010 2005 The Changing Computing Landscape Simulation by Keuckes-Williams 2006 ICM Satellite Meeting Collection II. New Ways of Doing Math AKPeters, October 2008 JMB’s Math Portal “The digital era has dramatically changed the ways that researchers search, produce, • and related subjects: Computer Science, publish, and disseminate their scientific work. These processes are still rapidly evolving due Statistics, Engineering, all Sciences, every other to improvements in information science, new subject …. for learning or for research achievements in computer science technologies, and initiatives such as DML and open access journals, digitization projects, – Experimentally on the Computer scientific reference catalogs, and digital – Visual or Haptic or Acoustic Output repositories. – Simulations and Emersions These changes have prompted many – With Web-services, Databases, Wikis, … mathematicians to play an active part in the developments of the digital era, and have led • Marvelous support tools for the Classroom mathematicians to promote and discuss new ideas with colleagues from other fields, such as technology developers and publishers. This •alsoNew Ways of Collaborating book is a collection of contributions by key leaders in the field, offering the paradigms and mechanisms for producing, searching, and exploiting scientific and technical scholarship in mathematics in the digital era.” 3 “The Crucible” Experimental Mathodology AKPeters November 2008 Science News 1. Gaining insight and intuition 2004 Experimental Math in Action M uch o more f vis use 2. Discovering new relationships ualiz “Computers are ation 3. Visualizinguseless,math they principles can 4. Testingonly giveand especially answers.” falsifying Experimental Mathodology conjecturesPablo Picasso 5. Exploring a possible result to see if it merits formal proof 6. Suggesting approaches for formal proof 7. Computing replacing lengthy hand derivations 8. Confirming analytically derived 2 2 2 4 results Comparing –y ln(y) (red)toy-y and y -y D-DRIVE Doug a haptic mascot Haptics and Light Paths Caveman Math + Physics = Computing ? Haptic Devices extend the world of I/O Caveman Geometry (2001)Geometry (2001) into the tangible and tactile • En français To test latency issues … 2 1 Links multiple devices so two or more users may interact at a distance (BC/NS Demo April 06) Sensable’s Phantom Omni Very cool for the one person with control • in Museums, Aware Homes, elsewhere - and very expensive: great genomic applications • Kinesiology, Surgery, Music, Art … 4 th 19th C Plaster Model Cost effective 3D visualization in 2007 19 C model Kline and Schwartz plus recent A second plaster model photograph and 21st C rendition I could be in Newcastle AG CARMA is coming Much like AMSI AG Content Dominates Form Computer Assisted Research Maths and its Applications Coast to Coast (‘C2C’) Seminar The Experience Jonathan Borwein, Dalhousie University High Quality Presentations Mathematical Visualization Fully interactive multi-way audio and video 2008: will focus on Lead partners: Uwe Glaesser, Simon Fraser University PhD presentations Semantic Blueprints of Discrete Dynamic Systems Dalhousie D-Drive – Halifax Given good bandwidth audio is Chile has now joined Nova Scotia much harder (if you rehearse) Peter Borwein, IRMACS IRMACS – Burnaby, The Riemann Hypothesis “No one explains chalk” British Columbia The closest thing to being in the same room Jonathan Schaeffer, University of Alberta Other Participants so far include: Solving Checkers Arvind Gupta, MITACS University of British Columbia, University The Protein Folding Problem of Alberta, University of Alberta, University of Saskatchewan, Lethbridge University, Shared Desktop for Przemyslaw Prusinkiewicz, University of Calgary Tuesdays 3:30pm (Atlantic) 11.30am (Pacific) Acadia University, MUN, Mt Allison, St Francis Xavier University, University of viewing presentations or Computational Biology of Plants Western Michigan, MathResources Inc, sharing software 9Chapter in Communicating Mathematics in the Karl Dilcher, Dalhousie University University of North Carolina, … Future Libraries will include Digital Era (AK Peters, Sept 2008) Fermat Numbers, Wieferich and Wilson Primes very complex objects 5 “Solving Checkers” A Colour and an Inverse Speaker in III. New Ways of Seeing Math CalculatorInverse and(1995 Colour &Calculators 2007) Aesthetic base for middle-school maths CheckersCheckers isis SolvedSolvedEdmonton (Nathalie Sinclair) Inverse Symbolic Computation Audience in • The Colour Calculator Vancouver Inferring mathematical structure from numerical data – numbers as pictures April 2007 Checkers solved Mixes large table lookup, integer relation methods and Science: one of top 10 • The Inverse Calculator intelligent preprocessing – needs micro-parallelism break-throughs of 2007 It faces the “curse of exponentiality” – numbers go in and symbols come out 2006: Poincaré Conjecture Implemented as identify in Maple 9.5 top breakthrough of year • The Top Ten Numbers Website 3.14626437 Input of π rt(3.)) qrt(2.)+sq identify(s • All at http://ddrive.cs.dal.ca/~isc/portal Mathematics and Beauty 2006 Roots of Zeros The ISC in Action WhatRoots you of Zeros draw is what you see (“visible structures in number theory”) Striking fractal patterns formed by plotting complex zeros for all polynomials in powers of x with coefficients 1 and -1 to degree 18 Coloration is by sensitivity of polynomials to slight variation around the values of the zeros. The color scale represents a normalized sensitivity to the range of values; red is insensitive to violet which is strongly sensitive. Input of •Allzeros are pictured (at 3600 dpi) • Figure 1b is colored by their local density • Figure 1d shows sensitivity relative to the x9 term • The white and orange striations are not understood • ISC+ runs on Glooscap A wide variety of patterns and features become visible, leading • Less lookup & more researchers to totally unexpected mathematical results algorithms than 1995 "The idea that we could make biology mathematical, I think, perhaps is not working, but what is happening, strangely enough, is that maybe mathematics will become biological!" Greg Chaitin, Interview, 2000.