Vaughan Pratt's Home Page.

ORCID 0000-0002-5490-4676

A one-page account of manmade global warming

We emit CO2, some of it accumulates in the atmosphere, causing Earth's surface to warm. This paper starts from 3x168 climate datapoints, for respectively CO2 emissions, atmospheric greenhouse gases, and land temperature, each for the 168 years 1851-2019, and boils them down to just the years 1851, 1977, which should suffice to give a clear picture of how we've been warming the planet since 1851.

Climate is (almost) always changing quickly: An uncertainty principle for climate

Abstract: IPCC's estimates of global climate in 2100 vary widely. We exploit an uncertainty principle for climate that trades off precision in time for precision in temperature. Assuming continuation of events, cycles, and trends since 1850, we obtain a usefully precise estimate of the extent of warming averaged over the 65 years within 32 years of 2100, namely 3.0-3.2 °C above preindustrial and 2.1-2.3 °C above today. Those who view the glass as half full can look forward to half of that period (suitably weighted) being colder than that while glass-half-empty types will be more focused on the other half. Variability in phase and duration of most cycles and events in modern climate makes it difficult to say which specific years will be the hotter ones.

My AGU19 poster on a closely related topic can be seen here.

Current research interests:
  • Global Environmental Change. (Model complexity of global climate)
  • Foundations of Geometry. (Euclid Book I via algebra instead of logic, cf. Pasch-Hilbert-Tarski-Birkhoff.)
  • Autonomous Vehicles. (Harmonic Predictive Control as a drop-in replacement for PID control.)
  • Foundations of Concurrency. (Chu Spaces over 4.)
  • Speech Recognition. (The Speech Manifold as a low-dimensional geometric object.)


    December 12: Calibrating centennial climate feedbacks by the Sun: Are we underestimating the climate feedbacks? . Poster, Session A41M, American Geophysical Union Fall Meeting 2019, Moscone Hall, San Francisco.


    April 27: The Class CAT of Locally Small Categories as a Functor-Free Framework for Foundations and Philosophy, talk at Berkeley Math and Philosophy Logic Colloquium,
    December 12: Sources of Variation in Climate Sensitivity Estimates. Poster, . Poster, Global Environmental Change session GC33H: The Rate of Global Warming on Decadal to Multidecadal Timescales: Hiatus Events, Surge Events, and Climate Sensitivity. Session GC33H, Posters, Wednesday December 12, Washington Convention Center, Hall A-C.


    April 27: Acceptance speech, University of Sydney 2017 Alumni Award for Innovation and Entrepreneurship.
    May 9: "Telling Climate Sensitivity by the Sun", talk at Brian Anderson Building, Australian National University.
    May 25: "Formality and Rigor in Treatments of Global Warming", Summer School in Formal Techniques, Menlo College.
    December 14: Magmatic Volatiles as an Amplifier of Centrifugal Volcanism . Poster, Perspectives on International Activities in Earth and Space Research and Supporting Informatics session IN43D, American Geophysical Union Fall Meeting 2017, Ernest N. Morial Convention Center, New Orleans.


    February 5: "Categories with Distinguished Objects", Invited talk, Fields Institute, Toronto. Slides (more recent version here), Video.
    See also these interviews at this meeting. Their lengths in units of tweets varied from about one to ten tweets; my three contributions came to respectively two, four, and two tweets in length. Speakers included Stephen Wolfram, Dana Scott, Harvey Friedman, Ingrid Daubechies, Jeremy Avigad, Georges Gonthier, and a number of representatives of the symbolic computation community. I was the only speaker west of Chicago, not sure what that says about western mathematics...
  • At 0:21:00 I said "The two big developments I see as being needed here are organizational and methodological. First off there ought to be a framework for organizing mathematical knowledge. [My favorite framework is typed Chu spaces.] And secondly there should be a method for reorganizing the extant body of mathematics within that framework. [Or any other framework for that matter. TBD.]"
  • At 1:06:34 I outlined my work on expressing Book I of Euclid's Elements in the equational style of linear algebra, group theory, ring theory, Boolean algebra, etc. but in the spirit of Euclid, namely without reference to numbers. I was able to capture exactly the affine fragment of Euclid's system, no angles or lengths, with an equational theory whose only operations were step and centroid. For the full theory with angles and lengths however I was unable to achieve this without resorting to a nonstandard extension of equational logic involving a certain pasting operation serving to enlarge the domains of the theory's partial operations.
  • At 1:27:52, under the heading "The nature of mathematics and its (mechanized?) future", I offered "What I would hope to see is an organization of mathematics that is accessible more to people than to computers, so it should be computers that should be doing the adapting rather than asking the humans to adapt to the computers."
  • April 18: My first tweet, attempting to explain quantum computing "better than [Canadian Prime Minister] Justin Trudeau". (Whereas the state space of 3 bits is a 3-dimensional space with 0-1-valued coordinates, the state space of 3 qubits is an 8-dimensional space with complex-valued coordinates.)

    October 9: Algebras and Bialgebras via Categories with Distinguished Objects, AMS Western Section Meeting, Denver, Colorado.

    November 2: Harmonic Predictive Control as a Variant of PID Control, tRFMO Model Strategy Evaluation Working Group, International Commission for the Conservation of Atlantic Tuna, Madrid, Spain.

    December 17: A Centrifugal Volcanism Mechanism for the Atlantic Multidecadal Oscillation . Poster, Global Environmental Change session GC13G, American Geophysical Union Fall Meeting 2016, Moscone Hall, San Francisco.


    May 14: "Academic Leadership". Invited talk, Global Leadership Development Program, Sydney University International House, Sydney, Australia.

    May 26: Euclid's Elements as an Equational Theory. Seminar, Mathematics Dept., University of Sydney, Sydney, Australia.

    August 21: Aristotle, Boole, and Chu: Duality since 350 BC. Plenary talk, George Boole Mathematical Sciences Conference, Cork, Ireland. (Conference in honour of Boole's 200th birthday.)

    October 12: Aristotle, Boole, and Categories. Invited paper, Parikh Festschrift, 2015.

    December 17: Model Complexity of Global Climate: Could Arrhenius have foreseen the hiatus? . Poster, Global Environmental Change session GC43C, American Geophysical Union Fall Meeting 2015, Moscone Hall, San Francisco.


    December 16: An Ekman Transport Mechanism for the Atlantic Multidecadal Oscillation . Poster, Global Environmental Change session GC21C, American Geophysical Union Fall Meeting 2014, Moscone Hall, San Francisco.


    August 5: A homogeneous algebraic definition of Euclidean space, Talk, Conference BLAST 2013, Chapman University, Orange, CA.

    July 18: Weiner's Repetition Finder. Invited talk, 24th Annual Conference on Combinatorial Pattern Matching, session "1973 + 40 = 2013", Bad Herrenalb, Germany.

    December 13: Reconciling multidecadal land-sea global temperature with rising CO2. Talk, SWIRL session GC53C "Understanding 400 ppm Climate: Past, Present and Future", American Geophysical Union Fall Meeting 2013, Moscone Hall, San Francisco. See also video of oral presentation.


    May 25: Geodesic spaces: Euclid's five postulates as an equational theory, starting with the second. Invited talk at The Constructive in Logic and Applications: A conference in honour of the 60th Birthday of Sergei Artemov. Video here.

    December 4: Multidecadal climate to within a millikelvin. Poster, Global Environmental Change session GC23C, American Geophysical Union Fall meeting 2012, San Francisco.


    February 12: Linear Process Algebra. Invited talk, International Conference on Distributed Computing and Internet Technology, Bhubaneswar, India. See also slides of talk.

    February 15: The Logic of Global Warming. Seminar, TATA Institute of Fundamental Research, Mumbai, India.

    February 15: Euclidean and non-Euclidean algebra. Seminar, TATA Institute of Fundamental Research, Mumbai, India.

    June 14: Euclidean and non-Euclidean algebra. Seminar, Maths Colloquium, Macquarie University, Sydney, Australia

    June 16: Linear Process Algebra. Colloquium, National Information and Communications Technology Australia (NICTA), Sydney, Australia.

    June 17: Linear Process Algebra. Seminar, School of Information Technology, University of Sydney, Australia.

    June 23: The Logic of Global Warming. Seminar, Australian National University, Canberra, Australia

    July 23: Structure from sorts, properties, and composition: A minimalist approach to topoalgebraic structure. Talk, International Conference on Category Theory, UBC, Vancouver, Canada.

    October 11: Linear Process Algebra. Math & CS Colloquium, Santa Clara University, CA.

    December 8: A three-component analytic model of long-term climate change . Poster, Global Environmental Change session GC43B, American Geophysical Union Fall meeting 2011, San Francisco.


    April 9: Tutorial on Chu spaces. Invited tutorial, Institut de Recherche et Coordination Acoustique/Musique (IRCAM), Paris, France.

    April 9: Presketches. Talk, IRCAM, Paris, France.

    April 13: Presketches. Seminar, Institute for Information, Logic, and Computation (IILC), University of Amsterdam, Netherlands.

    June 2: Topological algebra based on sorts and properties as free and cofree universes. Talk, Conference BLAST 2010, University of Colorado, Boulder, Colorado.

    June 5: Geodesic spaces : momentum :: Groups : symmetry. Talk, Conference BLAST 2010, University of Colorado, Boulder, Colorado.


    Mailing Address:
    2215 Old Page Mill Rd
    Palo Alto, CA 94304

    Publications: (complete list in vita)

  • HTML,
  • Abstracts of Concurrency group publications (HTML)
  • Chu Space Web Site (HTML)

  • Stanford Affiliations

  • CSD: Computer Science Department
  • EE: Department of Electrical Engineering (By courtesy)
  • AI Lab
  • Theory group
  • CSLI: Center for Studies in Language and Information

  • Other Affiliations

  • ACM: Association for Computing Machinery (Fellow)
  • IEEE: Institute of Electrical and Electronics Engineers (Life Senior Member)
  • AGU: American Geophysical Union (Life Member)
  • IGPL: Interest Group in Pure and Applied Logics (Editorial Board)
  • AMS American Mathematical Society (Member)
  • MAA Mathematical Association of America (Member)
  • AMS American Meteorological Society (Member)
  • Linux Counter Project Number: 119
  • Unix User ID: 11 (at Stanford CSD (1983-present), Sun Microsystems 1982-87, Tiqit Computers, and home)

  • M.Sc. Thesis: Translation of English into Logical Expressions, Sydney University, August 1969. Advisor: Jan B. Hext
    Abstract: A computer program to solve Lewis Carroll's syllogisms is considered. A logical decision method is evolved for dealing with syllogisms expressed as conjunctive normal form (CNF) propositions. For the translation of English into CNF, a theory of translation is presented. A computer program is exhibited which explicitly embodies each feature of the theory, and produces CNF translations of Carroll's syllogisms. It is claimed that the translation theory is the most significant result of the research. A translation approach to phrase-structure grammars enables their practical value to be studied more closely. It is shown that the position of phrase-structure grammars is stronger than that of transformational grammars in a utilitarian theory, as distinct from an explanatory theory.

    Ph.D. Thesis: Shellsort and Sorting Networks, Stanford University, December 1971.
    Advisor: Donald E. Knuth
    Former Ph.D. Students:
  • David Harel, MIT, 1978
  • Bob Streett, MIT, 1981 (coadvisor: Albert Meyer)
  • Jay Gischer, Stanford, 1984
  • Ross Casley, Stanford, 1991
  • Roger Crew, Stanford, 1991
  • Orli Waarts, Stanford, 1992
  • Gideon Avrahami, Stanford, 1994
  • David Magerman, Stanford, 1994 (coadvisor: Fred Jelinek)
  • Vineet Gupta, Stanford, 1994
  • Anna Patterson, U. Illinois, 1997 (coadvisor: Gul Aga)
  • Paul Fahn, Stanford, 1999 (coadvisor: Tom Cover)
  • Parham Aarabi, Stanford, 2001
  • Ramon Prieto, Stanford, 2003
  • Keyvan Mohajer, Stanford, 2006

  • Miscellaneous Thoughts