Show Reference: "Extending Ourselves: Computational Science, Empiricism, and Scientific Method"

Extending Ourselves: Computational Science, Empiricism, and Scientific Method (21 January 2007) by Paul Humphreys
    address = {USA},
    author = {Humphreys, Paul},
    day = {21},
    howpublished = {Paperback},
    isbn = {0195313291},
    keywords = {book, epistemology, methodology, philosophy, research, science, simulation},
    month = jan,
    posted-at = {2013-12-18 14:55:43},
    priority = {2},
    publisher = {Oxford University Press},
    title = {Extending Ourselves: Computational Science, Empiricism, and Scientific Method},
    url = {\&path=ASIN/0195313291},
    year = {2007}

See the CiteULike entry for more info, PDF links, BibTex etc.

Simulations are used to explore intractable mathematical models or in lieu of empirical experiments which are hard or impossible to conduct for some reason and pilot experiments .

``System S provides a core simulation of an object or process B just in case S is a concrete computational device that produces, via a temporal process, solutions to a computational model [...] that correctly represents B, either dynamically or statically. If in addition the computational model used by S correctly represents the structure of the real system R, then S provides a core simulation of system R with respect to B.''

A full simulation in Humphreys' sense is the combination of a core simulation with an output representation.

Graphical representations of numerical data are important to discover qualitative properties.

Vision is an important if not the most important source of sensory input for humans' (and other mammals').

Visualizations of numerical data are important in science.

For humans doing research, visualizations are not just handy—they are part of the research

For humans running simulations, visualizations (output representations) are not just handy—they are actually part of the simulations because without those, humans cannot interpret the results.

One of the goals of science is human understanding.

Without human understanding, at least one goal of science is not fulfilled.

According to Humphreys, simulation is a set of techniques rather than a single tool. It includes

  • numerical solution of equations,
  • visualization,
  • error correction on the computational methods,
  • data analysis,
  • model explorations

Simple systems can be hard to predict quantitatively without numerical techniques.

Simulations are different from experiments on the `real thing', but that is true also of all other kinds of theoretical model.

Computer simulations have benefits over empirical experiments:

  • wide ranges of initial conditions can be tested;
  • they can be replicated exactly;
  • they can be performed where the corresponding experiment would be impossible or unfeasible;
  • they are Gedankenexperimente without the psychological biases (well, somewhat);
  • they are more amenable to in-depth inspection regarding satisfaction of assumptions—code can be validated, reality cannot;
  • they can be used to guide analytical research;

We extend ourselves using technology in the sense that we build things that give us epistemological access to parts of reality which would otherwise be beyond our reach.

This includes instruments which help us perceive the world in ways not given to us naturally, like microscopes or compasses, and machines which help us think about our theories deeper than our cognitive limitations permit.

Models of real entities at lower dimensionalities than those entities can show certain qualitative features of these entities. However, sometimes they don't.

A simple, somewhat lacking definition of computational science is, according to Humphreys:

``computational science consists in the development, exploration, and implementation of computational models of nonmathematical systems using concrete computational devices.''

According to Humphreys, the difference between a simulation and a representation or computational model is that it the formulae are evaluated; The formula for an elliptic curve together with parameters (and initial conditions) is a representation of a planetary orbit and a specialized subset of Newtonian physics plus data is a computational model of it. But only the model plus solutions to the formulae for a finite number of time steps is a simulation. (My examples.)

A computational model has six components, according to Humphreys:

  1. A computational template', together with types of boundary and initial conditions—thebasic computational form';
  2. Construction assumptions;
  3. Correction set;
  4. An interpretation;
  5. Initial Justification of the template;
  6. An output representation.

A computational template in Humphreys diction, is a mathematical system (set of equations, logical formulae etc.) which is in itself out of context but can be applied to at least one area of discourse.

`Construction assumptions' in Humphreys' definition of computational models describe the correspondence between entities in the computational template and entities in the world together with the mismatch. They are a quintuple:

  1. Ontology
    which maps entities between computational template and world
  2. Idealizations
  3. Abstractions
  4. Constraints
  5. Approximations

The `correction set' seems to me to be a description of the knobs to turn to fit a computational model to empirical data.

A simulation can be thought of as a thought experiment: Given a correct mathematical model of something, it tries out how that model behaves and translates (via the output representation and interpretation) the behavior back into the realm of the real world.

A computer simulation then is a thought experiment carried out by a computer.

A computational model according to Humphreys seems to me to be a computational theory (in the logician's sense) and a manual for applying it to the world.