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CSC 599: Computational Scientific Discovery

Lecture 5a: The BACON systems. CSC 599: Computational Scientific Discovery. Outline. Bacon 1 Bacon 3 Bacon 4 Bacon 5 Glauber. Bacon 1. Idea Discover eqns w/products and ratios Method Objects have attributes For pairs of attrs rules see if: Attrs are same for all values ( constant ) ‏

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CSC 599: Computational Scientific Discovery

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  1. Lecture 5a: The BACON systems CSC 599: Computational Scientific Discovery

  2. Outline • Bacon 1 • Bacon 3 • Bacon 4 • Bacon 5 • Glauber

  3. Bacon 1 Idea Discover eqns w/products and ratios Method Objects have attributes For pairs of attrs rules see if: • Attrs are same for all values (constant)‏ • Note constant • Attrs linearly increase together (linear)‏ • Note slope & intercept • Attrs increase together (but not linear)‏ • Make new attr that is one divided by other • Attrs one increases while other decreases • Make new attr that is one multiplied by other

  4. Bacon 1 Example Rediscover Kepler's 3rd Law: Distance cubed (d) proportional period squared (p)‏ Planet D P D/P D2/P D3/P2 A 1.0 1.0 1.0 1.0 1.0 B 4.0 8.0 0.5 2.0 1.0 C 9.0 27.0 0.333 3.0 1.0

  5. Bacon 1 Rediscoveries Kepler's 3rd Law: c = D3/P2 Boyle's Law P = pressure V = volume PV = c Galileo's Law of Uniform acceleration X = -gt2

  6. Bacon 3 Idea: Vary independent attrs & observe dependent attrs Method: Have independent attrs A1 ... AN dependent attr D Fix A1 Fix A2 . . . Fix AN Find relationship between AN & D in each <A1,..AN-1> space Fix AN-1 Find relationship between AN-1 & D in each <A1,..AN-2> space

  7. Bacon 3 Example Ideal Gas Law P = pressure V = volume n = number of moles (# of molecules)‏ R = constant T = temperature (in Kelvin)‏

  8. Bacon 3 Example (2)‏ Bacon Std Const PV=a PV=k T,N PV=BT+c PV=k(T-273) N PV=DNT+eN PV=8.32N(T-273)‏

  9. Bacon 3 Rediscoveries Ideal Gas Law PV = nRT Coulomb's Law F = force D = distance between 2 point changes Q1 = charge of 1st point Q2 = charge of 2nd point FD2/Q1Q2 = 8.99e+9

  10. Bacon 4 Idea Want to posit intrinsic properties Density of Gold Conductivity of Copper Method If have symbolic attribute then propose new attr based on another symbolic value

  11. Bacon 4 Example Archimedes volume & density: Composition Obj V C W Silver A 100.0 105.326 55.923 Silver A 200.0 205.326 55.923 Silver A 300.0 305.326 55.923 Silver B 100.0 107.115 74.708 ... Gold D ... Lead G V = volume fluid (independent var)‏ C = combine volume (dependent var)‏ W = weight (dependent var)‏

  12. Bacon 4 Example Sequence of proposed attributes • SC,V: Linear Slope of line V=SC,V*C + IC,V • IC,V: Linear Intercept of line V=SC,V*C + IC,V • O: Define-Intrinsic O = IC,V • IC,V/O: Linear (tautological)‏ • W/O: Increase (constant for composition) That's density! Also rediscovered were: Black's Law of specific heat: Tf=(M1T1+M2T2)/(M1+M2)‏

  13. Bacon 5 Many equations are symmetric Snell's law of refraction: sin(1)/sin(2) = n1/n2 Bacon 5 had heuristics to prefer symmetric solutions if experimental setup was symmetric

  14. Glauber Discovers proper quantifiers for symbolic examples Input: (reacts inputs {HCL NH3} outputs {NH4CL})‏ (reacts inputs {HCL KOH} outputs {KCL})‏ Output: acid basesalt: (reacts inputs {acid base} outputs {salt})

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