Understanding Science 1. Proof © Colin Frayn,

Introduction Why science? –We care about the truth –We care about certainty –The inaccuracy of intuition –The limitations of dogma What is science? –How does it work? –Why does it work? –Why not do things differently? © Colin Frayn,

Assumptions of Science 1.The Universe operates according to stable underlying laws 2.Our senses give us accurate information about the world 3.Simplicity is preferable © Colin Frayn,

Occam’s Razor William of Occam ( ) There are always infinitely many potential explanations for any observation Gravity –Force proportional to product of masses –Inversely proportional to square of separation –Except for giraffes on Mars Which explanation should we prefer? © Colin Frayn,

More Occam’s Razor The simplest model is the most likely –It makes fewest unproved assumptions “We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.” (Isaac Newton) “Whenever possible, substitute constructions out of known entities for inferences to unknown entities.” (Bertrand Russell) Without this, no useful knowledge can be gained about anything, ever! © Colin Frayn,

Spectrum of Certainty © Colin Frayn, I’ve said that science is all about finding out what is true, but… Most claims are neither certainly true nor certainly false They lie on a spectrum between these values Certainly True Certainly False Neutral

Certain Proofs © Colin Frayn, Certainly True Certain knowledge Mathematical proofs Logical proofs There is no logically possible exception Certainly FalseNeutral = 3 10 < 5 a n + b n = c n for n>2 (Fermat) sqrt(2) = a/b = 2 10 > 5 a 2 + b 2 = c 2 (Pythagoras) Sound logical deductions Not much

Scientific Proofs © Colin Frayn, Science can rarely claim certainty Scientific theories are always tentative But we shouldn’t be neutral about them Science assigns probabilities to hypotheses Experimental “proofs” in maths e.g. Riemann Hypothesis Extremely Likely The sun will rise tomorrow Special relativity Age of Earth > 4 billion years Riemann Hypothesis is true Extremely Unlikely Gravity will reverse direction tomorrow Ghosts exist Alien abductions Mind reading

Scientific Process © Colin Frayn, Start with no knowledge Gradually add information Adjust assigned probabilities Continue until (sufficiently) certain Always be willing to move the arrow! Threshold

Scientific Theories Foundations for organising scientific knowledge Theories are –Supported strongly by evidence –Potentially falsifiable –Never certain Theories allow us to make predictions –Which is what science is all about! Examples –Newtonian Gravity –Special Relativity –Evolution © Colin Frayn,

Summary Science assigns probabilities –These can be updated with new knowledge Science makes a few assumptions –They enable us to make progress Very few things are absolutely certain –The Spectrum of Certainty –Absolute certainty is reserved for mathematics and logic –But we can be “practically” certain Beyond some suitable threshold A theory is a strongly-supported hypothesis –Can be used to make and test predictions –Can (in principle) be falsified © Colin Frayn,