Occam’s Razor: In need of sharpening?

In the first half of the 14th cen­tury, the Fran­cis­can friar and lo­gi­cian, William of Oc­cam pro­posed a heuris­tic for de­cid­ing be­tween al­ter­na­tive ex­pla­na­tions of phys­i­cal ob­serv­ables. As William put it: “En­tities should not be mul­ti­plied with­out ne­ces­sity”. Or, as Ein­stein re­for­mu­lated it 600 years later: “Every­thing should be made as sim­ple as pos­si­ble, but not sim­pler”.

Oc­cam’s Ra­zor, as it be­came known, was en­thu­si­as­ti­cally adopted by the sci­en­tific com­mu­nity and re­mains the un­ques­tioned crite­rion for de­cid­ing be­tween al­ter­na­tive hy­pothe­ses to this day. In my opinion, its suc­cess is trace­able to two char­ac­ter­is­tics:

o Utility: OR is not a log­i­cal de­duc­tion. Nei­ther is it a state­ment about which hy­poth­e­sis is most likely. In­stead, it is a pro­ce­dure for se­lect­ing a the­ory which makes fur­ther work as easy is pos­si­ble. And by fa­cil­i­tat­ing work, we can usu­ally ad­vance fur­ther and faster.

o Com­bin­abil­ity. OR is fully com­pat­i­ble with each the episte­molog­i­cal stances which have been adopted within sci­ence from time to time (em­piri­cism, ra­tio­nal­ism, pos­i­tivism, falsifi­a­bil­ity, etc.)

It is re­mark­able that such a widely ap­plied prin­ci­ple is ex­er­cised with so lit­tle thought to its in­ter­pre­ta­tion. I thought of this re­cently upon read­ing an ar­ti­cle claiming that the mul­ti­verse in­ter­pre­ta­tion of quan­tum me­chan­ics is ap­peal­ing be­cause it is so sim­ple. Really?? The mul­ti­verse ex­pla­na­tion pro­poses the cre­ation of an in­fini­tude of new uni­verses at ev­ery in­stant. To me, that makes it an egre­giously com­plex hy­poth­e­sis. But if some­one de­cides that it is sim­ple, I have no ba­sis for re­fu­ta­tion, since the no­tion of what it means for a the­ory to be sim­ple has never been speci­fied.

What do we mean when we call some­thing sim­ple? My naive no­tion is to be­gin by count­ing parts and fea­tures. A mil­ling de­vice made up of two stones, one sta­tion­ary one mo­bile, fit­ted with a stick for ro­ta­tion by hand be­comes more com­plex when we add de­vices to cap­ture and trans­mit wa­ter power for set­ting the stone in mo­tion. And my mo­bile phone be­comes more com­plex each time I add a new app. But these no­tions don’t serve to an­swer the ques­tion whether La­grange’s for­mu­la­tion of clas­si­cal me­chan­ics, based on ac­tion, is sim­pler than the equiv­a­lent for­mu­la­tion by New­ton, based on his three laws of forces.

Isn’t re­mark­able that sci­en­tists, so renown for their ex­ac­ti­tude, have been rely­ing heav­ily on so vague a prin­ci­ple for 700 years?

Can we do any­thing to make it more pre­cise?