mathematics

133:5.5Logic is valid in the ma­te­rial world, and math­e­mat­ics is re­li­able when lim­ited in its ap­pli­ca­tion to phys­i­cal things; but nei­ther is to be re­garded as wholly de­pend­able or in­fal­li­ble when ap­plied to life prob­lems. Life em­braces phe­nom­ena which are not wholly ma­te­rial. Arith­metic says that, if one man could shear a sheep in ten min­utes, ten men could shear it in one minute. That is sound math­e­mat­ics, but it is not true, for the ten men could not so do it; they would get in one an­other’s way so badly that the work would be greatly de­layed.

12:9.3Math­e­mat­ics, ma­te­rial sci­ence, is in­dis­pens­able to the in­tel­li­gent dis­cus­sion of the ma­te­rial as­pects of the uni­verse, but such knowl­edge is not nec­es­sar­ily a part of the higher re­al­iza­tion of truth or of the per­sonal ap­pre­ci­a­tion of spir­i­tual re­al­i­ties. Not only in the realms of life but even in the world of phys­i­cal en­ergy, the sum of two or more things is very of­ten some­thing more than, or some­thing dif­fer­ent from, the pre­dictable ad­di­tive con­se­quences of such unions. The en­tire sci­ence of math­e­mat­ics, the whole do­main of phi­los­o­phy, the high­est physics or chem­istry, could not pre­dict or know that the union of two gaseous hy­dro­gen atoms with one gaseous oxy­gen atom would re­sult in a new and qual­i­ta­tively super­ad­di­tive sub­stance—liq­uid wa­ter. The un­der­stand­ing knowl­edge of this one phys­io­chem­i­cal phe­nom­e­non should have pre­vented the de­vel­op­ment of ma­te­ri­al­is­tic phi­los­o­phy and mech­a­nis­tic cos­mol­ogy.

133:5.6Math­e­mat­ics as­serts that, if one per­son stands for a cer­tain unit of in­tel­lec­tual and moral value, ten per­sons would stand for ten times this value. But in deal­ing with hu­man per­son­al­ity it would be nearer the truth to say that such a per­son­al­ity as­so­ci­a­tion is a sum equal to the square of the num­ber of per­son­al­i­ties con­cerned in the equa­tion rather than the sim­ple arith­meti­cal sum. A so­cial group of hu­man be­ings in co-or­di­nated work­ing har­mony stands for a force far greater than the sim­ple sum of its parts.

12:9.5Your re­li­gion is be­com­ing real be­cause it is emerg­ing from the slav­ery of fear and the bond­age of su­per­sti­tion. Your phi­los­o­phy strug­gles for eman­ci­pa­tion from dogma and tra­di­tion. Your sci­ence is en­gaged in the age­long con­test be­tween truth and er­ror while it fights for de­liv­er­ance from the bond­age of ab­strac­tion, the slav­ery of math­e­mat­ics, and the rel­a­tive blind­ness of mech­a­nis­tic ma­te­ri­al­ism.

81:6.10Sci­ence teaches man to speak the new lan­guage of math­e­mat­ics and trains his thoughts along lines of ex­act­ing pre­ci­sion. And sci­ence also sta­bi­lizes phi­los­o­phy through the elim­i­na­tion of er­ror, while it pu­ri­fies re­li­gion by the de­struc­tion of su­per­sti­tion.

123:6.3About this time Je­sus met a teacher of math­e­mat­ics from Da­mas­cus, and learn­ing some new tech­niques of num­bers, he spent much time on math­e­mat­ics for sev­eral years. He de­vel­oped a keen sense of num­bers, dis­tances, and pro­por­tions.