To Infinity and Beyond: A Mind-Bending Documentary from the BBC

Infin­i­ty. It’s a puz­zling con­cept. Is it real, or a math­e­mat­i­cal fic­tion?

Aris­to­tle believed infin­i­ty could only be poten­tial, nev­er actu­al. To speak of an actu­al infin­i­ty, he argued, is to fall into log­i­cal con­tra­dic­tion: “The infi­nite turns out to be the con­trary of what it is said to be,” Aris­to­tle wrote in the Physics. “It is not what has noth­ing out­side it that is infi­nite, but what always has some­thing out­side it.”

Aris­totle’s log­ic rest­ed on com­mon sense: the belief that the whole is always greater than the part. But in the late 19th Cen­tu­ry, Georg Can­tor and Richard Dedekind turned com­mon sense upside down by demon­strat­ing that the part can be equal to the whole. Can­tor went on to show that there are many orders of infinity–indeed, an infin­i­ty of infini­ties.

But what rela­tion does the Pla­ton­ic realm of pure math­e­mat­ics have to the phys­i­cal world? Physics is an empir­i­cal sci­ence, but that has­n’t stopped the­o­rists from imag­in­ing the mind-bog­gling con­se­quences of an infi­nite uni­verse. To Infin­i­ty and Beyond, a one-hour BBC Hori­zon spe­cial fea­tur­ing inter­views with lead­ing math­e­mati­cians and physi­cists, is an enter­tain­ing explo­ration of a sub­ject which, by def­i­n­i­tion, you won’t be able to wrap your mind around.

Relat­ed Con­tent:

Dan­ger­ous Knowl­edge: 4 Bril­liant Math­e­mati­cians & Their Drift to Insan­i­ty

Futur­ist Arthur C. Clarke on Mandelbrot’s Frac­tals

Math­e­mat­ics in Movies: Har­vard Prof Curates 150+ Scenes