Balázs Faa: Dark Geo

Dark Geo is based on a geo­met­ri­cal sys­tem called pen­tap­le­xity or Pen­ro­se ti­l­ing, which un­li­ke, say, the Py­tha­go­re­an the­or­em or the de­ci­mal num­ber sys­tem, is som­eth­ing that ap­peared in ma­the­ma­tics only re­cently. It has a num­ber of in­ter­est­ing qu­a­li­ti­es, of which we now con­cent­ra­te on one, na­mely that the two rhom­bus­es form­ing the tiles never occur in a re­cur­r­ing order. The ti­l­ing is ape­ri­o­dic. The pat­tern pro­vi­ded by the Pen­ro­se ti­l­ing does not occur in na­tu­re, the qu­a­sicrys­tals it descri­bes were the re­sult of ela­bo­ra­te la­bo­ra­to­ry ex­pe­ri­ments.
My work was pro­du­ced by pla­cing dra­wings on the rhom­bus­es of the Pen­ro­se ti­l­ing. As the dra­wings meet where the sides of the rhom­bus­es do, a laby­rinth is crea­ted, or at least a net­work. There are two kinds of dra­wings on the rhom­bus­es; one can be seen by na­tu­ral light, the other by ult­ra­vi­o­let light. These are the facts.
What fol­lows is not a fact, but a con­jec­tu­re, spe­cu­la­ti­on, me­taphy­sics. Many think that ma­the­ma­tics is a coll­ec­ti­on of met­hods, which can be used to make bridges, el­ec­ti­on fo­re­casts or ato­mic bombs. One of those bor­ing things only idi­ots have an in­te­rest in. Ot­hers think ma­the­ma­tics is more than that. They think it descri­bes na­tu­re, and at such an ad­van­ced level that it al­most al­lows a view into the world of ide­als. The same people like to cont­rast moral cor­rupt­ion and human fra­ilty with the im­pe­ris­hab­le truths of ma­the­ma­tics. Ma­the­ma­tics is the only sci­en­ce, they claim, in which new the­ori­es do not overth­row old ones.
As a mat­ter of fact, con­tem­por­ary ma­the­ma­tics is no lon­ger in­ter­es­ted in na­tu­re. As I’ve said, the Pen­ro­se ti­l­ing does not occur in na­tu­re. The con­sis­tency of ma­the­ma­tics must de­rive from the fact that it is built en­ti­rely from sta­te­ments made by hu­mans. Even axi­oms are sta­te­ments which are based exc­lu­si­vely on human no­tions. Take for ins­tance the fol­lo­wing sta­te­ment:
If a equ­als b, and b equ­als c, then c equ­als a. Which is the kind of thing ma­the­ma­tics is based on. But how could they not be equal when the very no­ti­on of equ­a­lity is our own idea? This axiom says noth­ing about a and b, but mer­ely de­fi­nes equ­a­lity. And since it is an axiom, it ef­fects the de­fi­ni­ti­on by using itself. It is ob­vi­o­us what simp­lis­tic think­ing it would be to com­pa­re ma­the­ma­ti­cal equ­a­lity with so­ci­al equ­a­lity. It is no less than word magic.
I am in­ter­es­ted in ma­the­ma­tics as a vi­su­al ar­tist. Con­se­qu­ently what in­te­rests me is not what ma­the­ma­tics is, but what it means. I do not like the vi­su­al uni­ver­se as­so­ci­a­ted with ma­the­ma­tics. I do not think that works on ma­the­ma­tics sho­uld unc­ri­ti­cally emp­loy the vi­su­al qu­a­lity of geo­met­ric con­struc­ti­on. Lines, planes, sha­ded bo­di­es. All this is good for is a sce­nery to sci­en­ce.
What does ma­the­ma­tics mean? Why was it in­ven­ted, why is it pur­su­ed? Hindu sci­en­tist are fab­led to have had a con­test in num­bers: two Brah­mins tried to outdo each other in say­ing the lar­gest num­ber pos­sib­le. World eco­no­mics seems to ope­ra­te along the same lines. Ma­the­ma­tics, I think, also has a dark side.
Ma­the­ma­tics is the only sci­en­ce that does not deal with na­tu­re. It is built sol­ely from human sta­te­ments. If human in­tel­lect is not cons­idered a part of na­tu­re, then ma­the­ma­tics is the most un­na­tu­ral thing man is cap­ab­le of. Which might be the very point. Time and again we prove that we have left be­hind the stre­am­li­ned and ruth­less world of na­tu­ral being once and for all.