Sentence:  It was very radical because he also claimed that symmetry is a feature in mathematics and reality that is not just an infinitely accurate property, but a <WSD>transfinitely</WSD> accurate one. Like the modern idea of fractals—where we have this Mandelbrot type thinking of everything repeating itself all over again not just infinitely many times, but in such a way that the surface around it is <WSD>transfinitely</WSD> large. 
Meaning of the word marked with <WSD> tags:  Of transfinite degree.