topology and geometry , the difference

Reply Sun 30 May, 2010 06:56 pm
In the Discovery mag. June 2010 interview with SHING-TUNG-YAU started on pg.66

on pg.68 he says and I quote ;

" Geometry gives us the structure of that the willow tree is solid and extensive . Topology describes the overall shape of the tree without the details - but without the tree to start with, we would have nothing "

to quote further ;

" It has always amazed me to observe how different groups of people look at the same subject . My friends in physics look at space-time purely from the perspective of real physics , yet the general theory of realivity describes space-time in terms of geometry , because thats how Einstein looked at the problem "

the orginal question in the interveiw was ;

" DOES THAT MEAN geometry and topology are really two perspectives on the same thing ? "

---------- Post added 05-30-2010 at 08:58 PM ----------

[INDENT]to further dwell

same article , same pg. 68 ( but the question BEFORE the question and answer above )

the original question ;

What is topology ? Is it like geometry ?

" Geometry is specific and topology is general . Topologists study the large patterns and categories of shapes . For example , in geometry , a cube and sphere are distinct . But in topology they are the same because you can deform one into the other without cutting through the surface . The torus , a sphere with a whole in the middle , is a different form . It is clearly distinct from the sphere becuse you cannot deform a torus into a sphere no matter how you twist it . " [/INDENT]

---------- Post added 05-30-2010 at 10:36 PM ----------

therefore without the object there is nothing to base mathematics on , including time
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