Yes, that was indeed the point I was trying to convey! In an even sillier example, assume word vectors X, then calculate "proposal by proposal" similarities (i.e. inverse distances). Then duplicated X and concatenate [X,X], recalculate "proposal by proposal" distances (now for twice as many proposals)---those distances must now be less on average because each proposal has at least one "zero distance" neighbor. HOWEVER, why would you assert that the overall "idea space" has been reduced?
Yes, that was indeed the point I was trying to convey! In an even sillier example, assume word vectors X, then calculate "proposal by proposal" similarities (i.e. inverse distances). Then duplicated X and concatenate [X,X], recalculate "proposal by proposal" distances (now for twice as many proposals)---those distances must now be less on average because each proposal has at least one "zero distance" neighbor. HOWEVER, why would you assert that the overall "idea space" has been reduced?