Infinity, Impugned

I have a friend who is hostile to the concept of infinity.  He challenges everyone to find an instance of it in reality.

I fall back on infinity as a mathematical concept.  (In math all things that are within the rules are possible.)  Take a long piece of string.  Sever it in the center.  Throw away one half.  Sever the remaining half in the center.  Ad infinitum.  As long as your tiny scissors, your visual acuity and your underlying tremor cooperate in the exercise, it will never end.

I feel that when I do things now, things from which I derive pleasure, like visiting a lake, or organizing an interview with an admired judge, I am trying to sever the remaining piece of the string, with the further conceit that the very process of severing it will forestall getting to the end.  But we know that in reality the curtain will come down in the middle of the play, my little game erased along with everything else, simultaneously.  Which is why I am in a hunger for some sign of transcendence.  Transcendence is elusive.