There are infinitely more irrational numbers than there are rational numbers, hence proving that all life exists infinitely,
Hrm. This claim doesn't make sense: "all life exists infinitely" What does this mean exactly? Everything lives forever, or there is an infinite amount of life in the universe, or somethin else? Nevermind the fact that there's no logical link between the amount of irrational numbers and amount of life in the world, let's sort out the claim first.
because the world grows in patterns of sacred geometry
All approximations, for one thing. Second, it's not like every living organism in the world grows that way. Third, why is this geometry sacred? Does someone worship it?
Ever hear about how infinity can fit into a finite boundary?
How is this relevant? There are an infinite amount of numbers between 0 and 1, we know this. Or between any 2 numbers, for that matter. Are you proposing that there's some infinite-mass black-hole in space whose structure is comprised of the golden ratio?
Simply put, because the total mass of the universe is finite.
Well, that's quite a claim. Little bit early to say, don't you think?
Aside from that, Howler's point was that if atoms are composed of something, then whatever composes the atoms are composed by something smaller and smaller, on and on and on into infinity. What he doesn't realize, is that it doesn't matter, because the edge of a leaf or branch or whatever else he's talking about will be the boundary of the finitely-sized atoms which make it up, and all the quarks and gluons and whatever else are within the boundary of the atom, so don't matter when it comes to the length of the boundary. Since it's the atoms on the boundary, we're still dealing with finite sizes and therefore any ratio between some number of these atoms will only be an approximation of an irrational ratio like the golden ratio, since an irrational number cannot be represented as a fraction of two integers.
I would also like to point out the fact that the opening picture does not have any tetrahedrons in it, just equilateral triangles. I don't think anyone said this yet.