I disagree. If the universe expands and contracts, it must have a starting point somewhere.
Think of the graphs of cos/sin. They go up and down forever, but at any time T, we can determine if it is 'up' or 'down.'
The issue is, where do we start? If present time is assumed T=0, can tell what Sin was at t=-100 and t=100, but the question is, how do we know Sin existed -100time ago? We can only show what it would have looked like this far ago, but that doesn't tell us when it actually did start (which it must have).
Saw this before and didn't comment on it, but I feel like doing it now, so...
Sine is a function. You give it a number, it spits back out a number. The function sin(t) is defined for all real (and complex) numbers, which is how we "know" that sin(t) exists when t = 100. We don't even need trigonometry for this; the sine function can be defined simply using its Taylor series expansion: sin(t) = t - t^3/3! + t^5/5! - t^7/7! + t^9/9! - ... A sinusoidal curve, the
graph of a function, doesn't necessarily have anything to do with the function itself. It too does not need a "starting point".
In other words, your analogy isn't really appropriate here.
