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Over time, yes. And that's just what the evidence shows.
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Mathematics really should be required for a degree in evolutionary biology.
Time is not a factor in a continual, on-going process. It cancels out of the equations. That's why we can study stellar life cycles in human life times even though an individual star itself takes anywhere from a million to 20 billion years to go through its life cycle.
The point is, we shouldn't HAVE to look in a fossil record, we should be able to measure speciation occurring throughout the entire biosphere right now. We should be able to take sample populations, observe speciation vectors, distribution plots and harmonic resonances around a maximized form. These are all things mathematics predicts should be happening if evolution, as currently theorized, is accurate. We don't see any of this.
The dirty little secret is that biologists with a good math background already know this. That's why they keep resurrecting the theory of Punctuated Equilibrium, and then state that we are currently in an Equilibrium period.
> That's why we can study stellar life cycles in human life times even though an individual star itself takes anywhere from a million to 20 billion years to go through its life cycle.
That's becasue there are enough stars, and stars are sufficiently simple, that the life cycle is based not on watching individual stars, but on the differences between simialr stars. Just like the fossil record.
> we should be able to measure speciation occurring throughout the entire biosphere right now
Just like we should be able to mathematically predict future history, just like Hari Seldon, yes? Predicting the future of evolution in detail is like predicting who is going to win the 2020 Presidential election, and by how many electoral college votes. In principle, with enough information both should be possible.