[godelski]

Many times people will see an asymptote and say "Hey, what would happen if I crossed that? What would the math and physics look like?"

Tachyons are actually a great example of this. Taking the relativistic mass equation and asking "What would happen if I allowed for speeds larger than the speed of light?" Science is more a process of elimination. What does the math say? Can we observe what the math says should happen? Repeat.