the assumption that the natural processes operating in the past are the same as those that can be observed operating in the present.
This usually just summed up as "the present is the key to the past". I don't really like summing it up though because it glosses over something very very important: Uniformitarianism is an assumption. When I look at ripple marks in a 300 million year old sandstone (see below)
I assume they form in the same way ripple marks form today by water running over sand making little "waves" in the sand (I'm NOT a sedimentologist can you tell?) See below:
Like I said this is an assumption but I think it's a valid assumption. Really it's not more of an assumption than any scientist makes. More fundamentally uniformitarianism means that the "rules" don't change. What ever laws of physics operate to make ripples today operated in the past to make ancient ripples.
Wait a second.
That's the fundamental assumption that underlies ALL of science. If we didn't assume that the laws of nature don't change then there would be no way to figure anything out, no way to do science. So why do geologists and paleontologists make such a big deal out of it? (believe me we do, we gave it a big name and we talk about it a LOT). I mean it's not like in chemistry the Professor says " ok the ideal gas law states that pv=nrt and it has ALWAYS been that way. ??? No, pv=nrt it just does and you assume it always has.
Geologists and paleontologists have had to deal with something that chemists and physicists do not: People who think the Earth is 6,000 years old. What geologists are really saying when we talk about uniformitarianism is: "if you are going to insist on believing the Earth is 6,000 years old then you're also going to have to believe that the laws of physics change significantly because there is no way that the rock that is on the surface of the Earth today could have formed in 6,000 years"
Now my guess is that people who believe this who believe the 6,000 year time frame would just call the suspension of the laws of physics a miracle and get on with their lives. But if that's the case then what's the point of any kind of science? What's the point of anything? Why get up in the morning if gravity may well stop working at any time or why dry to drive as your car relies on the ideal gas law and it may stop working.
Ok this has degenerated a bit so here's the crux:
Uniformitarianism just means that the laws don't change... for anyone, not for physicists or chemists or geologists. So when geologists look for explanations for what we see in the rock record we look to what's going on now. Because the processes that are acting now are the same as the processes that were acting then.
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