Geology- working up from basic principles.

Why would it not be relevant before the flood? What would happen so differently that could invalidate the principle?

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It seems the LoS is set in place to promote old age earth ideas.

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Not so. It makes no assumptions about the age of the earth and is based purely on observational evidence and logic.

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How can we know the earth was not distorted from a catastrophe?

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Distorted in what way?Anyway, the law of superposition deals only with how rock is initially laid down. We do find evidence of distortion (eg folding and faulting) however this is irrelevant to superposition.

The the principle of original horizontality is more of a guideline. There are examples of rocks laid down with an angle of as high as 30 degrees from horizontal. All you are really supposed to take home from this is that if rock is heavily folded, near vertical etc then it was not laid down like that. As for why sediment must be [near] flat, this is due to a property called the angle of repose. This is the maximum stable slope that can be achieved on a pile of sediment before it gives way. We can observe and measure this in sediment today. The angle of repose for dry sand for example is nearly 30 degrees, and saturated sand closer to zero.

It doesn't say that sediment is deposited evenly. Here is the definition again:

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strata originally extended in all directions until they thinned to zero or terminated against the edges of their original basin of deposition.

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LinkThe point here is that if strata comes to an abrupt end (for example somewhere where it has been eroded, or reaches a fault, then this was probably not initially the end of the strata.

The principles we've covered so far are basically what were used to determine the order of the rock strata (particularly superposition and faunal succession/biostratigraphy). This wasn't simple or easy and it certainly didn't happen overnight, but with thousands of observations at thousands of localities a picture was built up of the extents of various formations and their relationships to one another.So how do we test if we got the order correct? Radiometric dating.
Radioactive isotopes are generally unstable and over time decay from their 'parent element' to a more stable form, the 'daughter element'. We can measure the rate at which this decay happens* and work out what is known as the half life. This is the time it takes one half of the parent elements to decay, and it forms an exponential curve. After one half life is over, half of the parent element remains. After two, a quarter, three an eighth, four a sixteenth etc etc. We determine the age by measuring the ratio of parent to daughter elements and see how many half lives of known length this equates to. There are a number of different elements we can use for dating, many with different half lives. Those with shorter half lives are suitable for younger material, and those with longer half lives for older. Misusing them will give erroneous results, for example carbon14 is good up to about 70,000 years. Try to date palaeozoic coal with it and it will give you a younger date. Likewise potassium argon dating is only good on material over 100,000 yrs. Try to date lava that is practically still warm and again you'll get an incorrect result.We can typically only date igneous material with most of these methods, however carbon dating is for biological material. Some metamorphic material may be dated with some techiques, but this will give the time of metamorphosis, not when the parent rock (rock that was metamorphosed) was formed. Here is a very good resouce on radiometric dating which deals with a lot of misconceptions about it as well as explaining numerous techniques.I don't want to dwell on this too much, but the point I'd like to make is that radiometric dating is an independent method that confirms the ordering of rocks as determined by other methods.For some more evidence that this dating is valid, I'd like to borrow from this excellent thread by Loudmouth. (edited out material not relevant to this thread where (snip) is written)It seems apparent that radiometric dating has confirmed that we have the order of rocks correct.*Just to clarify, it's not possible to predict when an individual atom will decay (correct me if I'm wrong here someone), however in their millions they behave predictably. Picture unweighted dice. If I were to roll and told you to guess the outcome, it would be purely by luck if you were correct as its is essentially random, however if I were to roll it a thousand times, you could bet good money that any given number would be rolled approximately one sixth of the time.

Apologies for lack of input here- I'm rather snowed under with uni work at the mo but do intend to keep adding things in the future.