The great breadths of time.

Hi Gigahound,
Most people have provided you with a general discussion of how it's very hard to imagine a large body of rock cooling rapidly. I'm going to provide a bit of math to further illustrate the difficulty of rapid cooling. I use Fick's laws to illustrate these phenomena. Fick's laws are phenomenological laws that describe how something must move across an area, and are essentially equations that describe the conservation of mass or energy for a given system. Fick's laws can be applied to temperature, as temperature is essentially energy and energy is conserved. You can find out a bit more about Fick's laws here: Fick's laws of diffusion - WikipediaFick's second law derives from his first law and states that the change in heat is proportional to the heat gradient across a body. In math terms this becomes:
dT......d² T
-- = K ------
dt......dx²where dT/dt is the change in temperature with respect to time, K is a constant, and the second term describes the change in the temperature gradient, or the temperature with distance profile. Sorry for the dots, but the board doesn't like the extra spaces. Luckily for a first order calculation this simplifies to:t = x² / K
where t is the time it takes a body of rock of size x to cool. K is constant for all rock and is ~10^-2 cm²/s, so the units work as well.Let's try a few examples. NosyNed describes walking on a lava field in Hawaii. The size of the rocks is on the order of 10 cm to 1 m. This gives:t = x² / Kt = (10 cm)² / 10^-2 cm²/swhich becomes ~10⁴ seconds or about an hour. Rock that is this small cools rapidly, and can be stepped on. For a rock 1 m in size, this stretches to several days to cool (10⁶ seconds).However, there are some huge bodies of rock that look very similar to rocks we see today, notably large plutons. Plutons are large bodies of magmatic rock that have cooled slowly underground. Consider the Idaho plutons (see here: Idaho Batholith ). These plutons are ~100 km in length, and we use a distance of about half of this as our distance. Using the same math as before,t = x² / Kt = (5000000 cm)² / 10^-2 cm²/st = several million years.The time it takes to cool these rocks is several million years. These are some of the largest igneous bodies, so even small rock bodies (a few km in size) take several thousands of years. These equations are great since they're so simple- they are essentially just the conservation of energy applied to a system.Some large plutons are young and are still hot as they haven't had time to cool down yet. These plutons are usually associated with geothermal activity like geysers, and Yellowstone national park is on top of one.I hope this gives you a little bit of appreciation for the math that goes behind how long it takes rock to cool. Enjoy!Edited by Matt P, : Fixed superscripts

Yes, ^ means raise to the power of, so 3^3 = 27. Sorry for not making that clear!Let me clarify one more thing: x^2 / K is equal to (x^2) / K, so K is not part of the exponent.Edited by Matt P, : No reason given.

Edited and changed. Thanks for the info!

Hi Gigahound, you have some good questions!JonF and Coragyps both provide good responses, and my response will build slightly on theirs.Fundamentally, this specific application of Fick's Law is a simple conservation of energy relation (energy is conserved during physical processes) coupled with the second law of thermodynamics (the spreading-out of energy through time). These relations are very well known and tested through and through.Compare this to the magnetic field argument: the origin of the Earth's magnetic field is still incompletely understood, the time evolution of the magnetic field is unclear, and there are no small scale tests that can be done with the Earth's field. Unlike the rock-cooling example, we can't simulate the origin and change of the Earth's magnetic field using smaller models (having a gravitationally bound sphere with a silicate shell containing a molten iron shell surrounding an iron-nickel core is not possible with modern technology). With all that's unclear creationists perform a definite disservice by attempting to back-extrapolate the modern data.I will be gone for the next week, so I'll leave others to answer your questions.