Just off the top of my head as a non engineer, the surface area to volume decreases as the size goes up, with less radiant cooling.
Regarding the “nuclear reactor” beneath our feet, most of it is shielded from us by lots of rock and dirt, such that the only harmful stuff is what we are sitting on. As long as it is not oozing radon gas or you don’t live in a uranium mine, you are OK.
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Righto- this summary of Kelvin’s work and wrong assumptions is nice and to the point:
Once it was discovered that radioactive isotopes are abundant in rocks and that radioactive decay releases tremendous amounts of heat, Kelvin’s assumption of a closed system and dwindling initial heat proved to be demonstrably false (Dalrymple, 37; Hallam, 124; Knopf, 16; Lewis, 47-48). Kelvin’s assumption of a solid Earth and heat transfer only by conduction also proved incorrect; the mantle does flow, and convection is the key method of heat transfer within the Earth (Dalrymple, 37). As Burchfield explains, radioactivity undermined the foundations for virtually all of Kelvin’s dating work (218). Lord Kelvin initially rejected the idea that radioactivity could emit significant heat, but he publicly abandoned this theory at the British Association Meeting of 1904 (Lewis, 55). In a debate two years later, however, it was clear that he never truly accepted radioactivity as the primary source of Earth’s internal heat (55). Accordingly, Kelvin never published a retraction of his overall theory, though he did privately concede to J.J. Thomson that the discovery of radioactivity rendered several of his assumptions unworkable (Hallam, 124).
It appears @WilliamDJ is doing calculations that use similar assumptions to Kelvin which are demonstrably incorrect assumptions to put in to one’s Earth cooling model that do not describe reality at all.
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A sphere of red hot fluid glass cools down in short time in the extreme cold (2K) of the vacuum of the universe, in the light of the sun, and a thin crust of 1% of its radius is formed in a few hours. The only reason to question this, is that you think you need 4,543 billion years for first order change to produce second order change. But that is impossible.
The claim that natural processes can transform simple molecules into an ever growing amount of complex molecules and structures of molecules, is pre-Victorian Alchemist faith. If natural processes could form an ever growing amount of more complex molecules, energy could be harvested for free, and chemical industry would close down. This is absurd. Therefore it is proven that natural processes cannot form an ever growing amount of more complex molecules and structures of molecules.
And please do not come up with bacteria as an example of natural processes, because bacteria are completely automated biochemical nano factories. Bringing them up as proof is circular reasoning.
And that is not a good model to use. Why do you assume the earth was entirely molten in the first place? Why do you assume the scaling factor is simply a linear function of the radius?
Lord Kelvin was opposed to evolution and so his figures are not an attempt to save it. Yet he still came up with 20 to 400 million years for the age of the earth.
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We have had this discussion before. See my posts in the biologos thread ‘Can the age of the earth be a litmus test for what counts as science?’ , and you will find the answer to your question on the linearity of the scaling factor, as well as many more empirical facts that contradict the claim that the earth is 4,543 billion years old.
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Please accept the mathematical fact that changing a system in its parameters cannot produce change in its dimensions: (a1, b1) → (a2, b2) cannot produce (a1, b1) → (a2, b2, c2) . Even if 1000 billions of years would be available, first order change (for instance the variation of the beaks of Darwin finches), cannot be extrapolated to second order change (for instance the transformation of a land animal into a whale).
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See further the 5 conclusions in my post nr. 126
@WilliamDJ Yes we have had this discussion before and you have never presented anything that would support a linear scaling factor. You have simply made it up.
Now since the scaling factor is probably related to the volume of the sphere, bigger takes longer to cool down obviously, I would say the scaling factor should be r cubed. So the scaling factor would be 2.5E23. This gives an age of the earth as 4.9 E18 years. Going with a scaling factor of r squared interesting enough gives an age of the earth as 0.7 billion years which is getting close, order of magnitude, to the correct value.
None of which are correct. This has been pointed out repeatedly but it doesn’t seem to make any difference to you.
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This is not at all a mathematical fact. A function can be mutated such that the dimensionality of its range can change.
I have in fact performed such mutations to inter-system computational interfaces. Thus the dimensionality of the domain is held constant while the dimensionality of the range increases.
There is no constraint in science or mathematics to a mutation in a biological process that would change the dimensionality of a range. Or for a mutation in the dimensionality of a domain. Or both, for that matter.
In spite of the fact that I have actually performed that which you asserted is impossible, based on your past behavior I predict you will continue to insist it is impossible, William. I dare you to prove my prediction wrong!
Blessings,
Chris Falter
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