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Nor did I find any post, by truedream, which shows how the orbit of Mercury can be calculated - according the truedream ATM idea. Could someone please point me to the relevant truedream posts? If there are no such, then I have two questions for truedream, about the ATM idea presented in this thread (they are already covered by Swift and Fortis; I'm just asking in a (slightly) different way): 1) How does the truedream idea of gravity differ from General Relativity, quantitatively? 2) Please show how to calculate - quantitatively - the orbit of the planet Mercury, according the truedream idea. |
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More than 30 years ago (was it really that long ago?) I took a course at the university called "High Speed Computation". It was a rather free-wheeling, informal course in which problem sets were assigned, we would do as many as we could, but (most important thing!) we would explain how we did it. We were allowed to use whatever language we liked from the compilers offered at that time. This meant Fortran (WATFIV), PL/I, LISP, even BASIC. In the case of FORTRAN, we had access to the various subroutine libraries. One problem we were assigned was this: to generate the set of all integers of the form 2k*3l*5n less than 1 million and list them in order. Everyone else in the class chose to generate an array containing (say) all the powers of 2, then add the products of these with powers of three to the array, call the sort routine from the subroutine library, then multiply these numbers by powers of 5, and call the sort routine one last time. But I had an insight: if x is an element of this set, then so are 2*x, 3*x, and 5*x. I know that 1 is an element of the set, so the next element must be the minimum of 2*1, 3*1, and 5*1, so the next element is 2. Knowing this, the next element must be the minimum of 2*2, 3*1, and 5*1, which is 3. The next element must be the minimum of 2*2, 3*2, and 5*1, which is 4. We have to be careful whenever we have two or all three of these candidates equal, because we must advance the index for each of the candidates to the next element of the set. For example, 2*15, 3*10, and 5*6 are 30, so after adding 30 to the array we must advance the index of each of these numbers to the next one, so that the next candidate is the minimum of 2*16, 3*12, and 5*8, which is 32. The professor was amazed. No one had thought of actually generating them in order before. Now in the past, I used to describe this as "out of the box" thinking, and I suppose it is "out of the box" thinking if you consider the box to be "Use FORTRAN and the math subroutine libraries". But I realize now that "the box" was really the definition of the set, and that understanding "the box" was the key to realizing that its membership could be generated inductively from its first member, the number one. BTW: My program was written in crummy FORTRAN-esque spaghetti-code about 30 lines long. One of my classmates was so impressed by my algorithm that he rewrote it in RATFOR (an early structured version of FORTRAN) and got it down to 18 lines. That impressed me enough to learn structured programming and I haven't looked back. ![]()
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Microsoft is over if you want it. The bar has been lowered for the promotion of ATM ideas; the bar for the acceptance of ATM ideas must remain high. |
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You're right, the anecdote doesn't really illustrate " 'out of the box' is a justification for slovenly, uncritical thinking", it's more an illustration of the importance of "understanding the box". But I did mention that in the past I would have characterized my solution as "out of the box". Guess it's just "slovenly, uncritical thinking" on my part!
![]() I'm not sure why; now that you mention it, sorting is necessary only once. Unless you generate them in order as I did, then it's not necessary at all.
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Microsoft is over if you want it. The bar has been lowered for the promotion of ATM ideas; the bar for the acceptance of ATM ideas must remain high. |
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When I have a problem, my tools are still in the toolbox, and I keep my toolbox nearby. Some people only have that pocketknife.
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Numbers are not case sensitive. (me) |
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FWIW, my own view of 'out of the box thinking' has at least two critical components:
one is the one most of us seem to think of upon hearing the term - something (completely!) different, a fresh approach, creativity, ...; the other relates to CM's tale: the thinking must actually solve the problem the thinking was intended to address in the first place! |
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In reality it is more due to the increase in the energy of the atoms that happens as the temperature increases. (Think about what happens when you increase the speed of an object in orbit around the earth. Eventually it will reach escape velocity and fly away without ever coming back.) Quote:
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