Many of us will be familiar with , in which someone spins counterclockwise to slow down the rotation of the earth and make the night longer.  The mass of an individual human is not all that much compared to the earth, so the gesture is poetic but futile. On the other hand, the mass of forty 3,300 pound cars driving counterclockwise is quite a lot more considerable.  How much does an individual NASCAR race affect the rotation of the earth? How much time does an individual NASCAR race remove from (or add to) the length of a day on our planet?  Let's assume we're operating on the 's not-quite-oval outer track , with 200 laps of a 2.5 mile track made by forty cars weighing exactly 3,300 pounds each. The race lasts approximately three hours.
We walk or ride on our vehicles to our destinations daily. Does our movement have any effect on the rotation of the earth according to Newton's law? What will be the effect if we move all the peoples along with their vehicles at their maximum velocity in one line in one direction along the equator? How much effect will it make?
Original sentence:     Prince Andrew, looking again at that genealogical tree, shook his head, laughing as a man laughs who looks at a portrait so characteristic of the original as to be amusing.    (War and Peace, Tolstoy, English translation)     In the sentence above, shouldn't the comma before laughing be omitted if this is about the participle clause denoting "an action that happens at the same time in the past"?  I mean it should be      Prince Andrew…shook his head laughing as a man…   Plus, shouldn't the verb laugh after a man be in the past tense in order to be in accordance (agreement) with shook his head?   You know, the whole sentence should be consistent…. In Chiswell's Mathematical Logic, there is the following problem is posed using the language of propositions (LP):     In some systems of logic (mostly constructive systems where 'true' is taken to mean 'provable') there is a rule      if $(\Gamma\vdash(\phi\,\lor\psi))$ is a correct sequent then at least   one of $(\Gamma\vdash\phi)$ and $(\Gamma\vdash\psi)$ is also correct.      By giving a counterexample to a particular instance, show that this is   unacceptable as a rule for LP. [Start by giving counterexamples for   both the sequents $(\vdash p_0)$ and $(\vdash(\neg p_0))$.]   In my , it was answered that one can let $\Gamma = \{p_0\,\lor\,(\neg p_0)\}$.  From there, one can deduce neither $(\Gamma\vdash p_0)$ nor $(\Gamma\vdash (\neg p_0))$.  But this does not proceed by the counterexample route that the author suggests.  Namely, he seems to imply that we should (1) take an interpretation of propositional variables $p_0,\,p_1,\,\ldots$ (setting each one equal to T or F), and (2) write $\phi$ and $\psi$ as functions of these propositional variables, and (3) pick sentences for $\Gamma$ which are all T, all with the conditions that (A) $(\phi\,\lor\psi)$ is evaluated as T, yet (B) both $\phi$ and $\psi$ are evaluated as F.  This, of course, seems impossible.  What, then, am I missing?  It seems that taking a concrete interpretation of the propositional symbols makes the constructivist's rule irrefutable.  (Note: this is supposed to be a very simple problem set, and I am an elementary logician). Is there an IDictionary implementation that, on missing key, returns the default value instead of throwing? How do I use multirow in LaTeX? How to delete GRUB entirely from GRUB rescue and boot Windows only I am looking at  (dual low-voltage power amplifier). 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