As comic book guy might say, "Worst. Acronym. Ever." MoND refers to a theory in physics, especially cosmology and astrophysics, that suggests that there is no real need to posit "dark matter". The case for dark matter has always been that the amount of observable matter in galaxies is not enough to understand how fast galaxies rotate. Either our views of gravity or our views of mass must change to cover these rotations. MoND opts for changing the view of gravity, rather than postulating vast quantities of mass. Here is Sabine Hossenfelder's explanation of the point. https://backreaction.blogspot.com/?fbclid=IwAR0Eild3WJDSYbL1NjgSjMsmenRUf6wbPy9HQE7DEkIrfLnlxHbvzp0g9Xc Advocates of Modified Newtonian Dynamics propose changes of the Newtonian theory of gravity. Of course, the Einstein revolution did already modify Newton. The point though was that another differently-motivated modification will be necessary, and that scientists from six score ye...
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Throughout school, I took what I have come to think of as a guess-and-test approach to math word problems. This was never the 'official' approach, so I eventually had to learn to dress my answers up to seem more official. But they were derived from guess-and-test. Simple example. There are two school buses, A and B. A has 18 more seats in it than B does. Together, they have 96 seats. Find the number of seats in each. Guess-and-test. Hmmm. Sixty is a nice round number lower than 96. Let us see if the big bus could have 60 seats. That would mean the small bus has 18 fewer seats than that. Hmmmm. 60 + 42 = 102 NOT 96. Okay, each bus has to have fewer seats than that. Let us guess that the big one has 55. Does that work? 55 + 37 = 92 NOT 96. Oops. But we do...
I mentioned Whitehead's apparent sympathy with Heraclitus in my last post about him. My reading had not yet at that point discovered Process and Reality. Part II, Chapter Ten , which takes the form of an extended meditation on the sentiment "all things flow." In Heraclitus' Greek, panta rhei. The sympathy is here made explicit. Indeed, a full understanding of that sentiment is said to be one of the main goals of philosophizing at all. Some of the thinkers of the early modern world tried to ban flow, or fluency, from their picture of the world. But Whitehead adds, "Newton, that Napoleon of of the world of thought, brusquely ordered fluency back into the world, regimented into his 'absolute, mathematical time, flowing equably without regard to anything external.' He also gave it a mathematical uniform in the shape of his Theory of Fluxions." What a marvelous packing of two concise sentences! Almost as magnificent as Heraclitus' two words. ...
The relationship is complicated. Let us take four points. First. both were path-breaking mathematicians. Descartes’ invention of analytic geometry made possible, a generation later, Newton’s (and Leibniz') development of calculus. Second, they had very different ideas about matter and how different chunks of matter interact. Descartes wanted to get rid of the idea of “occult” causes and effects, or what some call teleology. To speak very roughly, mechanistic explanations involve pushing and teleological ones involve pulling. For Descartes, everything that happens in the material world had to be explained by things pushing each other around. There could be no “action at a distance,” no pull, just as things didn't happen because inanimate objects (or non-human animals!) wanted them to happen. So the Cartesians of the following generation argued against Newton’s law of gravity — in their eyes Newton was trying to bring back those occult causes, pulling at each other across vast d...
think it would be great to come up with ideas that people were still trying to improve upon in a century. That is the situation with Einstein's structure of ideas, especially the general theory of relativity. Physicists are probing its limits not in the hope that they can somehow over come it and erase it from the blackboard of history -- that won't happen --but in the expectation that in time somebody will do to Einstein what he did to Newton. Roughly speaking, Einstein showed that Newton was right about a special case within a broader situation. Outside of this special case (a stable framework for observations, within which objects move at slow velocities) things work in non-Newtonian ways. Could even Einstein's understanding of physics turn out to be a special case within a broader situation. It is almost certain that this WILL happen. The question is: where do the Einsteinian rules break down? Find that out, and come up with the broader theory, and your name my frie...
The idea of inertia is not new. It was not invented by Newton, or even by Galileo. Galileo did make a fascinating elaboration on it, though. Let's look at the famous thought experiment in which he talked about dropping balls of different sizes from the Tower of Pisa. The point of the experiment is that, although there are in principle two ways of measuring mass, they come out to be the same. One can measure mass by inertia, or one can measure it in terms of gravity. If mass (gravity) is the important variable in our thought experiment, then one would expect the heavier ball -- say a cannon ball -- to fall to the ground more quickly than the small one, say, the pebble. On the other hand, if mass (inertia) in the important variable than one would expect the cannonball to move more slowly than the pebble. Inertial mass holds it back from the free fall the pebble enjoys. The only way that the cannonball and the pebble fall at the same ...
As is well known (at least in certain nerdy circles), the immaterialist philosopher George Berkeley sharply criticized Isaac Newton, and the branch of mathematics Newton had founded, in 1734. Berkeley's book of that year, THE ANALYST, said that calculus depends upon presuming that an "infinitesimal" is something at a certain point in one's reason, then assuming it is nothing at another point. That is internally incoherent. Berkeley thus earned himself a place within the usual story about calculus. The story goes -- Newton proposed certain rough-and-ready ideas, not yet fully developed. He developed them just far enough, and just deep enough, to figure out orbital mathematics. But he left holes in his reasoning. Berkeley saw the holes and called Newton out on this. Subsequent theorists re-worked the foundations to render this branch of mathematics safe from Berkeleyan assaults. That, as I say, is the usual story. In 1987, a fellow named David Sherry wrote an ar...
"Color itself is a degree of darkness." German polymath Johann Wolfgang von Goethe said that, and much else, in his publication Theory of Colors. Brain pickings recently ran an appreciation of this Treatise, calling it "an absorbing account of the philosophy and artistic experience of color." It was also part of the romantic rebellion against classicism -- Goethe was taking on boring clockworks-loving old Newton. Here's a link to the Amazon page which will allow you to look inside Goethe's text if you're so inclined. https://www.amazon.com/exec/obidos/ASIN/0262070375/braipick-20
The story of another candidate for numberhood, the infinitesimal, is even stranger than the story of the irrationals or the imaginaries. The infinitesimal is the limit of a process, where the method stipulates that the end of that process can never be reached. Consider: can a single mathematical point have a slope? Our intuitive answer, trained by Euclid, is: no. A point is pure position. It isn’t a line, it isn’t even a tiny part of a line, so it can’t have a slope! Can there be a smallest possible line? How short can a line get and still have a slope! That’s a question that Euclid taught us not to ask. It is akin to suggesting that we can have two adjacent points. If we could have two adjacent points, then they would presumably constitute the smallest possible line and they would have a slope. But we can’t. Between any two points, properly speaking, infinity of other points can fit. In the seventeenth century it was common for the mathematicians at its cuttin...