181–190 of 335 posts
> 17. At any given moment on the earth's surface, there exist 2 antipodal points (on exactly opposite sides of the earth) with the same temperature and barometric pressure: youtube.com/watch?v=cchIr1OXc8E This is not necessarily true. They say a picture is worth 1000 words: https://media.deseretdigital.com/file/5894488349 Regardomg Gabriel's Horn and Banach-Tarski, the paradox is described as a trumpet, or a ball, ma…
Number 19 is a clinker. Banach-Tarski applies only to objects in real-number space, but there are no such objects. For that to work, objects have to be infinitely divisible, but all of our objects are made out of atoms. Real-numbered space is a good enough approximation to our experience that we hardly ever encounter a model failure like this one.
> 17. At any given moment on the earth's surface, there exist 2 antipodal points (on exactly opposite sides of the earth) with the same temperature and barometric pressure: youtube.com/watch?v=cchIr1OXc8E This is not necessarily true. They say a picture is worth 1000 words: https://media.deseretdigital.com/file/5894488349 Regardomg Gabriel's Horn and Banach-Tarski, the paradox is described as a trumpet, or a ball, ma…
I don't get what thought that picture is supposed to provoke.
Earlier quoted context omitted.
Although the more I think about this the more I think the difference between technical and colloquial is actually that "weight" in colloquial use refers to mass, because force is not commonly relevant.
"Weight" historically referred to mass, in common speech dating back forever. It’s the Germanic word which has been used throughout the history of English, whereas "mass" comes from Latin via French, like 5–6 centuries ago. The two words are almost exact synonyms, in historical/colloquial use. Both historically and today, a "pound" (Roman libra) is a unit of mass. People use a pound-force as a unit of force only in s…
When someone mentioned "weight" just in a qualitative way, as a burden, they might have thought at the force that presses someone down, but whenever they referred to weight in a quantitative way, they referred to the weight as measured with a weighing scale, which gives the ratio between the mass of the weighed object and the mass of a standard weight, independently of the local acceleration of gravity.
Methods that measure the force of gravity and then the mass is computed from the measured force, i.e. with the force measured either mechanically with springs or electrically, have appeared only very recently.
The distinction between force of weight and mass became important only since Newton, who used "quantity of matter" for what was renamed later to the more convenient shorter word "mass".
Perhaps it would have been better to retain the traditional words like weight and its correspondents in all other languages with the meaning of "mass", because this meaning has been used during more than 5 millennia and use a new word, e.g. gravitational force, for the force of weight, because we need to speak about this force much more seldom than about the mass of something.
Earlier quoted context omitted.
Without the math: Radius is always proportional to circumference, so a circle twice the size is twice as big around. Take the case of two identical circles. To move a point on the first circle from 12 o'clock back to 12 o'clock, it only goes halfway around the other circle, which you can prove to yourself by imagining you've wrapped a string around the circle and marked it at 12 and 6 o'clock. If you unwrap half of t…
It’s interesting to read others reasoning on this. I find it hard to follow and much harder to generalize without some notation (and a diagram which this comment box struggles to reproduce)
Hold center of small circle still, rotate big circle once counter clock wise, small one rotates 3x clockwise.
Glue them together, rotate big circle once clockwise, small circle also rotates once clockwise.
Sum them together, 0 rotations for big circle, 4 for small. I'm not at all sure how to rigorously generalize.
Surprising fact about the sun: it actually produces less heat per unit volume than a compost pile - this makes sense when you consider that fusion events are very rare. The reason the sun is so hot is that it has an enormous ratio of volume to surface area. Heat emission due to radiative cooling is proportional to the surface area, but heat creation due to fusion is proportional to the volume.
The density of the sun is very low, like much lower than the atmosphere (throughout most of it, anyway,) But yes it has an enormous volume.
Errr, the Earth doesn’t ‘roll around the sun’ - hence the author’s (+1) is wrong, I think (hope!). It’s 365.256 according to Wikipedia.
Earlier quoted context omitted.
The density of the sun is very low, like much lower than the atmosphere (throughout most of it, anyway,) But yes it has an enormous volume.
Given vastness of sun, it's age and existence of extremophiles, I would be surprised if there is no life there.
Here is one of my favorites. Take a light source and shine it at a filter that is polarized up/down that is in front of a filter that is polarized left/right. None of the light will get through: the first filter removes all of the L/R components of the light, and the second filter removes all the remaining light. Now add a third filter, between the two, which is polarized at 45 degrees. Now some of the light goes thr…
It makes more sense if you think of the polariser sheets as fences with vertical bars, and light like a string going through between two bars and being wiggled. If the direction of the waves in the string are at right-angles to the slit, the wave can't propagate through the bars. If the wave is at an angle, then some of the wave gets through, with a maximum of 100% when the wave wiggles up and down in the same direct…
Number 7: “The Earth makes 366.25 rotations around its axis per year.” Errr, the Earth doesn’t ‘roll around the sun’ - hence the author’s (+1) is wrong, I think (hope!). It’s 365.256 according to Wikipedia.