The Physics of Information Processing Superobjects: Daily Life Among the Jupiter Brains

nibble pdf study article essay ratty bostrom physics lower-bounds interdisciplinary computation frontier singularity civilization communication time phys-energy thermo entropy-like lens intelligence futurism philosophy software hardware enhancement no-go data scale magnitude network-structure structure complex-systems concurrency density bits retention mechanics electromag quantum quantum-info speed information-theory measure chemistry gravity relativity the-world-is-just-atoms dirty-hands skunkworks gedanken ideas hard-tech nitty-gritty intricacy len:long spatial whole-partial-many frequency neuro internet web trivia cocktail humanity composition-decomposition instinct reason illusion the-self psychology cog-psych dennett within-without signal-noise coding-theory quotes scifi-fantasy fiction giants death long-short-run janus eden-heaven efficiency finiteness iteration-recursion cycles nietzschean big-peeps examples

april 2018 by nhaliday

nibble pdf study article essay ratty bostrom physics lower-bounds interdisciplinary computation frontier singularity civilization communication time phys-energy thermo entropy-like lens intelligence futurism philosophy software hardware enhancement no-go data scale magnitude network-structure structure complex-systems concurrency density bits retention mechanics electromag quantum quantum-info speed information-theory measure chemistry gravity relativity the-world-is-just-atoms dirty-hands skunkworks gedanken ideas hard-tech nitty-gritty intricacy len:long spatial whole-partial-many frequency neuro internet web trivia cocktail humanity composition-decomposition instinct reason illusion the-self psychology cog-psych dennett within-without signal-noise coding-theory quotes scifi-fantasy fiction giants death long-short-run janus eden-heaven efficiency finiteness iteration-recursion cycles nietzschean big-peeps examples

april 2018 by nhaliday

How do you measure the mass of a star? (Beginner) - Curious About Astronomy? Ask an Astronomer

december 2017 by nhaliday

Measuring the mass of stars in binary systems is easy. Binary systems are sets of two or more stars in orbit about each other. By measuring the size of the orbit, the stars' orbital speeds, and their orbital periods, we can determine exactly what the masses of the stars are. We can take that knowledge and then apply it to similar stars not in multiple systems.

We also can easily measure the luminosity and temperature of any star. A plot of luminocity versus temperature for a set of stars is called a Hertsprung-Russel (H-R) diagram, and it turns out that most stars lie along a thin band in this diagram known as the main Sequence. Stars arrange themselves by mass on the Main Sequence, with massive stars being hotter and brighter than their small-mass bretheren. If a star falls on the Main Sequence, we therefore immediately know its mass.

In addition to these methods, we also have an excellent understanding of how stars work. Our models of stellar structure are excellent predictors of the properties and evolution of stars. As it turns out, the mass of a star determines its life history from day 1, for all times thereafter, not only when the star is on the Main Sequence. So actually, the position of a star on the H-R diagram is a good indicator of its mass, regardless of whether it's on the Main Sequence or not.

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We also can easily measure the luminosity and temperature of any star. A plot of luminocity versus temperature for a set of stars is called a Hertsprung-Russel (H-R) diagram, and it turns out that most stars lie along a thin band in this diagram known as the main Sequence. Stars arrange themselves by mass on the Main Sequence, with massive stars being hotter and brighter than their small-mass bretheren. If a star falls on the Main Sequence, we therefore immediately know its mass.

In addition to these methods, we also have an excellent understanding of how stars work. Our models of stellar structure are excellent predictors of the properties and evolution of stars. As it turns out, the mass of a star determines its life history from day 1, for all times thereafter, not only when the star is on the Main Sequence. So actually, the position of a star on the H-R diagram is a good indicator of its mass, regardless of whether it's on the Main Sequence or not.

december 2017 by nhaliday

What is the connection between special and general relativity? - Physics Stack Exchange

november 2017 by nhaliday

Special relativity is the "special case" of general relativity where spacetime is flat. The speed of light is essential to both.

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november 2017 by nhaliday

What is the difference between general and special relativity? - Quora

november 2017 by nhaliday

General Relativity is, quite simply, needed to explain gravity.

Special Relativity is the special case of GR, when the metric is flat — which means no gravity.

You need General Relativity when the metric gets all curvy, and when things start to experience gravitation.

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Special Relativity is the special case of GR, when the metric is flat — which means no gravity.

You need General Relativity when the metric gets all curvy, and when things start to experience gravitation.

november 2017 by nhaliday

GPS and Relativity

november 2017 by nhaliday

The nominal GPS configuration consists of a network of 24 satellites in high orbits around the Earth, but up to 30 or so satellites may be on station at any given time. Each satellite in the GPS constellation orbits at an altitude of about 20,000 km from the ground, and has an orbital speed of about 14,000 km/hour (the orbital period is roughly 12 hours - contrary to popular belief, GPS satellites are not in geosynchronous or geostationary orbits). The satellite orbits are distributed so that at least 4 satellites are always visible from any point on the Earth at any given instant (with up to 12 visible at one time). Each satellite carries with it an atomic clock that "ticks" with a nominal accuracy of 1 nanosecond (1 billionth of a second). A GPS receiver in an airplane determines its current position and course by comparing the time signals it receives from the currently visible GPS satellites (usually 6 to 12) and trilaterating on the known positions of each satellite[1]. The precision achieved is remarkable: even a simple hand-held GPS receiver can determine your absolute position on the surface of the Earth to within 5 to 10 meters in only a few seconds. A GPS receiver in a car can give accurate readings of position, speed, and course in real-time!

More sophisticated techniques, like Differential GPS (DGPS) and Real-Time Kinematic (RTK) methods, deliver centimeter-level positions with a few minutes of measurement. Such methods allow use of GPS and related satellite navigation system data to be used for high-precision surveying, autonomous driving, and other applications requiring greater real-time position accuracy than can be achieved with standard GPS receivers.

To achieve this level of precision, the clock ticks from the GPS satellites must be known to an accuracy of 20-30 nanoseconds. However, because the satellites are constantly moving relative to observers on the Earth, effects predicted by the Special and General theories of Relativity must be taken into account to achieve the desired 20-30 nanosecond accuracy.

Because an observer on the ground sees the satellites in motion relative to them, Special Relativity predicts that we should see their clocks ticking more slowly (see the Special Relativity lecture). Special Relativity predicts that the on-board atomic clocks on the satellites should fall behind clocks on the ground by about 7 microseconds per day because of the slower ticking rate due to the time dilation effect of their relative motion [2].

Further, the satellites are in orbits high above the Earth, where the curvature of spacetime due to the Earth's mass is less than it is at the Earth's surface. A prediction of General Relativity is that clocks closer to a massive object will seem to tick more slowly than those located further away (see the Black Holes lecture). As such, when viewed from the surface of the Earth, the clocks on the satellites appear to be ticking faster than identical clocks on the ground. A calculation using General Relativity predicts that the clocks in each GPS satellite should get ahead of ground-based clocks by 45 microseconds per day.

The combination of these two relativitic effects means that the clocks on-board each satellite should tick faster than identical clocks on the ground by about 38 microseconds per day (45-7=38)! This sounds small, but the high-precision required of the GPS system requires nanosecond accuracy, and 38 microseconds is 38,000 nanoseconds. If these effects were not properly taken into account, a navigational fix based on the GPS constellation would be false after only 2 minutes, and errors in global positions would continue to accumulate at a rate of about 10 kilometers each day! The whole system would be utterly worthless for navigation in a very short time.

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physics
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applications
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More sophisticated techniques, like Differential GPS (DGPS) and Real-Time Kinematic (RTK) methods, deliver centimeter-level positions with a few minutes of measurement. Such methods allow use of GPS and related satellite navigation system data to be used for high-precision surveying, autonomous driving, and other applications requiring greater real-time position accuracy than can be achieved with standard GPS receivers.

To achieve this level of precision, the clock ticks from the GPS satellites must be known to an accuracy of 20-30 nanoseconds. However, because the satellites are constantly moving relative to observers on the Earth, effects predicted by the Special and General theories of Relativity must be taken into account to achieve the desired 20-30 nanosecond accuracy.

Because an observer on the ground sees the satellites in motion relative to them, Special Relativity predicts that we should see their clocks ticking more slowly (see the Special Relativity lecture). Special Relativity predicts that the on-board atomic clocks on the satellites should fall behind clocks on the ground by about 7 microseconds per day because of the slower ticking rate due to the time dilation effect of their relative motion [2].

Further, the satellites are in orbits high above the Earth, where the curvature of spacetime due to the Earth's mass is less than it is at the Earth's surface. A prediction of General Relativity is that clocks closer to a massive object will seem to tick more slowly than those located further away (see the Black Holes lecture). As such, when viewed from the surface of the Earth, the clocks on the satellites appear to be ticking faster than identical clocks on the ground. A calculation using General Relativity predicts that the clocks in each GPS satellite should get ahead of ground-based clocks by 45 microseconds per day.

The combination of these two relativitic effects means that the clocks on-board each satellite should tick faster than identical clocks on the ground by about 38 microseconds per day (45-7=38)! This sounds small, but the high-precision required of the GPS system requires nanosecond accuracy, and 38 microseconds is 38,000 nanoseconds. If these effects were not properly taken into account, a navigational fix based on the GPS constellation would be false after only 2 minutes, and errors in global positions would continue to accumulate at a rate of about 10 kilometers each day! The whole system would be utterly worthless for navigation in a very short time.

november 2017 by nhaliday

The Moon And Tides

november 2017 by nhaliday

Why does the Moon produce TWO water tides on the Earth and not just one?

"It is intuitively easy to understand why the gravitational pull of the Moon should produce a water tide on the Earth in the part of the ocean closest to the moon along the line connecting the center of the Moon with the center of the Earth. But in fact not one but TWO water tides are produced under which the Earth rotates every day to produce about two high tides and two low tides every day. How come?

It is not the gravitational force that is doing it, but the change in the gravitational force across the body of the Earth. If you were to plot the pattern of the Moon's 'tidal' gravitational force added to the Earth's own gravitational force, at the Earth's surface, you would be able to resolve the force vectors at different latitudes and longitudes into a radial component directed towards the Earth's center, and a component tangential to the Earth's surface. On the side nearest the moon, the 'differential' gravitational force is directed toward the Moon showing that for particles on the Earth's surface, they are being tugged slightly towards the Moon because the force of the Moon is slightly stronger at the Earth's surface than at the Earth's center which is an additional 6300 kilometers from the Moon. On the far side of the Earth, the Moon is tugging on the center of the Earth slightly stronger than it is on the far surface, so the resultant force vector is directed away from the Earth's center.

The net result of this is that the Earth gets deformed into a slightly squashed, ellipsoidal shape due to these tidal forces. This happens because if we resolve the tidal forces at each point on the Earth into a local vertical and horizontal component, the horizontal components are not zero, and are directed towards the two points along the line connecting the Earth and the Moon's centers. These horizontal forces cause rock and water to feel a gravitational force which results in the flow of rock and water into the 'tidal bulges'. There will be exactly two of these bulges. At exactly the positions of the tidal bulges where the Moon is at the zenith and at the nadir positions, there are no horizontal tidal forces and the flow stops. The water gets piled up, and the only effect is to slightly lower the weight of the water along the vertical direction.

Another way of thinking about this is that the gravitational force of the Moon causes the Earth to accelerate slightly towards the Moon causing the water to get pulled towards the Moon faster than the solid rock on the side nearest the Moon. On the far side, the solid Earth 'leaves behind' some of the water which is not as strongly accelerated towards the Moon as the Earth is. This produces the bulge on the 'back side' of the Earth."- Dr. Odenwald's ASK THE ASTRONOMER

org:junk
nibble
space
physics
mechanics
cycles
navigation
gravity
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oceans
explanation
faq
objektbuch
rhythm
"It is intuitively easy to understand why the gravitational pull of the Moon should produce a water tide on the Earth in the part of the ocean closest to the moon along the line connecting the center of the Moon with the center of the Earth. But in fact not one but TWO water tides are produced under which the Earth rotates every day to produce about two high tides and two low tides every day. How come?

It is not the gravitational force that is doing it, but the change in the gravitational force across the body of the Earth. If you were to plot the pattern of the Moon's 'tidal' gravitational force added to the Earth's own gravitational force, at the Earth's surface, you would be able to resolve the force vectors at different latitudes and longitudes into a radial component directed towards the Earth's center, and a component tangential to the Earth's surface. On the side nearest the moon, the 'differential' gravitational force is directed toward the Moon showing that for particles on the Earth's surface, they are being tugged slightly towards the Moon because the force of the Moon is slightly stronger at the Earth's surface than at the Earth's center which is an additional 6300 kilometers from the Moon. On the far side of the Earth, the Moon is tugging on the center of the Earth slightly stronger than it is on the far surface, so the resultant force vector is directed away from the Earth's center.

The net result of this is that the Earth gets deformed into a slightly squashed, ellipsoidal shape due to these tidal forces. This happens because if we resolve the tidal forces at each point on the Earth into a local vertical and horizontal component, the horizontal components are not zero, and are directed towards the two points along the line connecting the Earth and the Moon's centers. These horizontal forces cause rock and water to feel a gravitational force which results in the flow of rock and water into the 'tidal bulges'. There will be exactly two of these bulges. At exactly the positions of the tidal bulges where the Moon is at the zenith and at the nadir positions, there are no horizontal tidal forces and the flow stops. The water gets piled up, and the only effect is to slightly lower the weight of the water along the vertical direction.

Another way of thinking about this is that the gravitational force of the Moon causes the Earth to accelerate slightly towards the Moon causing the water to get pulled towards the Moon faster than the solid rock on the side nearest the Moon. On the far side, the solid Earth 'leaves behind' some of the water which is not as strongly accelerated towards the Moon as the Earth is. This produces the bulge on the 'back side' of the Earth."- Dr. Odenwald's ASK THE ASTRONOMER

november 2017 by nhaliday

Stability of the Solar System - Wikipedia

november 2017 by nhaliday

The stability of the Solar System is a subject of much inquiry in astronomy. Though the planets have been stable when historically observed, and will be in the short term, their weak gravitational effects on one another can add up in unpredictable ways. For this reason (among others) the Solar System is chaotic,[1] and even the most precise long-term models for the orbital motion of the Solar System are not valid over more than a few tens of millions of years.[2]

The Solar System is stable in human terms, and far beyond, given that it is unlikely any of the planets will collide with each other or be ejected from the system in the next few billion years,[3] and the Earth's orbit will be relatively stable.[4]

Since Newton's law of gravitation (1687), mathematicians and astronomers (such as Laplace, Lagrange, Gauss, Poincaré, Kolmogorov, Vladimir Arnold and Jürgen Moser) have searched for evidence for the stability of the planetary motions, and this quest led to many mathematical developments, and several successive 'proofs' of stability of the Solar System.[5]

...

The planets' orbits are chaotic over longer timescales, such that the whole Solar System possesses a Lyapunov time in the range of 2–230 million years.[3] In all cases this means that the position of a planet along its orbit ultimately becomes impossible to predict with any certainty (so, for example, the timing of winter and summer become uncertain), but in some cases the orbits themselves may change dramatically. Such chaos manifests most strongly as changes in eccentricity, with some planets' orbits becoming significantly more—or less—elliptical.[7]

Is the Solar System Stable?: https://www.ias.edu/ideas/2011/tremaine-solar-system

Is the Solar System Stable?: https://arxiv.org/abs/1209.5996

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perturbation
math
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papers
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data
org:mat
The Solar System is stable in human terms, and far beyond, given that it is unlikely any of the planets will collide with each other or be ejected from the system in the next few billion years,[3] and the Earth's orbit will be relatively stable.[4]

Since Newton's law of gravitation (1687), mathematicians and astronomers (such as Laplace, Lagrange, Gauss, Poincaré, Kolmogorov, Vladimir Arnold and Jürgen Moser) have searched for evidence for the stability of the planetary motions, and this quest led to many mathematical developments, and several successive 'proofs' of stability of the Solar System.[5]

...

The planets' orbits are chaotic over longer timescales, such that the whole Solar System possesses a Lyapunov time in the range of 2–230 million years.[3] In all cases this means that the position of a planet along its orbit ultimately becomes impossible to predict with any certainty (so, for example, the timing of winter and summer become uncertain), but in some cases the orbits themselves may change dramatically. Such chaos manifests most strongly as changes in eccentricity, with some planets' orbits becoming significantly more—or less—elliptical.[7]

Is the Solar System Stable?: https://www.ias.edu/ideas/2011/tremaine-solar-system

Is the Solar System Stable?: https://arxiv.org/abs/1209.5996

november 2017 by nhaliday

The First Men in the Moon | West Hunter

october 2017 by nhaliday

But what about the future? One generally assumes that space colonists, assuming that there ever are any, will be picked individuals, somewhat like existing astronauts – the best out of hordes of applicants. They’ll be smarter than average, healthier than average, saner than average – and not by just a little.

Since all these traits are significantly heritable, some highly so, we have to expect that their descendants will be different – different above the neck. They’d likely be, on average, smarter than any existing ethnic group. If a Lunar colony really took off, early colonists might account for a disproportionate fraction of the population (just as Puritans do in the US), and the Loonies might continue to have inordinate amounts of the right stuff indefinitely. They’d notice: we’d notice. We’d worry about the Lunar Peril. They’d sneer at deluded groundlings, and talk about the menace from Earth.

https://westhunt.wordpress.com/2014/09/29/the-first-men-in-the-moon/#comment-58473

Depends on your level of technical expertise. 2 million years ago, settlement of the Eurasian temperate zone was bleeding-edge technology – but it got easier. We can certainly settle the Solar system with near-term technology, if we choose to. And you’re forgetting one of the big payoffs: gafia.

west-hunter
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migration
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technology
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conquest-empire
gravity
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vitality
ability-competence
Since all these traits are significantly heritable, some highly so, we have to expect that their descendants will be different – different above the neck. They’d likely be, on average, smarter than any existing ethnic group. If a Lunar colony really took off, early colonists might account for a disproportionate fraction of the population (just as Puritans do in the US), and the Loonies might continue to have inordinate amounts of the right stuff indefinitely. They’d notice: we’d notice. We’d worry about the Lunar Peril. They’d sneer at deluded groundlings, and talk about the menace from Earth.

https://westhunt.wordpress.com/2014/09/29/the-first-men-in-the-moon/#comment-58473

Depends on your level of technical expertise. 2 million years ago, settlement of the Eurasian temperate zone was bleeding-edge technology – but it got easier. We can certainly settle the Solar system with near-term technology, if we choose to. And you’re forgetting one of the big payoffs: gafia.

october 2017 by nhaliday

forces - The Time That 2 Masses Will Collide Due To Newtonian Gravity - Physics Stack Exchange

october 2017 by nhaliday

If two particles of dust are placed in an empty universe 1 light year apart from each other, how long will it take for them to collide due to the effects of gravity?: https://www.reddit.com/r/theydidthemath/comments/3rum1p/request_if_two_particles_of_dust_are_placed_in_an/

How long for 2 particles to collide due to gravity?: https://www.physicsforums.com/threads/how-long-for-2-particles-to-collide-due-to-gravity.698767/

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How long for 2 particles to collide due to gravity?: https://www.physicsforums.com/threads/how-long-for-2-particles-to-collide-due-to-gravity.698767/

october 2017 by nhaliday

newtonian gravity - Newton's original proof of gravitation for non-point-mass objects - Physics Stack Exchange

september 2017 by nhaliday

This theorem is Proposition LXXI, Theorem XXXI in the Principia. To warm up, consider the more straightforward proof of the preceding theorem, that there's no inverse-square force inside of a spherical shell:

picture

The crux of the argument is that the triangles HPI and LPK are similar. The mass enclosed in the small-but-near patch of sphere HI goes like the square of the distance HP, while the mass enclosed in the large-but-far patch of sphere KL, with the same solid angle, goes like the square of the distance KP. This mass ratio cancels out the distance-squared ratio governing the strength of the force, and so the net force from those two patches vanishes.

For a point mass outside a shell, Newton's approach is essentially the same as the modern approach:

picture

One integral is removed because we're considering a thin spherical shell rather than a solid sphere. The second integral, "as the semi-circle AKB revolves about the diameter AB," trivially turns Newton's infinitesimal arcs HI and KL into annuli.

The third integral is over all the annuli in the sphere, over 0≤ϕ≤τ/20≤ϕ≤τ/2 or over R−r≤s≤R+rR−r≤s≤R+r. This one is a little bit hairy, even with the advantage of modern notation.

Newton's clever trick is to consider the relationship between the force due to the smaller, nearer annulus HI and the larger, farther annulus KL defined by the same viewing angle (in modern notation, dθdθ). If I understand correctly he argues again, based on lots of similar triangles with infinitesimal angles, that the smaller-but-nearer annulus and the larger-but-farther annulus exert the same force at P. Furthermore, he shows that the force doesn't depend on the distance PF, and thus doesn't depend on the radius of the sphere; the only parameter left is the distance PS (squared) between the particle and the sphere's center. Since the argument doesn't depend on the angle HPS, it's true for all the annuli, and the theorem is proved.

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The crux of the argument is that the triangles HPI and LPK are similar. The mass enclosed in the small-but-near patch of sphere HI goes like the square of the distance HP, while the mass enclosed in the large-but-far patch of sphere KL, with the same solid angle, goes like the square of the distance KP. This mass ratio cancels out the distance-squared ratio governing the strength of the force, and so the net force from those two patches vanishes.

For a point mass outside a shell, Newton's approach is essentially the same as the modern approach:

picture

One integral is removed because we're considering a thin spherical shell rather than a solid sphere. The second integral, "as the semi-circle AKB revolves about the diameter AB," trivially turns Newton's infinitesimal arcs HI and KL into annuli.

The third integral is over all the annuli in the sphere, over 0≤ϕ≤τ/20≤ϕ≤τ/2 or over R−r≤s≤R+rR−r≤s≤R+r. This one is a little bit hairy, even with the advantage of modern notation.

Newton's clever trick is to consider the relationship between the force due to the smaller, nearer annulus HI and the larger, farther annulus KL defined by the same viewing angle (in modern notation, dθdθ). If I understand correctly he argues again, based on lots of similar triangles with infinitesimal angles, that the smaller-but-nearer annulus and the larger-but-farther annulus exert the same force at P. Furthermore, he shows that the force doesn't depend on the distance PF, and thus doesn't depend on the radius of the sphere; the only parameter left is the distance PS (squared) between the particle and the sphere's center. Since the argument doesn't depend on the angle HPS, it's true for all the annuli, and the theorem is proved.

september 2017 by nhaliday

Physics 152: Gravity, Fluids, Waves, Heat

september 2017 by nhaliday

lots of good lecture notes with pictures, worked examples, and simulations

unit
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mechanics
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symmetry
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examples
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simulation
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fluid
waves
oscillation
thermo
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p:whenever
accretion
math.CA
hi-order-bits
nitty-gritty
linearity
spatial
space
entropy-like
temperature
proofs
yoga
plots
september 2017 by nhaliday

Centers of gravity in non-uniform fields - Wikipedia

september 2017 by nhaliday

In physics, a center of gravity of a material body is a point that may be used for a summary description of gravitational interactions. In a uniform gravitational field, the center of mass serves as the center of gravity. This is a very good approximation for smaller bodies near the surface of Earth, so there is no practical need to distinguish "center of gravity" from "center of mass" in most applications, such as engineering and medicine.

In a non-uniform field, gravitational effects such as potential energy, force, and torque can no longer be calculated using the center of mass alone. In particular, a non-uniform gravitational field can produce a torque on an object, even about an axis through the center of mass. The center of gravity seeks to explain this effect. Formally, a center of gravity is an application point of the resultant gravitational force on the body. Such a point may not exist, and if it exists, it is not unique. One can further define a unique center of gravity by approximating the field as either parallel or spherically symmetric.

The concept of a center of gravity as distinct from the center of mass is rarely used in applications, even in celestial mechanics, where non-uniform fields are important. Since the center of gravity depends on the external field, its motion is harder to determine than the motion of the center of mass. The common method to deal with gravitational torques is a field theory.

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In a non-uniform field, gravitational effects such as potential energy, force, and torque can no longer be calculated using the center of mass alone. In particular, a non-uniform gravitational field can produce a torque on an object, even about an axis through the center of mass. The center of gravity seeks to explain this effect. Formally, a center of gravity is an application point of the resultant gravitational force on the body. Such a point may not exist, and if it exists, it is not unique. One can further define a unique center of gravity by approximating the field as either parallel or spherically symmetric.

The concept of a center of gravity as distinct from the center of mass is rarely used in applications, even in celestial mechanics, where non-uniform fields are important. Since the center of gravity depends on the external field, its motion is harder to determine than the motion of the center of mass. The common method to deal with gravitational torques is a field theory.

september 2017 by nhaliday

Why is Earth's gravity stronger at the poles? - Physics Stack Exchange

september 2017 by nhaliday

The point is that if we approximate Earth with an oblate ellipsoid, then the surface of Earth is an equipotential surface,11 see e.g. this Phys.SE post.

Now, because the polar radius is smaller than the equatorial radius, the density of equipotential surfaces at the poles must be bigger than at the equator.

Or equivalently, the field strength22 gg at the poles must be bigger than at the equator.

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Now, because the polar radius is smaller than the equatorial radius, the density of equipotential surfaces at the poles must be bigger than at the equator.

Or equivalently, the field strength22 gg at the poles must be bigger than at the equator.

september 2017 by nhaliday

Does your weight change between the poles and the equator? (Intermediate) - Curious About Astronomy? Ask an Astronomer

september 2017 by nhaliday

You are right, that because of centrifugal force you will weigh a tiny amount less at the Equator than at the poles. Try not to think of centrifugal force as a force though; what's really going on is that objects which are in motion like to go in a straight line and so it takes some force to make them go round in a circle. (Centrifugal force is a fictitious force that shows up in the equations of motion for an object in a rotating reference frame - such as on Earth's Equator.)

So some of the force of gravity (centripetal force) is being used to make you go around in a circle at the Equator (instead of flying off into space) while at the pole this is not needed. The centripetal acceleration at the Equator is given by four times pi squared times the radius of the Earth divided by the period of rotation squared (4×π2×R/T2). Earth's period of rotation is a sidereal day (86164.1 seconds, slightly less than 24 hours), and the equatorial radius of the Earth is about 6378 km. This means that the centripetal acceleration at the Equator is about 0.03 m/s2 (metres per second squared). Compare this to the acceleration due to gravity which is about 9.8 m/s2 and you can see how tiny an effect this is - you would weigh about 0.3% less at the equator than at the poles!

There is an additional effect due to the oblateness of the Earth. The Earth is not exactly spherical but rather is a little bit like a "squashed" sphere (technically, an oblate spheroid), with the radius at the Equator slightly larger than the radius at the poles. (This shape can be explained by the effect of centrifugal acceleration on the material that makes up the Earth, exactly as described above.) This has the effect of slightly increasing your weight at the poles (since you are close to the centre of the Earth and the gravitational force depends on distance) and slightly decreasing it at the equator.

Taking into account both of the above effects, the gravitational acceleration is 9.78 m/s2 at the equator and 9.83 m/s2 at the poles, so you weigh about 0.5% more at the poles than at the equator.

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So some of the force of gravity (centripetal force) is being used to make you go around in a circle at the Equator (instead of flying off into space) while at the pole this is not needed. The centripetal acceleration at the Equator is given by four times pi squared times the radius of the Earth divided by the period of rotation squared (4×π2×R/T2). Earth's period of rotation is a sidereal day (86164.1 seconds, slightly less than 24 hours), and the equatorial radius of the Earth is about 6378 km. This means that the centripetal acceleration at the Equator is about 0.03 m/s2 (metres per second squared). Compare this to the acceleration due to gravity which is about 9.8 m/s2 and you can see how tiny an effect this is - you would weigh about 0.3% less at the equator than at the poles!

There is an additional effect due to the oblateness of the Earth. The Earth is not exactly spherical but rather is a little bit like a "squashed" sphere (technically, an oblate spheroid), with the radius at the Equator slightly larger than the radius at the poles. (This shape can be explained by the effect of centrifugal acceleration on the material that makes up the Earth, exactly as described above.) This has the effect of slightly increasing your weight at the poles (since you are close to the centre of the Earth and the gravitational force depends on distance) and slightly decreasing it at the equator.

Taking into account both of the above effects, the gravitational acceleration is 9.78 m/s2 at the equator and 9.83 m/s2 at the poles, so you weigh about 0.5% more at the poles than at the equator.

september 2017 by nhaliday

GALILEO'S STUDIES OF PROJECTILE MOTION

august 2017 by nhaliday

During the Renaissance, the focus, especially in the arts, was on representing as accurately as possible the real world whether on a 2 dimensional surface or a solid such as marble or granite. This required two things. The first was new methods for drawing or painting, e.g., perspective. The second, relevant to this topic, was careful observation.

With the spread of cannon in warfare, the study of projectile motion had taken on greater importance, and now, with more careful observation and more accurate representation, came the realization that projectiles did not move the way Aristotle and his followers had said they did: the path of a projectile did not consist of two consecutive straight line components but was instead a smooth curve. [1]

Now someone needed to come up with a method to determine if there was a special curve a projectile followed. But measuring the path of a projectile was not easy.

Using an inclined plane, Galileo had performed experiments on uniformly accelerated motion, and he now used the same apparatus to study projectile motion. He placed an inclined plane on a table and provided it with a curved piece at the bottom which deflected an inked bronze ball into a horizontal direction. The ball thus accelerated rolled over the table-top with uniform motion and then fell off the edge of the table Where it hit the floor, it left a small mark. The mark allowed the horizontal and vertical distances traveled by the ball to be measured. [2]

By varying the ball's horizontal velocity and vertical drop, Galileo was able to determine that the path of a projectile is parabolic.

https://www.scientificamerican.com/author/stillman-drake/

Galileo's Discovery of the Parabolic Trajectory: http://www.jstor.org/stable/24949756

Galileo's Experimental Confirmation of Horizontal Inertia: Unpublished Manuscripts (Galileo

Gleanings XXII): https://sci-hub.tw/https://www.jstor.org/stable/229718

- Drake Stillman

MORE THAN A DECADE HAS ELAPSED since Thomas Settle published a classic paper in which Galileo's well-known statements about his experiments on inclined planes were completely vindicated.' Settle's paper replied to an earlier attempt by Alexandre Koyre to show that Galileo could not have obtained the results he claimed in his Two New Sciences by actual observations using the equipment there described. The practical ineffectiveness of Settle's painstaking repetition of the experiments in altering the opinion of historians of science is only too evident. Koyre's paper was reprinted years later in book form without so much as a note by the editors concerning Settle's refutation of its thesis.2 And the general literature continues to belittle the role of experiment in Galileo's physics.

More recently James MacLachlan has repeated and confirmed a different experiment reported by Galileo-one which has always seemed highly exaggerated and which was also rejected by Koyre with withering sarcasm.3 In this case, however, it was accuracy of observation rather than precision of experimental data that was in question. Until now, nothing has been produced to demonstrate Galileo's skill in the design and the accurate execution of physical experiment in the modern sense.

Pant of a page of Galileo's unpublished manuscript notes, written late in 7608, corroborating his inertial assumption and leading directly to his discovery of the parabolic trajectory. (Folio 1 16v Vol. 72, MSS Galileiani; courtesy of the Biblioteca Nazionale di Firenze.)

...

(The same skeptical historians, however, believe that to show that Galileo could have used the medieval mean-speed theorem suffices to prove that he did use it, though it is found nowhere in his published or unpublished writings.)

...

Now, it happens that among Galileo's manuscript notes on motion there are many pages that were not published by Favaro, since they contained only calculations or diagrams without attendant propositions or explanations. Some pages that were published had first undergone considerable editing, making it difficult if not impossible to discern their full significance from their printed form. This unpublished material includes at least one group of notes which cannot satisfactorily be accounted for except as representing a series of experiments designed to test a fundamental assumption, which led to a new, important discovery. In these documents precise empirical data are given numerically, comparisons are made with calculated values derived from theory, a source of discrepancy from still another expected result is noted, a new experiment is designed to eliminate this, and further empirical data are recorded. The last-named data, although proving to be beyond Galileo's powers of mathematical analysis at the time, when subjected to modern analysis turn out to be remarkably precise. If this does not represent the experimental process in its fully modern sense, it is hard to imagine what standards historians require to be met.

The discovery of these notes confirms the opinion of earlier historians. They read only Galileo's published works, but did so without a preconceived notion of continuity in the history of ideas. The opinion of our more sophisticated colleagues has its sole support in philosophical interpretations that fit with preconceived views of orderly long-term scientific development. To find manuscript evidence that Galileo was at home in the physics laboratory hardly surprises me. I should find it much more astonishing if, by reasoning alone, working only from fourteenth-century theories and conclusions, he had continued along lines so different from those followed by profound philosophers in earlier centuries. It is to be hoped that, warned by these examples, historians will begin to restore the old cautionary clauses in analogous instances in which scholarly opinions are revised without new evidence, simply to fit historical theories.

In what follows, the newly discovered documents are presented in the context of a hypothetical reconstruction of Galileo's thought.

...

As early as 1590, if we are correct in ascribing Galileo's juvenile De motu to that date, it was his belief that an ideal body resting on an ideal horizontal plane could be set in motion by a force smaller than any previously assigned force, however small. By "horizontal plane" he meant a surface concentric with the earth but which for reasonable distances would be indistinguishable from a level plane. Galileo noted at the time that experiment did not confirm this belief that the body could be set in motion by a vanishingly small force, and he attributed the failure to friction, pressure, the imperfection of material surfaces and spheres, and the departure of level planes from concentricity with the earth.5

It followed from this belief that under ideal conditions the motion so induced would also be perpetual and uniform. Galileo did not mention these consequences until much later, and it is impossible to say just when he perceived them. They are, however, so evident that it is safe to assume that he saw them almost from the start. They constitute a trivial case of the proposition he seems to have been teaching before 1607-that a mover is required to start motion, but that absence of resistance is then sufficient to account for its continuation.6

In mid-1604, following some investigations of motions along circular arcs and motions of pendulums, Galileo hit upon the law that in free fall the times elapsed from rest are as the smaller distance is to the mean proportional between two distances fallen.7 This gave him the times-squared law as well as the rule of odd numbers for successive distances and speeds in free fall. During the next few years he worked out a large number of theorems relating to motion along inclined planes, later published in the Two New Sciences. He also arrived at the rule that the speed terminating free fall from rest was double the speed of the fall itself. These theorems survive in manuscript notes of the period 1604-1609. (Work during these years can be identified with virtual certainty by the watermarks in the paper used, as I have explained elsewhere.8)

In the autumn of 1608, after a summer at Florence, Galileo seems to have interested himself in the question whether the actual slowing of a body moving horizontally followed any particular rule. On folio 117i of the manuscripts just mentioned, the numbers 196, 155, 121, 100 are noted along the horizontal line near the middle of the page (see Fig. 1). I believe that this was the first entry on this leaf, for reasons that will appear later, and that Galileo placed his grooved plane in the level position and recorded distances traversed in equal times along it. Using a metronome, and rolling a light wooden ball about 4 3/4 inches in diameter along a plane with a groove 1 3/4 inches wide, I obtained similar relations over a distance of 6 feet. The figures obtained vary greatly for balls of different materials and weights and for greatly different initial speeds.9 But it suffices for my present purposes that Galileo could have obtained the figures noted by observing the actual deceleration of a ball along a level plane. It should be noted that the watermark on this leaf is like that on folio 116, to which we shall come presently, and it will be seen later that the two sheets are closely connected in time in other ways as well.

The relatively rapid deceleration is obviously related to the contact of ball and groove. Were the ball to roll right off the end of the plane, all resistance to horizontal motion would be virtually removed. If, then, there were any way to have a given ball leave the plane at different speeds of which the ratios were known, Galileo's old idea that horizontal motion would continue uniformly in the absence of resistance could be put to test. His law of free fall made this possible. The ratios of speeds could be controlled by allowing the ball to fall vertically through known heights, at the ends of which it would be deflected horizontally. Falls through given heights … [more]

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With the spread of cannon in warfare, the study of projectile motion had taken on greater importance, and now, with more careful observation and more accurate representation, came the realization that projectiles did not move the way Aristotle and his followers had said they did: the path of a projectile did not consist of two consecutive straight line components but was instead a smooth curve. [1]

Now someone needed to come up with a method to determine if there was a special curve a projectile followed. But measuring the path of a projectile was not easy.

Using an inclined plane, Galileo had performed experiments on uniformly accelerated motion, and he now used the same apparatus to study projectile motion. He placed an inclined plane on a table and provided it with a curved piece at the bottom which deflected an inked bronze ball into a horizontal direction. The ball thus accelerated rolled over the table-top with uniform motion and then fell off the edge of the table Where it hit the floor, it left a small mark. The mark allowed the horizontal and vertical distances traveled by the ball to be measured. [2]

By varying the ball's horizontal velocity and vertical drop, Galileo was able to determine that the path of a projectile is parabolic.

https://www.scientificamerican.com/author/stillman-drake/

Galileo's Discovery of the Parabolic Trajectory: http://www.jstor.org/stable/24949756

Galileo's Experimental Confirmation of Horizontal Inertia: Unpublished Manuscripts (Galileo

Gleanings XXII): https://sci-hub.tw/https://www.jstor.org/stable/229718

- Drake Stillman

MORE THAN A DECADE HAS ELAPSED since Thomas Settle published a classic paper in which Galileo's well-known statements about his experiments on inclined planes were completely vindicated.' Settle's paper replied to an earlier attempt by Alexandre Koyre to show that Galileo could not have obtained the results he claimed in his Two New Sciences by actual observations using the equipment there described. The practical ineffectiveness of Settle's painstaking repetition of the experiments in altering the opinion of historians of science is only too evident. Koyre's paper was reprinted years later in book form without so much as a note by the editors concerning Settle's refutation of its thesis.2 And the general literature continues to belittle the role of experiment in Galileo's physics.

More recently James MacLachlan has repeated and confirmed a different experiment reported by Galileo-one which has always seemed highly exaggerated and which was also rejected by Koyre with withering sarcasm.3 In this case, however, it was accuracy of observation rather than precision of experimental data that was in question. Until now, nothing has been produced to demonstrate Galileo's skill in the design and the accurate execution of physical experiment in the modern sense.

Pant of a page of Galileo's unpublished manuscript notes, written late in 7608, corroborating his inertial assumption and leading directly to his discovery of the parabolic trajectory. (Folio 1 16v Vol. 72, MSS Galileiani; courtesy of the Biblioteca Nazionale di Firenze.)

...

(The same skeptical historians, however, believe that to show that Galileo could have used the medieval mean-speed theorem suffices to prove that he did use it, though it is found nowhere in his published or unpublished writings.)

...

Now, it happens that among Galileo's manuscript notes on motion there are many pages that were not published by Favaro, since they contained only calculations or diagrams without attendant propositions or explanations. Some pages that were published had first undergone considerable editing, making it difficult if not impossible to discern their full significance from their printed form. This unpublished material includes at least one group of notes which cannot satisfactorily be accounted for except as representing a series of experiments designed to test a fundamental assumption, which led to a new, important discovery. In these documents precise empirical data are given numerically, comparisons are made with calculated values derived from theory, a source of discrepancy from still another expected result is noted, a new experiment is designed to eliminate this, and further empirical data are recorded. The last-named data, although proving to be beyond Galileo's powers of mathematical analysis at the time, when subjected to modern analysis turn out to be remarkably precise. If this does not represent the experimental process in its fully modern sense, it is hard to imagine what standards historians require to be met.

The discovery of these notes confirms the opinion of earlier historians. They read only Galileo's published works, but did so without a preconceived notion of continuity in the history of ideas. The opinion of our more sophisticated colleagues has its sole support in philosophical interpretations that fit with preconceived views of orderly long-term scientific development. To find manuscript evidence that Galileo was at home in the physics laboratory hardly surprises me. I should find it much more astonishing if, by reasoning alone, working only from fourteenth-century theories and conclusions, he had continued along lines so different from those followed by profound philosophers in earlier centuries. It is to be hoped that, warned by these examples, historians will begin to restore the old cautionary clauses in analogous instances in which scholarly opinions are revised without new evidence, simply to fit historical theories.

In what follows, the newly discovered documents are presented in the context of a hypothetical reconstruction of Galileo's thought.

...

As early as 1590, if we are correct in ascribing Galileo's juvenile De motu to that date, it was his belief that an ideal body resting on an ideal horizontal plane could be set in motion by a force smaller than any previously assigned force, however small. By "horizontal plane" he meant a surface concentric with the earth but which for reasonable distances would be indistinguishable from a level plane. Galileo noted at the time that experiment did not confirm this belief that the body could be set in motion by a vanishingly small force, and he attributed the failure to friction, pressure, the imperfection of material surfaces and spheres, and the departure of level planes from concentricity with the earth.5

It followed from this belief that under ideal conditions the motion so induced would also be perpetual and uniform. Galileo did not mention these consequences until much later, and it is impossible to say just when he perceived them. They are, however, so evident that it is safe to assume that he saw them almost from the start. They constitute a trivial case of the proposition he seems to have been teaching before 1607-that a mover is required to start motion, but that absence of resistance is then sufficient to account for its continuation.6

In mid-1604, following some investigations of motions along circular arcs and motions of pendulums, Galileo hit upon the law that in free fall the times elapsed from rest are as the smaller distance is to the mean proportional between two distances fallen.7 This gave him the times-squared law as well as the rule of odd numbers for successive distances and speeds in free fall. During the next few years he worked out a large number of theorems relating to motion along inclined planes, later published in the Two New Sciences. He also arrived at the rule that the speed terminating free fall from rest was double the speed of the fall itself. These theorems survive in manuscript notes of the period 1604-1609. (Work during these years can be identified with virtual certainty by the watermarks in the paper used, as I have explained elsewhere.8)

In the autumn of 1608, after a summer at Florence, Galileo seems to have interested himself in the question whether the actual slowing of a body moving horizontally followed any particular rule. On folio 117i of the manuscripts just mentioned, the numbers 196, 155, 121, 100 are noted along the horizontal line near the middle of the page (see Fig. 1). I believe that this was the first entry on this leaf, for reasons that will appear later, and that Galileo placed his grooved plane in the level position and recorded distances traversed in equal times along it. Using a metronome, and rolling a light wooden ball about 4 3/4 inches in diameter along a plane with a groove 1 3/4 inches wide, I obtained similar relations over a distance of 6 feet. The figures obtained vary greatly for balls of different materials and weights and for greatly different initial speeds.9 But it suffices for my present purposes that Galileo could have obtained the figures noted by observing the actual deceleration of a ball along a level plane. It should be noted that the watermark on this leaf is like that on folio 116, to which we shall come presently, and it will be seen later that the two sheets are closely connected in time in other ways as well.

The relatively rapid deceleration is obviously related to the contact of ball and groove. Were the ball to roll right off the end of the plane, all resistance to horizontal motion would be virtually removed. If, then, there were any way to have a given ball leave the plane at different speeds of which the ratios were known, Galileo's old idea that horizontal motion would continue uniformly in the absence of resistance could be put to test. His law of free fall made this possible. The ratios of speeds could be controlled by allowing the ball to fall vertically through known heights, at the ends of which it would be deflected horizontally. Falls through given heights … [more]

august 2017 by nhaliday

Isaac Newton: the first physicist.

august 2017 by nhaliday

[...] More fundamentally, Newton's mathematical approach has become so basic to all of physics that he is generally regarded as _the father of the clockwork universe_: the first, and perhaps the greatest, physicist.

The Alchemist

In fact, Newton was deeply opposed to the mechanistic conception of the world. A secretive alchemist [...]. His written work on the subject ran to more than a million words, far more than he ever produced on calculus or mechanics [21]. Obsessively religious, he spent years correlating biblical prophecy with historical events [319ff]. He became deeply convinced that Christian doctrine had been deliberately corrupted by _the false notion of the trinity_, and developed a vicious contempt for conventional (trinitarian) Christianity and for Roman Catholicism in particular [324]. [...] He believed that God mediated the gravitational force [511](353), and opposed any attempt to give a mechanistic explanation of chemistry or gravity, since that would diminish the role of God [646]. He consequently conceived such _a hatred of Descartes_, on whose foundations so many of his achievements were built, that at times _he refused even to write his name_ [399,401].

The Man

Newton was rigorously puritanical: when one of his few friends told him "a loose story about a nun", he ended their friendship (267). [...] He thought of himself as the sole inventor of the calculus, and hence the greatest mathematician since the ancients, and left behind a huge corpus of unpublished work, mostly alchemy and biblical exegesis, that he believed future generations would appreciate more than his own (199,511).

[...] Even though these unattractive qualities caused him to waste huge amounts of time and energy in ruthless vendettas against colleagues who in many cases had helped him (see below), they also drove him to the extraordinary achievements for which he is still remembered. And for all his arrogance, Newton's own summary of his life (574) was beautifully humble:

"I do not know how I may appear to the world, but to myself I seem to have been only like a boy, playing on the sea-shore, and diverting myself, in now and then finding a smoother pebble or prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me."

Before Newton

...

1. Calculus. Descartes, in 1637, pioneered the use of coordinates to turn geometric problems into algebraic ones, a method that Newton was never to accept [399]. Descartes, Fermat, and others investigated methods of calculating the tangents to arbitrary curves [28-30]. Kepler, Cavalieri, and others used infinitesimal slices to calculate volumes and areas enclosed by curves [30], but no unified treatment of these problems had yet been found.

2. Mechanics & Planetary motion. The elliptical orbits of the planets having been established by Kepler, Descartes proposed the idea of a purely mechanical heliocentric universe, following deterministic laws, and with no need of any divine agency [15], another anathema to Newton. _No one imagined, however, that a single law might explain both falling bodies and planetary motion_. Galileo invented the concept of inertia, anticipating Newton's first and second laws of motion (293), and Huygens used it to analyze collisions and circular motion [11]. Again, these pieces of progress had not been synthesized into a general method for analyzing forces and motion.

3. Light. Descartes claimed that light was a pressure wave, Gassendi that it was a stream of particles (corpuscles) [13]. As might be guessed, Newton vigorously supported the corpuscular theory. _White light was universally believed to be the pure form_, and colors were some added property bequeathed to it upon reflection from matter (150). Descartes had discovered the sine law of refraction (94), but it was not known that some colors were refracted more than others. The pattern was the familiar one: many pieces of the puzzle were in place, but the overall picture was still unclear.

The Natural Philosopher

Between 1671 and 1690, Newton was to supply definitive treatments of most of these problems. By assiduous experimentation with prisms he established that colored light was actually fundamental, and that it could be recombined to create white light. He did not publish the result for 6 years, by which time it seemed so obvious to him that he found great difficulty in responding patiently to the many misunderstandings and objections with which it met [239ff].

He invented differential and integral calculus in 1665-6, but failed to publish it. Leibniz invented it independently 10 years later, and published it first [718]. This resulted in a priority dispute which degenerated into a feud characterized by extraordinary dishonesty and venom on both sides (542).

In discovering gravitation, Newton was also _barely ahead of the rest of the pack_. Hooke was the first to realize that orbital motion was produced by a centripetal force (268), and in 1679 _he suggested an inverse square law to Newton_ [387]. Halley and Wren came to the same conclusion, and turned to Newton for a proof, which he duly supplied [402]. Newton did not stop there, however. From 1684 to 1687 he worked continuously on a grand synthesis of the whole of mechanics, the "Philosophiae Naturalis Principia Mathematica," in which he developed his three laws of motion and showed in detail that the universal force of gravitation could explain the fall of an apple as well as the precise motions of planets and comets.

The "Principia" crystallized the new conceptions of force and inertia that had gradually been emerging, and marks the beginning of theoretical physics as the mathematical field that we know today. It is not an easy read: Newton had developed the idea that geometry and equations should never be combined [399], and therefore _refused to use simple analytical techniques in his proofs_, requiring classical geometric constructions instead [428]. He even made his Principia _deliberately abstruse in order to discourage amateurs from feeling qualified to criticize it_ [459].

[...] most of the rest of his life was spent in administrative work as Master of the Mint and as President of the Royal Society, _a position he ruthlessly exploited in the pursuit of vendettas_ against Hooke (300ff,500), Leibniz (510ff), and Flamsteed (490,500), among others. He kept secret his disbelief in Christ's divinity right up until his dying moment, at which point he refused the last rites, at last openly defying the church (576). [...]

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The Alchemist

In fact, Newton was deeply opposed to the mechanistic conception of the world. A secretive alchemist [...]. His written work on the subject ran to more than a million words, far more than he ever produced on calculus or mechanics [21]. Obsessively religious, he spent years correlating biblical prophecy with historical events [319ff]. He became deeply convinced that Christian doctrine had been deliberately corrupted by _the false notion of the trinity_, and developed a vicious contempt for conventional (trinitarian) Christianity and for Roman Catholicism in particular [324]. [...] He believed that God mediated the gravitational force [511](353), and opposed any attempt to give a mechanistic explanation of chemistry or gravity, since that would diminish the role of God [646]. He consequently conceived such _a hatred of Descartes_, on whose foundations so many of his achievements were built, that at times _he refused even to write his name_ [399,401].

The Man

Newton was rigorously puritanical: when one of his few friends told him "a loose story about a nun", he ended their friendship (267). [...] He thought of himself as the sole inventor of the calculus, and hence the greatest mathematician since the ancients, and left behind a huge corpus of unpublished work, mostly alchemy and biblical exegesis, that he believed future generations would appreciate more than his own (199,511).

[...] Even though these unattractive qualities caused him to waste huge amounts of time and energy in ruthless vendettas against colleagues who in many cases had helped him (see below), they also drove him to the extraordinary achievements for which he is still remembered. And for all his arrogance, Newton's own summary of his life (574) was beautifully humble:

"I do not know how I may appear to the world, but to myself I seem to have been only like a boy, playing on the sea-shore, and diverting myself, in now and then finding a smoother pebble or prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me."

Before Newton

...

1. Calculus. Descartes, in 1637, pioneered the use of coordinates to turn geometric problems into algebraic ones, a method that Newton was never to accept [399]. Descartes, Fermat, and others investigated methods of calculating the tangents to arbitrary curves [28-30]. Kepler, Cavalieri, and others used infinitesimal slices to calculate volumes and areas enclosed by curves [30], but no unified treatment of these problems had yet been found.

2. Mechanics & Planetary motion. The elliptical orbits of the planets having been established by Kepler, Descartes proposed the idea of a purely mechanical heliocentric universe, following deterministic laws, and with no need of any divine agency [15], another anathema to Newton. _No one imagined, however, that a single law might explain both falling bodies and planetary motion_. Galileo invented the concept of inertia, anticipating Newton's first and second laws of motion (293), and Huygens used it to analyze collisions and circular motion [11]. Again, these pieces of progress had not been synthesized into a general method for analyzing forces and motion.

3. Light. Descartes claimed that light was a pressure wave, Gassendi that it was a stream of particles (corpuscles) [13]. As might be guessed, Newton vigorously supported the corpuscular theory. _White light was universally believed to be the pure form_, and colors were some added property bequeathed to it upon reflection from matter (150). Descartes had discovered the sine law of refraction (94), but it was not known that some colors were refracted more than others. The pattern was the familiar one: many pieces of the puzzle were in place, but the overall picture was still unclear.

The Natural Philosopher

Between 1671 and 1690, Newton was to supply definitive treatments of most of these problems. By assiduous experimentation with prisms he established that colored light was actually fundamental, and that it could be recombined to create white light. He did not publish the result for 6 years, by which time it seemed so obvious to him that he found great difficulty in responding patiently to the many misunderstandings and objections with which it met [239ff].

He invented differential and integral calculus in 1665-6, but failed to publish it. Leibniz invented it independently 10 years later, and published it first [718]. This resulted in a priority dispute which degenerated into a feud characterized by extraordinary dishonesty and venom on both sides (542).

In discovering gravitation, Newton was also _barely ahead of the rest of the pack_. Hooke was the first to realize that orbital motion was produced by a centripetal force (268), and in 1679 _he suggested an inverse square law to Newton_ [387]. Halley and Wren came to the same conclusion, and turned to Newton for a proof, which he duly supplied [402]. Newton did not stop there, however. From 1684 to 1687 he worked continuously on a grand synthesis of the whole of mechanics, the "Philosophiae Naturalis Principia Mathematica," in which he developed his three laws of motion and showed in detail that the universal force of gravitation could explain the fall of an apple as well as the precise motions of planets and comets.

The "Principia" crystallized the new conceptions of force and inertia that had gradually been emerging, and marks the beginning of theoretical physics as the mathematical field that we know today. It is not an easy read: Newton had developed the idea that geometry and equations should never be combined [399], and therefore _refused to use simple analytical techniques in his proofs_, requiring classical geometric constructions instead [428]. He even made his Principia _deliberately abstruse in order to discourage amateurs from feeling qualified to criticize it_ [459].

[...] most of the rest of his life was spent in administrative work as Master of the Mint and as President of the Royal Society, _a position he ruthlessly exploited in the pursuit of vendettas_ against Hooke (300ff,500), Leibniz (510ff), and Flamsteed (490,500), among others. He kept secret his disbelief in Christ's divinity right up until his dying moment, at which point he refused the last rites, at last openly defying the church (576). [...]

august 2017 by nhaliday

Philosophiæ Naturalis Principia Mathematica - Wikipedia

august 2017 by nhaliday

Newton Papers : Philosophiæ naturalis principia mathematica: https://cudl.lib.cam.ac.uk/view/PR-ADV-B-00039-00001/1

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august 2017 by nhaliday

gravity - Gravitational collapse and free fall time (spherical, pressure-free) - Physics Stack Exchange

august 2017 by nhaliday

the parenthetical regarding Gauss's law just involves noting a shell of radius r + symmetry (so single parameter determines field along shell)

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august 2017 by nhaliday

How large is the Sun compared to Earth? | Cool Cosmos

august 2017 by nhaliday

Compared to Earth, the Sun is enormous! It contains 99.86% of all of the mass of the entire Solar System. The Sun is 864,400 miles (1,391,000 kilometers) across. This is about 109 times the diameter of Earth. The Sun weighs about 333,000 times as much as Earth. It is so large that about 1,300,000 planet Earths can fit inside of it. Earth is about the size of an average sunspot!

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august 2017 by nhaliday

Tidal locking - Wikipedia

august 2017 by nhaliday

The Moon's rotation and orbital periods are tidally locked with each other, so no matter when the Moon is observed from Earth the same hemisphere of the Moon is always seen. The far side of the Moon was not seen until 1959, when photographs of most of the far side were transmitted from the Soviet spacecraft Luna 3.[12]

never actually thought about this

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never actually thought about this

august 2017 by nhaliday

The Earth-Moon system

august 2017 by nhaliday

nice way of expressing Kepler's law (scaled by AU, solar mass, year, etc.) among other things

1. PHYSICAL PROPERTIES OF THE MOON

2. LUNAR PHASES

3. ECLIPSES

4. TIDES

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1. PHYSICAL PROPERTIES OF THE MOON

2. LUNAR PHASES

3. ECLIPSES

4. TIDES

august 2017 by nhaliday

Aether theories - Wikipedia

august 2017 by nhaliday

Mechanical explanations of gravitation: https://en.wikipedia.org/wiki/Mechanical_explanations_of_gravitation

Newton’s aether model: https://arxiv.org/pdf/physics/0011003.pdf

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Newton’s aether model: https://arxiv.org/pdf/physics/0011003.pdf

august 2017 by nhaliday

Roche limit - Wikipedia

july 2017 by nhaliday

In celestial mechanics, the Roche limit (pronounced /ʁɔʃ/) or Roche radius, is the distance within which a celestial body, held together only by its own gravity, will disintegrate due to a second celestial body's tidal forces exceeding the first body's gravitational self-attraction.[1] Inside the Roche limit, orbiting material disperses and forms rings whereas outside the limit material tends to coalesce. The term is named after Édouard Roche, who is the French astronomer who first calculated this theoretical limit in 1848.[2]

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july 2017 by nhaliday

Interstellar travel - Wikipedia

july 2017 by nhaliday

https://en.wikipedia.org/wiki/Space_travel_using_constant_acceleration

https://twitter.com/gcochran99/status/886766460365832192

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https://twitter.com/gcochran99/status/886766460365832192

july 2017 by nhaliday

Low g | West Hunter

july 2017 by nhaliday

https://en.wikipedia.org/wiki/Effect_of_spaceflight_on_the_human_body

https://westhunt.wordpress.com/2017/07/06/low-g/#comment-93406

https://en.wikipedia.org/wiki/The_Integral_Trees

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https://westhunt.wordpress.com/2017/07/06/low-g/#comment-93406

https://en.wikipedia.org/wiki/The_Integral_Trees

july 2017 by nhaliday

Laws of science - Wikipedia

concept list skeleton minimum-viable physics mechanics gravity relativity thermo electromag quantum chemistry metabuch identity levers wiki reference nibble cheatsheet summary hi-order-bits synthesis 🔬 science space applicability-prereqs theory-practice

june 2017 by nhaliday

concept list skeleton minimum-viable physics mechanics gravity relativity thermo electromag quantum chemistry metabuch identity levers wiki reference nibble cheatsheet summary hi-order-bits synthesis 🔬 science space applicability-prereqs theory-practice

june 2017 by nhaliday

Project Orion (nuclear propulsion) - Wikipedia

may 2017 by nhaliday

https://en.wikipedia.org/wiki/Nuclear_pulse_propulsion

https://en.wikipedia.org/wiki/NERVA

https://en.wikipedia.org/wiki/Nuclear_thermal_rocket

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https://en.wikipedia.org/wiki/NERVA

https://en.wikipedia.org/wiki/Nuclear_thermal_rocket

may 2017 by nhaliday

Lucio Russo - Wikipedia

may 2017 by nhaliday

In The Forgotten Revolution: How Science Was Born in 300 BC and Why It Had to Be Reborn (Italian: La rivoluzione dimenticata), Russo promotes the belief that Hellenistic science in the period 320-144 BC reached heights not achieved by Classical age science, and proposes that it went further than ordinarily thought, in multiple fields not normally associated with ancient science.

La Rivoluzione Dimenticata (The Forgotten Revolution), Reviewed by Sandro Graffi: http://www.ams.org/notices/199805/review-graffi.pdf

Before turning to the question of the decline of Hellenistic science, I come back to the new light shed by the book on Euclid’s Elements and on pre-Ptolemaic astronomy. Euclid’s definitions of the elementary geometric entities—point, straight line, plane—at the beginning of the Elements have long presented a problem.7 Their nature is in sharp contrast with the approach taken in the rest of the book, and continued by mathematicians ever since, of refraining from defining the fundamental entities explicitly but limiting themselves to postulating the properties which they enjoy. Why should Euclid be so hopelessly obscure right at the beginning and so smooth just after? The answer is: the definitions are not Euclid’s. Toward the beginning of the second century A.D. Heron of Alexandria found it convenient to introduce definitions of the elementary objects (a sign of decadence!) in his commentary on Euclid’s Elements, which had been written at least 400 years before. All manuscripts of the Elements copied ever since included Heron’s definitions without mention, whence their attribution to Euclid himself. The philological evidence leading to this conclusion is quite convincing.8

...

What about the general and steady (on the average) impoverishment of Hellenistic science under the Roman empire? This is a major historical problem, strongly tied to the even bigger one of the decline and fall of the antique civilization itself. I would summarize the author’s argument by saying that it basically represents an application to science of a widely accepted general theory on decadence of antique civilization going back to Max Weber. Roman society, mainly based on slave labor, underwent an ultimately unrecoverable crisis as the traditional sources of that labor force, essentially wars, progressively dried up. To save basic farming, the remaining slaves were promoted to be serfs, and poor free peasants reduced to serfdom, but this made trade disappear. A society in which production is almost entirely based on serfdom and with no trade clearly has very little need of culture, including science and technology. As Max Weber pointed out, when trade vanished, so did the marble splendor of the ancient towns, as well as the spiritual assets that went with it: art, literature, science, and sophisticated commercial laws. The recovery of Hellenistic science then had to wait until the disappearance of serfdom at the end of the Middle Ages. To quote Max Weber: “Only then with renewed vigor did the old giant rise up again.”

...

The epilogue contains the (rather pessimistic) views of the author on the future of science, threatened by the apparent triumph of today’s vogue of irrationality even in leading institutions (e.g., an astrology professorship at the Sorbonne). He looks at today’s ever-increasing tendency to teach science more on a fideistic than on a deductive or experimental basis as the first sign of a decline which could be analogous to the post-Hellenistic one.

Praising Alexandrians to excess: https://sci-hub.tw/10.1088/2058-7058/17/4/35

The Economic Record review: https://sci-hub.tw/10.1111/j.1475-4932.2004.00203.x

listed here: https://pinboard.in/u:nhaliday/b:c5c09f2687c1

Was Roman Science in Decline? (Excerpt from My New Book): https://www.richardcarrier.info/archives/13477

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piracy
physics
canon
science
the-trenches
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broad-econ
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frontier
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conquest-empire
giants
economics
article
growth-econ
cjones-like
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empirical
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truth
rot
zeitgeist
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big-peeps
civilization
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roots
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britain
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social-structure
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cycles
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mechanics
math
geometry
gravity
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is-ought
flexibility
trends
reason
applicability-prereqs
theory-practice
traces
evidence
La Rivoluzione Dimenticata (The Forgotten Revolution), Reviewed by Sandro Graffi: http://www.ams.org/notices/199805/review-graffi.pdf

Before turning to the question of the decline of Hellenistic science, I come back to the new light shed by the book on Euclid’s Elements and on pre-Ptolemaic astronomy. Euclid’s definitions of the elementary geometric entities—point, straight line, plane—at the beginning of the Elements have long presented a problem.7 Their nature is in sharp contrast with the approach taken in the rest of the book, and continued by mathematicians ever since, of refraining from defining the fundamental entities explicitly but limiting themselves to postulating the properties which they enjoy. Why should Euclid be so hopelessly obscure right at the beginning and so smooth just after? The answer is: the definitions are not Euclid’s. Toward the beginning of the second century A.D. Heron of Alexandria found it convenient to introduce definitions of the elementary objects (a sign of decadence!) in his commentary on Euclid’s Elements, which had been written at least 400 years before. All manuscripts of the Elements copied ever since included Heron’s definitions without mention, whence their attribution to Euclid himself. The philological evidence leading to this conclusion is quite convincing.8

...

What about the general and steady (on the average) impoverishment of Hellenistic science under the Roman empire? This is a major historical problem, strongly tied to the even bigger one of the decline and fall of the antique civilization itself. I would summarize the author’s argument by saying that it basically represents an application to science of a widely accepted general theory on decadence of antique civilization going back to Max Weber. Roman society, mainly based on slave labor, underwent an ultimately unrecoverable crisis as the traditional sources of that labor force, essentially wars, progressively dried up. To save basic farming, the remaining slaves were promoted to be serfs, and poor free peasants reduced to serfdom, but this made trade disappear. A society in which production is almost entirely based on serfdom and with no trade clearly has very little need of culture, including science and technology. As Max Weber pointed out, when trade vanished, so did the marble splendor of the ancient towns, as well as the spiritual assets that went with it: art, literature, science, and sophisticated commercial laws. The recovery of Hellenistic science then had to wait until the disappearance of serfdom at the end of the Middle Ages. To quote Max Weber: “Only then with renewed vigor did the old giant rise up again.”

...

The epilogue contains the (rather pessimistic) views of the author on the future of science, threatened by the apparent triumph of today’s vogue of irrationality even in leading institutions (e.g., an astrology professorship at the Sorbonne). He looks at today’s ever-increasing tendency to teach science more on a fideistic than on a deductive or experimental basis as the first sign of a decline which could be analogous to the post-Hellenistic one.

Praising Alexandrians to excess: https://sci-hub.tw/10.1088/2058-7058/17/4/35

The Economic Record review: https://sci-hub.tw/10.1111/j.1475-4932.2004.00203.x

listed here: https://pinboard.in/u:nhaliday/b:c5c09f2687c1

Was Roman Science in Decline? (Excerpt from My New Book): https://www.richardcarrier.info/archives/13477

may 2017 by nhaliday

Futuristic Physicists? | Do the Math

march 2017 by nhaliday

interesting comment: https://westhunt.wordpress.com/2014/03/05/outliers/#comment-23087

referring to timelines? or maybe also the jetpack+flying car (doesn't seem physically impossible; at most impossible for useful trip lengths)?

Topic Mean % pessim. median disposition

1. Autopilot Cars 1.4 (125 yr) 4 likely within 50 years

15. Real Robots 2.2 (800 yr) 10 likely within 500 years

13. Fusion Power 2.4 (1300 yr) 8 likely within 500 years

10. Lunar Colony 3.2 18 likely within 5000 years

16. Cloaking Devices 3.5 32 likely within 5000 years

20. 200 Year Lifetime 3.3 16 maybe within 5000 years

11. Martian Colony 3.4 22 probably eventually (>5000 yr)

12. Terraforming 4.1 40 probably eventually (> 5000 yr)

18. Alien Dialog 4.2 42 probably eventually (> 5000 yr)

19. Alien Visit 4.3 50 on the fence

2. Jetpack 4.1 64 unlikely ever

14. Synthesized Food 4.2 52 unlikely ever

8. Roving Astrophysics 4.6 64 unlikely ever

3. Flying “Cars” 3.9 60 unlikely ever

7. Visit Black Hole 5.1 74 forget about it

9. Artificial Gravity 5.3 84 forget about it

4. Teleportation 5.3 85 forget about it

5. Warp Drive 5.5 92 forget about it

6. Wormhole Travel 5.5 96 forget about it

17. Time Travel 5.7 92 forget about it

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s:*
c:**
🔬
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referring to timelines? or maybe also the jetpack+flying car (doesn't seem physically impossible; at most impossible for useful trip lengths)?

Topic Mean % pessim. median disposition

1. Autopilot Cars 1.4 (125 yr) 4 likely within 50 years

15. Real Robots 2.2 (800 yr) 10 likely within 500 years

13. Fusion Power 2.4 (1300 yr) 8 likely within 500 years

10. Lunar Colony 3.2 18 likely within 5000 years

16. Cloaking Devices 3.5 32 likely within 5000 years

20. 200 Year Lifetime 3.3 16 maybe within 5000 years

11. Martian Colony 3.4 22 probably eventually (>5000 yr)

12. Terraforming 4.1 40 probably eventually (> 5000 yr)

18. Alien Dialog 4.2 42 probably eventually (> 5000 yr)

19. Alien Visit 4.3 50 on the fence

2. Jetpack 4.1 64 unlikely ever

14. Synthesized Food 4.2 52 unlikely ever

8. Roving Astrophysics 4.6 64 unlikely ever

3. Flying “Cars” 3.9 60 unlikely ever

7. Visit Black Hole 5.1 74 forget about it

9. Artificial Gravity 5.3 84 forget about it

4. Teleportation 5.3 85 forget about it

5. Warp Drive 5.5 92 forget about it

6. Wormhole Travel 5.5 96 forget about it

17. Time Travel 5.7 92 forget about it

march 2017 by nhaliday

Which one would be easier to terraform: Venus or Mars? - Quora

february 2017 by nhaliday

what Greg Cochran was suggesting:

First, alternatives to terraforming. It would be possible to live on Venus in the high atmosphere, in giant floating cities. Using a standard space-station atmospheric mix at about half an earth atmosphere, a pressurized geodesic sphere would float naturally somewhere above the bulk of the clouds of sulfuric acid. Atmospheric motions would likely lead to some rotation about the polar areas, where inhabitants would experience a near-perpetual sunset. Floating cities could be mechanically rotated to provide a day-night cycle for on-board agriculture. The Venusian atmosphere is rich in carbon, oxygen, sulfur, and has trace quantities of water. These could be mined for building materials, while rarer elements could be mined from the surface with long scoops or imported from other places with space-plane shuttles.

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First, alternatives to terraforming. It would be possible to live on Venus in the high atmosphere, in giant floating cities. Using a standard space-station atmospheric mix at about half an earth atmosphere, a pressurized geodesic sphere would float naturally somewhere above the bulk of the clouds of sulfuric acid. Atmospheric motions would likely lead to some rotation about the polar areas, where inhabitants would experience a near-perpetual sunset. Floating cities could be mechanically rotated to provide a day-night cycle for on-board agriculture. The Venusian atmosphere is rich in carbon, oxygen, sulfur, and has trace quantities of water. These could be mined for building materials, while rarer elements could be mined from the surface with long scoops or imported from other places with space-plane shuttles.

february 2017 by nhaliday

Mars is Hard - Casey Handmer

people speculation prediction engineering physics space papers analysis electromag gravity technology frontier links reading caltech spock nitty-gritty 2016 the-world-is-just-atoms new-religion fermi applications wild-ideas 🔬 definite-planning ideas article mechanics white-paper dirty-hands expansionism

february 2017 by nhaliday

people speculation prediction engineering physics space papers analysis electromag gravity technology frontier links reading caltech spock nitty-gritty 2016 the-world-is-just-atoms new-religion fermi applications wild-ideas 🔬 definite-planning ideas article mechanics white-paper dirty-hands expansionism

february 2017 by nhaliday

Orthogonal — Greg Egan

february 2017 by nhaliday

In Yalda’s universe, light has no universal speed and its creation generates energy.

On Yalda’s world, plants make food by emitting their own light into the dark night sky.

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On Yalda’s world, plants make food by emitting their own light into the dark night sky.

february 2017 by nhaliday

Richard Feynman: Physics is fun to imagine | TED Talk | TED.com

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january 2017 by nhaliday

feynman physics curiosity :) video interview classic insight org:edge lens giants nibble virtu communication cartoons exposition metameta thinking hi-order-bits science meta:science synthesis visual-understanding worrydream vitality dynamic org:anglo thermo mechanics electromag phys-energy better-explained teaching the-world-is-just-atoms presentation wisdom waves space gravity wordlessness oscillation quantum concrete minimum-viable s:*** new-religion energy-resources big-picture 🔬 info-dynamics

january 2017 by nhaliday

The Secret Histories | West Hunter

january 2017 by nhaliday

WW2 and the Civil War: https://westhunt.wordpress.com/2016/12/30/the-secret-histories/#comment-86474

the great divergence:

https://westhunt.wordpress.com/2016/12/30/the-secret-histories/#comment-86588

Untrue. Drastically wrong. Who has made a greater contribution to human knowledge – James Clerk Maxwell [ one guy !] , or East Asia over the past five hundred years?

https://westhunt.wordpress.com/2016/12/30/the-secret-histories/#comment-86527

When people talk about the “Great Divergence”, they don’t seem to place much emphasis on the fact that at the very top, Western Europe was enormously more intellectually sophisticated than China. Europeans were using Jupiter’s moons as a clock in 1800 and directly measuring the gravitational force of a 12-inch lead ball. European physics & mathematics were far advanced over China’s at that point. Indeed, you could argue that Hellenistic science and mathematics were far advanced over those of China in 1800.

Cavendish experiment: https://en.wikipedia.org/wiki/Cavendish_experiment

Torsion balance: https://en.wikipedia.org/wiki/Torsion_spring#Torsion_balance

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the great divergence:

https://westhunt.wordpress.com/2016/12/30/the-secret-histories/#comment-86588

Untrue. Drastically wrong. Who has made a greater contribution to human knowledge – James Clerk Maxwell [ one guy !] , or East Asia over the past five hundred years?

https://westhunt.wordpress.com/2016/12/30/the-secret-histories/#comment-86527

When people talk about the “Great Divergence”, they don’t seem to place much emphasis on the fact that at the very top, Western Europe was enormously more intellectually sophisticated than China. Europeans were using Jupiter’s moons as a clock in 1800 and directly measuring the gravitational force of a 12-inch lead ball. European physics & mathematics were far advanced over China’s at that point. Indeed, you could argue that Hellenistic science and mathematics were far advanced over those of China in 1800.

Cavendish experiment: https://en.wikipedia.org/wiki/Cavendish_experiment

Torsion balance: https://en.wikipedia.org/wiki/Torsion_spring#Torsion_balance

january 2017 by nhaliday

Fiction: Missile Gap by Charles Stross — Subterranean Press

october 2016 by nhaliday

- flat-earth scifi

- little tidbit from fictional Carl Sagan: behavior of gravity on very large (near-infinite) disk

in limit, no inverse square law, constant downward force: ∫ G/(a^2+r^2) a/sqrt(a^2+r^2) σ rdr dθ = 2πGσ independent of a

for large but finite radius R, asymptotically inverse square but near-constant for a << R (check via Maclaurin expansion around a and x=1/a)

- interesting depiction of war between eusocial species and humans (humans lose)

fiction
space
len:long
physics
mechanics
magnitude
limits
gravity
🔬
individualism-collectivism
xenobio
scifi-fantasy
- little tidbit from fictional Carl Sagan: behavior of gravity on very large (near-infinite) disk

in limit, no inverse square law, constant downward force: ∫ G/(a^2+r^2) a/sqrt(a^2+r^2) σ rdr dθ = 2πGσ independent of a

for large but finite radius R, asymptotically inverse square but near-constant for a << R (check via Maclaurin expansion around a and x=1/a)

- interesting depiction of war between eusocial species and humans (humans lose)

october 2016 by nhaliday

bundles : physics

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