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Feature Detection with Automatic Scale Selection
The (lengthy) article on scale invariance that leads to SIFT and SURF amongst others
coink  computer  vision  math  scale  invariance 
june 2018 by paunit
Uniformitarianism - Wikipedia
Uniformitarianism, also known as the Doctrine of Uniformity,[1] is the assumption that the same natural laws and processes that operate in the universe now have always operated in the universe in the past and apply everywhere.[2][3] It refers to invariance in the principles underpinning science, such as the constancy of causality, or causation, throughout time,[4] but it has also been used to describe invariance of physical laws through time and space.[5] Though an unprovable postulate that cannot be verified using the scientific method, uniformitarianism has been a key first principle of virtually all fields of science.[6]

In geology, uniformitarianism has included the gradualistic concept that "the present is the key to the past" (that events occur at the same rate now as they have always done); many geologists now, however, no longer hold to a strict theory of gradualism.[7] Coined by William Whewell, the word was proposed in contrast to catastrophism[8] by British naturalists in the late 18th century, starting with the work of the geologist James Hutton. Hutton's work was later refined by scientist John Playfair and popularised by geologist Charles Lyell's Principles of Geology in 1830.[9] Today, Earth's history is considered to have been a slow, gradual process, punctuated by occasional natural catastrophic events.
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january 2018 by nhaliday
Is the speed of light really constant?
So what if the speed of light isn’t the same when moving toward or away from us? Are there any observable consequences? Not to the limits of observation so far. We know, for example, that any one-way speed of light is independent of the motion of the light source to 2 parts in a billion. We know it has no effect on the color of the light emitted to a few parts in 1020. Aspects such as polarization and interference are also indistinguishable from standard relativity. But that’s not surprising, because you don’t need to assume isotropy for relativity to work. In the 1970s, John Winnie and others showed that all the results of relativity could be modeled with anisotropic light so long as the two-way speed was a constant. The “extra” assumption that the speed of light is a uniform constant doesn’t change the physics, but it does make the mathematics much simpler. Since Einstein’s relativity is the simpler of two equivalent models, it’s the model we use. You could argue that it’s the right one citing Occam’s razor, or you could take Newton’s position that anything untestable isn’t worth arguing over.

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november 2017 by nhaliday
Power of a point - Wikipedia
The power of point P (see in Figure 1) can be defined equivalently as the product of distances from the point P to the two intersection points of any ray emanating from P.
nibble  math  geometry  spatial  ground-up  concept  metrics  invariance  identity  atoms  wiki  reference  measure  yoga  calculation 
september 2017 by nhaliday Friday Q&A 2015-11-20: Covariance and Contravariance
The astute reader may notice that the title of the article contains these two terms which I have carefully avoided using this whole time. Now that we're firm on the concepts, let's talk about the terminology. Covariance is when subtypes are accepted.
contravariance  covariance  invariance  programming  type  variance 
september 2017 by pitiphong_p
rotational dynamics - Why do non-rigid bodies try to increase their moment of inertia? - Physics Stack Exchange
This happens to isolated rotating system that is not a rigid body.

Inside such a body (for example, steel chain in free fall) the parts move relatively to each other and there is internal friction that dissipates kinetic energy of the system, while angular momentum is conserved. The dissipation goes on until the parts stop moving with respect to each other, so body rotates as a rigid body, even if it is not rigid by constitution.

The rotating state of the body that has the lowest kinetic energy for given angular momentum is that in which the body has the greatest moment of inertia (with respect to center of mass). For example, a long chain thrown into free fall will twist and turn until it is all straight and rotating as rigid body.


If LL is constant (net torque of external forces acting on the system is zero) and the constitution and initial conditions allow it, the system's dissipation will work to diminish energy until it has the minimum value, which happens for maximum IaIa possible.
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august 2017 by nhaliday

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