Proportional Quotes - page 3
It was one lesson he never forgot.You don't sit back when you or a loved one is being assaulted.And you don't act like the goverment with their "proportional responses" and all that nonsense.If someone hurts you,mercy and pity must be put aside,You eliminate the enemy.You scorch the earth.
Harlan Coben
Few Christians understand the concept of eternal rewards, even thought the Lord dedicated a great deal of His precious time on earth to teaching about them. The one certainty is that our position in the Lord's kingdom will be inversely proportional to how we indulge ourselves in this lifetime.
Larry Burkett
It was early 1932, when Einstein and I both were at the California Institute of Technology in Pasedena, and we just decided to look for a simple relativistic model that agreed reasonably well with the known observational data, namely, the Hubble recession rate and the mean density of matter in the universe. So we took the space curvature to be zero and also the cosmological constant and the pressure term to be zero, and then it follows straightforwardly that the density is proportional to the square of the Hubble constant. It gives a value for the density that is high, but not impossibly high. That's about all there was to it. It was not an important paper, although Einstein apparently thought that it was. He was pleased to have a simple model with no cosmological constant. That's it.
Willem de Sitter
In both the solutions A and B the curvature is positive, in both three-dimensional space is finite: the universe has a definite size, we can speak of its radius, and, in the case A, of its total mass. In the case A... the density is proportional to the curvature... Thus, if we wish to have a finite density in a static universe, we must have a finite positive curvature.
Willem de Sitter
In February 1917, it was found that a static solution with a positive curvature-the solution A-was not possible without the λ. In fact the curvature is proportional to λ (in solution A, λ is equal to the curvature; in B... it is three times the curvature). Thus, at the time when we had only the two static solutions A and B, and thought that these were the only possible ones, here was a plausible physical interpretation of the meaning of λ: it was the curvature of the world, and the square root of its reciprocal, the radius of curvature, could be conceived as providing a natural unit of length.
Willem de Sitter
The careful experiments of Joule, who developed heat in various ways by the application of mechanical force, establish almost to a certainty, not only the possibility of increasing the quantity of heat, but also the fact that the newly-produced heat is proportional to the work expended in its production.
Rudolf Clausius
... If a distant galaxy is moving relative to us, its entire spectrum is Doppler-shifted in frequency. Its spectral lines are displaced relative to those of stationary light sources. Thanks to this effect, we know that distant galaxies recede from the solar system at speeds proportional to their distances from us. That's the effect that told us of the expanding universe, and of its birth, long ago, in the Big Bang.
Sheldon L. Glashow
![The Rule of Three, or Golden Rule of Arithmeticall whole Numbers. Be the three termes given 2 3 4. ...To finde their fourth proporcionall Terme: that is to say, in such Reason to the third terme 4, as the second terme 3, is to the first terme 2 [Modern notation: \frac{x}{4} = \frac{3}{2}]. ...Multiply the second terme 3, by the third terme 4, & giveth the product 12: which dividing by the first terme 2, giveth the Quotient 6: I say that 6 is the fourth proportional terme required. (Simon Stevin)](https://cdn.quotesdtb.com/img/quotes_images_webp/70/simon-stevin-dividing-fourth-961470.webp)
Jacob Bekenstein found... in 1971 that every black hole must have an entropy proportional to the area of its horizon... Stephen Hawking then refined this by showing that the constant of proportionality must be... exactly one quarter. ...entropy is supposed to correspond to a measure of information ...Loop quantum gravity... [gives] a detailed description of the microscopic structure of a black hole. ...a horizon can have, for each quantized unit of area, a finite number of states. Counting them, we get exactly Bekenstein's result...
Lee Smolin
Many facts have lately transpired which tend to overthrow the hypothesis that heat is itself a body, and to prove that it consists in a motion of the ultimate particles of bodies. If this be so, the general principles of mechanics may be applied to heat; this motion may be converted into work, the loss of vis viva in each particular case being proportional to the quantity of work produced.
These circumstances, of which Carnot was also well aware, and the importance of which he expressly admitted, pressingly demand a comparison between heat and work, to be undertaken with reference to the divergent assumption that the production of work is not only due to an alteration in the distribution of heat, but to an actual consumption thereof; and inversely, that by the expenditure of work, heat may be produced.
Rudolf Clausius
E = mc2 really applies only to isolated bodies at rest. In general, when you have moving bodies, or interacting bodies, energy and mass aren't proportional. E = mc2 simply doesn't apply. ...For moving bodies, the correct mass-energy equation is
E=\frac {mc^2} {\sqrt{1-\frac{v^2} {c^2}}}
where v is the velocity. For a body at rest (v=0), this becomes E = mc2. ...we must consider the special case of particles with zero mass... examples include photons, color gluons, and gravitons. If we attempt to put m = 0 and v = c in our general mass-energy equation, both the numerator and denominator on the right-hand-side vanish, and we get the nonsensical relation E = 0/0. The correct result is that the energy of a photon can take any value. ...The energy E of a photon is proportional to the frequency f of the light it represents. ...they are related by the Planck-Einstein-Schrödinger equation E = hf, where h is Plank's constant.
Frank Wilczek
