“These… are the two observational facts about our neighbourhood, which have to be accounted for by the theory: there is a finite density of matter, and there is expansion, i. e. the mutual distances are increasing, and therefore the density is decreasing.”

Kosmos (1932), Above is Beginning Quote of the Last Chapter: Relativity and Modern Theories of the Universe -->

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Willem de Sitter44

Dutch cosmologist 1872–1934

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“The "universe" is an hypothesis, like the atom, and must be allowed the freedom to have properties and to do things which would be contradictory and impossible for a finite material structure. What we observe are the stars and nebulae constituting "our neighbourhood." All that goes beyond that, in time or in space, or both, is pure extrapolation. The conclusions derived about the expanding universe depend on the assumed homogeneity and isotropy, i. e. on the hypothesis that the observed finite material density and expansion of our neighbourhood are not local phenomena, but properties of the "universe." It is not inconceivable that this hypothesis may at some future stage of the development of science have to be given up, or modified, or at least differently interpreted.”

Willem de Sitter (1872–1934) Dutch cosmologist

Kosmos (1932), Above is Beginning Quote of the Last Chapter: Relativity and Modern Theories of the Universe -->

“In the beginning of 1917, two solutions of the field equations for a homogeneous isotropic universe had been found, which I… call the solutions "A" and "B."… at that time only static solutions were looked for. It was thought that the universe must be a stable structure… In one of these solutions (B) the average density was zero, it was empty; the other one (A) had a finite density…. In B, to get the real universe, we should have to put in a few galactic systems, in A we should have to condense the evenly distributed matter into galactic systems. The universe A… has an average density, but no expansion. It is therefore called the static universe. B, on the other hand… expands, and it could only parade in the garb of a static universe because there is nothing in it to show the expansion. B is therefore called the empty universe. Thus we had two approximations : the static universe with matter and without expansion, and the empty one without matter and with expansion. The actual universe… has both matter and expansion… In 1917… the actual value of the density was still entirely unknown, and the expansion had not yet been discovered.”

Willem de Sitter (1872–1934) Dutch cosmologist

Kosmos (1932), Above is Beginning Quote of the Last Chapter: Relativity and Modern Theories of the Universe -->

“Observations give us two data, viz. the rate of expansion and the average density, and there are three unknowns: the value of λ, the sign of the curvature, and the scale of the figure, i. e. the units of R and of the time. The problem is indeterminate.”

Willem de Sitter (1872–1934) Dutch cosmologist

Kosmos (1932), Above is Beginning Quote of the Last Chapter: Relativity and Modern Theories of the Universe -->

“We… come to the conclusion… that the actual universe is neither the static nor the empty one. It differs so much from both of these that neither can be used as an appropriate grand scale model. We must thus look for other solutions of the general field-equations. On account of the expansion our solution must necessarily be a non-static one, and it must have a finite density. There is only one possible static solution possessing a finite density, viz. our old friend A, but of non-static solutions with finite density there exists a great variety.”

Willem de Sitter (1872–1934) Dutch cosmologist

Kosmos (1932), Above is Beginning Quote of the Last Chapter: Relativity and Modern Theories of the Universe -->

“There is no direct observational evidence for the curvature [of space], the only directly observed data being the mean density and the expansion, which latter proves that the actual universe corresponds to the non-statical case. It is therefore clear that from the direct data of observation we can derive neither the sign nor that value of the curvature, and the question arises whether it is possible to represent the observed facts without introducing the curvature at all. Historically the term containing the 'cosmological constant λ' was introduced into the field equations in order to enable us to account theoretically for the existence of a finite mean density in a static universe. It now appears that in the dynamical case this end can be reached without the introduction of λ.”

Willem de Sitter (1872–1934) Dutch cosmologist

Joint memoir with Einstein (1932) as quoted by Gerald James Whitrow, The Structure of the Universe: An Introduction to Cosmology (1949)

“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 (1872–1934) Dutch cosmologist

Kosmos (1932), Above is Beginning Quote of the Last Chapter: Relativity and Modern Theories of the Universe -->

“It is easy to compute the density of a static universe of a radius of two thousand million lightyears, and it comes out only very little larger than the observed density. The actual universe is thus very far from empty, it is, on the contrary, nearly full.”

Willem de Sitter (1872–1934) Dutch cosmologist

Kosmos (1932), Above is Beginning Quote of the Last Chapter: Relativity and Modern Theories of the Universe -->

“That part of the air which is nearest to the wing which presses on it, will have the greatest density.”

Leonardo Da Vinci (1452–1519) Italian Renaissance polymath

The Notebooks of Leonardo Da Vinci (1938), XVII Flight

“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 (1872–1934) Dutch cosmologist

As quoted by Helge Kragh, Masters of the Universe: Conversations with Cosmologists of the Past (2014)

“This is Phobos… Its mean density is known, and it is consistent with organic matter. Deimos… same story.”

Carl Sagan (1934–1996) American astrophysicist, cosmologist, author and science educator

The Varieties of Scientific Experience: A Personal View of the Search for God (2006)

“These… are the two observational facts about our neighbourhood, which have to be accounted for by the theory: there is a finite density of matter, and there is expansion, i. e. the mutual distances are increasing, and therefore the density is decreasing.”

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