THE RELATIONSHIP BETWEEN THE NUMBERS 1.19, 1.23, AND 0.724

AND WHAT THIS SUGGESTS FOR THE ORIGIN OF THE UNIVERSE.

By T. Frank Lee, geologist. 2008.

(This short paper was printed in my small book “Further Studies of the Solar System – studies from 1994 to early 1997”, ISBN 0 646 31840 3, and is being placed in this web page in the belief that it may interest those with a mathematical and astronomical bent.)

At the end of the previous paper it was shown that 1.19^1.19 = 1.23 -------------------A

A few days after making this discovery in February, 1997 it was realised that if instead of using 0.724 one used its reciprocal - 1.38121547 – then:

1.19 x 1.23 x 1.38 = 2.019906, within 0.995% of 2 and 0.726% of 1.19⁴ ---------B

The previous studies have shown fairly emphatically that 0.724 is correct for the Solar System; but should the product be equal to 2 or 1.194 for Universe calculations? I suggested to Dr. P. Pesteil of Nice, France the day before discovering this simple equation that 0.98 (= 0.724^1/16) outside the Solar System should be 0.981. This leads to testing the product equal first to 2, then to 1.19⁴, ie.,

1.19 x 1.23 x y = 2 gives y = 1.3664002 = 0.73185^-1 = 0.9806779 ^-16 ------------C

1.19 x 1.23 x y = 1.19⁴ gives y = 1.3700480 = 0.72990^-1 = 0.9805145^–16 -------D

The number should have some simple relationship to the other numbers because of the geometrical relationships revealed in the paper “Ratios”. Trial and error showed that:

1.23^1.232 = 1.3677838 = 0.7311097 ^–1 = 0.9806159 ^–16 ---------------------------------E

and this lies between those of C and D. It also compares with 0.9809223, the fifth power of the ratio of the masses of Jupiter (1999x10²⁴ kg) and protoJupiter immediately after the hypothesised separation of Saturn (2201.1x10²⁴ kg). [These two values are in error. They should read 1899 and 2101.1, respectively. Their ratio equals 0.9038123 and this is 0.0127% from 0.98⁵. F.L., 2008.]

The formula a x b x c = 2 very closely, where a = 1.19, b = 1.23, and c = 1.36778 can therefore be written as: a x a^a x (a^a)(aa)2 = 2 very closely.

It seems to me most unlikely that the equation is accidental but is one of significance and suggests support for the geometrical relationship argued previously for the three numbers 1.19, 1.23, and 0.724.

Is the number at E significant? First, substituting it in the formula 1.19 x 1.23 x y gives the product 2.0020251, suggesting that the product should equate to 2, not to 1.19⁴. (But see below, which suggests the number should be close to, but a little larger than 2.)

Note that if 1.23^1.5 is used, because 1.23 may only be an approximation for 1.5^½, then the product is 1.99669; and if (1.5^½)) to the power (1.5^½)² is used the product is 0.98390. The number to obtain 2 or 1.19⁴ must therefore be 1.23 to the power 1.23² and not these alternatives; in turn suggesting 1.23 is correct, 1.5^½ is not.

A test is required for the significance of the number 1.23^1.232.

First note that in Table 3, “Fundamental Dimensionless Numbers”, in Kokus (Apeiron No. 20, 1994, p.3) the Fine Structure constant is given as 137, which is 1/(1.37 x 100). This is very suggestive of 1.23 to the power 1.23² times 1/100. There just may be a relationship.

Pesteil (Apeiron, Autumn 1991, p.13) states that the m_neutron/m_electron ratio is 1838.684,

and m_proton/m_electron ratio is 1836.1527;

and gives as an approximation for these numbers 150^3/2= 1837.117

The number 150^3/2 suggests (1.23²)^1.232 x 100^1.232 or more simply (y x 10^1.232)², where y is the number at E above.

The product comes to 1985.339971. Does this have a rlationship to one of the electron ratios? It would seem so, for using the proton/electron ratio (surely the most proper?);

1836.1527/1985.339971 = 0.92485554 = 0.98066⁴.

The number 0.98066 is virtually identical to the number at E and even closer to the number at C and suggests writing the formula (0.9806² x y x 10^1.232)², where y = 1.23 to the power 1.23². The product is within 0.024% of the proton/electron ratio.

Accidental? I doubt it, as it mirrors similar differences in some Solar System ratios as briefly noted later in this paper. It would then suggest that the figure 1.36778 (or 0.73111) is a figure of importance for Universe calculations.

Of course, because of the above (0.724/0.73111)² = 0.9806447

and this is equivalent to 0.98³² /0.980600³³ = 1.

I have done sufficient work to be certain that the number 0.724 is closely correct for the Solar System and therefore suggest that in the case of Universe relationships, where the ratio appears it should be 0.73111. Why? In my opinion bodies big and small rarely divide exactly as mathematical theory requires. A slight variation in composition or conditions normally occur, leading to a slight variation in the ratios. I suggest this is what occurred for the Universe and the Solar System.

Pesteil (In brief: Apeiron Vol. 3 No.2, 1996) quotes four dimensionless ratios obtained in his extensive studies of the origin of the Universe, which ratios relate items within various physical phenomena. The numbers 1.192, 1.2283, 137.036, and 210. It is immediately obvious that the numbers bear a striking resemblance to the ratios determined for the Solar System, leading to the suggestion that:

1.192 x 1.2283 x 137.036 = 210? (equivalent to 1.192 x 1.2283 x 1.37036 = 2.10?

No, the right hand side does not equate to the left hand side, but it nearly does if 210 is multiplied by 0.9806² (= 201.931). The difference is +0.64% different (LHS = 200.639). However, I am not aware at present of how accurate the number 210 is and so cannot comment further. The figures are suggestive.

(The discussion cannot be ended without commenting that

1.19 x 1.23 x 1.38 = 2.10 x 0.98² = 2.10/1.38^1/8, within 0.14%.)

Why the number 0.9806²? It has been my observation during study of the Solar System that a change from one configuration to the next, from one stage to the next, is often (usually?) accompanied by a decrease in the property studied and the decease is usually 0.98 or an even power of 0.98. For example, in the very early pages of my 1994 book it was shown that there was a loss of (1 – 0.98) of force on Mars stripping from the silicate core, (1 – 0.98⁶⁴) for Earth, and (1 – 0.98¹⁶) for Venus. Also, in the paper “Suggestive Supporting Evidence from the Satellites” given in this book the radii of succeeding stages of the silicate core after stripping of the “medium icy” and “silicate” satellites showed a 0.98² relationship. Therefore, if the measure 210 is of a property post-breakup, and the other three numbers are of properties in the next stage of development then one would expect a 0.98 relationship. But note: I am not aware that this condition is so; the relationship suggests this to be the case.

Fortunately, the accuracy does not affect a conclusion which can be made for the two groups of numbers 1.19, 1.23, 1.37 and 1.192, 1.2283, 137.036, 210. My studies of the Solar System have shown that the first group of numbers, which appear so frequently in Solar System body relationships, appeared at the beginning of the break-up of the body. They relate to and are a reflection of the geometrical relationships of and within the partly differentiated, prolate ellipsoidal body when the body reached the first Jacobi bifurcation point. That is, the group of numbers and the relationships of the numbers one to another came into being due to the body’s break-up and reflect the mechanism which caused the break-up. Even if the “cold body break-up” [in 2008 read Single Body Breakup] hypothesis is incorrect it is still a valid supposition that the four numbers are a reflection of the mechanism which caused the Solar System to develop.

Now to turn to the Universe group of numbers. Two of these – 1.192 and 1.2283 – may be considered to be identical to 1.19 and 1.23, and the remaining two are closely 100x greater than 1.38 and 2. So that when put in the form:

1.192 x 1.2283 x 137.036 = 210k, the equation can be validly written as:

1.192 x 1.2283 x 1.37036 = 2.10k, where k very nearly equals 1.37036^–1/8.

The closeness of the four numbers thus obtained to those of the four numbers for the Solar System, together with them producing a like equation, strongly suggests that a similar mechanism of break-up occurred at the instant the Universe came into being as that which formed the Solar System. This is not to say their subsequent histories would be the same; that would depend on other factors such as their composition. The equality of the groups of numbers merely suggests a like instantaneous beginning.

There is a rule of thumb in Archaean structural geology to the effect that the macro-structure of a formation is reflected by the micro-structure of that formation. In this case the Solar System is the micro-structure and shows the same general characteristics – its four numbers and their relationships – that can be related to origin as does the Universe, which is the macro-structure. This leads to the conclusion that the Universe and Solar Systems both came into being in the same way. However, the Universe is currently argued as having come into being by a “Big Bang”, and the Solar System is currently argued as having come into being by the differentiation of a nebula disc about a protostar. If the two systems began in a similar manner as argued above then three conclusions must follow. They are:

Either (1) the Universe did not form by a “Big Bang”;

(2) the Solar System did not form from a nebula disc;

(3) neither formed as the present popular postulates argue.

There is ample evidence to show that the Universe did not develop from a nebula, and the stability of the Solar System (even ignoring my development of cold-body break-up) strongly suggests it did not develop as an explosion. Therefore it must be concluded, on the basis of the similarity of numbers and formulae reflecting a like beginning, that neither Universe nor Solar System formed as the presently popular postulates state.

How, then, could have the Universe formed? The following is only a suggestion relating to the “Big Bang”. [I prefer a simpler development. 2008] Other suggestions will probably present themselves.

Assume the whole of the Universe matter – mass, light, etc. – concentrated to form a steadily developing prolate ellipsoidal body, increasing in rotation as the body built up. On the body attaining that of the first Jacobi bifurcation point, the body began to disintegrate in “catherine wheel” fashion. In giving this suggestion I should point out that I am aware of the current ideas of the effects of hyper-pressure on mass. Fortunately, the origin of the Universe is not a part of this paper. What is a part is the conclusion that the Universe cannot have formed from a “Big Bang” nor the Solar System from a nebula ring.

To end this informal paper I make what will probably be dismissed as a fatuous suggestion but the idea interests me.

ln X/log X = 2.302585093 = 1.2318389224, within +0.64% of 1.23⁴;

and e¹ = 2.718281828, so that:

e¹/(lnX/logX) = 1.180534798, within –0.08% of 1.19 --------------F

If lnX/logX should be 1.234 and 1.19 the right hand side of equation F, then for the Universe calculations would a base E = 2.723751028 be better than e = 2.718281828 where e occurs in calculations? (a difference of 0.20%)

Just a thought which will probably lead nowhere.