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The Scot Science Journal

Contents

1. News In Science

2. Impact Series

3. Puzzle

4. Chess Problem

Dr. J . c.· Keister

Associate Editors

Dr. J.C. Keister Mr. Ray Dameron Dan 1\rown

Physics and Mathematics Artwork and Layout Psychology

Vol. VI, #5, March 1977 Covenant College, Lookout Mountain, Tennessee 37350

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1. NEWS IN SCIENCE

Talk About Long Proofs, ..

Godel has shown that in any mathematical system (for example, as complicated as the number system) there is a need for an infinite number of ax:i.oms to supply all the "tr"+:hs " contained in the system. Many times when a conjecture is made, it is not known whether or not the conjecture is provable, or whether one must accept either the conjecture, (or its contradiction) as an axiom.

In the February issue of Science, pg. 767, is an account of two proofs of a conjecture that a finite number of subsets of the count­ing numbers will contain at least one subset which has arithmetic progressions of all lengths. One proof (in number theory) took 100 pages while a somewhat shorter proof from ana l ys is in probability theory t ook 82 pa ges to establish. Besides showing the interdis ci­plinary connection between probability theory

and number theOt:'y, these two· the-Ot'ies· ·shOW - ­that persistence pays off. The existence of the two theorems has led to speculation that the fields of probability theory and number theory may be more closely related than pre­viously supposed.

Another conjecture has be_en made - namely, that if the sums of the reciprocals of t he integers in a subset d_everge, the subset will contain _arithmetic progressions of arbitrary length. The author of the conjecture (Erdos) is offering a $3000.00 reward to any­one who can piove or disprove the conje c ture. Since it was Erdos who offered a $1000.00 reward for the previous conjec t ure , it l ooks as though we may be in for a 300 page proof. ~ ne author of the article sugges ted a Revela ­tion as a possible necessity f or the so l u tion of this problem. No doubt it would help.

The Evolutionists Strike Back

In the J an-Feb 1977 issue of the Humanist, a gr oup of 180 scientists (including author Isaac Asimov, Carl Rogers, B.F. Skinner and Linus Pauling) signed a statement affirming that evolution is the only scientific explana­tion for the diversity of life as seen today. In particular , they make such statements as this, "There are no alternative theories to the principle of evolution, with its tree of life pattern, tha t any competent biologist of today takes seriously." Also, they make such statements as this:"(The Biblical view of creation) is a purely religious view held by some religious sects and persons .. . Evolution is the only presently known scientific and not religious explanation for the existence of liv-

ing organisms. It is therefore the only view wluch should be expounded in public school courses on science."

As indicated in the Chattanooga Times of Feb. 10, 1977, Prof. Kurtz of Buffalo State said that he didn't expect to convert any creationists, but that he hoped to in­fluence school board members to oppose the creationists. The Times article goes on to say that Kurtz et al used the same strategy against astrology in 1975, but had to admit

that astrology was growing in spite of such efforts. Perhaps we should pray that he incr~<!_~ his efforts against c·reationism? !

On a more serious note: One of t he funda­mental pillars of science is this: a theory must in principle be falsifiable by obse rva­tional experiment in order to qualify as being sc ientific. Since no experiment can be run (or has ever been run) at any time of the order of millions of years ago, it is i mpos­sible to experimentally verify (or falsify) any statement about evolution, or non-evolu­tion of life on earth, for times of the order of millions of .years ago. There fore, evolu­tionary theories about events on the earth which supposedly happened befo re scientific investigations were made are by their very nature non-scientific . Since no observation can be made (or were made), we must rely on other sources to verify (for example) whethe r or not all processes going on today have always been going on. (Note that this is one of the fundamental tenets of evolutionary theory.) Relying on any such source must involve faith - or, simply rely ing on the assumption that proc.esses have never changed is also an article of faith. Thus it is tha t creationists and evolutionists alike rely on non-scientific presuppositions of faith for their stand.

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Why Is the Night Sky Dark?

In a previous issue of the SSJ , we pre­sented an article by E. F. Harrison on why the sky was dark - t~e article was based on a published paper in Physics Today, Vol. 28 U2, 1975, p. 69. The explanation presented at that time was that the lifetime of the stars (estimated at 1010 years, based on the so-called evolutionary track of the Hertz­sprung-Russel diagram for stars) was too short to allow the stars to light up the uni­verse.

The explanation of the Physics Today article was not all that clear . Harrison has written a second article in the American Journa l of Physics, Vol 45, Feb. 1977, which appears to clarify his ideas considerabl , . To understand his explanation and its ramifi­cations, we need to examine the so-called black night paradox, as follows:

In a uniform universe, (where.in a large enough volume,the star distribution is more or l ess identical everywhere), the star light from each spherica l. shell surrounding any one point in the universe contributes the s,am~ light and heat as every other spherical shell sui'rounding that point. With an infinite uni­verse, and an infinite number of these shells, the al!lvunt of energy contributing to that po int (assuming the stars to be point sources) would be infinite. The effect of having finite size stars reduces the total energy i mput t o a finite amount, because each star absorbs some of thi! energy, and in effect shows to any observer a h~t "wal~" 0£

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number of stars. But, this hot wall , once equilibrium has been reached, will raise the temperature of every point within the "wall" to the surface temperature of the stars •he~­sel,·es, which is very hot indeed! This is the paradox, because we know that the temperature is !}Q!. as this analysis says; the question is: What is wrong with the analysis?

Note the several presuppositions to this parade·:: a uniform universe, at steady state, hav ing existed for all time. Suppose some of these conditions are relaxed; for example, the red shift of distant gallaxies suggest that the universe is expanding and is not static. Harrison states that calculations show this expansion factor will reduce the energy input at a point by at most a factor of 2. Tlds would still be pl , 1ty enough to fry everything in sight. Therefore , one

(or both) of the other two assumptions mus t be relaxed. For example, suppose th e uni­verse was composed of nested gallaxies, and never is uniform, no matter how large a scale is taken. In such a case, there could be considerable empty space, and th e enc l of ing 11wall" of stars would have numerous gaps and holes. If the gaps and ho les were many factors of 10 larger in observed area than the star area, the energy received at any one point would be cor r espondingly reduced. The author takes the o ther possibility; namely, that the stars either have not exist­ed for all time, or have a finite lifetime, or both. In such a situation, we would not see the stars fur ther away than light would have time to travel to get here. Then, as the stars "burnL.J out", they would no longer provide energy or light. Thus, a thin shell of stars (of thickness in light yea r s co rres­ponding to the lifetime of the stars) would provide all the starlight and star ene rgy we experience. As time progressed, this shell would recede, since the light would start coming from more distant stars, while local stars progressively burned out. With typical calculated star life times of 1ol0 years, the shell thickness would be 1ol0 light years. The author has calculated a distance of 1023 light years which corres­ponds to the distance where an observer 1 s line of sight would be completely blccked by stars. But, since a shell of only 1olO light years of stars are visible, the ratio of energy from the entire :phere o10stars 23 must be reduced by the rat1~ of 10 to 10 or by a factor of 1013. Such a reduction of energy would indeed explain why the sky is dark, within the framework of evolutionary presuppositions.

To sum up: In order to explain why the sky is black at night, one or more of the fol1-owing conditions must be met, within the framework of consistent - cause and effect relationship, and where God is as­sumed to have no role:

A. The universe is not uniform, but consists of gallaxies of stars, so clustered that no matter how large a volume is selected, the distribution of stars is non-uniform. This raises the natural question: If condi­tions are not uniform in space, why should we necessarily expect conditions to remain uniform in time?

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Why Is the Night Sky Dark?

B. The lifetime of stars is too short to permit the entire visible space from being blocked off by luminous stars. In such .a sit uation, there will be a thin shell of luminous stars, which r ecedes away from an observer with time. Thus, conditions are not uniform in time. Should conditions neces­sarily be uniform in space?

C. The universe is expanding in time, and the corresponding volume is so large that equilibrium conditions have not been me t for stars to heat up the interstellar space. Thus conditions are not uniform in time - and, (once again), can we necessarily assume they would be uniform in space?

In any event, we must have non-uniform conditions existing either in time, or space, or both. While such conditions fit in very well with the concept of creation, they do not fit .in well at ' all with the ultimate

presuppositions of cosmological evolution . In fact, the only viable "evolutionary" theory of the, universe is the so- called "Big Bang" Theory, which in itself does not explain how the "Big Bang" started in the first place. One is reminded of a passage from Romans Chapter 1, verse 20 and 21:

For the invisible things of him from the creation of the world are clearly seen, being understood by the things t hat are made, even his. eternal power and Godhead; so that they are without excuse:

Because that, when they knew God, they glorified him not as God, neither were thankful ; but became vain in their imagina­tions, and their foo lish heart was darkened.

3. PUZZLE

ADAM Ai'lD EVE

ON A

RAFT

Answer to Last Month's Problem

6068 6068 1015 1015 620 620 130 130 919 939 949 979

32 12 73 43 6 6 1 1

7645 7645 2168 2168

This Mo nth's Problem

X = l+ =l'-~-'----- ----2 + 1 ---------1 +=1 _____ _

2 + 1 _l_+_l __ _

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Determine the value of x (in closed form)

1017 1017 160 160 949 959

56 46 1 1

2183 2186

----.

:- .

1. n-k2!

4. CHESS PROBLEM

Solution to Last Month's Problem

1. Qxkr (if ... 1. Qxqr, 2. rxP, mate. If ... 1. Kxkr, q-b3 mate. If . .. l. Kxqr, q-r3 mate. If •.. 1. - P-B-2 or B-3, 2. rxQ_mate. If .. . l. P-R-2 or R-3, 2. rxQ, mate.)

2. rxP, mate.

This Month's Problem

(Taken from the Manchester Guardian) White to mo ve and mate in three

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