TestingWorldviews.com
"The unexamined life is not worth living." - Socrates |

(A Mathematical Proof)

- by R. Totten (c)2000

Gazing up at the immense night sky has left most people wondering how the cosmos ---including the sun, moon and earth--- came to be. This article will set out to show that discoveries of modern astronomers and astrophysicists are now increasingly demonstrating that the universe is, in highest probability, the product of intelligent design. Although some people have speculated that there may be life on other planets throughout the universe, what are the chances that the universe ---with all bodies and forces it contains--- could be randomly suited to be hospitable to life? This article purposes to outline a statistical mathematical proof, which demonstrates that the cosmos is indeed intelligently designed to be compatible for life ---as opposed to coming about by random chance processes.

**The Method of "Proof"**

Technically, a formal "proof" is absolutely air-tight, and with no possible exceptions, such as one would find in geometry. However, such a proof cannot exist in actual history involving real physical objects. -- Since this article considers physical occurrences in nature, I'll be using probabilities, in which (strictly speaking) there could be a remotely possible chance (however miniscule) that an event might occur. ---Thus, if the probability is extremely vanishingly small, then the chance of something occurring randomly should reasonably be considered to be virtually zero. Likewise, (since chance is "ruled out") the occurrence of such an event should reasonably be considered to be virtually 100% proven to be "NOT chance," which means that the event must be intentionally caused (namely, by an intelligence). In this article, the probability numbers will be based on a comparison of the full range of possibilities as compared to the narrow range required for the existence of living things somewhere in the cosmos.

The Factors in PhysicsScience has determined that in order for living things to exist in the cosmos, there are a number of constants in physics --such as the gravitational constant, and the strength of the weak and strong nuclear forces-- which must fall within a very narrow range. The probability that all of these constants would fall into the narrow range required for each one, is unimaginably small.
In this regard, Scientist Francis Collins states: "When you look from the perspective of a scientist at the universe, it looks as if it knew we were coming. There are 15 constants --the gravitational constant, various constants about the strong and weak nuclear force, etc.-- that have precise values. If any one of those constants was off by even one part in a million, or in some cases, by one part in a million million, the universe could not have actually come to the point where we see it. Matter would not have been able to coalesce, there would have been no galaxy, stars, planets or people."
This article will be utilizing numbers based largely on the analysis of astrophysicist Hugh Ross, Ph.D. ---who is a post-doctoral fellow at the California Institute of Technology--- found in his book, |

**1. The "Big Bang"**

It has been known for about 70 years, that the galaxies of the universe are moving apart and away from each other, in a similar fashion to raisins moving apart and away from each other in an expanding lump of dough. In 1929, astronomer Edwin Hubble's measurements of more than 40 galaxies established that the galaxies of the universe are indeed receding away from each other at several hundred miles per second, as an explosion would propel exploded pieces from each other. That "explosion"-event is now popularly called the "Big Bang" --- and this event is evidenced by left-over heat (or "background radiation") throughout the universe which (along with much other evidence) leaves little doubt that this hot explosive event occurred.

In addition, recent research, such as data from the "__BOOMERANG__ experiment" (short for "Balloon Observations of Millimetric Extragalactic Radiation and Geophysics") have determined that the geometry and "**"shape" of the universe**," is **"flat"** (as opposed to having "curved" space). A **"flat" universe** means that Euclidian geometry applies throughout space, and every "straight" line (as people normally think of straightness) in the universe does not curve with the fabric of space --even over a very long distance. It doesn't matter that gravity causes light to curve --the __geometry__ of space is still flat. This means that there is an approximate "center" to the material universe (since there is a finite number of galaxies).

One of the implications of the universe being "flat" is that it will expand forever --and in fact, there is experimental confirmation that the universe is actually __accelerating__ in its expansion rate. All of this means that the expansion will never reverse and bring the universe back together into a "Big Crunch," because there's not enough gravity in the mass of the universe to stop the expansion. -- Therefore, we know that the universe has not been on an endless cycle of bang, crunch, bang, crunch, etc. And because of this, we know that the universe is not an eternal entity.

In the following video, Dr. William Lane Craig discusses this current cosmological evidence:

Astrophysicists (such as Stephen Hawking) determined that the evident starting point just before the Big Bang involved something called a "singularity," which is**:** all the cosmos's potential mass (matter), energy, and dimensions --and time-- reduced down to an infinitely small point of **zero** volume. ---Thus, matter, 3-dimensional space, and time virtually did not exist before the Big Bang.

The expanding universe is an important discovery, because if we "reverse the film" of that expansion, then we arrive back at a starting-point for its beginning ...and if there is a beginning, there must logically be a "beginner" to initiate the Big Bang. The beginner of the Bang precedes and is outside of (transcends) all matter, dimensions and time. In light of this, the thoughts of many people go to the first verse of the Bible, which states, "In the beginning God created the heavens and the earth" (Gen. 1:1).

This powerful evidence contradicts worldviews and religions that posit an eternally existing universe (such as older materialism), ... or views which posit the idea of cosmic "reincarnation" with an oscillating universe that eternally expands and contracts (such as Hinduism, Buddhism, & New Age philosophies); ---*but instead*, --the Big Bang would support the biblical view of a transcendent God; that "the universe was formed at God's command, so that what is __seen__ was __not__ made out of what was __visible__" - Hebrews 11:3. In addition, ---unlike any other supposedly "holy writings"--- the Bible __alone__ says that there was a "beginning of time" (2Tim. 1:9 & Titus 1:2), ---and God was causing effects before that beginning (John 17:5 & Col. 1:16-17).

** The Balance of the Bang:** In order for life to be possible in the universe, the explosive power of the Big Bang needed to be extremely closely matched to the amount of mass and balanced with the force of gravity, so that the expansion speed is very precise. This very exact expansion speed of the universe is called the "Cosmological Constant." If the force of the bang was slightly too

Science writer Gregg Easterbrook explains the required explosive power-balance of the Big Bang, saying that, "Researchers have calculated that, if the ratio of matter and energy to the volume of space ...had not been within about ** one-quadrillionth** of

In terms of the expansion rate of the universe as a result of the Big Bang: "What's even more amazing is how delicately balanced that expansion rate must be for life to exist. It cannot differ by more than **one** part in **10 ^{55}** from the actual rate." (My emphasis.) (Ref: H.Ross, 1995, as cited above, p.116). (Note: 10

** THE PROBABILITY:** The chances we can conservatively assign to this: It was about

Design and Cosmology

In the following video, Dr. William Lane Craig discusses this current cosmological evidence:

**Next ---** Several of the following items deal with strengths of the four (known) basic forces of physics in the material universe, which hold everything together. Those four basic forces are: the force of __gravity__, the __strong__ nuclear force, the __weak__ nuclear force, and the __electromagnetic__ force. The strengths of these four forces are extremely finely tuned and balanced with each other and with the amount of matter in the universe, which makes life possible in the present cosmos. ---What is the chance that such fine-tuning happened by chance? --- (Note: If a scientist can improve the accuracy in the numbers used for probabilities here, such information would be appreciated.)

**2. The Force of Gravity**

It is now known that if the force of gravity were any __weaker__, stars would not have compacted tight enough together so that nuclear fusion would occur. Fusion is necessary to produce the heavier elements upon which life depends (such as carbon, nitrogen and oxygen) ---and without fusion, there would only be hydrogen and helium in all the universe. On the other hand, if gravity were any __stronger__, stars would burn so hot that they would burn up in about one year or so (ref. G. Easterbrook, cited, p.26). As it is, the gravitational force is so finely tuned, that the average star is capable of burning in a stable fashion for about 80 billion years (ref. H. Ross, cited, p.60).

How finely tuned is gravity? -- Well, the strength of gravity could be at any one of 14 billion billion billion settings, but there is only one setting which is adequate (and optimal) for a universe with intelligent life to exist.

-- To illustrate: This is as if you had a measuring tape with one-inch sections stretched across the known universe, it would be 14 billion billion billion inches long, and only **one** or two of those inches in the middle is the optimal strength-setting for gravity. If you moved the strength-setting to the right or left just a couple of inches, then intelligent life could not exist (though bacterial life might survive with gravity stronger or weaker by one setting up or down).

** THE PROBABILITY:** Although the force of gravity could obviously have attained a large number of wrong magnitude-ranges, the chance of it being correct for intelligent life to exist, is one chance out of 14 billion billion billion. --Thus, we can conservatively say that it was about

**3. The Strong Nuclear Force**

This is the force which binds the protons and neutrons together in atomic nuclei.

If the strong nuclear force were very slightly __weaker__ by just __one__ part in 10,000 billion billion billion billion, then protons and neutrons would not stick together, and the __only__ element possible in the universe, would be hydrogen only. There would be no stars, and no planets or life in the universe. (Ref., Dr. Robin Collins of Messiah College).

However, if the strong nuclear force were slightly too __strong__ by the same fraction amount, the protons and neutrons would tend to stick together so much that there would basically only be heavy elements, but no hydrogen at all --If this were the case, then life would also not be possible, because hydrogen is a key element in water and in all life-chemistry.

** THE PROBABILITY:** If the strong nuclear force were slightly weaker or stronger than it, in fact, is, then life would be impossible. Therefore, we can very conservatively say that it was about

**4. The Weak Nuclear Force**

The weak nuclear force is what controls the rates at which radioactive elements decay. If this force were slightly __stronger__, the matter would decay into the heavy elements in a relatively short time. However, if it were significantly __weaker__, all matter would almost totally exist in the form of the lightest elements, especially hydrogen and helium ---there would be (for example) virtually no oxygen, carbon or nitrogen, which are essential for life.

In addition, although heavier elements necessary for life are formed inside giant stars, those elements can only escape the cores of those stars when they explode in supernova explosions, however, such supernova explosions can only occur because the weak nuclear force is exactly the right value. As Professor of astronomy, Paul Davies, describes this situation: "If the weak interaction were slightly __weaker__, the neutrinos would not be able to exert enough pressure on the outer envelope of the star to cause the supernova explosion. On the other hand, if it were slightly __stronger__, the neutrinos would be trapped inside the core, and rendered impotent" (My emphasis.) (ref. P.C.W. Davies, *The Accidental Universe*, London, 1982, p.68.)

** THE PROBABILITY:** Considering the fine-tuning of the weak nuclear force for both the rate of radioactive decay as well as the precise value required to allow supernova explosions, it is probably conservative to say that it was

**5. The Electromagnetic Force**

If the electromagnetic force (exerted by electrons) were somewhat __stronger__, electrons would adhere to atoms so tightly that atoms would not share their electrons with each other ---and the sharing of electrons between atoms is what makes chemical bonding possible so that atoms can combine into molecules (e.g., water) so that life can exist. However, if the electromagnetic force were somewhat __weaker__, then atoms would not hang onto electrons enough to cause any bonding between atoms, and thus, compounds would never hold together. In addition, this fine-tuning of the electromagnetic force must be even more stringent if more and more elements are to be able to bond together into many different types of molecules.

** THE PROBABILITY:** Considering the range of electromagnetic force that might have occurred, it is reasonable to say that the probability of the electromagnetic force being balanced at the right level for many thousands of compounds to function for the making of chemical compounds necessary for life, is

**6. The Ratio of the Electromagnetic Force to the Gravitational Force**

It has been established that if the ratio of the electromagnetic force were barely __stronger__ relative to the gravitational force by just __one__ part in 10^{40}, then only small stars would form. On the other hand, if the ratio of the electromagnetic force were __weaker__ compared to the gravitational force by a mere __one__ part in 10^{40}, then only very large stars would form. The problem is, that __both__ types of stars are necessary for life to be possible, because the larger stars is the place where life-essential elements are produced by thermonuclear fusion, ---and the smaller stars (like our sun) are necessary because only such stars burn long enough, and in a stable manner, to support life near to them. (ref. H.Ross, cited, p.117).

In a similar vein, cosmologist Paul Davies explains: "If gravity were *very* slightly weaker, or electromagnetism *very* slightly stronger, (or the electron slightly less massive relative to the proton), __all__ stars would be red dwarfs. A correspondingly tiny change in the other way, and they would __all__ be blue giants" (His italics; my underline). (Ref. P. Davies, cited above, '82, p.73). ---The problem with red dwarfs and blue giants, is that the color spectrum given off by either color of star cannot sustain life because the photosynthetic reaction would be inadequate. (ref. H. Ross, cited, p.139).

** THE PROBABILITY:** As required for photosynthesis, ---since the ratio of the electromagnetic force cannot vary from the gravitational force by any more than (plus or minus) one part in 10

**7. The Ground State Energies of Carbon, Oxygen, Helium & Beryllium**

In the years around 1980, Fred Hoyle discovered that the ground state energies of carbon, oxygen, helium and beryllium had to be within 4% of each other, or else the universe would not have enough carbon or oxygen for life to exist. (Ref. Hoyle, "The Universe: Past and Present Reflection", *Annual Reviews of Astronomy... 20*, '82, p.16). Realizing the unlikelihood of this situation just happening by itself, Hoyle (who was an anti-theist), declared that for all four of those life-essential elements to randomly hit within 4% of the same "bulls-eye", was so unlikely that it seemed like "a superintellect has monkeyed with physics, as well as with chemistry and biology" (Ref. Hoyle, last citation, p.16).

** THE PROBABILITY:** For a single one of those elements to randomly "hit the bulls-eye" to within 4% accuracy of the target energy level, could be conservatively said to be one chance out of 20. ---However, to have the

When we follow through for all four elements, using the same procedure of calculating the probability, the final result is: The chance that the ground state energies of all __four__ elements would randomly hit the same energy level required (allowing life to exist), is conservatively **one** chance out of **100,000**. ---(...since 1 chance out of 20x20x20x20 = 1 chance out of 160,000).

**8. The Number of Electrons Compared to Protons**

Astronomer Hugh Ross explains that the universe must have a fine balance of electrons (with a negative charge) as compared to protons (with a positive charge), and this balance must be very precise. He states: "Unless the number of electrons is equivalent to the number of protons to an accuracy of **one** part in 10^37, or **better**, electromagnetic forces in the universe would have so overcome gravitational forces that galaxies, stars, and planets never would have formed" (My emphasis) (Ref. H.Ross, as cited, p.115). --This is a __minimum__ accuracy for the required balance of electrons compared to protons in the universe.

This would mean that if the Big Bang produced a billion (or 10^9) protons for every billion-and-__one__ electrons, then no galaxies (etc) would have formed (and thus, no life either). The balance must be much better. --- Going further: If a trillion (10^12) protons were produced for every trillion-and-__one__ electrons, there would be no galaxies (etc) or life. The balance must be much better. --- And further: If a quadrillion (10^15) protons were produced for every quadrillion-and-__one__ electrons, there would be no galaxies (etc) or life. --- This same sort of tiny un-balance would make the formation of galaxies or life impossible, by merely adding **one** extra electron to a perfectly balanced number of both particles... even if the number 10^36 is reached for both particles. (10^36 is the number 1 with 36 zeros after it.) Merely adding one particle of either type would produce enough imbalance to render the existence of life impossible.

** THE PROBABILITY:** Because of the extremely fine balance required, it would be safe to say that in order for life to be possible, the probability that the necessary balance between protons and electrons was achieved by a random result of the Big Bang, would be

**Summary of The Probabilities**

As explained in the article "A Mathematical Proof of Intelligent Design in Nature," if the probability of something happening by random processes is vanishingly small enough, such a random chance explanation for that event's occurrence is virtually ruled out as a reasonable possibility. In that same article, it was also explained that French mathematician Emile Borel set the probability of **1** chance out of **10^50** as having a statistical chance of **zero** that it could happen.

**Calculating Probabilities Together**

In order to calculate the chance that two probabilities could happen together, we must __multiply__ the probabilites together. For example, the chance of flipping a two-sided coin so that we get "heads," is one chance out of 2 ---and the chance of flipping two heads in a row, is the product of the two flips, or one out of 2 times 2, --or-- one chance out of 4.

To calculate the probability that our first **two** attributes of the universe could both occur at random so that life could exist, we must multiply them together. (Those first two attributes were: **#1**: that the force of the Big Bang could have randomly been properly balanced with the mass & gravity of the universe ; and **#2**: that the force of gravity might have randomly attained such an advantageous strength for the making of life-necessary elements in the stars).

---The chance that the first attribute could have happened randomly, was one chance out of 10^{21}, and the chance for the second attribute's random occurrence, was also one chance out of 10^{21}. Thus, by __multiplying__ the two, we see that the chance that both could occur randomly together, is **one** chance out of **10 ^{42}**.

The chance of the **#3** attribute happening at random, was 1 chance out of 10^{12}, therefore, when we multiply to get the chance that the first three attributes could all happen together at random, we get **one** chance out of **10 ^{54}**.

The chance of **#4** happening was 1 out of 1000. Thus, the chance of the first four happening together randomly is **1** out of **10 ^{57}**.

The chance of **#5** was also 1 out of 1000. So, the chance of the first five all happening randomly is **1** out of **10 ^{60}**.

The chance of **#6** was 1 out of 10^{30}. So, the chance of the first six all happening randomly is **1** out of **10 ^{90}**.

The chance of **#7** was 1 out of 10^{5}. So, the chance of the first seven all happening is **1** out of **10 ^{95}**.

The chance of **#8** was 1 out of 10^{30}.

So, the chance of all eight attributes randomly happening together in the cosmos, thus permitting life to exist, is **1** chance out of **10 ^{125}**.

The actual number should be __many__ times slimmer than this, since our probability estimates were so conservative... and there are many other factors we could have figured in.

**Analysis**

So, how remote is 1 chance out of 10^{125}?

---Well, the known cosmos is made up of about 10^{84} sub-atomic particles (such as electrons, protons and neutrons), therefore, 10^{125} is about the number of sub-atomic particles contained in 10^{41} universes the size of our cosmos. ---Thus, this chance of the properties of our present cosmos happening at random, would be equivalent to marking one single sub-atomic particle in 10^{41} of our universes, mixing it in thoroughly, and then successfully finding that marked particle by __one__ totally random selection.

In light of this vanishingly small probability, we can quite confidently say that the attributes of the cosmos (described above), which make it possible for life to exist, did not occur together as a random chance combination of events.

If it was not a chance occurrence, then the other rational and logical option is that purposeful intentionality caused the cosmos to originate as it did, and to have the attributes that it does, so that life may exist.

You may read about a similar sort of study, in which Hugh Ross has put together a list of factors to give an estimate of the Probability for a Life Support Body arising in the universe without the purposeful work of an intelligent designer.

**Identity of The Designer**

In light of the above considerations, we therefore have a virtual "proof" that the cosmos was intentionally designed by the purposeful work of a designer, however, the specific identity of the designer does not seem to be (as yet) apparent from an investigation of only nature. It does not even appear that we can necessarily conclude that the designer is an omnipotent being, since all of the designed things we might consider are finite things, for which a finite designer could be adequate (...however, it would seem that an almost unfathomably powerful and intelligent designer would be necessary, due to the magnitude of the universe, and the complexity of designed things).

---Still, if you will read further in this website, you may agree that there is an excellent body of evidence which indicates that the Bible is a supernaturally produced piece of literature, the true Word of God. ...and the Bible claims to identify the living God (and Jesus Christ) who did the intelligent designing of all things. If you want to read about such evidence concerning the Bible, click on this link: "Prophecy Proves the Bible's Authority."

---Concerning Jesus Christ, the Bible says: "Through him **all** things were made; without him **nothing** was made that has been made" (John 1:3). Similarly, it says: "For by him **all** things were created: things in heaven and on earth, visible and invisible" (Colossians 1:16).

**YOU**, dear reader are loved by God, and that's why Jesus Christ came!

**Related Sites & Articles:**

- Reasons to Believe - with Dr. Hugh Ross - Showing how breakthrough discoveries in the sciences confirm Intelligent Design and enhance the scientific case for the God of the Bible.

- The Fine-Tuning Design Argument - by Robin Collins

- The Designed 'Just So' Universe - by Walter L. Bradley, Ph.D.

- How to Calculate Probabilities - by Dr. Hale

- GOD AND THE BIG BANG...and Other Arguments... - by Mike Poole