Fractal Geometry and the Bible, Part 1--the argument:
FULFILLS FN4 OF HUB#4:
1. This hub begins to complete footnote#4 of hub#4, Proof the Bible is God's Word.
TWO PILLARS UPON WHICH TO BASE BIBLE STUDY:
2. There is a chain of reasoning which led me to the conclusion that fractal geometry is mentioned in the Bible. The foundation of this reasoning is based on personal axioms( self--evident truths) concerning God, and His Word( our compiled Bible): 1. God is God; i.e. He is omniscient, omnipotent, and is the Creator. 2.God's prophets and servants were inspired( 2Timothy 3:16) by God to write the 66 books of the Bible; therefore, those words in Scripture are God's words. These two pillars are foundational to understanding Scripture, to being saved( forgiven of sins and going to heaven), and to knowing God. This is the first link in this chain of logic.
THE QUESTIONS GOD HAS POSED TO US:
3. Whenever God wanted to prove to us that He is God, He would often refer to His creation. There are many verses in which this was done including Psalms 102:25; 104:2,3,5,6,24,25,30; 136:5--9; Isaiah 45:7; 48:13; 51:13; Jeremiah 5:22; 10:12; 27:5; 31:35, and many, many more. So when God intended to remind us that He is God, and we are not God, He would pose questions to us which we could not answer. This is what He did with Job at Job chapters 38 and 39. Job could not answer God's questions, and the effect God intended from this was fulfilled at Job 42:1--3. This is the 2nd link.
GOD, THE CREATOR AND RULER OF TIME:
4. The 3rd link in this chain of reasoning involves 3 Scriptures: 1. Isaiah 46:9 and 10( "I am God, and there is none like me, Declaring the end from the beginning"), 2. Isaiah 57:15( "For thus saith the high and lofty One that inhabiteth eternity . . . "), 3. 2Timothy 3:16 and 17( "all Scripture is given by inspiration of God, and is profitable . . . That the man of God may be perfect . . . "). What those verses are saying in Isaiah is that God knows every detail of the future. Not only can He predict general trends of the future as He did in Daniel 12:4 concerning the proliferation of knowledge that we are experiencing now, but He knew, when making that prediction in Daniel's time, that I would be taking a sip of my potent coffee while accessing that knowledge on my computer. Keep this fact in mind as we continue with our chain of reasoning.
IF YOU WERE GOD:
5. The 4th link is questions I have asked myself, and I'll pose it to you: If you were God, and you wanted to prove to all generations that you were God, then would you ask anyone a question that you knew the human race would eventually come up with the answer? The questions you would ask would have to be extremely difficult--impossible!-- to answer; otherwise, would you not loose credibility as God if your creation could eventually answer the impossible questions of which only you could know the answers?
GOD'S CREDIBILITY AND HIS WORD JEOPARDIZED:
6. Not only would God's credibility be jeopardized but so would His word, the Bible. Christians are not, in my opinion, reluctant to put the credibility of God or His Word on the line. They boldly stand by God's Word, and they unequivocally believe in its accuracy and inerrancy. This is one of the signs of a true Christian. So if God asks a question in His Word whose purpose it is to dwarf our knowledge, and put us in our place as creations of God, rather than the other way around, then we should never be able to answer that question, not even closely. God knows the future, and He knows if we will ever be able to answer one of those questions.
OH BOY! GOD AND HIS WORD ARE IN BIG TROUBLE!
7. Nevertheless, isn't this precisely what happened in the book of Job( written about 1,845 BC)? In chapters 38 and 39 God is asking Job questions to prove to Job that He is God, and Job isn't. So we get to Job 38:18 and God asks, "Have you perceived the breadth of the earth? Declare if you know it all." God knew that in less than 1,600 years, in 250 BC, Eratosthenes would come up with a pretty close answer to that question. Now, over 2,260 years after Eratosthenes provided his answer to that question, we believe we have an answer so accurate that the earth's slightly ellipsoidal shape is taken into consideration. So are we catching up to God? Are we beginning to rival God in knowledge? Are we able to say to God, "Well now, god, just exactly what do you want to know? Do you want to know the circumference around the polar axis, or the equatorial axis? There is a difference you know. You do know that, don't you?"
WE ARE SIMPLISTIC AND OUR SCIENCE IS RUDIMENTARY:
8. If there is anything we should be able to boast about, it would be our complicated gadgets, sophisticated toys, and highly advanced technology and sciences. If we could take our stuff back a few hundred years we would be perceived as gods, and why not?--what with our near omniscience and all. Do you think the children of yesteryear would have the audacity to compare their horse and buggy to our Boeing 747, or their bows and arrows to our guided missiles, or their catapults to our Saturn V rockets? Who do those grasshoppers think they are anyway? And yet in our heart--a good argument can be made for this--this is precisely our attitude toward God. Who are we to compare the complexity of our computers to the complexity of God's organic creations, including us, or the power of our Saturn V rockets to the power of God's Quasars, or our ability to travel long distances in short times to God's omnipresence? What kind of grasshoppers( Isaiah 40:22) do we think we are anyway? In our best state ever--past, present, or future-- we will be nothing more than simpleminded imbiciles compared to God. Besides, everything we create we do so with the stuff God already created and put on earth; not to mention we use the forces of nature that God created, as the electromagnetic force. We are just a bunch of kids playing with tinker toys that Daddy gave to us.
ARE WE NOW ABLE TO ANSWER GOD'S QUESTION TO JOB ?
9. No, not even closely. If we are going to measure the circumference of the earth with our crude measuring instruments then we will come up with a mean answer of 24,902.63 miles. An answer of 25,000 miles is what we normally hear when the question is asked. This is a good answer because 25,000 miles is well within 1 percent of 24,902.63 miles. God being gracious, I will bet He would be willing to accept an answer from us that was within 40 percent, but I'm afraid we must give God the same answer Job gave Him nearly 4,000 years ago: " therefore have I uttered that I understood not; things too wonderful for me, which I knew not." The reason we must give God the same answer is we do not know what measuring instrument God has( no mistake on tense--->Isaiah 57:15) in mind when He asked this question. This is a very big deal!
FRACTAL GEOMETRY AND THE MEASURING INSTRUMENT:
10. In fractal geometry, the length of what you are measuring, in many cases, depends on the length of the measuring instrument, and it is not a trivial amount. For example, the Koch Snowflake is initially represented as an equilateral triangle( all sides of equal length), but it does not stay that way. If we begin with each of the three sides being 1cm long( about as long as your little fingernail is wide) then we have a perimeter of 3cm( slightly over an inch). As the koch snowflake is constructed with more and more iterations going toward smaller and smaller scales the perimeter of the snowflake tends toward infinity. What began as a perimeter of 3cm at L1( see the calculations below) goes to nearly 2 miles after 40 iterations at L4. After 80 iterations at L5 the perimeter of our tiny triangle( although distorted now) is 184,328 miles or a distance of 7.37 times around the earth. I've included 3 links, with introductions, which will explain the koch Snowflake,its construction, and fractal geometry.
- Fractal Geometry :: Fractals in Nature
Dosters has a good hub here on fractals in nature(creation). About 6 pictures down in his hub is the Koch curve, and the 7th picture is a real time construction of the Koch Snowflake.
- The Chaos Theory Part - 2
About 6 paragraphs down Aravindb1982 does a good job of describing the koch snowflake and its construction. He also mentions string theory. String theorists state that these strings have enormous tension, which coincides with Psa.104:2; Isa.40:22 etc
- Fractal Geometry
In this hub RicardoE describes many properties of Fractal Geometry. Here he has pictures of the Mandelbrot Set and the Julian Set, both of which are fractals constructed with complex numbers.
MY FIRST ENCOUNTER WITH FRACTAL GEOMETRY:
11. My first encounter with the Koch Snowflake( KS) was one of disbelief. The author said the KS represented an infinite line enclosing a finite area. My first thought was, " What a moron. That is ridiculous." I actually threw the book across the desk, and was mad at my self for buying it. Later I calmed down and took another look at it. I do not remember having the simple formula at L1 above. I just started doing iterations as I watched the perimeter getting longer and longer. Mathematics, God's language, can do that; it can make the unbelievable, believable. I trusted the math, and believed in the reality that an infinite line can enclose a finite area. Of course in real life I suppose there would be a limit to how small the measuring instrument can be, as for example the Plank Length, which is about 1.61 X 10^( -35) meters.
CONCLUSION OF OUR LOOK INTO JOB 38:18
12. What started out to be just a footnote for hub#4 is turning out to be more than one hub. In part 2 of this subject we will look at a real life example of how Great Britain's coastline got to be longer and longer as they kept using smaller measuring sticks to determine its length. It is a classic, and practical, example of how fractal dimensions and fractal geometry is no fairy tale. The math, logic and evidence proves we do not have any Idea of what is the circumference of the earth; thereby proving God's question to Job is still valid.
GOD IS THE DESIGNER, NOT US:
13. One may be tempted to argue that this whole idea is stupid. The circumference of the earth is 25,000 miles. Who is going to be dumb enough to measure the earth's circumference with a measuring stick the size of his hand, or an ant, or a bacterium. Well, that is really easy for us to say since none of us designed the earth. You may ask someone how long is the suspension cables are on the Golden Gate Bridge. He may say, "Well, now, I'll tell ya. It looks to me to be, well lets see . . . well I reckon that duffer be aboot . . . well, I walk once, so I reckon it be . . . oh, I'm thinkin . . . I'm calculatin them duffers be bout . . . . ok what you question? Oh yah. I reckon aboot, you know, aboot 6,000 to . . . oh aboot 8,000 fat footies, I'm thinkin. Yah. That's what I reckon tis is." Even though such in depth analyses would rival the brightest minds, the engineers who designed the bridge know that the 2 main cables are each 7,650 feet long and 36.375 inches in diameter; however, the actual length of the cables that compose the main cables have a total length of 80,000 miles. This analogy applies to God and us. It is easy for us to take a simple-minded approach to God's creation, and that may be good enough to get us by in a functional way, but God did not have that luxury when He designed the earth. He had to consider the earth's foundations( Job 38:4), and how those foundations related to the stretching of space( Psalms 136:6) in a possibly 2 or more dimensional way( Isaiah 42:5). Oh yes, God used a measuring stick at Job 38:5, but Job 38:5 also implies that His measuring device was( or is) constantly changing its length to coincide with the stretching of space( Isaiah 42:5; 45:12). God measured everything(Isaiah 40:12). It is possible that the measuring instrument that God uses is space itself( Jeremiah 31:37) but we can't measure it because God is constantly stretching( Isaiah 44:24--present tense) and spreading( Job 9:8--present tense) space. People use the Golden Gate Bridge everyday but very few of them are aware of the complex design that went into it. So also we function fine on earth without knowing the intricate engineering God put into it. Simple-minded and vacuous thinking does fine when you want to use something, but it doesn't do any good when it comes to designing it. So we may not think the size of the measuring instrument is relevant, but God does.