Smith Contemplating Infinity

A Mathematical Insight Into God's Nature
1. Auflage 2017
ISBN: 978-1-925590-27-2
Verlag: Vivid Publishing
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 200 Seiten

'Contemplating Infinity' gives a glimpse into the nature/character of God that is reflected in our mathematics.' This nature is the same as that seen in the Scriptures. For example, the book shows that mathematics is logical (requiring a logical beginning). Mathematics has infinity as a character, a dual nature (one part is easily envisaged, the other is not). It has majesty (which commands obedience to principles), and it offers the joy of enquiry to those willing to follow these principles. The book also gives an apologetic for special creation based on probability, and evidence from the natural world. 'Contemplating Infinity' also delves into special numbers of interest, such as pi and the speed of light, the Fibonacci Sequence, the Golden Ratio and Fractals. It explains why we can see stars that are millions of light-years away (a problem for many sceptics). The book is replete with mathematical examples, which those at senior high school level can easily do. At the end of each section, there are Review Questions (with many maths questions) to re-enforce learning for the student or enquiring adult. Answers to these appear at the back, along with a Glossary of all the major terms.

Autoren/Hrsg.

Smith, Fiona

Leseproben

The Character of Numbers Gives an Insight into the Nature of God   Introduction “For the invisible things of Him from the creation of the world are clearly seen, being understood by the things that are made, even His eternal power and Godhead; so that they (the unbelievers or defiant) are without excuse.” —Romans 1:20 All of creation cries out “creation by an omniscient and caring Creator”. You see this in the magnificent lifeforms that inhabit this planet. You also see it in the provisions they are all given, in order to have a comfortable existence. You also see it in the numbers that form the basis of the physics laws underlying the functioning of the Universe, and our ability to understand and use these numbers. This book investigates some of the aspects that we can learn about our Creator by studying mathematics. For those with a joy of mathematics, problems are added for you to solve.   Mathematics is Logical Mathematics is the study of the relationships and properties of quantity and space. This quantity or magnitude is conveyed by numbers. By this definition, mathematics cannot be arbitrary, which means it must be logical. It must allow us to understand our world, but only by following a consistent manner of reasoning. Otherwise, such a study would be pointless. Similarly, the reliability of our senses and memories to use this mathematics must also be non-arbitrary. If our senses and memories were not reliable we couldn’t understand the world through mathematics, even if it were put together logically. The character of the logic in mathematical reasoning and the ability of us to follow this necessitates an adequate cause…. One that is at least intelligent enough to be logical, and to create beings capable of following such reasoning. An unplanned, explosion of super-dense, sub-atomic particles does not provide an adequate cause. A Creator of fearsome intelligence does. As Dr. J. Lisle wrote in his book ‘The Ultimate Proof of Creation’ (ref. {1} p.40.), “The ultimate proof of creation is this: if biblical creation were not true, we could not know anything.” Review Questions for Mathematics is Logical. Answers for the Review Questions are found on p. 169 (If you answer in complete sentences, then your answers can serve as your notes.) Define ‘mathematics’. Why must mathematics be logical? Why must our senses and memories be reliable? What does Dr. Lisle claim to be the ultimate proof of Biblical creation? Reference {1} J. Lisle, ‘The Ultimate Proof of Creation – Resolving the Origins Debate’, 2011, Master Books, Arizona, USA.   Numbers are Real, Unchanging, Universal and They Existed before We Did As a concept, mathematics and numbers are abstract in nature. This means that they are separated from matter and particular examples. They are not concrete. Yet mathematics and numbers are very, very real. In other words, while we can’t hold a ‘one’ or a ‘ten’ in our hands, we certainly know that the quantity, itself, exists. Numbers are so real that we even have laws to describe how they can be manipulated to derive a reasonable result. (e.g. commutative law, associative law) These laws are invariant, which means that they don’t change with time or place. Like the laws of physics and chemistry, laws of mathematics don’t evolve. These laws are universal, as are the laws of physics and chemistry. This means that (as far as we know) they apply in the same way in all parts of the Universe. Laws of mathematics were and are discovered by people. Therefore, they existed before people existed. For example, the relationship of the circumference of a circle divided by its diameter (which is equal to pi or p on a flat surface) was there before Archimedes determined its value. Similarly, the orbits of the planets around the sun – as discovered by Johannes Kepler existed before human beings described them. Humans discover mathematical relationships. They don’t invent them. Dr. J. Lisle in his article ‘Evolutionary Math?’ (ref. {1}) describes numbers as a “reflection of God’s thoughts”. He explains, “Numbers existed before people because God’s thoughts existed before people. The internal consistency of mathematics is a reflection of the internal consistency within the Godhead.” Since God doesn’t change (Malachi 3:6), His thoughts do not change with time and, thus, neither do the laws of His mathematics. “For I am the LORD, I change not; therefore ye sons of Jacob are not consumed.” —Malachi 3:6 Since God is omnipresent (Jeremiah 23:24), the laws of mathematics apply everywhere. “Can any hide himself in secret places that I shall not see him? saith the LORD. Do not I fill heaven and Earth? saith the LORD.” —Jeremiah 23:24 Dr. Lisle writes “mathematics are real and, yet, not physical—just as God is real and not physical in His essential nature.” Human beings are able to think about and use mathematics because we are made in the image of God. His thoughts are embedded in us when we think rightly about anything. The Secular Dilemma The correspondence of abstract mathematical laws to material things cannot be understood from a secular standpoint. How can one accident of nature (we, humans) understand another accident of nature? How can we have mathematical consistency across the span of the Universe without a physical absolute underlying the reality that we know? In 1960, the physicist Eugene Wigner published a classic article from his secular point of view on the topic of why the physical universe obeys mathematical laws. The title of the article was “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”. In his closing paragraph, E. Wigner stated, “The miracle of the appropriateness of the language of mathematics for the formulation of laws of physics is a wonderful gift which we neither understand nor deserve.” (ref. {2}) The Creationist Can Understand Why We Understand Mathematics In contrast, the appropriateness of the language of mathematics is easily understood by those who accept that we have been created from the same mathematical mind that formed the Universe, and that we have been given the gift to comprehend it. Review Questions for Numbers are Real, Unchanging, Universal and Existed Before We Did. Answers for the Review Questions are found on p. 169 (If you answer in complete sentences, then your answers can serve as your notes.) While numbers are abstract in quality, how do we know that they are real? Numbers and their laws are ‘invariant’. What does this mean? Numbers and their laws are ‘universal’. What does this mean? How does J. Lisle describe that numbers are a reflection of God’s thought? What is the dilemma with regard to abstract mathematical laws and the physical world for secular mathematicians, according to E. Wigner? How does a creationist explain the reality of the universal appropriateness of mathematics? Reference {1} J. Lisle, ‘Evolutionary Math?’, 2012, ICR, Acts & Facts. 41 (12): 11-13, http://www.icr.org/article/evolutionary-math {2} E. Wigner, 1960, The Unreasonable Effectiveness of Mathematics in the Natural Sciences. Communications on Pure and Applied Mathematics. 13(1):1-14.   Numbers have Infinity as a Character Defining Infinity There are some really, impressively big numbers! e.g. a googol is 10100 – i.e. a 1, followed by 100 zeroes. 10,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000 In his book, ‘The Emperor’s New Mind’ (ref. {1}), R. Penrose an English mathematical physicist, estimated that there are approximately1080 subatomic particles in the Universe. So, a googol is even greater than all of the sub-atomic particles that make up all of the atoms in the known Universe! However, infinity is much larger! 1080, 10100, even 1080^100000 are all finite numbers, and they are all smaller than infinity. Note: ^100000 means that this 1080 is, itself, raised to the power of 10000. Finite numbers have an identifiable value on the number line. We say they are ‘limited’ or ‘bounded’. We can always find a number bigger than a given finite number. E.g. 1080^100000 + 1 is bigger than 1080^100000. Infinity does not have a definable value. It’s beyond any finite number that we can name, and it is not bounded. We define it as being ‘unlimited’, ‘unbounded’ or ‘endless’. Note: This does not mean that the number sequence is presently ‘getting larger’ continually....