- Coins?

“And God called the light Day, and the darkness he called Night. And the evening and the morning were the first day.” – Genesis 1:5

When my children were young, their mom and I regularly gave them a few coins before we would go to the store so they might get something they wanted. Over time, we used this habit to teach them how to select one thing over another, how different denominations of coins related to each other, and to learn the value of money as compared to the things they wanted. But before they knew the value of the coins, they recognized that the number of coins was important.
As we would get ready to go to the store, they would hold out their little open hands expectantly. You could watch the eyes dart from between each other’s palms as they prepared to quickly compare their treasure. I had their undivided attention. They laughed at my little attempts at humor; their eyes sparkled as I dropped a coin in one hand and then the other.
Eventually it was time for a lesson; I gave five nickels to one and to the other I gave one quarter. As it became clear that I was done with my giving, a little pair of eyes caught mine and the corners of a mouth started to drop; the eyes seemed to ask, “Why only one coin? She has more.” The other little face seemed just as sad, “But his coin is bigger than all my coins.”
As I attempted to explain to my children the difference in value between nickels and quarters, it was like the world slowed down to a crawl. I could have sworn the temperature in the room dropped four degrees. Their little faces lost all emotion; I was met with blank stares. But, with a little patience, it didn’t take long for them to understand. We had entered a new phase in their education.

My children recognized when one had fewer coins than their sibling. They hadn’t likely applied the very simple mathematical principle of arithmetic by counting coins. Instead, they were unhappy because one pile looked bigger than the other. But that comparison brought on a lesson, and after the lesson they understood that different coins were assigned different values. Later, they advanced to counting coins and to adding the different values of coins. They learned to divide so they could determine how many of something they could get with their money. They learned multiplication allowing them to quickly calculate how much they had if they had a certain number of coins. Their mathematical education was continuous. They learned to apply mathematical principles which help them in life.
But what’s this got to do with self-evident truth? Thinking of coins helps me remember the importance of mathematics. It leads me to suggest as one of my three self-evident or universally recognized truths:
Correctly applying mathematical principles can lead to correct answers.

My friend and I discussed this briefly. He had always been good at math and agreed that there were rules that had to be followed, and if a person did so, they should come up with the right answer.

There is one argument I’ve heard against this truth; it attacks a person’s fundamental understanding of mathematics. Expressed in the form of a question, the argument begins: How do you know one plus one equals two? This is usually followed by the claimed possibility that: Perhaps 1 plus 1 equals 3; some can even go on to cite some formula as proof.
So how do we know that 1+1=2? Believe it or not, the answer is not found in mathematics. The answer is found by using our first self-evident truth. Do you remember my story about sex? It turned out my young son was asking for the English translation of the German word sex which is six in English. This served as our memory aid to remember that: Words have definitions.
Knowing that words have definitions, we can look at the definition of the word “two” which may be defined as: a cardinal number, the result of adding 1 plus 1. In other words, one plus one equals two because it is enshrined in the very definition of the words themselves. The word two is so basic, that you find it used in other word definitions. Words like pair and couple are harder to define if we don’t use the word two. And two is a cardinal number, the result of adding 1 plus 1.
So how do we know that 1+1=2? We know it because that is the definition. (Besides, there is usually an error in the mathematical formula when someone gets another answer.)

This truth is important because later in this book there are two mathematical disciplines introduced; a person should be familiar with these disciplines when considering the truthfulness of Christianity. The two disciplines are probability and statistics.
For now, let’s apply this to Christianity by looking at the question of the beginning of the universe. Do you think mathematics proves an old earth? Shall we see?

Billions vs. Thousands
After Charles Darwin’s theory was accepted, it was thought that the universe had existed forever and the imagined process of natural selection (evolution) was not limited by time. It seemed logical to conclude, and many did, that our evolution was a foregone conclusion given the foundational belief of seemingly infinite time. However, with Albert Einstein’s theories of relativity, that supposedly firm foundation was shown to be weaker than many thought. People were able to calculate the amount of time since the beginning of space, time, energy, and matter. Once people realized that the evolution of everything had to happen within the calculated period, evolution was restricted to that window of time.
While it wasn’t great for the evolutionist who thought unlimited time was necessary, neither was it great for those who believed in a young earth based on the biblical creation account or biblical genealogical history. Initially, mathematicians had calculated the beginning of the universe to about 13.7 billion years (now they are calculating it at over 15 billion years); but credible theologians calculated the biblical timeline as only accounting for about 6,000 years, and part of that were the six days of creation recorded in the first chapter of the book of Genesis. Even stretching it out, Christians could only get to maybe ten thousand years. But 10,000 years is a long way from billions of years. Which is true?
While the 13.7 to 15 billion years were the figures that some evolutionist could work with, Exodus 20:11 and 31:17 clearly taught that “in six days the LORD made heaven and earth”. And with rabbinical and evangelical teachers concluding that the Hebrew word used in scripture for a “day” represented a 24-hour period, there was a paradox (an apparent contradiction) between evolutionist’s theory and the Judeo-Christian creation account. Were the evolutionists interpreting the mathematics correctly? Were the theologians interpreting the Bible correctly?
In this case, I trusted both mathematics and the Bible as true. This had to be a paradox and not a contradiction. I knew there had to be an answer that would solve this problem, and I got the answer one day from a radio program.

Chuck Missler was reviewing Isaiah, chapters 40 through 43. In a sidebar he began with an introduction of a friend of his, Doctor Gerald L. Schroeder, an experienced nuclear physicist, who wrote a book called Genesis and the Big Bang. In a letter to Mr. Missler, Doctor Schroeder shared something interesting, but I’ll let Mr. Missler tell it. Oh, he refers to Doctor Schroeder as “Gerry”:

“We talk about six days [of creation]. Did God create the world in six days, right? And yet we measure astronomically and know that the universe is roughly 13 billion years old by some other accounting. And of course in the Genesis study we did point out that by using Einstein’s Theory of General Relativity, time dilates in accordance with mass and acceleration. That means that when you talk time, whether it’s six days on the earth or somewhere else, you have to deal with gravity and time; and time is neither linear nor absolute.
“Gerry went and did the equations recently. He took the mass of the universe, which we now know; he took the mass of the earth. He put an observer on the surface of the earth and plugged that into Einstein’s General Theory, took the mass of the universe and imagined [an observer] on the perimeter of the universe, [then] put that into Einstein’s Theory of Relativity, and the 13 billion years at the perimeter of the universe by Einstein’s General Theory equates to guess how long on the earth? Six days. [Isn’t] that kind of fun?
“The foolishness of God puts to naught the wisdom of men.”

Just in case you missed that, or started to read it and felt like the room was spinning, let me summarize. In short, Dr. Schroeder contends that the results of Einstein’s calculations must be based on the observer. When the observer is at the perimeter of the universe we get the figure of over 13 billion years, now 15 billion years. But, when the observer is on the surface of the Earth, we get the figure of six days. This still holds true even when the calculations made from the perimeter of the universe exceeds 15 billion years. This was later updated by Dr. Schroeder on his website. (See his article on the Age of the Universe)
Now when I hear about conclusions that contradict clear Biblical meaning – to say the least – I am skeptical as to the validity of the interpretation of data.

Conclusion
Coins are a wonderful learning device for children. Ultimately, we can use coins and take a child from understanding less about numbers and counting to understand more about numbers and counting. This can lead to an education in multiplication, division, and more.
Therefore, thinking of coins, helps me remember the importance of mathematics and leads me to suggest as a self-evident truth: Correctly applying mathematical principles can lead to correct answers. In other words, I can trust mathematics.

What does the Bible say?
Does the Bible support mathematics? Of course it does, and right from the very first chapter! The first chapter of the first book introduces us to numbering when it tells us about the first six days of creation in which God creates the first day (verse 5) , a second day (verse 8), a third day (verse 13), the fourth day (verse 19), the fifth day (verse 23), and the sixth day (verse 31). Division was introduced as God separated light from darkness (verse 4), the waters from the waters (verse 5), and the day from night (verse 14). Sets were introduced as days, years, water creatures, fowl, and cattle. The concept of measuring was introduced by measuring time with a day defined as an evening and a morning. And multiplication was introduced when God told the creatures in the water and fowl (verse 22) to multiply or increase.
A person may find other mathematical concepts throughout the scriptures. Here is something to look for: I’m told the building of Noah’s ark introduces a reader to the concept of algebra. I haven’t looked for this yet, so I’ll leave it to you to find this and leave it to you to possibly find the introduction of other mathematical concepts.
I’ll close with a verse I’ve already mentioned, “And God called the light Day, and the darkness he called Night. And the evening and the morning were the first day.” – Genesis 1:5

Quick Review
On the front cover are pictures of a map of the United States of America and six cups of coins. These pictures remind us:
The Founding Fathers of the United States of America wrote a Declaration of Independence in which they refer to “self-evident truth”.
Sex is the German word that is translated to “six” in English; it is used as a reminder that if we don’t know what language a person is speaking, we may not know the definition of the word they are using. This is important because: We understand each other’s words based on our common language.
A cup can have something in it or not have something in it. Even a child can recognize the contradiction that a cup is not both “empty” and “not empty” at the same time in the same respect. Even the child realizes that: Contradictions can’t be true.
Thinking of coins helps me remember the importance of mathematics and leads me to suggest as a self-evident truth: Correctly applying mathematical principles can lead to correct answers.

Up next
After the section summary, we will proceed to answers concerning certain philosophical questions.