My friend Justina recently gave me a rambling math history book entitled Here’s Looking at Euclid, by Alex Bellos.  Besides the punny name, it starts right out in chapter zero with a math finding that echoes the idea of general and special revelation found in Romans 1 and Hebrews 1.

What?  Math supports the Bible? Check this out. 

Romans 1.19-20 says “For what can be known about God is plain to them, because God has shown it to them.  For his invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made.” Everyone has enough evidence to conclude there is a creator God – general revelation.  Hebrews 1.1-2  tells us there is more to know: “Long ago, at many times and in many ways, God spoke to our fathers by the prophets, but in these last days he has spoken to us by his Son, whom he appointed the heir of all things, through whom also he created the world.” The Son, Jesus, who was present at creation and is the heir of all things, is also the one who was given so that whoever believes in him would not die but would have eternal life (John 3.16) – special revelation.

Now from the math side, Bellos describes the efforts of researcher Pierre Pica with the Munduruku, a tribe of Amazonian Indians whose language has no words for numbers larger than five.  He wanted to know how they process those larger counts.  Here is his research technique:

“Since the Munduruku don’t have numbers, Pica tested them using sets of dots on a screen.  Each volunteer was shown an unmarked line on the screen.  To the left side of the line was one dot, to the right ten dots.  Each volunteer was then shown random sets of between one and ten dots.  For each set the subject had to point at where on the line he or she thought the number of dots should be located. Pica moved the cursor to this point and clicked.  Through repeated clicks, he could see exactly how the Mundruuku spaced numbers between one and ten. “

What seems obvious to us is that the numbers would be spaced evenly on the line. But the uneducated Indians have a different view of magnitude.  They see large intervals between one, two and three, and progressively smaller intervals as the numbers increase.  The author’s explanation: “Imagine a Munduruku is presented with five dots.  He will study them closely and see that five dots are five times bigger than one dot, but ten dots are only twice as big as five dots.”  Ratios are more important than counting.

It turns out that the natives’ perceptions are the same as those of young children. Other researchers did the same experiment with kindergartners, first graders, and second graders.  The Kindergarten response is like the Munduruku – large spaces between small numbers, and decreasing spaces as the numbers get larger.  The second grade response has the numbers falling in equal spacing – a linear model.  First graders are making the transition.

The Amazonians and the unschooled children have an intuitively logarithmic view of quantity.  There are many lasting impressions that come from logarithms – our idea of the passing of time shows up as we remember time passing so slowly when we were younger, but it is zipping by now.    Yesterday seems longer than all of last week.

But exact numbers and equal spacing, which must be taught, are necessary for measurements and they facilitate calculations.  The linear model provides the doorway to deeper understanding of number theory, calculus, binary systems used in computers, and waves of “higher” math.

We all have an innate, general revelation understanding of logarithms.  But there is more to know.  We are taught the special revelation of linear and other numbering systems that allows us to understand more fully the math world around us.  Both are real and valuable, but you can’t send men to the moon with just logarithms.  Similarly, it is wonderful to see the beauty of the creator in nature, but you can’t appreciate the wonderful grace of Jesus Christ without being taught the basics of God’s plan as revealed in the Bible.