The Power of Numbers

6 pack divided by 2 = 3

AD (childhood and current friend)

My response:

When did you ever split a sixpack? Maybe 24 divided by 3 = 8.

• AD response: that’s advanced Math.
• My response: only after having the 8

Fun with numbers:

Some numbers are simply better at certain jobs. And most have a really neat history. Two, six, ten, twelve, sixty, 360, have shaped everything from ancient calendars to modern computers. The more I learn about them, the more I realize numbers aren’t arbitrary—they each have histories and dare I say, even personalities.

Six is one of my favorite numbers. It is both the sum and the product of one, two and three. It just seems so versatile. And that is an attractive quality in numbers. 

Ancient Sumerians built much of their mathematics with the number 60. Each of your fingers has three knuckles. Excluding the thumb, that’s 12. After counting to 12 you can tally that set with a finger from the other hand. Since your hands have five fingers, 12 X 5 = 60. They used a sexagesimal system as opposed to our decimal system. It was more useful to them for counting things, surveying land for farming and tax collection, and record keeping. It was also used later by the Babylonians for Astronomical measurement and making calendars.

And while 60 is very flexible, the top dog of flexible numbers must be 360. It is evenly divisible by 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360. That is 24 factors! I know, you must be as amazed as I am!

The year is roughly 360 days long. And one lunar cycle (a moonth) is about 30 days long. So there should be 12 equal months in a year. Since the motion of Earth around the sun (year) is not physically related to the turning of Earth about its axis (day), these numbers are not related nor accurate enough for our level of time-keeping. But for the Ancient Sumerians, Babylonians, and Egyptians- it was close enough. It allowed for accurate planting and sowing times as well as creating a detailed map of the night sky and motions of the sun, moon, and planets. 

This flexibility is why a circle is defined as 360°. It could have been defined by any number you choose. The ancient Babylonians had a number system based on 60 opposed to our decimal system (based on 10). So they chose 360° for a circle as it is evenly divided by 60. Things would still be the same if the circle were defined with a different number of degrees, like 100, but it would not be as easy to divide. 100 only has 9 factors (1, 2, 4, 5, 10, 20, 25, 50, 100). So 360° is easier to make calculations from than if you defined a circle as 100°. In our current system a third of a circle is 120°. It would be 33.3° using the 100° system. 

There are some times when using degrees doesn’t fit in with the best way to work with a circle, so you can use radians instead. This incorporates how the circumference of a circle is related to its diameter (C= πD). 360° is equal to 2π radians. If you have a circle with a radius of one foot, you would travel 2π feet around it.

And where I like 6 because of its versatility, I am also intrigued by numbers like 7 for their inflexibility. Prime numbers, those numbers that are not evenly divisible by any integer but themselves, are also pretty cool. One would think that something that is as unique as a prime (1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, …) might not have many uses, but there are many times we use primes.

Each time you make a secure online purchase, log onto a website, or use mobile banking, prime numbers are working behind the scenes to protect your personal information. It’s their uniqueness that makes them so valuable for computer encryption and data storage.

While encryption uses prime numbers, computers themselves rely mostly just on one prime- the number 2. Binary systems are what make our modern electronics work so well. A computer chip has tens of billions of transistors that can do one of two things. They can either be on or off. Those two states represent the binary digits 0 and 1, called bits. Eight bits make up a byte. But combine the output of those transistors and one can make logic gates that create situations like the letters showing up on the screen as I type. Or they may display the answer of 4 when you type 2 + 2 into your calculator.

Since everything is base two, the memory and operating systems display this when you buy a computer or phone. When I first used a computer, it had 16 MB of RAM. This is the computer’s working memory. Memory storage is separate and would be larger. 16 MB is 16 million bytes doing the calculations. As computers became more advanced and powerful, 16 MB went to 32 MB, then 64 MB, then 128, 256, 512, and 1024 MB or a gigabyte. 16=2⁴, 32=2⁵, 64=2⁶, 128=2⁷, 256=2⁸ 512=2⁹, 1024=2¹⁰. It all goes back to that prime number, 2!

Today, most computers you use will have at least 32 GB of working memory. This means an average computer today has over 1000X as much RAM as my first computer! Memory storage is typically measured in terabytes now. My first floppy disks (~1983) could hold 160 KB. So I would need almost seven million floppy disks to equal the memory storage of one typical computer today. 

So what am I trying to tell you with this story of calendars, circles, and computers? The power of numbers is astounding! While most of us don’t think much about why we use “weird” numbers like 360 or 2, their ability to organize our observations and ideas is infinite.

We often think of numbers as just symbols, but they have shaped civilization. They determined how ancient people measured the heavens, how we tell time, how engineers divide a circle, how computers store information, and how your bank protects your account today. Behind nearly everything is a number that happens to be especially good at its job.