These are a few of my favorite things

I hate it when a website gives asks you for security questions.  They are things like:

What it your FAVORITE band?
What is your FAVORITE  color?
What is your FAVORITE sports team?
etc.

I generally don't have favorites.

Except I do have favorite girl.

I suspect Julie Andrews had this problem as well.  When she sang her famous song in The Sound of Music, her list of  "favorite things" was rather long, leading me to think she had no real favorite things as well.

As for me, I don't have a favorite color, high school teacher, vacation spot, band, sports team, etc.

I may perhaps have a favorite piece of music (Pachelbel's canon in D major), but since I haven't even listened to that in a while, I'm not sure it's true.

But then, the other day, I was reading someone's facebook post about how to calculate exponentials.  As I was playing around with that, I calculated 2 to the 1/2 power, and there was may favorite number--well one of two favorite numbers (they go together).

√2 and √0.5

Or, to round to 3 decimals:

1.414 and 0.707

Such fun numbers to play with.

   √2 = 1.414; 1.414² = 2

   √0.5 = 0.707; 0.707² = 0.5

   0.707 + 0.707 = 1.414

   1/1.414 = 0.707

   1/0.707 = 1.414

   cos(45) = sin(45) = 0.707

   RMS = 0.707 * peak

   Peak = 1.414 * RMS

These two magical numbers are memorable to me because the play into some interests of mine: soil science, map making and electronics.

My favorite numbers and soil science

When I was a freshman at university studying for a degree in forestry, I had to take a class in soil science.  Soil Science?!  I didn't know there was such a field of study.

The professor who taught the class was known for his love of teaching about soil.  I carried on with some of his techniques in my later years.  But one of the things he stressed was how, when we took shortcuts across the grass, we contributed to soil compaction which led to the death of the very grass we liked walking across.

I was a good student.  I quit (taking short cuts).  I lost walking companions because they wanted to shortcut and I didn't.  But I was a very fast walker and still beat most people going across campus.  So how much further did I actually go? (To answer this I reach into another interest area of mine, map-making).

Your most basic short cut involves taking the shortest route to evade a 90 degree corner.  In the diagram below, assume you are going from A to B.  The sidewalk follows the path a + b.  The shortcut follows path c.

The basic nature of this shortcut involves a 45-45-90 triangle, where A and B are both 45 degrees and C is 90 degrees. We'll assume that the shortcut (c) has a length of 1.  To calculate the length of side (a) we can either use the sine of A or the cosine of B, which is that magical number 0.707 (the square root of 0.5) and multiply it by the length of (c), which in this case is 1, so we can just leave it alone.

You can double-check these with the Pythagorean theorem

a² +b² = c²

(√0.5)² + (√0.5)² = 1²

0.5 + 0.5 = 1

The shortcut length is 1
The long way is 0.707 + 0.707 = 1.414

So the shortcut is 1/1.414 or 0.707 times the distance (70.7%) of the long way.
or, to look at it the other way
the long way is 1.414/1 or 1.414 times the length of the shortcut.

Now, not all shortcuts are created equal, some involve a greater and some involve a lesser amount of distance savings.  But one could estimate that by NOT taking shortcuts, I walked about 41% more than my peers who did.

My favorite numbers and electronics

I used to tell people that I got my first license when I was 15.  Of course, I would leave out the fact that this was a ham radio license and not a drivers license.

To get a ham radio license, I had to study a bit of electronics.   This was in the day when our radios might not have even had a single transistor in it, let alone a chip.

One of the things we studied was waves, such as one might have with AC (alternating current).

Here in Thailand, our voltage is 220 volts.  But what does that mean?  Since with AC current, the voltage varies over time in a pattern call a sine wave.

If the voltage is the path of the blue line, then you can see it varies from 0, up to some peak value, then back to 0 again.

To measure the voltage of these AC currents, we use a value called the Root Mean Square or RMS as an average.

The RMS is 0.707 time the peak value.
Or, to look at it the other way,
the peak value is 1.414 * the RMS value.

So here in Thailand where the voltage is 220, the peak voltage is actually 1.414 times that, or about 311 volts.

And there are my favorite numbers, once again.

While it may almost seem like magic how these numbers pop up in different places, it should not be surprising that there is an order or pattern to these things. Scientists, mathematicians, engineers and many others can do amazing things because there are fundamental laws or principles that govern how things work.  And while we may not totally understand the "why" behind all these laws and principles, we can still do things like launch a satellite and have it intersects with a small moving target like Pluto, many years and several billion miles away.  We can build planes that fly in the sky and huge steel ships that sail in the sea.  We can build wrist watches that run a very fancy computers powered by minute amounts of electricity or that use very precise gears and require no electricity at all.

We read in Colossians 1:15-17 (NLT)
¹⁵  Christ is the visible image of the invisible God. He existed before anything was created and is supreme over all creation,
¹⁶  for through him God created everything in the heavenly realms and on earth. He made the things we can see and the things we can’t see— such as thrones, kingdoms, rulers, and authorities in the unseen world. Everything was created through him and for him.
¹⁷  He existed before anything else, and he holds all creation together.



God, through Jesus, holds all creation together.

How does He do that?

One of the ways creation is held together is by the universal laws and principles that we so often take for granted.

But these laws and principles aren't there so that we can boast in ourselves when we figure them out.  They are there so that we will marvel at the Creator Who put them in place.