Macro

It's the week between Christmas and New Year's Day, and while I have many Christmas photos to post, I have also enjoyed extra time to work on another part of my hobby- macro photography.

The following pictures were taken of our table centerpiece using a reversed 50mm lens on extension tubes.





[Editors note: These photos are uncropped.]

Rainbows

There are 10 kinds of people in the world...

... a note on binary.

Our normal decimal system is a base 10 system, meaning that each digit represents 10 to a different order of magnitude. We learned in school that there is a ones place, a tens place, a hundreds place, a thousands, place, etc. Each of these places can also be represented by the number 10 raised to an exponent. The ones place is 10⁰, the tens place is 10¹, the hundreds place is 10², the thousands place is 10³, and so on. (This is also true for the tenths, hundredths, and thousandths, places, except 10 is raised to the -1, -2, and -3 powers respectively.

The digits in each place are then multiplied by that base, and added together.

Let’s use 1234 as an example. Here are several different ways of writing it out:

1234 = 1234
(1 x 10³) + (2 x 10²) + (3 x 10¹) + (4 x 10⁰) = 1234
(1 x 1000) + (2 x 100) + (3 x 10) + (4 x 1) = 1234
1000 + 200 + 30 + 4 = 1234

Each digit can only be 0 to 9, since 10 or more would carry over to the next place.

Now take those principles and apply them to binary. Binary is a base 2 system, so each place can be represented by the number 2 to an exponent: 2⁰ = 1, 2¹ = 2, 2² = 4, 2³ =8, etc. Instead of ones, tens, hundreds, and thousands places, we have ones, twos, fours, and eights places.

When writing a number in binary, each digit will only be 0 or 1, since 2 or more would carry over to the next place.

In binary, the decimal 2 is written as 10. The 1 digit is in the 2¹ (twos) place, and the 0 digit is in the 2⁰ (ones) place. Multiplying out like we did before, we see:

10 = 2 (decimal)
(1 x 2¹) + (0 x 2⁰) = 2 (decimal)
(1 x 2) + (0 x 1) = 2 (decimal).

The decimal 13 would be written as 1101:
1101 = 13 (decimal)
(1 x 2³) + (1 x 2²) + (0 x 2¹) + (1 x 2⁰) = 13 (decimal)
(1 x 8) + (1 x 4) + (0 x 2) + (1 x 1) = 13 (decimal)

This can be done using any base. Another common base is 16, referred to as “hexadecimal”. However, in order to use single digits, the decimals 10, 11, 12, 13, 14, and 15 are replaced with A, B, C, D, E, and F respectively. Remember the digits for any base may only go from 0 to one less than the base, so hexadecimal digits go from 0 to 15, or more appropriately, 0 to F.

For practice, solve the following problems and check your answers in the back of the book...

(Just kidding.)

Vision

Every few months (or weeks, or days) it seems I find myself looking at a new lens, thinking that if I only have one more, I will be taking better photographs. Before I left on my trip, I found a few new pieces that honestly did make my life a lot easier while traveling, however most of the time this idea is just an illusion. I have been doing well for years with what I already have, and I often return to the same pieces of equipment over and over again.

I was reminded today on a photography blog that good photography is all about capturing the vision of the photographer. The best equipment in the world is useless in the hands of someone who lacks an artistic perspective, and the simplest, most inexpensive cameras can be used by a master to great effect. The right camera and the right lens do not make excellent photographs, they only make it easier for the photographer to do his work.

This is true in our relationship to God. In his hands, the most inadequate of us is wholly useful for accomplishing his purpose. At the same time, without his masterful touch, those of us who think we are the best and most capable cannot accomplish anything of value. Our value is not in what we are, but what he makes of us. It is his vision and how he uses us that makes all the difference.

Summertime

Happy Birthday Dad (Grandpa)

Why hasn't Adam blogged in six months?