Tuesday, December 9, 2008

The High Order Bits

In the number 1375, 1 is the most significant digit and 5 is the least significant. When doing mathematical operations you can do some funny magic by being inconsistent with which end is most significant, as illustrated by the Kettle's:







We actually do this in computer science all the time: given the two bytes 0x0200, we can get very different numbers depending on if the first byte is most significant (it's 768) or the second (it's 3). It turns out that some computer hardware always treats the first as most significant, and some computer hardware always treats the last as most significant. This is known as Endianness and we talk about "big endian" and "little endian" to refer to the two systems. It is absolutely essential that we are careful to make sure that all operations are done in the right endianness. If we're inconsistent, bad things happen.

Another interesting aspect of the Kettle's little performance there is that they are 100% convinced that they are right, and that their son is left speechless -- astounded at what is happening.

Unfortunately, each of us runs into the same situation nearly every day (the frequency is increasing at an alarming pace): someone expressing a point of view which is arrived at by swapping the importance of things, and which too often leaves us dumbfounded and speechless due to their ignorant confusion. What does one say when presented with an argument that is clear and precise (like that of Pa Kettle's) and in which the presenter obviously completely believes is sound and true and correct, and yet we know that they are totally off base? Further, what do we do when we discover that presenting the truth is like trying to straighten out Pa Kettle?

Often, my response is like Pa's son: try a couple times, realize the situation I'm in, and throw up my hands. But what should I do when the topic is an important one? What if the topic is one of critical importance to my country? to my family? to my finances? to my friend's health?

The long-term solution is education. I'm not talking about education regarding the things that are taught in our wonderful primary schools (reading, writing, 'rithmetic, etc.), I'm talking about education regarding 1) things as they really are, and 2) critical thinking skills. Part of this blog is an attempt to stand up and contribute to the educated-ness of the people in this world. But what about the short-term? When a significantly large portion of the population is making arguments like the Kettle's, on topics that are pressing and relevant in our day, what is one to do?

Nobody is "Blind"
From centuries ago comes the philosophical question: If a man is born blind, does he ever really know what it means to be blind? I'm not talking about people's eyeballs here, I'm talking about the "eyes of their understanding." How do we correct the confusion in the world that occurs when people do not realize they are blind?

Personally, I do not believe anyone is totally blind: I believe that all people have the potential to see. But many people do not realize that they are not doing their math right, arriving at bogus solutions via arguments which invert priorities, confuse endianness, and are inconsistent. And how to correctly teach the Kettle's the truth when they have been so well indoctrinated by faulty math? It is easier to educate than to correct mis-education, and it's especially hard when urgency comes into play.

The Good and the Better

There is a lot of merit to the saying that "the Good is the enemy of the Best" but there's also much merit to Voltaire's notion that "Perfect is the enemy of Good." How do we decide which is the right saying to apply in a given case? Well, math saves the day again:

In the number 1375, the 5 is important: It contributes, it should be looked after, it should be taken care of, nobody should say ill of it, nobody should knock it, etc. But the 1 is more important. If you have to be fuzzy or imperfect on one of them, make it the 5 and not the 1. When we swap endianness arbitrarily, math like the Kettles' is the result. To Voltaire and the other wise folk I say: Do your very best on the important things, and be happy with "good enough" on the less important things. There are important issues in this universe, one's that shouldn't be knocked, nobody should speak ill of, etc. But if there are more important issues, than we need less ruckus about the less important ones.

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This post is not news to anyone, we all already knew these things. We all know that it's important to prioritize things and to get those relative priorities correct. This post is not a call for more prioritization, it's a call for people to start standing up for the things that really are most important. Many of the most important things are getting eclipsed these days by lots of noise and attention being given to less important things.

Today is the day for those who see things as they really are, to stand and teach. Teach the truth, and encourage people to sharpen their critical thinking skills -- we'll all need as much of that as we can get. Do not be afraid to say that "1 is more important that 5" -- assuming it actually is. There are people who disagree with you on what is most important. How does one know what is actually most important? That post is coming. But if you ask me, I'll tell you straight: 1 is more important than 5.

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