Religious ramble

Inspiration hit this weekend and I let it out... very rough, but I feared what would happen if I let myself edit too much on this one.  Hopefully more to come soon regarding my writing, both the experience with the novel and the direction I would like to head in next.  Also debating a brief, non-partisan discussion of certain terms and concepts, but it might be better if I have another four years to get that one together.

My Unique Message

The story of my faith, like that of any aspect of my life, is a long, and sometimes incoherent, ramble. Much like the scripture I hold dear, each part reflects important truths that can be used to instruct, encourage, assure or guide or, conversely, be taken out of context from the entirety to portray something completely different. Given my love of writing and passion for sharing those things most dear to me (from NASCAR to politics, Christian faith to charitable causes, once I get going, it is difficult to control the volume of voice and magnitude of hand movement until I have exhausted all I have to day), it has been a frustration to me that I have a message, a desire to share it and the capability to write with a love of doing so, and yet, I have no idea where to start. I have blogged on the errancy of the church in how they pretend to “love the sinner and hate the sin” and shared some of my own experience and views on faith in my novel, but both are only sound bites whose motivations were more based on life events demanding they be written than what was inside of me.

So I find myself asking, what is the message I am supposed to start with? Is it one of tolerance, like the blog post? This is something important to me and needed today, but I have done that and believe the next step is action more than additional words. Is it a message of forgiveness, endurance or compassion? I certainly can speak from experience on these subjects, but there are many who are more gifted in the methods of encouraging and motivating on these fronts. How about unity? One of the biggest problems I have seen today is division within the church on things that matter little and lack of focus on the important points we all agree on. But again, that is far from my area of expertise and thus, probably not where I am supposed to start.

This is where the major revelation comes in and I have the answer. Except that really it is where I come up with something that is not obviously wrong. The place that seems to me the best starting point is that which is unique to me. Because anyone who knows me, knows I AM unique; some call me “Sheldon”, after the uber-genius, socially inept character from Big Bang Theory (while I must point out that I am more creative and romantic than Sheldon, I must also concede the unconventional thought processes and autistic tendencies that make those things the exceptions that prove the rule); more often than not, I miss non-verbal cues that everyone else gets, am oblivious to subtleties in flirting and tend to take things far too literally. Given that, some part of me feels that any message too personal and specific to me might be totally irrelevant to most people. But it is that very thing that makes it a message I am uniquely qualified to share and I can only hope and pray it has application to someone else.

The Skeptical Approach

I have a tendency to accept nothing as truth until I have checked it out for myself and to question all motives (others' and my own) for the conclusions we reach. This has led me to change political and economic philosophies, move much closer to the Calvinist end of the spectrum and become convinced that I am never to be too certain of being right (as well as being fully convinced that those most convinced of being right are least likely to be so). It is not an easy trait to live with, as any change of religious or political philosophy is akin to treason from the perspective of those who still maintain those perspectives and at the same time, there is a certain comfort in a consistent identity with an ideology that a constant search for truth preempts. It also means a greater need to always be credible and certain that natural biases are dealt with and conclusions can be backed up with confidence.

One of the best examples of this for me is the Armenian-ism - Calvinism debate (I bring it up here not to convince the reader of my own conclusion, but to illustrate how I approach these kinds of questions). I was raised to believe in a Free Will dogma, that God did not create us to be robots and that He would not force us to come to Him any more than He would predestine someone to be lost; I not only was indoctrinated from childhood to believe this, I found it fit well with my sense of “fairness” and self-determination that so fit with the conservative American principles I knew and valued. My problem with it was that many intelligent Christians disagreed with it. I had to find out for myself and decided the best way was to read the Bible with the intent of discerning what each author believed.

I expected the end of my research to come down to a weighing of evidence, where my interpretations of each author put them at various points along the spectrum; what I found was that I could not find a single New Testament author who did not at least come close to the absolute extreme position in favor of Calvin; they all seemed to believe that those who were saved came to that salvation by being predestined, called and saved by God's grace – none who was lost had it in them to even seek God on their own or accept His word upon hearing it without intervention on His part; Old Testament readings fed into this in some instances and none went beyond neutral on the subject. My lifelong belief was shot down and despite my need to believe otherwise in the name of what I thought was right or fair, I could not object to those who knew Christ firsthand and whose messages, when approached without agenda, seemed to indicate the opposite of what I believed. And eventually, I gained new perspective on all of it by opening myself up to truth that was at odds to what I wanted to believe (one insight I gained was that if we were all truly free to choose, the only logical choice would be the one that leads to life, but since all do not choose that, we must be without free will in our bondage to sin and thus can only be free to choose otherwise through some action on God's part that has nothing to do with our own will or action).

I will stop there before I get too far down the rabbit trail and forget where I am supposed to be going.

In the search for truth, I have studied scripture and science, commentary and text, academic and lay/pop targeted writings. I can not call myself an expert on either front, but neither am I a slouch. I have read various translations and tried to learn a little about the original texts on the biblical front; in science, I start easy and dig deep, then start on something over my head and do the background research to be able to grasp it. Before I get to the final intellectual conclusion of this search (“conclusion” being a word used very loosely), I must diverge into what I have seen of my own basis for faith and the rationales I have heard from others.

Neil de Grasse Tyson once wrote of a concept he calls “God of the gaps” (a concept I do not believe he invented, but one he expresses very well); while I do not agree with him on the subject of religion and see in him an illogical animosity toward the God he claims to doubt the existence of, he makes a valid point on the way in which we erroneously conclude a need for God. In short, he says that our need for God begins where our understanding of science ends. Before we understood the way orbits worked, we proclaimed that God must hold the planets in place (something with a Biblical basis, depending on how literally you apply certain verses); once we had gravity down, we found it to be unstable enough to need help... until we learned that the orbit of the planets were elliptical; once we got that down, we needed God to intervene where the gravitational forces of the various bodies caused problems... until we figured out how to solve the three-body problem. And that is just three steps along the way in figuring out one tiny sliver of how our universe worked. I heard (and still hear) people exclaiming how they know God exists because they see a tree and know someone created it or they know God exists because he put the Earth in a perfect place with perfect conditions for life, without understanding that life exists in volcanic ocean vents that are dark and hot and exists in arctic cold, dry and wet, all extremes found on our planet; wherever life springs forth, it does so in a way suited to its environment, not because it had an environment suited to bringing life.

Why does any of this matter? There are two reasons.

First, such teaching is a stumbling block to those who are educated, or at least intellectually inclined toward understanding science. Though most of us (science nerds) excuse a non-scientist thinking that the big bang was supposed to have happened when two Higgs Bosons collided as a harmless inaccuracy from one trying to keep up, some of the inaccurate claims and straw man arguments from Christians send a message that the Christian faith is only suited to those with limited knowledge (especially those that ridicule complex science from an oversimplified perspective); if the proof of God's existence or the flaw in contrary theories is based in a false premise, what use is Christianity other than as a myth to placate the uneducated?

Some in the church might care little for this consequence of their statements, as many in the upper reaches of scientific work will not be reached regardless of our sensitivities in the public discourse. Some might say just as well, as they would just as well not have to associate with “Sheldon” in church (though I do not claim these people are the majority, I know for a fact they exist in not-so-small numbers). For such people, I throw out the second problem in God of the gaps theology, which applies as well to taking too hard a stand on whatever the current scripture vs science debate is.

For Galileo and Copernicus, evidence that all the bodies of the heavens did not orbit the Earth went contrary to church teaching and could mean punishment as severe as death. In the latter case, he kept his mouth shut, in the former, he went on trial. In both cases, what they believed went against contemporary interpretation of scripture and in favor of scientific inquiry; that belief is one that science has held firm on and Biblical interpretation has shifted to accept (and yes, I know that the interpretation of that time did not agree with earlier interpretations; we easily accept our current interpretation as the only one, while wondering how stupid people must have been to take “it [the Earth] shall never be moved” as a literal declaration that the universe revolved around us, without considering what future generations will think of us). Today, there are debates over the age of the Earth, evolution, cosmology and even environmental issues that pit the Bible against science (sadly, some will argue for a 6000 year old planet without knowing where that number came from or any arguments for or against its accuracy; some will even insist that the Bible says it is so; but again I diverge...). Beyond what these debates say to the intellectual seeker, they also place the faith of believers on shaky ground (a subject I undertake without reference to the previously mentioned Armenian-Calvinist debate); if belief in God depended on the Earth being flat or the Sun and planets orbiting it, then when that debate is done away with and the opposite is shown to be true, what happens to the reason, need or argument for God? If belief in God depends on Him making the Earth in the perfect location for life, then what happens if we discover life on Mars or Europa or some less “perfect” place? Do we really want the faith of our children to be based on an absolute stand on shaky science after so many centuries of Biblical interpretation shifting to accept new discoveries? I would argue that at a minimum, we should admit our uncertainties on these points and take the unyielding positions on such things as God's omnipotence, the free gift of salvation and who wins in the end.

God of the Gaps Revisited

Hopefully, the science vs religion rant has not set so much of a negative tone as to miss its original intent, but it is part of “my” story and provides background to the conclusion, because now that I have shot holes all in the God of the gaps approach to religion, I hope to patch a few of them (but not so many as to excuse that form of apologetics altogether).

I hate to use tired cliches (more than the reader can know), but when it comes to the issue of proof and God, you can no more disprove Him than disprove unicorns. No matter how many places you show a unicorn not to be, there are always more places to look; no matter how many things science explains a method for that does not require a deity, the lack of need for one does not demand that one not exist and just because the planets orbit the sun in accordance with Newtonian physics (with the adjustments made by Einstein) does not mean that God does not have His hand on them, moving them in a way that looks like physics, or (more to my liking, which means nothing) that He did not create the Universe to act in accordance with physical laws He created. Either way works.

And so, my short answer comes out here: intellectually, I find the odds of God to be 50/50. No matter how far down I go through Newton and Einstein, into quantum physics and string theory, I find that at any point, God has just as good a chance of being in the mix as not. Having no knowledge that takes us around the next bend at any given point, it is just as likely that two m-branes coming in contact sparked the big bang as it is that God set it off (I know that giving God a 50/50 chance of having intervened at any point along the line actually gives him an extremely high likelihood of having intervened at some point, 1 – (0.5)^n, to be exact, but I will no more get into that than I will enter into the semantic argument over chance being the nothing that something supposedly came from). There is just no way of knowing and at some point, we are so far out of our own reality for causation that all bets are off. The only point I want to make from this intellectual conclusion is that I am very suspect of so-called scientists who are open minded on most subjects being so militant and angry in their objection to God's existence (as in the case of NdGT, mentioned earlier).

So with even odds using only logical means, do we just flip a coin or take Pascal's wager (which in itself is flawed, since it does not address who God is if He does exist and therefore has no answer for whether Judaism or Islam, protestant Christian or Catholic or any of the polytheistic religions are correct)?

In my case, since it takes little to tip the scales when started at an even balance between God and no God, all I need is anything, no matter how insignificant. But I find so much more, though I must admit upfront, that much of what I find is imperfect and personal in nature. I make no apology for this.

Beauty is Truth

Where a look at two or three failures in God of the gaps theology might convince one of a pattern of that line of thinking failing and thus lead them to abandon any call for God to fill in the blanks, I find something else. I find beauty in the way it all plays out. But even more, I find opportunities for science to illustrate His work.

I just heard a sermon that used the weaving metaphor for God's creation and find it fitting in relation to the development of scientific knowledge and belief in God. Where we might have had a simple rough weave of creation that left us with a choice between a simple scientific theory and a simple creationist theology, what we find is increasingly intricate detail at each level with reflections of God manifesting at each; while the threads become ever more fine and higher in count, His filaments are always present if you look close enough. For instance, if Newtonian physics worked all the time and atoms were the basic building block of everything, it would be easier to settle on science, as all the answers would be there and lack nothing for God to fill in; at the same time, the arguments against faith would be fewer – it would only take crediting God for atoms and simple physical laws to get there. Of course, if Newtonian physics did not work and improvement on the math was deemed impossible, the opposite would hold true.

Einstein, when faced with the probabilistic nature of quantum physics is said to have proclaimed, “God does not play dice” and I commented earlier on arguments I have heard about the “chance” that is supposed to be the nothing that everything came from being logically inconsistent. But both play out well and seem to be proven time and again in scientific experiments (as well as such inconsistencies as wave-particle duality and the ability of quantum particles to be in two places or two states simultaneously); both also throw a wrench in the deterministic argument that classical physics sought, while leaving the door wide open for divine intervention; what if the “chance” or “probability” that science says rules all is actually the hand/will of God (I do not propose that it is, as this leaves open the same false basis for faith that I eschewed earlier; I put this forth as a small part of a bigger picture that I find necessary to move from the agnostic fulcrum that our knowledge leaves us with)? As another example, go a couple steps beyond the atomic level and you find that the subatomic particles many of us were taught as being the basic building blocks for all (specifically protons and neutrons) are made up of quarks; it takes three of these quarks (two of one kind and one of another) to make one of these particles, which have specific and similar masses. But these quarks, by themselves, have no mass; they appear to be just bundles of energy that can not exist outside of these special combinations; to me, this sounds like something coming from nothing, that concept both offensive to those who don't believe in chance and yet key to the Genesis creation. All of this energy, force without mass, combining in ways that create mass, making up the universe (in my imperfect understanding of current physical models, this is where the Higgs Fields, of which the famous Boson is a less than critical component, comes into play, with the interaction of particles and field creating mass), it has echoes of God speaking the universe into existence, the breath He used to bring us into existence the energy, His words the field that brings it all together and the fact that there is no end to it all appears to me as the fingerprint of the Creator who spoke to Job of how lacking he was in understanding the great mysteries to which God was privy.

Following this line of thought one step further into the building blocks of the universe, if everything is made up of different frequencies of vibrating “strings”, then once again, we have a singular building block (breath of a single God?) operating in different ways (words of that God) manifesting in every trace of mass (omniscient) and every force (omnipotent).

Must it be this way because it fits? No. All of these theories are secular in nature and exist independent of God. But my heart says when centuries of scientific investigation show a universe that winks at me with the fulfillment of Biblical truth at every level of inquiry, it can not be ignored. Science does not disagree, either. John Archibald Wheeler, the scientist credited with the discovery of black holes, believed that they must exist because they can. He theorized their existence, proved the math and only later was shown to be correct; in fact, we can't see black holes and must conclude their existence and location by the observed effects (which were theorized, also), but still, these exotic entities, which break most of the laws of classical physics, were believed to be true because of the elegant truths that came along with them and were accepted as proved because the predicted effects have been observed and shown to fit the model (Wheeler also tells of the possibility of particles moving back and forth in time throughout the universe, which means you can add eternal to the adjectives for God's word and breath to the list given in the last paragraph). The Higgs Boson was important for the same reason: its existence at a certain energy level fit perfectly with a beautiful model of physics that called for a Higgs Field that included such a boson; string theory, too, is ardently supported by a group of mathematicians and physicists because of the way it so perfectly fits and explains all, despite the fact that many think it is an impossible theory to test (putting it squarely in the same boat with God... except that God actually has personal implications). Ian Stewart (in the book from which I stole the title as the heading for this section) also comments on the beauty of patterns in nature and the way certain numbers and symmetries occur.

So, I do not place my faith in any of the things I have said, but I have found the beauty of God's character, His hand, His work, in all I have learned. There is nothing to disprove, as I don't care if something new is discovered to explain quarks; in fact, I believe that whatever it is will show some piece of God in how it works. It is fine with me if strings do not exist or if they are made up of yet another particle, wave or whatever. God is in the gaps and has created endless levels to the physical world that we might never get to the bottom of it all.

Beyond the Science

Many use their personal experience as their primary evidence for God. Internally, I can do the same, but again, my intellect and understanding of cause and effect leave me skeptical enough of others' perceptions and anecdotal evidence to do the same. I know that human emotion can be shaped by belief in something that does not exist. I know that these emotions can have effects on behavior and attitude that can bring about positive changes in both attitude and life outcomes. Even having experienced manifestations of a pentecostal (or holy-roller) nature, I know that we can cause ourselves to pass out, our hearts to race, our eyes to tear, our minds to become confused and even medical science has proven a placebo effect that can not be explained by current biological, chemical and physical knowledge (whether with or without a religious belief).

But I still do not do justice to the work of God in my life if I ignore the personal aspect completely.

I have seen healings and I have seen unanswered prayers whose purposes were only later revealed; these have helped my faith, if they neither proved it nor were necessary to it. There have been relationships restored, forgiveness brought about and emotional healings delivered, all of which count as more to me than the physical prayers and border on being sufficient for me, whether they mean anything to anyone else or not; still they are not necessary to my faith, nor do these miracles sustain my faith long enough to make a lifelong difference. I have even seen events that I (with a graduate certificate in statistics and skeptical approach to the use of coincidence as evidence for the supernatural) can not allow credit for to go anywhere but God; these really help to keep me believing, but given time enough without them, they fade. I have to admit that the anger of many atheists (and the fact that so many supposedly intelligent and rational people prefer that title to the agnostic label that they finally concede when backed into a corner) also serves to build my faith; there must be something or someone there for that anger to be focused on; but still, that is a weak premise for such a significant conclusion.

No, after I finish with the logical inquiry and proceed with the more liberal intellectual inquiries into what fits and what seems right and review all the evidence in my life's story, I still struggle and feel that God would not have me pretend that I do not. He created me, He knows me and He is no fan of hypocrites. Perhaps my struggles have been a “thorn in the side” such as Paul had, either to keep me humble (very possible) or to keep me sympathetic to others who struggle – maybe both.

Finally, as much as I would like to ignore the bedrock of my faith here and know that it is the hardest of all to explain, I know I must go there.

When, at my lowest points, when I least feel the presence of God and am least convinced that He even exists, I know that He forgives my doubts. It sounds ironic that a God whose existence is called into question can forgive, but it is the most real of all to me and the most rational. In the end, it brings me back around to Him. Faith is a gift of the Spirit, given by God; if faith lacks, then it is reason to ask to be granted more; if faith is a weakness, it is more evidence of His love and faithfulness that it is not precondition to His acceptance of us.

Maybe no one will understand, but it is the message I have and am most qualified to give.

A story of money

This is a presentation done as a piece of a larger project explaining the differences between macro and micro economics, based on my own limited knowledge of the subject.
The original was done in odp format and then exported as a swf, so the animations and slide transitions are not present in this version. Any feedback is welcome and I hope (as in many other things) to get some more work done on the subject in the future.
If the file does not open when downloaded (or asks which application to open with), any browser should be able to view it.

Work in progress

Working on a flash or presentation based math tutorial, but thought I would paste one of my early attempts at conveying one way a conceptually based math brain sees things...

Visualizing percentages

The big little numbers and their exclamatory friend

aka...exponents and arrows and the math nerds who love them.

Is 4000 a big number? How about 1.2 million? 632, 415, 906, 255? What about 10¹⁵? As this is obviously a trick question, even the non-mathematic are likely guessing that the last of these is the biggest. Ten to the fifteenth power is a sixteen-digit number (as compared to the 12 digits of the next largest number mentioned above). Knowing that still doesn’t give a fair representation, though. Which seems larger: 1,000,000,000,000,000 or 10¹⁵?

Of course, neither really means anything to us.

Multiple exponents can make even larger numbers seem small. How big is (10³)x(10³)? Or (10³)³? How about 10^3³ (the ^ means to the power of, so 10^3=10³ and 10^3³ just means raise 10 to the 3³ power)? How do these two number compare to the numbers at the end of the last paragraph?

First, 1,000,000,000,000,000 and 10¹⁵ are the same; anytime you raise 10 to a power, the result is a one with that number (the power) of zeroes after it. When multiplying a number to a power by the same number to a power, add the exponents ((10³)x(10³)=10⁶ or 1,000,000). When raising a number to a power and then raising the result to a power, such as (10³)³, you multiply the exponents. So (10³)³ yields 10⁹ or 1,000,000,000. Finally, raising a number to a power that is raised to a power, the power in the exponent must be done first (following order of operations), so 10^3³ is 10²⁷ or 1,000,000,000,000,000,000,000,000,000. So minor changes in the use of these little numbers (the exponents) or movements of the parentheses can make a huge difference in the scale of the result. We can also represent unwieldy numbers in very small notations through careful use of exponents. In addition to the notations used above, the up arrow, ↑, indicates an exponential use of powers, such as 10^(3↑↑3) (this is Knuth’s up-arrow notation, for those who care) means 10^(3^(3^3)), which is 10^(3^27) or 10^7625597484987. This number is a one with over 7 trillion zeroes after it, which I represented with four digits, three arrows and a pair of parentheses (and only then because I wanted to keep using 10 to a power and used threes to keep the final exponent small enough to show here. The addition of a third arrow does not mean a third cubing of the 7 trillion digit number; instead, it means to do the double arrow operation three times: 3↑↑↑3= (3↑↑(3↑↑3), which is 3 cubed 7625597484987 times (a number far too large to represent in any form other than that already used here). Multiple arrows, even with small numbers, will yield numbers that have minimal, if any, use.

Taking our extreme number game a step further, Graham’s number is a number that makes creative use of the up-arrow notation. First, calculate 3↑↑↑↑3; this will be called g(1). To calculate g(2), calculate 3↑↑….↑↑3, with number of arrows between the 3’s being equal to g(1). Of course, remembering what 3 up arrows did to the threes in the previous example and the fact that an additional arrow means to do the triple arrow operation 3 times (3↑↑↑(3↑↑↑3), which is unwieldy when reduced to the already impressive double arrow notation. So, if g(2) is a pair of 3’s with g(1) arrows, this number is not only large beyond imagination, we cannot even comprehend how large the result is in comparison to g(1). Moving on, Graham’s number is g(64)….that’s right, a mind blowing ratio between mind blowing numbers 64 TIMES! Ridiculous!

So, The Math Factor (broadcast on KUAF, an NPR associate, and available on podcast) had a contest to see who could express the largest number on the fly. The contestants (Agustín Rayo against Adam Elga) took turns one-upping each other until Rayo introduced us to the number now known as Rayo’s Number. Simply put (sort of), Rayo’s Number is the smallest number larger than the largest finite number that can be expressed in the language of first order set theory (common math and logic symbolism) using no more than a googol (one with one hundred zeros after it or 10^100) symbols. A bit of a cheat, but the winner of the contest.

Math Factor Website

Lumberjack music

The logarithmic scale, which few of us think we understand and most of us kind of do...

First a math joke...what is another term for lumberjack music?

Logger rhythms...

Now on to the column...

How large a number can you comprehend?

The answer to that question really depends on how you define 'comprehend'. This may seem a little like what the meaning of 'is' is, but the distinction is important here.

We all can focus on one object (whatever that object is) and follow its movement and characteristics easily. Two objects are also fairly easy for the human brain; beyond three, we are very limited in our ability to track dynamic objects, unless we group them, such as the 11 players on an NFL team. For four or five objects, we must continually shift focus, as we are unable to track them all simultaneously.

But for static objects, most of us can easily count five or six (or more) on sight and perceive the difference in quantities at this level without taking the time to count them. So already, we can see that our mental ability to comprehend a number depends on whether we want to be able to follow these objects' activity or just count them quickly.

Beyond single digit numbers, we do fairly well in games that require us to remember the location of specific items (think matching games like concentration). Going on to three or four digit numbers, most of us can comprehend how tightly we need to control our money if we go on a three day trip with two-hundred dollars in spending money or how far a thousand miles is. Up to the scale of one million, we can see all the individual components as well as the collection (there is a wall with one million tiny dots on it at the Science Museum Of Virginia in Richmond; you can step back to the point of seeing the whole wall at once and still be able to see the dots...take this much farther, say 10 or 20 million, and to back up far enough to see the whole thing at once, the dots would blur together). Of course, we can think of 20 of these walls, but we are again on a different scale of comprehension. Thinking of a trillion (a million million), we would have to think of each dot being another wall of a million, at which point, we still have some idea of the scale, but not in the same way we did with a million.

Thinking of this another way, you can perceive in detail what a foot of road looks like, down to the imperfections in the pavement. A mile is not too difficult to walk and can be driven very quickly and easily; though the two modes of mobility will yield vast differences in how we think of the distance and in the detail we notice in our surroundings during the trip. How many of us have flown across country in a couple of hours? It doesn't seem that far, but driving it gives us a different impression of what those three thousand miles consist of and walking it yet again yields a different perspective. Carry that out to man going to the moon and it changes again (consider that the space shuttle orbits the Earth in about an hour and a half-far faster than a jet and orders of magnitude above driving or walking). Yet all of these distances can be understood in some manner.

This is the logarithmic scale at work. When we are dealing with one, two or three things, each is very significant. At a scale of one-hundred, the individuals matter less-think of how much time you save walking when you cut to the inside of a turn versus how little it matters which lane you are driving in around a particular bend on a hundred mile drive.

At a scale of one thousand, even a few dozen are less significant. There is an economic theory based on this fact that talks of the decreasing marginal value of a dollar; basically, when you are very poor, an extra dollar may mean eating or not eating, the next dollar may mean eating enough to not feel hunger pains, while another may mean feeling satisfied...on up to the point where a dollar means very little or, for those of greater means, a dollar on the side walk is not worth the time to pick it up (they say that if you based the value of Bill Gate's time on his net worth, the amount on the sidewalk would have to exceed 10 thousand dollars to be worth his time to pick it up).

So what exactly is the logarithmic scale?

Logarithms are numbers that you raise 10 (or some other number, like 2) to in order to get a specific number. So if you think of a normal chart (say the time it takes fifth graders to run a hundred yards), you may see a scale of evenly incremented numbers along the bottom...say 10 second intervals. But a logarithmic chart would change in scale as you go from left to right. This is useful with data that has multiple events (or items) early on, but which stretches out very far. If you were to chart income, you would see that the vast majority are clumped around some range (say 20 to 100 thousand per year), but a scale using increments of 10 thousand would have to be very long to reach the billions (10 thousand goes into a billion 100 thousand times), but using an evenly incremented scale that reaches a billion in the width of a sheet of paper (and is large enough print to decipher) would require increments of 5 million or so and the first part would have all of the data. So instead, we might start with 10 thousand, then double to 20, then 40, then 80, 160, 320, 640, 1.2 million, etc, and a billion would only require 18 increments. We might also do this for time based events: say we dropped a million pennies in a field from an airplane and gave a prize to anyone who found one (or more). If the field was relatively small, we might have several finds in the first minute, more in the second and so on. After some time (the length of which depends on the size of the field, height of the airplane and number of people looking), we may have the same number of finds in an hour or day as we did in the first minute. Unless we have an organized archeological team working, we will likely have some left in the field after the first group gives up looking. Likely, pennies will turn up years later (assuming people still return to look occasionally), at which point, charting by hours or days might even be pointless. Perhaps the field will be abandoned for a century or longer and records of the penny drop will be discovered by future generations who actually do initiate a dig at the site (though at this time, the person maintaining the chart may be long in the grave, we will assume that the chart is found, scanned and updated by some future Indiana Jones.

Does any of this matter to the average Joe? Probably not, though if he read this column, he may be able to sound slightly smarter by using the term 'logarithmic scale' properly to his buddies in the bar. And it serves as a prelude to another column I am posting on large numbers.

Finally, for those who understand logarithms and like bad humor, there is a math joke involving Noah's Ark (as well as some other poor puns) here:

http://www.lhup.edu/~dsimanek/noahfool.htm

State of the Union Perspective

Check out this sampling of State of the Union quotes:

"When I visited this chamber last year as a newcomer to Washington, critical of past policies which I believe had failed, I proposed a new spirit of partnership between this Congress and this Administration and between Washington and our state and local governments...seldom have the stakes been higher for America. What we do and say here will make all the difference to auto workers in Detroit, lumberjacks in the Northwest, steelworkers in Steubenville who are in the unemployment lines, to black teen-agers in Newark a nd Chicago; to hard-pressed farmers and small businessmen and to millions of everyday Americans who harbor the simple wish of a safe and financially secure future for their children...To understand the State of the Union, we must look not only at where we are and where we're going but where we've been. The situation at this time last year was truly ominous...The last decade has seen a series of recessions...If we had not acted as we did, things would be far worse for all Americans than they are today...The economy will face difficult moments in the months ahead. But, the program for economic recovery that is in place will pull the economy out of its slump and put us on the road to prosperity and stable growth by the latter half of this year...Our current problems are not the the product of the recovery program that's only just now getting under way, as some would have you believe...because our economic problems are deeply rooted and will not respond to quick political fixes, we must stick to our carefully integrated plan for recovery...-The only alternative being offered to this economic program is a return to the policies that gave us a trillion-dollar debt...and unemployment...Now the budget deficit this year will exceed our earlier expectations. The recession did that. It lowered revenues and increased costs...We look forward to the enactment of a responsible Clean Air Act to increase jobs while continuing to improve the quality of our air...The Federal Government will still subsidize 95 million meals every day. That's one out of seven of all the meals served in America. Head St art, senior nutrition programs, and child welfare programs will not be cut from the levels we proposed last year. More than one-half billion dollars has been proposed for minority business assistance. And research at the National Institutes of Health will be increased by over $100 million. While meeting all these needs, we intend to plug unwarranted tax loopholes and strengthen the law which requires all large corporations to pay a minimum tax..."

Sounds like what we heard a few nights ago? This was from Reagan's 1982 State of the Union speech. I have my opinions on this (I agree with both of them for the most part; whether good or bad, most policy on such a large takes time for the impact to be seen), but the main thing that has stood out for me in the current debates is the lack of consistency. Most of my friends and relatives have different views than I do and I respect that. However, I find myself questioning the sincerity of many of the arguments I hear when they run contrary to those they exhibited under a different administration. If deficits are bad, then they are bad under either party; if large health care entitlements are bad, it doesn't matter who proposes it; if a president is held to account for a failed terrorist attack, this should apply to all presidents. Again, I am not trying to convince anyone of any point of view, only asking that all stop to consider whether they truly believe in a philosophy or principle or if they are merely trying to help their team by attacking the other side.

All of this is not said because of offense taken at the humor; I think both sides need to be able to laugh at themselves and politics as a whole. The context merely brought up something that I had been wanting to address for some time now.

A Fond Farewell aka What's in a Name?

It has been a while since I have posted. That does not mean that I have not been thinking. I have a very long list of ideas and a few partly written posts; I just have not had much time to write. Hopefully I will get a few more out on a regular basis, but I expect it to be more fits and starts as I work several at one time and occasionally finish multiples together. We will see....

On with this post...

What's in a name? that which we call a rose


By any other name would smell as sweet;

-Shakespeare, Romeo and Juliet

18 Feb 1930 – 18 Aug 2006

RIP, Pluto

On August 18, we marked the third anniversary of the passing of an old friend. On that date, five percent of scientists voted to pull the rug out under Pluto’s claim to planethood. This is not the first time this has happened. Ceres, discovered in 1801, was named a planet at one point. Later, the planets Pallas, Juno and Vesta (1802, 1804 and 1807, respectively) were added to the list. Over subsequent decades, several more bodies were found orbiting the sun between Mars and Jupiter, were named and given symbols in the manner of other planets. By the mid-1800’s, their number grew to the point that scientists had to acknowledge their definition of a planet was too liberal and had to be modified. At that point, the terms ‘asteroid’ and ‘minor planet’ came to be used for bodies in the asteroid belt, excluding the first four, which were still planets. Eventually (there is no definite time of death for them), the first four planetary homicides were committed by mankind. This took place through the delisting of them as planets in astronomical almanacs or alterations in nomenclature in such journals and in scientific observation.

Ceres, which went through several designations of planet, minor planet and asteroid (and was even given dual designation for a time), settled into what appeared to be permanent status as an asteroid until 2006. Ironically, it was in that year, simultaneous with the reduction in Pluto’s status, Ceres was once again elevated to minor planet. No one is quite sure if Ceres still carries the second designation as asteroid along with being a minor planet.

So why all the executions and exhumations? Scientists would have us believe it is all in the name of precision; we must be most careful and accurate in the way we classify. In fact, the careful precision is a necessary by product of practicality, born partly of shame from the lack of foresight that allowed us into this predicament.

If the total number of bodies sizeable enough to achieve a semi-spherical shape was in the single or low double digits, we could name them all planets and no one would say ‘boo’ (at least until we explored another solar system in which this was not the case). But, as going about things in this freewheeling manner results in a fairly large number of planets, with multiples sharing the same orbits, things get ugly in a hurry. So, we have to create constraints to bring the numbers back down. But is it necessary to rescind planetary status in order to do this?

It would be a simple enough thing to say, ‘this much and no more’, limiting planets to those bodies already bearing the definition. We could also say, ‘future discoveries must meet certain criteria to be designated planets’, allowing for minimal expansion, while grandfathering existing planets. All of these offend scientific sensibility because they rely on sentiment or tradition rather than a well-defined system of classification.

So there it is, in the name of consistency and scientific discipline, we must sacrifice our beloved nine (or ten or fourteen) planet solar-system and forever declare our planet to be one of eight, right? Well, no….

Many scientists claim that the agreed upon definition of planet excludes Earth, Jupiter and Neptune because they have not ‘cleared their neighborhood’ of other orbiting objects. This does not mean that they are not planets, as all eight planets are named in footnotes, but this could be done without even including a definition.

But all of this is beside the point. The criteria described for qualification as a planet is clearly worded to include the eight named planets and exclude Pluto, Eris, Ceres and the rest of the ‘dwarf planets’. This is quite an unscientific way to go about things; they just as easily could have created a definition to include some of the smaller planets (as some proposals did); it is also quite easy to imagine a scenario involving a body that all agree is a planet, but does not meet the criteria.

Of course, it is easy to criticize and much harder to offer solutions to the problem. This is where I go out on a limb as a non-scientist and offer my proposal:

First, I think the easiest way to go about this is to subdivide the category of planets (as is done with animals, flora, etc) into groups such as dwarf planets, minor planets, intermediate planets and major planets (and possibly superplanets, for use with some of the larger bodies discovered orbiting other stars). It might even be useful to have a multi-faceted definition including such descriptions as terrestrial, gas and ice, as well as double and triple. Using this, Pluto may be a triple or quadruple ice dwarf planet, while Earth would be a single intermediate terrestrial planet. Complicated? Yes, but it would be a consistent definition that would likely prove useful in extra-solar discoveries. It would also still be possible to define a group we call ‘historical planets’, which would include the nine I grew up with, along with Ceres and possibly Eris, which is the ninth largest known body orbiting the sun and largest in Pluto’s neighborhood (Kuiper belt); I would argue that this list is significant for more than sentimental reasons, as it outlines the expansion of our knowledge of the solar system.

JMHO, one of many I have (and believe make at least as much sense as those of the ‘experts’).