Monday, November 19, 2007

Numb and Number

Two cows were talking in a field and the first one said to the second, “Say, old chap, this Mad Cow disease has me in a bit of a tizzy.”
“Not me,” replied the second, “I’m a duck.”

I like irony. I don’t know exactly what it is, but I know it when it hits me. I can’t say I know it when I see it because I suspect there is good deal of irony that gets lost on me – which is ironic, for someone who likes irony.

Irony has many cousins and many bedfellows. Humor is one of irony’s favorite bedfellows, and the oxymoron is often a cousin and a bedfellow, which is a clue that something isn’t right. The funny thing is the oxymoron often isn’t ironic until it is pointed out; how many times do you see Jumbo Shrimp and not even think about it? How about the Great Depression? Shouldn’t it have been called the Bad Depression? The oxymoron is often hidden in plain sight; how oxymoronic – or is it ironic? It’s not sardonic, and there isn’t even a word called sardony or sardon. I find that ironic.

There are a lot of missing words. I was looking for the opposite of exceed the other day and I’ll be damned if inceed is not a word. It should be, if you follow the rules; inhale, exhale, inceed, exceed, incest, excest. Nothing is the opposite of exceed as best as I can tell.

Two freaks crashed into each other at the intersection. When asked about it, the chief of police said, “We’ve seen an increase of freak accidents lately.”

Yes, it is irony, but it’s too obvious. It’s like 3rd degree irony.

Some of the best irony lives below the surface. Here’s some 1st degree irony that also involves freaks and has the added bonus of being true:

The rock band, Alice in Chains, has a CD which shows a photograph of a three-legged dog on the front and a photograph of a three-legged man on the back. I like it very much because on the one hand, it’s ironic that the dog is missing a leg and the man has an extra leg, but on the other hand they both simply have three legs. It’s ambiguously ironic, which has a great sound rolling of the tongue.

Take a look at the next sentence:

This sentence has threee erors.

That is cold-blooded, premeditated irony. Its overall truthfulness requires two levels to establish. First there are the two spelling errors, and then there is the error in the number of errors. The sentence is only correct because everything is wrong.

Let’s say you have a car in your garage that you have been slowly fixing up for quite some time. When you can afford it, you buy a new part that is in perfect condition and install it, throwing the old part in the old-part pile. You keep doing this for every part on the car until that great day when you have replaced the very last part. Somehow it’s a bit anticlimactic because the whole time that you’ve been fixing it up, you’ve been driving it around. Two years go by and you are bored. You begin tinkering in the old-part pile and before you know it, you have assembled all the parts from the pile back into a working car that looks remarkably similar to your other car.Which car is your new car?

Is that a paradox? I don’t think so. I think a paradox is the strict and impossibly stubborn cousin of irony. A paradox is intractable. Its truth is impossible to ascertain. Paradoxes can break things… and breaking things can be a lot of fun.

If you are standing exactly at the North Pole, and you are asked to go 3 steps north, which way do you go?

I’ve never had a problem with North, East, South, and West before; the compass directions had always worked just fine for me until I went to the North Pole and then they broke. I complained to the Bureau of Weights and Measures and here’s what they said:

“But these directions worked for you everywhere else?”

“Yes, though I haven’t been to the South Pole.”

“Well, I think you will have to give them a little latitude.”

“Is that it? Is that your answer?”

“Well, alright; we’ll throw in longitude as well.”

“Why didn’t you do that to begin with? Why have N, E, S, W?”

“Well, it would make compasses quite large. It’s all relative with NEWS.”

“Relative? No it’s not! North is absolutely north.”

“To a point. It’s relatively absolute; you can’t have only one absolute because it creates a problem of magnitude which, in your case, is 3 steps. It’s unfortunate they didn’t make it relatively easy and ask you to go 3 steps forward.”

Speaking of relativity, Einstein had a theory about it. Science does a reasonably good job owning up to its mistakes, but then again; it has had plenty of practice because remarkably few scientific theories stand the test of time. Only the great theories survive, and a great theory is one that can be used to predict things with great accuracy and agree with real world observations. I mention this because you have to appreciate the hole Einstein dug for himself. First, he basically said that the grand master scientist, Isaac Newton was wrong, even though Newton’s theories seemed to work beautifully. Second, he took the generally agreed upon fact that the speed of something is always relative, and threw it out the window. The light from a car’s headlights will speed up when the car speeds up, everyone knows that. You would have to be a lunatic to think otherwise.

Einstein said no, the speed of light will always appear the same to any observer, no matter how fast they are going – he made the speed of light absolute.

So why do they call it the theory of relativity?

Well, to make the speed of light absolute, he had to change a few other things because the math wouldn’t work out otherwise. What he did was make time relative to an observer’s speed, and space (or distance) relative to an observer’s speed. He also threw in mass and made that relative too. Oh, and he curved space around mass too. To summarize, if you are traveling at any velocity, then time has slowed down, space has shrunk in the direction you are moving, you are heavier, and a straight line curves near mass but is still straight. He also said he had some good news, and some bad news; the good news was he had a formula for potential energy and it was e=mc2, or energy equals mass times the speed of light squared. The bad news was he had to change the formula for kinetic energy from e=mv, or energy equals mass times velocity, to this:

This one had an interesting implication. At normal speeds, it was essentially the same as the old formula because m was being divided by a value damn close to 1, which just leaves the same number. However, at 90% the speed of light, mass better than doubles. At 99%, mass is 7 times larger, and at 99.9999999999%, mass is over 700,000 times larger. He was sorry to say that it would require infinite energy to get all the way to 100% because mass would be infinite. Therefore, faster-than-light travel was not allowed.

Like I said, Einstein dug himself quite a large hole. Sure the math worked out, but the whole thing is too weird; it couldn’t be right, because we don’t experience anything like that, do we? It turns out there were a few pesky problems that had been known to science for some time but they were mostly hidden from the public. One problem had to do with the observed orbit of the planet Mercury. It wasn’t quite where it should be according to Newton’s laws. Now mind you, the discrepancy was miniscule, but it was still there, and either the formula worked or it didn’t, so that is why it nagged at scientists. When other scientists applied Einstein’s new formulas to this problem, they found it solved the Mercury perihelion precession problem, perfectly – sorry if that made you spit on your screen.

The speed of light being defined as universally absolute in something called the Theory of Relativity is not the only irony to be found here. It is also ironic that Einstein never won the Nobel Prize for his astonishing, reality changing discovery. Instead, he won the prize for a paper he published on the photoelectric effect. Even more ironic is the fact that unbeknownst to him, that paper helped lay the foundation for quantum theory – a theory Einstein refused to accept, but one which we now know works. It was too weird for him, if you can believe it.

Einstein dismissed quantum theory with the statement, “God doesn’t play dice with the universe.”

What prompted his comment was that until then, all the formulas discovered that governed physics were deterministic. What that means is if you know the precise state of a system, then you can predict what it will look like after some amount of time has elapsed. If you knew where the planet Saturn was, and you knew its mass, its distance from the sun, and the mass of the sun, then you could know where Saturn was for all of time. The universe seemed to run like a clock, and that fit in well with the belief that there was a plan for the universe when God made it, and that plan would proceed in an orderly manner.

When looking at the planets closely, any discrepancy from prediction was sure to have a cause; it just had to be found. So certain of this they were, that the planet Neptune was actually discovered when somebody called an observatory and told them where to aim their telescope. Based on a slight wobble with the orbit of Uranus that had been observed over time, someone (I forget who) actually calculated that the wobble could only be accounted for by an unknown planet located at a specific place. When the telescope was aimed at that precise spot in the sky, sure enough there was a planet. How smug they must have felt. This just reinforced the notion of the universe, and all things in it, running like a clock.

I find it ironic that I don’t know the name of the person who predicted the existence of Neptune, yet I have heard of Nostradamus, who never actually predicted anything, let alone Neptune. As best as I can tell, his predictions are actually post-dictions made by others who fit events to his vague and vapid writings to sell books. Here’s a clue: if it needs to be interpreted, it’s not a prediction.

Quantum theory did violence to the notion of a deterministic universe. It doesn’t just allow for non-determinism, it demands it. Quantum theory definitely was not a bolt from the blue. It had, and continues to have many contributors, some of who were extremely reluctant to put forth their ideas because the implications were so profoundly obscene. Quantum theory has remarkable predictive powers, which is ironic for something that forbids the certainty of knowledge about the thing it is predicting. It says the world of the tiny is governed only by probabilities and that nothing can be said about a particle with certainty. Some of the quantum laws were governed by such things as the Heisenberg Uncertainty Principle, and the Pauli Exclusion Principle. Quantum theory is so bizarre that there is an official interpretation of it called the Copenhagen Interpretation, which ironically makes no attempt to explain what quantum theory is, only what it can predict – and predict it does. It has been reconciled perfectly with all sub-atomic processes and even with electromagnetism. Unfortunately, it has not been reconciled with gravity, nor with general relativity. That goal has been sought for so long by the world’s greatest scientists that some have come to believe that Einstein was correct in his assessment of it, and believe there is something even more fundamental that is governing the universe. Like algebra to a dog, it’s possible that a more fundamental theory is currently beyond our ability to perceive. We may be on the cusp of changing that, and I’ll explain why in a bit. First, let me tell you how foolish I am in making that last statement and tell you of another time we were “on the cusp” of something profound.

The following two sentences form a paradox which was used to break something so thoroughly that, to anyone trying to fix it, included the warning “Abandon all hope, ye who enter here.”

The two sentences are:

The following sentence is a lie.

The previous sentence is true.

It really loses something in the translation. This killer was originally written in the language of formal mathematics by a person whose name was Kurt Gödel (pronounced Girdle). He broke formal mathematics with it. You have to have proverbial balls the size of grapefruits to try and break math because there is a 100% chance that you are either a brilliant super genius or a foaming lunatic. Personally, I’m just smart enough to know that if I think I’m brilliant enough to break math, then I’m a lunatic.

Gödel ‘s Incompleteness Theorem states that any axiomatic system that is powerful enough to describe itself will always contain in it, statements whose truth cannot be ascertained. English is an axiomatic system, and it’s talking about itself right now. Math is too, and though I’m not fluent, I would just like to say:

Gödel actually scored 200% on my statement above. Sure he broke math but, ironically, he died of starvation while living in New Jersey. That’s bad when you forget to eat to death; it points to something not being right (on a side note, Gödel used to take walks every day with… Albert Einstein! Neither would ever reveal what they talked about during these walks.)

In the everyday world of typical average people, Gödel’s revelation really wasn’t that big of a deal. For all purposes, it was just a pile of poop to step around when encountered. What made it profound was at the time (1931), there was a lot of talk about man being on the cusp of systematizing all of mathematics. There was crazy talk of machines that would automatically be able to solve any math problem, and in fact, of machines that would set to work on creating, from first principals, every true statement of mathematics. The scientists thought they would just sit around the machine reading the tape that it spit out and go “Oooo, Ahhh, We did not know that.”

Foolish mortals; it wasn’t that long before that people were still putting beaks on their flying machines. Gödel actually did the scientists a favor and sent them packing. Had he not come up with rigorous proof of their futility, they might still be at it. It makes me wonder how much we are spinning our wheels today. I guess it depends on which poet or philosopher you ask.

Knowing when some exercise is futile has tremendous value. A British mathematician by the name of Alan Turing was great at it. Turing was probably responsible for saving more lives in WWII than any other single individual when he broke the Nazi codes. He was rewarded for that by being kicked out of the service and labeled unfit because it was discovered he was gay. I guess it’s bad when a gay person saves thousands of lives.

Turing anticipated the invention of the computer. He actually invented a machine called a Turing machine that was not a real machine, but rather a hypothetical machine that would read a tape (program) and carry out the instructions on it one step at a time. The instructions were simple statements of math and some control instructions to move the tape back and forth. The programs he “wrote” for this machine were not Pac Man or anything tangible; in fact, he skipped writing any programs and went straight to the heart of determining what the “boundaries” of such a machine could be.

He showed, without the use of a real computer, what the limits of a real computer would be by determining what was computable and what wasn’t. He showed that there was an algorithm (or formula) for computing the digits of pi. Now because pi goes on forever, it is technically non-computable. Turing wasn’t interested in that and reasoned that the machine could be instructed to stop after however many digits were desired. What he was interested in were algorithms for solving problems whose successful completion could never be ascertained before hand. For instance, is there a program that could be written to find the first time 19 sevens occur in a row in the number pi? He proved that the answer to that is no. The best the program could do is to start generating the digits of pi and look for the sevens until it finds them, but the program is never guaranteed to find them; it may run forever.

That problem may seem foolish or obvious at first glance, but by looking closely at these kind of problems led to many insightful things. For instance, he found that some problems would indeed lend themselves to being computable and would be certain to find the answer, but how long it took was indeterminate. This trait could be exploited for secure communications. If it can be shown that the only way to discover an encryption key is by systematically trying all possibilities, then the law of averages says you will find it after trying half the possible keys. Computer security today depends on picking a key size that the fastest known computer would take on average millions of years to try half of all possible keys to decode a message.
The very nature of computability owes a great deal to Alan Turing. It’s an easy thing to characterize a function that take a number for its input, and outputs the square of that number. It just multiplies that number by itself and returns the answer. The answer is always found in the same amount of time for any number, and the answer is never less precise than the input. Now, what about the reverse function that takes a number for its input and returns the square root of the number for the answer?

That’s a big problem; there is no known deterministic way or finding a square root. The only thing a computer can do is try a number, square it, and see if it is the same as the input number. The question is what is the best scheme for doing this? It can obviously be done by picking a precision - say 10-thousandths - and starting at 0.0001, test it, and if it is not correct, then incrementing to 0.0002 and check that, and on and on until it finds the closest number to the input. That could take a long time, but is there a better way?

Yes. Let’s use a real example; to find the square root of 10, set a lower bound to 1, and an upper bound to 10. Now, take the middle of the two and run the square test. In this case we would square the value 5.5 and see that it is 30-something, which is too high. Because of this, we know the square root has to be lower than 5.5 so we set a new upper bound to 5.5 and perform the mid-point test again. We will round the mid-point up to 3 and square it to get 9. This is smaller than 10 so we set the lower bound to 3. We are progressively zeroing in on it. We can keep doing this, getting closer by half to the desired value each time we do. We can characterize the function as having an indeterminate, but finite running time as long as we agree beforehand to some level or precision. This also means the output might only be an approximation of the real answer.

We can see that enormous complexity can arise by simply reversing a trivial process. We went from a function that always returns a precise value in one step (multplying a number by itself) to a function that cannot ensure a precise answer and whose time to produce the answer cannot be predicted beforehand. Where does the complexity arise? Is there some essence we are missing? People look very hard at these things because they help us understand the boundaries of a problem. If you know the boundaries, then you might be able to identify if a problem lies outside the boundaries and you better look elsewhere for a solution.

We see computers now that sport dual-core, or quad-core technology. These are arising because scientists’ years ago plotted the course of semiconductor advances and saw that the relentless miniaturization and speedups would start to bump into physical barriers. The days of doubling the speed of computers by using faster clocks are over. The manufacturers of semiconductors are now saying, “Here; this chip has two microprocessors in it for the price of one.” Now the onus is on the software engineers to exploit ways of using two processors at the same time to tackle a problem. This is an extremely difficult thing to do and has alarmed many researchers. I find extremely ironic that giving an extra microprocessor to a programmer has made his or her job more difficult rather than easier.

I still don’t know if I like philosophy or not. So much of it seems so… philosophical. I guess the thing I do like about it is that it seems to form a necessary willingness to give even absurd ideas a chance at redemption and even fruition. Many of the timeless personalities throughout history who shaped and shifted our perception of reality did so not by accident, but by seeking and finding answers in places that others just wouldn’t look at. We hear that penicillin was discovered by accident, but someone did have a Petri dish open and someone did look through the microscope; that’s no accident.

My days of idealism are over, and I find that sort of liberating. It’s a messy world in which we live and that is all the more reason I try to keep my mind open. I let it all wash over me, but that doesn’t mean that I accept everything that comes my way; in fact, my bullshit detector has never worked better. Deception vies for our attention all the time… even our own. I used to scoff at what passes for news and entertainment. I still don’t really care what is happening with Paris Hilton, but I can understand why people do. She is much… nicer than vague threats from Homeland Security and wondering how much better at swimming polar bears will have to become now that they are running out of ice.

It gets hard to sort it all out. America is the beacon of democracy in the world and people hate us for our freedom. We are not like other countries who torture people and eavesdrop on their own citizens. We only go to war as a last resort and when we do, the mission is accomplished within a couple of months and we come home. We would not linger around while 1/3rd of its citizens are killed, maimed, or displaced as refugees. We would never give chemical weapons technology to another country, and we would never supply arms to both sides of a war because that could come back to haunt us. We would never put a price tag on the health of our children, and our American companies would never make toys for our children that are poisonous. Our religious leaders would never have gay sex and take drugs, nor would they molest children. The government would never suppress science, or interfere with justice, and it would never, ever abandon one of our cities in a time of need. Give us your tired, your hungry, your poor.
Know nothing, and question everything.

Science is the study of probabilities and religion is the study of absolutes.
That’s one of those self-righteous smug slogans masquerading as a humble observation. It sarcastically implies that only science can be trusted for objective truth; at least that’s what I read into it.

Religion has been abused, and for all the wrong reasons. In fact, its history is littered with the corpses of the innocent who fell victim in one way or another to the church. It is second only to science. Science can scoff all it wants at religion but if you ever saw a broken down old reverend or priest holding the door open late at night to a makeshift community center in a dangerous part of a city too poor to have a church of his own, give comfort to a lost soul who is crawling on his knees and praying to sweet Jesus for the strength to go just one more day without touching the bottle then, my friend, you don’t know anything about religion. Real or not, when your life is coming to a close and that warm hand touches yours and begins saying words for your soul, you will never be so glad you kept your mind open to the possibility that you might be slipping away here, but going somewhere better. Nobody deserves to die alone, even scientists.

Things have to be flexible, that's just the nature of everything. A one point science had the earth at the center of the universe and all the stars and the Sun whirled around us. Then it was decided that the earth spun around and the stars were fixed in space. Then Copernicus showed us it was the Sun that was at the center of the universe and everything whirled around it. Then the universe shrunk down to the Milky Way. Then the universe became much larger when the fuzzy nebulae turned into other galaxies. All those reality shifts by science.

Right now, science is telling us that we are just a little piss-ant planet circling a completely average star in the back woods of the outer arm of a completely average galaxy which is part of a cluster of galaxies known as the Local Cluster. Wow! What an original name! I wonder if any aliens over in Andromeda call it the Local Cluster too. Andromeda is the closest galaxy to ours at 6 trillion miles away. To give you a sense of how far that is, shrink all of space so that the earth is one foot from the sun; at that scale, Andromeda is about 11 miles away, and that’s our nearest neighbor galaxy.

The extent of the universe and the age of the universe are things that have changed quite a bit over time. At one point the age of the universe was younger that the age of the earth, if you can believe that. The geologists and astronomers had to have a powwow over that. The extent of the universe has been shown to be finite by a very clever line of reasoning that goes like this:

The distribution of stars and galaxies appears to be very smooth at large scales and that lends itself nicely to statistics. If the universe was infinite, then there would be an infinite number of stars in any direction you looked, no matter how small of a region you looked. That means the sky should be ablaze with light of unimaginable intensity. It doesn’t matter how far away they are, an infinite number of stars adds up to blinding light. It was suggested that there might be a shell of dust and gasses obscuring the rest of the stars but it was pointed out that in no time, an infinite amount of stars would heat up the shell of dust and gas so that it too glowed with great intensity. There is really no way around it; space is not infinite. Like a loaf of raisin bread cooking, the universe is expanding and the raisins are all moving away from each other.

Many times we have known the “objective truth” only to have our picture of reality altered with a new, better “truth”. Science is fantastically successful at proving itself wrong, but at least it admits it’s wrong.

There are a lot of questions that science does not have the answer to, and there are a lot science “preachers” who either reject many of these questions as absurd or just shrug them off because they don’t have answers to them. I think it’s ironic that scientists are supposed to be dedicated to the pursuit of new, truthful knowledge, but many only like to discuss what they already know.

I was on site at a company once and there was a person that I needed to deal with whose title was Scientist of Information Theory. He was about 9 pay grades and 8 academic degrees above me but he was a chatty chap.

“I’m not very familiar with information theory,” I said to him. “I know it always takes some amount of energy to transmit information, and I know it can never be transmitted faster than the speed of light.”
He just smiled politely and said, “Well there you go; you can skip the eight years of college.”

I ignored his sarcasm and asked, “Has anyone ever speculated on how fortune tellers, and psychics, and those people who talk to dead relatives for a fee get their information, and what medium it might be transmitted in?”
“From the UFO’s,” he said.
“I don’t believe in UFO’s.”
“Really, Why?” he asked.
“Information theory,” I teased. “Space is big. If a planet were close to us, say 50,000 light years, and they just now pointed their telescopes at us, they would be looking at images from 50,000 years in our past. They wouldn’t see any cities, or hear any radio, or anything. Even worse, they would have had to start out 50,000 years ago and travelled at near light speed to be here now. That’s fantastically improbable in my book. It seems like a lot of work to go through when they could just listen and watch instead. If they came all the way here, I’m afraid it would be because they had to physically be near us and there’s only one reason for that.”

He seemed to enjoy that and said, “Yes, it would be the smart thing for them to do. We are only on one planet now but someday we will have to leave, and they might worry we will take all their oil.”

“Good thing there are no UFO’s,” I said. “So seriously, where would a fortune teller get her information?”
“You are kidding, right?”

“No! I’m not saying there are real fortune tellers; I’m only asking if there is the possibility of information lurking in mediums that we can’t tune in yet. There are all kinds of real crap that we don’t have the answers to.”

“Like what?” he asked.
“Well, have you ever had the feeling someone is looking at you, and sure enough they are?”
“That’s not real,” he said. “You just think that because your subconscious saw the person looking at you a moment before.”
That was lame but I didn’t want to argue. “OK, then why is it when my girlfriend massages my scalp or scratches my arm with her finger nails, that I cannot generate the same electric feeling when I try it on myself? I can exactly reproduce her touch but not the sensation.”
That one stopped him dead in his tracks for a moment.
“It’s probably because the brain can’t both coordinate the arm movements and the sensory input at the same time and produce the same feeling.”
Oh, he was good!
I went on; “Why is it that when I look in the mirror, reflections are flipped right and left but not up and down? Why does one spatial axis get favored over the other?”
“Oh, I’ve heard that one before,” he said. “I forget what the answer is… something about perception.”
“So all the things I mentioned have their answers rooted in some mental reflex.”
“More or less, yes,” he said. “Those are my best objective answers.”
“You mean subjective,” I corrected. “My questions were objective because we all experience the same thing, but your answers were all subjective.”
“Whatever. The brain is a pattern matching machine and it will fill in the blanks on its own sometimes – it’s called inductive reasoning and we fight it all the time because it can carry us away to places that are far from reality. A normal, functioning brain is supposed to take in input and, using the information it already has to augment its decision making process, arrive at a conclusion that is, if not correct, at least rooted in reality. When it doesn’t have enough information, it will ask for it. If it still lacks information, it will manufacture it to keep moving forward.”
There was a good deal of sense to what he said but the brain cannot always be trusted to operate in such an objective manor. I came across an ethical dilemma once that really slammed that point home. It contrasts two seemingly equivalent problems and asks, “Is this behavior acceptable?” The “correct” answers to each are at such odds with one another that it offends the senses. The worst thing about it is, articulating the reasons for the different answers is nearly impossible, and what reasons are given usually don’t hold up to close examination. The first part of the dilemma is this:
An engineer is driving his train through a very narrow canyon when he rounds a corner and sees up ahead that 3 people are hopelessly trapped on the tracks. There was no way he can stop the train in time to avoid killing the people. His only option is to throw a switch that would send the train onto a side rail where there is only 1 person hopelessly trapped.
The question is: would it be morally acceptable to throw the switch and kill 1 person in order to save 3 people?
Common sense says yes, and there is probably not a jury in the land that would convict the engineer for doing anything criminal. The second part of the dilemma is this:
A surgeon has 3 extremely sick patients, each waiting for a different organ transplant. Death is imminent for all three unless they have the surgery. The surgeon also has a patient coming in to get his tonsils removed and he can’t help but notice this patient is a perfect donor match for his 3 very sick patients.
The question is: would it be morally acceptable to kill the 1 patient in order to save the other 3 patients?
To me, the very thought of it is repugnant and I think it would land him in prison.
In the first situation, it’s unfortunate but acceptable to kill 1 person to save 3, but in the second, it is unacceptable to kill 1 person to save 3.
So what is different about the two situations?

It’s ironic that I have bumped into information theory once again since meeting my scientist friend. I would have liked to press a few more questions on him about some conclusions I have drawn from the new knowledge I have acquired. As so often happens, this insight began with a seemingly harmless statement about something called information density; something I had never thought about before.

If you are like most people, you are reading this essay one word at a time. If I were clever enough, I might have been able to arrange the words so that a whole different story could be read by skipping every other word. That would double the information density of the used words. I may have even been able to add a 3rd story at every 3rd word. I may have also been able to change the shape of the letters and spacing between lines so the white on the page also formed letters between the lines. Instead of 26 letters, I could have created a symbol for each word much like Oriental scripts and then performed the same skipping tricks and positive/negative tricks. I don’t mean to disappoint you, but it sounded like too much work so I didn’t even try.

People think about this stuff and clever people exploit it. The information density of a picture stored on your computer is so inefficient that it is easily exploited for passing secret messages. At the expense of just a little bit of image fidelity that would only be noticed by an expert, you could email a picture of grandma that had the Colonel’s secret recipe buried in it.

I have come to understand what my scientist friend was talking about a little better when he said that the brain fills in the blanks all by itself. This too can be exploited in information density theory but only under the right circumstances. In many cases, it can be quite dangerous. Consider this:
A small meteorite hits earth and is witnessed by many people who race to the impact site. They are amazed to discover the meteorite is a stone cube, and one of its sides has the following engraving:
. .
. . .

What can be learned from the six dots? The crowd seems to already have some ideas and as you walk around, some of the things you hear are:
“The aliens are showing us they know how to count – 1, 2, 3.”
“No, the aliens are showing us they know the first 3 prime numbers – 1, 2, 3.”
“No, the aliens are showing us they know how to add – 1 plus 2 equals 3.”
“No, the aliens are the same one’s who built the pyramids.”
“No, the aliens are pointing to something.”
“No, the aliens are showing they are on top, and all others are below them.”
Hmm. That sure is a lot of information for 6 dots. Where did it come from? If I knew the answer to that, you would be watching me on Oprah, not reading this. All I know is that we are the undisputed masters at finding patterns and filling in the blanks.

Personally, I think the correct answer to the above question is nothing; no judgment of truth can be made with any certainty as to its meaning. The problem is, as you move around the crowd telling them the six dots mean nothing and not to draw any conclusions, you are likely to reinforce their beliefs and raise suspicion about yourself and your obvious motive to hide the true meaning of the dots. With just a few well-placed words such as “you were not meant to see this,” you could possibly place yourself as the authority on the real meaning of the dots. That’s another form of information density – or disinformation density as the case may be. If you managed to exploit your position of authority, then you might go to great lengths to suppress any future messages that could contradict the fiction you concocted around the original message. It would be tough to explain that the dots on the first cube were a hat for a smiley face on the next cube that fell from the sky.

Information density is the most likely reason why the shape of the brain is all wrinkled. The highest densities of neural cells are at the surface of the brain, and the wrinkled structure greatly increases the surface area when compared to a smooth dome. People think about these things and clever people exploit them. I speculated above that a more fundamental theory of nature that unifies the strange but undeniable existence of quantum theory with that of gravity and Relativity might currently be beyond our ability to perceive much the same way that algebra is beyond the perception of a dog. I then cryptically alluded to the possibility that we might be on the cusp of changing that.

Several years ago the sequencing of the human genome was completed after a massive effort. Furious work is now underway to decode the genome so that a full understanding of which parts of the DNA control all the various metabolic processes that make us human and keep us healthy. Already, the largest computer in the world has been constructed by IBM for the sole purpose of tracking the legal patents that will be arising from this knowledge. Proving that you have fully decoded all the genes responsible for the production of hemoglobin in red blood cells, and proving that your modifications to these genes that can enable people to run twice as far will not interfere with normal body functions or intrude on other patents is tricky business.

If this was indeed your business, you might very well have a hard time staying away from finding the gene or genes that control the amount of wrinkling in the brain, or how fast synaptic connections in the brain are formed. This would represent the first time man has taken a direct, active roll in our intelligence. Until that moment arrives, all our learning will have been passive. We read and learn, and maybe write something that contributes a little more to the collective body of knowledge for others to read and learn. It’s a relatively slow process. If you learned how to double the surface area of the brain, it is possible that those brains might gain a deeper perception of reality and might even figure out further improvements to perform on the brain. It is not out of the realm of possibility that a self-reinforcing process could be established where, in a very short period of time, our mental capabilities undergo a hyperbolic increase leading to who-knows-what. Our natural brains would have proven to be just smart enough to learn how they work and then, something not fully human, would have taken over from there. It is truly a frightening thought unless of course you allow for the possibility that these… neo-people learned whole new levels of love and appreciation for life, the arts, the sciences, and quite possibly elevated their perception to reach God directly. He may be waiting for them - us. Who knows?

I know I could love some little bulb-headed child who communicated by telepathy and levitated furniture… as long as she or he still needed a hug every now and then.
Let’s come way back down to earth and do something mundane. Since this essay is entitled
numb and number, maybe a little bit of boring math is due. Let’s do something simple like count the number of atoms in the universe.
We don’t have to do them one at a time; we’ll just take a close approximation. Since this number is likely to be a bit large, a quick review of numerical exponentiation is in order. We can write the number one-million, in a couple of ways. The first is to write out all the zeros as in 1,000,000 and another way is to write 10 and the number of zeros, as in 106. Writing 106 is the same as saying 1, followed by 6 zeros. It is also the same as saying 10 to the 6th power. Not only does this save space, but it allows us to multiply two of these numbers together by adding the powers together as long as both numbers are base 10. 106 X 106 = 1012 or, one million times one million is one trillion – 1 followed by 12 zeros.
Each time 1 is added to the power, the number is ten times larger. If 106 is one million then 107 is ten million. The secret to counting the atoms in the universe is to know how much an atom weighs and then weigh the universe.
Chemists use a unit of measure called a mole to weigh chemicals. A mole of one substance has the same number of molecules as a mole of a different substance, even though they weigh different amounts. The number of molecules in a mole was selected to be the strange number, 6.03 X 1023, but we will round it to 1024 . Ten to the 24th power is one-trillion-trillion and it was chosen because that is the number of atoms in one gram of hydrogen, which is the lightest element.
Lucky for us, stars are mostly made of hydrogen and stars make up nearly 100% of the mass of the visible universe. So…
1 gram of hydrogen is 1024 atoms, and 1000 grams (103), which is 1-kilogram, has 1027 atoms.
1000 kilograms (103) is one metric ton and that has 1030 atoms.
We know that a trillion is 1012, so a trillion tons of hydrogen has 1042 atoms.
A trillion-trillion tons is 1054, and ten-thousand-trillion-trillion tons is 1058; that is how many atoms of hydrogen is in our sun.
We will assume that our sun is an average sized star. The accepted estimate of the number of stars in our Milky Way galaxy is one-hundred-billion, or 1011. That means the number of atoms in the Milky Way is 1069 atoms.
An estimate of the number of galaxies in the universe is also one-hundred-billion so that means there are 1080 atoms.
The number of atoms in the universe is roughly 1080, and ten universes would have 1081 atoms.
Why did I take you through this exercise? Because I wanted to show you how ridiculously small the number of atoms in the universe is. Now we are going to go inside the nucleus of a cell to count something really big.

A real hot-button issue that has been in the news is the subject of intelligent design. As is so normal, the controversy is much ado about nothing, and I say that not as a slight to intelligent design, but because of attempts to present it as an alternative to the Theory of Evolution. Why does it have to be either/or? If you are going to claim a new theory, especially one with “intelligence” in its name, isn’t it possible that Natural Selection is simply a designed-in feature of the new theory? Natural selection is a beautiful feature for a self-replicating entity to have. It allows it to adapt to a changing environment and promotes species survival in unfavorable conditions.
The strict “Darwinists” can’t conceivably lay claim to exclusive and absolute knowledge of the origins of man either. It’s possible we started out as slime on a rock, but then again, maybe we had some help. The dogmatic refusal to concede the possibility that man, or life on earth in general, arose purely by chance is asinine.
One thing that would have helped would be if the Bible alluded to the fine structure of life since it is so awesome.

I’d like to outline something here that grossly simplifies a number of processes. I will quickly run through the difficulties that arise in thinking that the genetic code could happen purely at random. Many will correctly claim that it is unfair to think it had to happen in the piecewise manner I am ready to outline. At the end, I will touch on this. Please bear with me for a moment just to get a flavor of the process.

The entire genetic code for nearly all living creatures on earth is stored in a complex molecule called DNA that resides in the nucleus of living cells. A strand of DNA looks like a long ladder that twists in a right-hand spiral. The building blocks of DNA are four different chemicals abbreviated A,C,G,T, and they can interlock with each other. There are approximately 3 billion rungs on the human DNA ladder but the ladder can be divided into roughly 25,000 sections, where each section represents a gene.
A gene can be thought of as a sequence of instructions for the construction of a specific protein or enzyme. These 25,000 different proteins carry out all the metabolic functions in our body. It’s a very complicated dance.
The DNA molecule itself does nothing. It simply provides a template from which something called RNA can receive instructions or programming to construct a protein. Conceptually, the RNA will have brushed up against a specific spot on the DNA strand and took with it an impression, or recording of the chemical sequence of that part of the strand. It might detach from the DNA carrying the genetic code GATTACA. Each letter is called a nucleon and they form triplets called a nucleotide. Since each nucleon can be one of 4 values (A,C,G,T), and since they group by 3, that means a nucleotide can assume one of 43, or 64 different values. Each of these different values codes for an amino acid but there is some redundancy in the coding and it turns out that there are only 23 different amino acids. There are also a couple of special values that can be thought of as instructions to start and stop the creation of a protein.To make things easy, we will pretend that instead of 23 different amino acids, there are only 10. That way, we can think of a nucleotide as representing a single digit, and a series of nucleotides is a series of digits that make up a larger number. Four nucleotides can represent the numbers 0000 to 9999, or ten-thousand different values, but a typical gene may have thousands of digits.
RNA resembles a flat ribbon much like a tape. This ribbon is fed into a factory called a ribosome. The ribosome “reads” a start instruction and begins assembling a protein from the basic amino acids. Each digit adds an amino acid to the protein until the ribosome reads a stop instruction and then snips the protein off to float away and do its duty. The protein might be hemoglobin which carries an oxygen molecule for delivery by a red blood cell, or it might be a protein to remove lactic acid from a recently exerted muscle cell.
The protein has a primary structure which is the sequence of amino acids. It also has a secondary structure which is the shape of the amino acids. Finally it has a third, or tertiary structure which is how the amino acids are “folded” in 3-D space when chained together. It turns out that this tertiary structure is a very important aspect of proteins and allows them to assume specific 3-D shapes that fit into chemical receptors designed only to receive the specific shape of a certain protein. That is why proteins can “drift” in a cell; they will only be delivered where they are needed by unlocking a receptor designed for their shape.
Now, let’s take a look at some preliminary numbers. If we take 3 billion base pairs in a strand of DNA and divide that by 25,000 genes, we get an average length of 120,000 base pairs; grouping the base pairs by 3 yields 40,000 nucleotides (digits) per gene on average. The fact is, much of our DNA is junk, and not all of it is used. For our purposes, we will use a simple gene that is a mere 110 digits long, which can assume one of 10110 possible values – only one of which will work correctly. Remember that the number of atoms in the universe is 1080, so 10110 is 1030, or one-million-trillion-trillion times larger than the number of atoms in the universe.
We may as well go crazy with assumptions. Let’s suppose each atom in the universe is actually a nucleotide that can mutate into any of the digits 0-9. Let’s also suppose these mutations happen one-billion times a second. We will take all the matter in the universe, all 1080 nucleotides, and group them into roughly 1078 110-nucleotide groups and see how long it takes until one group hits on the exact 110-digit number that our gene needs in order to create the right shape to fit in a receptor.
If there are 10110 possible combinations, then the law of averages says we will have to try ½ of the number of combinations on average before we randomly roll the right value. To keep things simple, I’ll assume luck is on our side and we will hit the right number after only trying 10% of the combinations. That means we will hit the correct value within 10109 tries.
Let’s further assume that there are 100 seconds in a minute, 100 minutes in an hour, and 100 hours in a day. That means there are 100 X 100 X 100 = 1003 = 1 million seconds in a day. We will make years long too; 1000 days in a year means there are 1 billion seconds in a year. So after one year, we have 1078 groups mutating 109 times per second, for 109 seconds which is 1096 mutations in one year.
After 1 million years, 10102 mutations would have been tried. After 1 billion years, 10105 mutations would have been tried, and after 1 trillion years, 10108 mutations would have been tried.
It would take all the matter in the universe, mutating 1 billion times a second, about 10 trillion years to randomly hit upon the magic value for our one gene. That’s 1000 times the age of the universe.
That’s just for one gene. If we threw away 99% of the DNA as junk DNA and only kept 1%, then 3 billion base pairs grouped by three nucleons, is 1 billion nucleotides (or digits). One percent of one billion is ten million, so 1010,000,000 combinations would have to be tried at random to hit upon the whole 1% of our genetic code. That’s a 1 followed by ten-million zeros.

There is no reason to think this process had to rely on pure chance, which is the worst case. It is possible there is some minimum length sequence that has just enough functionality to replicate. That could represent a huge advantage over a random process because once replication was attained, it could keep churning out copies and, pardon the expression, grow legs from there.
A primitive multi-cellular organism living on the ocean floor may have undergone a mutation that caused a group of cells to become sensitive to changes in light intensity so that a sudden change from light to dark, such as a shadow, caused the organism to retract and therefore avoid an opportunistic predator that was drifting by. This could prove to be such a great survival feature that the photosensitive cells were pressured to improve until something resembling an eye emerged. Who knows?

The first time I read about gene expression I got the distinct sense that the process was artificial. It seemed too deliberate, almost like a cell is a computer processor and the DNA/RNA is a program. I still get that sense even now. Instead of writing software in a computer language such as Pascal or FORTRAN, we were written in DNA. Instead of machines made from silicon and metal that are tasked to do one thing, we are made from proteins built around a calcium framework and can perform a variety of tasks autonomously.
Our efficiency is off the charts compared to even the most efficient machine. Mankind is a long way off from building something as small as a fly that can land on ceilings or buzz around in circles virtually all day on just a tiny bit of sugar. A bee can buzz around, identify flowers, identify threats, attack threats, construct elaborate structures, participate in a hierarchical society, employ communication, and other bee things. It has a brain the size of a speck. There are viruses that behave almost the same way and they have no brain at all.

The above exercise was done to get a sense of the enormous precision of the genetic code. It is remarkable how stable this very large molecule is. Our DNA today is nearly identical to the DNA of the earliest man. Of course, it is also within 1% of that from a chimpanzee, and within a few percent of any mammal.

In fact, there is enough common in all DNA (even plants) that some consideration must be given to the idea that it all came from the same origin. The Darwinists would nod their head in agreement at this as the right conclusion. The creationists might take exception to this and remind us of, “Let there be life.” There is another possibility that doesn’t solve the origin problem, but is a possibility nonetheless.

We know that someday the sun will swell up during its death throws and scorch the earth, only to recede back and eventually die. For us to survive, we will have to move. In science fiction we apply this migration to ourselves and imagine the construction of giant spaceships that will sustain us for great journeys. The sun won’t die out for a few billion years and maybe this type of voyage will be possible then, but what if we found out that a meteor was going to hit the earth in 10 years and destroy it? How would we manage our survival?
One way could be to redefine what “our” survival means and take a long term view of things. We already know of hundreds of other planets but even if we didn’t, we know roughly what the “habitable” distance from a star is. A cheap and hasty way to propagate life might be to encase DNA in rock and scatter them by the millions toward the habitable zones of stars. We would never know what happened of course, but it’s just possible that after enough time some creature might look up at the stars and wonder how they came to exist.

Two neo-humans were standing at the edge of a cliff gazing in silence over a beautiful valley. The first one suddenly started laughing and said, “I just figured out the secret of gravity, and it’s beautiful. Watch this, I’m going to fly to the other side of this valley.”The second neo-human put her hand on his shoulder and said, “Maybe you should take off from the ground first.”


Seven Star Hand said...

Hey Mouse ,

Here’s a clue: if it needs to be interpreted, it’s not a prediction.

Want overwhelming proof to the contrary?

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Nostradamus Lost Book Bombshells


Rosemary said...

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