Subject: Random mutation, selection and low probabilities Newsgroups: talk.origins Date: 1 December 2003 Message-ID: email@example.com
The recent discussion with Walter got me to thinking about a process we use in Geophysics and while I was driving home from Thanksgiving, I mentally calculated the number of possible acoustical impedance models one gets in geophysics. So I wrote it up.
Anti-creationists make a huge deal about the odds against finding a single sequence of protein or DNA which they think is useful. The odds against finding the workable solution are usually in the range of 10^-100 to 10^-300. Dembski claims that 10^-150 probability is some sort of universal probability bound, in which anything with odds less than that simply must be designed. He writes:
"In The Design Inference I justify a more stringent universal probability bound of 10^-150 based on the number of elementary particles in the observable universe, the duration of the observable universe until its heat death and the Planck time. A probability bound of 10^-150 translates to 500 bits of information. Accordingly, specified information of complexity greater than 500 bits cannot reasonably be attributed to chance. This 500-bit ceiling on the amount of specified complexity attributable to chance constitutes a universal complexity bound for CSI." William A. Dembski, Intelligent Design, (Downers Grove: Intervarsity Press, 2001), p. 166
In my business we deal with probabilities which make those numbers absolutely pale by comparison. The system I will describe has one chance in 10^126,000,000,000 of being right. That is 10 raised to the 126 billionth power. This is much greater than this supposed probability bound. To help you understand, I must explain a bit of geophysics.
In seismic exploration, we set off airguns or dynamite charges on the surface of the ocean or land (respectively for each type of source--dynamite is not used offshore). We then listen for the echoes of sound bouncing back to the surface off of the various rock layers. This is important. We record the sound wave field every 2 milliseconds and we record to 8 seconds or more in time. This is equivalent to something like 40,000 feet deep and we end up with a seismic trace which consists of a sequence of 4000 numbers which represent the amplitude of the sound waves reflected off the rocks under the earth. We record the data in such a manner that we end up with a seismic trace every 25 meters in one direction and every 40 meters in another direction and the size of some surveys is so large that they extend a hundred kilometers or more in both directions. Most field seismic data is around 10 km by 10 km for 100 sq. km of data. Thus we have 100,000 seismic traces, each with 4000 different numbers. This would be a typical 3D seismic program over an oil field.
The reflection of the sound (which is what causes the echo) is controlled by the change in acoustic impedance from the upper layer to the lower rock layer. Acoustic impedance (AI) is merely the multiplication of the rock's density by the velocity of sound in that rock.
AI = rho x vel
AI is what causes the seismic reflections:
Sound going: Down Up \ / \ / AI in rock 1 \ / ----------------\/----------------- AI in rock 2
We would really like to know the AI rather than what the seismic readily offers which is energy of sound reflection. AI is tied to the rock lithology and properties so it is more useful than merely knowing how much sound energy is reflected back. We use this AI data to help us understand the porosity of the rocks and to determine rock type.
To get to this information we do what is called an inversion. We guess at the AI pattern and make a model acoustic impedence trace, then we apply the reflection laws to it to produce a model seismic trace, compare that model to the real seismic trace, and if it differs by a certain amount, we guess again (randomly mutate the model), make a model seismic trace, compare it to the real seismic trace etc. We continue this iterative process until the model AI produces a model synthetic seismogram which matches closely the observed data.
Now, what are the probabilities of us getting the right AI? All we know is the seismic data which we have sampled every 2 milliseconds and have 4000 numbers for each seismic trace. We know that the density in rocks we are interested in generally extend from 2 to 2.5 grams per cc and the velocity of sound generally ranges from 5,000 to 12,000 feet per second. Thus, if we let the density values go from 2 to 2.5 in steps of .01 and the velocity of sound vary from 5,000 feet per second to 12,000 feet per second in increments of 1 foot per second, we have 50 x 7000 = 350,000 different possibilities for each sample of the seismic data. Remember we have 4000 samples. So the total possible AI solutions for a given seismic trace is
Total number of AI solutions = 4000^350,000 = 10^1,260,720.
This is 10 raised to the 1.2 millionth power!! The odds against finding the correct answer is so much smaller than finding the ‘correct' answer with protein that one would bet on the protein long before betting on geophysics. Protein probabilities are in the order of one chance in 10^300. But this is merely the probability of getting ONE seismic trace AI correct. We have 100,000 other traces, so that the probability of getting the correct model for the entire seismic survey is an astounding one chance in
Or ten followed by 126 billion zeros.
If the anti-evolutionary probability arguments were correct, we geophysicists would have no chance of finding anything useful in this procedure. If one searched 10 quadrillion models per second for the age of the universe we would only have searched 10^33 of the models to date. But, I will tell you that we always find usable models via this technique. We do reduce the number of samples we run the inversion over so in general we only use 200 samples but that still gives us one chance in 10 followed by 80 billion zeros. We only do this for the reason that an oil field only occupies that much of the time series. But even with odds against us of 10 followed by 80 billion zeros, we always get a useful AI output. Why?
Well, it is because we don't have to have absolutely the correct answer to get a workable and useful answer. Billions upon trillions upon gazillions of the AI inversions will give the very same answer (provide the very same functionality). In other words, the answers are not unique. This is the same reason that the probability arguments given by the anti-evolutionists fail to impress. Those who are familiar with such systems know that one doesn't have to find the best solution to have a workable solution. Hemoglobin is not the very best oxygen carrier anywhere among all possible protein sequences; but it is a workable carrier. Cytochrome c as found in humans is not the very best at that functionality; it is certainly a workable solution. All through the biopolymers, this statement can be said. And experiment shows that this is the case:
Andrew Ellington and Jack W. Szostak "used small organic dyes as the
target. They screened 10^13 random-sequence RNAs and found molecules
that bound tightly and specifically to each of the dyes.
"Recently they repeated this experiment using random-sequence DNAs and arrived at an entirely different set of dye-binding molecules.
"That observation reveals an important truth about directed evolution (and indeed, about evolution in general): the forms selected are not necessarily the best answers to a problem in some ideal sense, only the best answers to arise in the evolutionary history of a particular macromolecule." --Gerald F. Joyce, "Directed Evolution," Scientific American, Dec. 1992, p. 94-95.
Low probabilities for finding the correct answer is only a meaningful argument if one and only one solution works. We know this to be false in geophysics and in biology. Cow, sheep, etc all have different proteins, but we often have used their proteins to support our lives because their different chemicals work fine and dandy in us and thus when we are sick we live. But it means that there are more than one biological solution to the functionality in question. The anti-evolutionary arguments simply won't stand up to scrutiny.
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Subject: Re: Explaining Hominid stratigraphy Newsgroups: talk.origins Date: 26 November 2003 Message-ID: 3FC48D06.14809EB4@sgi.com
Elzie Kai wrote:
> "Thomas H. Faller" wrote in message news:3FC31E4C.261546D3@sgi.com...
> > Really cool idea, Elzie. And it also makes sense that all sorts of
> > other objects and artifacts associated with hominids are sorted
> > by altitude, so that the "earliest" and most primitive hand tools
> > are relegated to the lower caste deformed members of society.
> Though you're being sarcastic here, it is perfectly reasonable to
> expect different castes to use different quality tools. The term
> "primitive" would be inaccurate; the tools of the lower castes would
> have been cheaper or of lower quality, but contemporaneous with, and
> therefore not more "primitive" than the tools used by the upper
> castes. You wouldn't expect to see a the Indian Vaisyas and Sudras to
> drink out of the same quality cups as the Brahman or Kishatryas
> castes, would you?
Elzie, I was being sarcastic with the idea in the back of my head that you were handing your thoughts to us as a parody, not as a real explanation. While that may seem harsh, there's a very good reason for it, and I hope you'll read through to see why.
First, I'm a geologist. I've studied the deposition of sediments through books and in the field. I've mapped the distribution of sediments and examined drill cores through them (taken from wells) which show how they vary in thickness, composition of material and fossil content over large areas. I've studied paleontology, and I've also studied anthropology, history and sociology, so I've got some background in sediments in general, but I understand your argument about social stratification as well.
The problem with your argument is that it doesn't fit the real world at all. It's not just a little off, it's way off. Let me start from the beginning.
Where do the upper classes live? At upper altitudes, you suggest. Where do upper altitudes come from? You could say, from mountain building. Mountains push up all the time, even today. And there are plenty of hills around.
The trouble is, where mountains push up, they're pushing up rock and sediment that were already there, rocks which already have fossils in well-defined sequences of fossil patterns. And although there are some hills which are early mountains, almost all the variation in altitude you see around you, every example which you are familiar with is created by water eroding existing layers of rock down, cutting slopes and valleys. The rock under the hills is also made of layers of fossilized rock, all of it. Let's say you want to claim that before the Flood, these fossil-bearing rocks weren't there yet. Okay, then all hills and mountains are made of granite or basalt or what we now call "basement" rock.
Now basalts and granites are tough rock, which is why we use them for building. They wear very slowly. Rock like that isn't likely to form soil quickly, certainly not within a few thousand years. Most mountains which have soil are made of softer sedimentary rock which weathers easier, or they've been worn by glaciers. So if these mountains and hills have soil for agriculture, or even for grass and trees, it was put there by a Creator, who ground up rock, mixed different types (like you'd add lime to acid soil) and grain sizes, then mixed dead stuff (from where?) for humus and to give plants the nutrients to grow. Except that this looks a lot like erosion and long-term death already.. Hmmm.
But this soil would only be as deep as it needed to be in order to grow plants. There wouldn't be much use to pile thousands of feet of dirt into a valley if people were only going to need the top few inches. So we put people there and animals and crops and lakes and everything else, and we let it run for dozens of generations and then we look at it.
Sure enough, the rich people live on top of the hills and bury their dead there. They've already got a Bronze Age culture going, which is where the Bible picks them up, so we don't need to worry about all of the Stone Age tools. Maybe they're just used by the people in the valleys. But there are a dozen "ages" of Stone Age tool, from very primitive chopping stones to advanced delicate flaked tools like spear points and arrowheads. Even if we bury the primitive stuff at the lowest level, there's only room enough for a few feet worth of difference between the top and bottom layers, unless the valleys get inundated by floods every year which would mean that the soil from the upper slopes is getting stripped off and mixed with the lower sediments. More complications.
Your basic problem in our limited case so far is that there isn't enough dirt to go around to bury everything deep enough and still preserve social differences except in limited areas. Sure the rich live in higher areas and the poor in lower, but the higher and lower areas are separated geographically as well. If you dig for artifacts in the rich guy area, all you see are rich guy artifacts. The poor guys live over there, down the slope. In the time before the flood, you'll never get any poor guy artifacts under the rich guy sites, and you won't get any rich guy stuff deposited only on top the poor guy artifacts in the valleys; it can only be mixed in. This even works if you assume all sites were poor initially, and only the higher elevations got richer. There's a geographic pattern to artifacts, as well as a stratigraphic pattern that we just don't see in real life.
I'm spending a lot of time discussing this because it's what you focused on, but in the real world, it's only the tiniest part of the sedimentary evidence. First of all, I mentioned that the hills and mountains you see around you are actually layers of sedimentary rock, even very large mountain ranges like the Rockies or the Himalayas. They are thousands of feet of sands, shales, limestones and interbedded volcanics in places. Sands are mostly quartz, and quartz comes from the weathering of granite over a long time. Quartz particles show, by their size and degree of rounding, how much weathering they've gone through before they were deposited. Some layers are pebble sized particles, and are pieces of previously deposited rocks that have been broken up and worn down again - a single pebble in a conglomerate layer may show mixing and layering from a previous life, and it might be sitting next to a limestone pebble or a metamorphosed pebble. I've actually handled rocks like these in Utah - you can't find an explation for them that doesn't require huge amounts of time.
Next, most areas of the world have underlying strata of limestone, which is produced by biologic activity only. You can see the shells of former animals and remains of plants, representing single individuals which took time to grow to their size (you can see growth rings, like you see on present organisms), and then time to fossilize. Often, limestones are interbedded with sands and shales, indicating times when the sea level rose and fell, making the area a beach, or a deep offshore plain, far from sources of sand and below the depth where light could penetrate.
You can't just mix these via water currents during a Flood, as each layer shows traces of long stability during its deposition (burrows preserved in multiple layers), and evenness of grain size that points to a single stable source of sediment.
You also have to deal with the volume of sediments. Sands have to be eroded from somewhere. There isn't enough time in Flood scenarios to erode miles of layers of sand from the hills and weather it. Any current big enough to break up rocks in that volume will leave house-sized boulders mixed in. Sands come in layers that show long periods of weathering, long periods of sorting out different sizes of grains, and patterns of deposition (like layering in stream beds, beaches and deltas) that can't be achieved quickly. Shales are even more indicative of time, since they're made of more finely ground sand and the chemicals (muds) of weathered rock.
But finally, you have to deal with the volume of fossilized life in limestones. It's difficult to picture how much this is, but in one example, there's a fossil layer of crinoids, an ocean animal that looked like a plant, that is made of thousands of feet of crinoid parts, spread over hundreds of square miles. That's enough to cover the earth to a few inches in crinoids. And that's just one layer in one area. There are fossil coral reefs along the western slopes of the Appalachians, buried now under hundreds of feet of other rocks in places like Kentucky and Ohio. There are sediments over and under these reefs, indicating long periods of stable conditions - not just hundreds of years, not just thousands, but millions of years.
Even if you want to sort artifacts by altitude, there are many places in the world where there isn't any, to speak of. Vast stretches of the continents, where people have lived, are nearly flat. People tend to farm and hunt on flat land, near quiet rivers where there is soil deposited by occasional flooding, making the land rich and productive. In the Mississippi Valley, where thousands of wells are dug for water each year, where the sediments extend down to seven miles below the surface, we have never found any human artifacts except right at the surface, and they all show one of two cultures - pre-Columbian or post-Columbian. In thousands of othr sites around the globe, whether the terrain is smooth or hilly, human artifacts are never found at or near the bottom of the stratigraphic column, near where you'd expect them to be if humans lived in valleys or lowlands before a Flood.
> > they get the ancestral varieties of plant and animal life while the upper
> > classes get the "mature" species, and they get to cook over the
> > "earlier" dated campfires with older wood, while the rich folks use
> > the younger wood.
No. There is no evidence anywhere that humans ever cooked and ate trilobites, dinosaurs, Archaeopteryx, giant ferns, or any of the billions of species that are "ancestral" to the ones from the past million years. We've never made campfires over any species of wood that became extinct over a million years ago. We've never gathered extinct species of plants, so that their pollen or seeds would be found in our excavated dwellings. We hunted mammoth and cave bear, but we never hunted their ancestors. We ate horses, but never any of the hundreds of ancestral horses, which would have tasted just as good. There's no crossover. All of those animals and plants were dead and gone long before we ever happened.
> In my interpretation, the wood would be of the same age, while the
> flora of different altitudes would of course differ. Radioisotopic
> dating is a problem for creation science, but I doubt it's an
> insurmountable one.
It isn't just dating, it's species. Whole hosts of species, from both higher and lower elevations, were inaccessible to man because they were extinct long before he arrived.
> At first blush, I'd guess radioisotopes to vary in
> abundance with altitude to some extent or another. This might explain
> why the lower fires would yield "older" radioisotope dates.
Nope. You can check this today.
> > In some cases, you can even see where the lower
> > case guys had to live in a forest, while their upper caste friends
> > had their own front-yard savanna or even lake to play around in.
No, I mean that most of the fossils we have found of humans have come from areas which were flat, and either covered with trees or grass with lakes, much like Central Africa today. You could make a name for yourself if you found "upper-caste" fossils on the slopes of the mountains of Africa today. There are plenty of reasons from the real world why you wouldn't, but none I can think of from your scenario.
What I was saying was that the "lower-caste" fossils are from human ancestors who originally lived in or near trees, but as Africa dried up, they adapted to savannas, and occasionally fell into and died in lakes. The later, "upper-caste" types of humans lived in a different environment, but on the same flat African plain as their ancestors. The environment changed, not the altitude.
> You've never been to a mountain lake? Never heard of savannah-covered
> plateaux? Some types of forests do occur more frequently in riparian
> settings than in high altitudes. Anyway, you can find instances of
> each caste in a variety of settings.
> > It's pretty impressive that they could maintain this sorting even
> > in the same location, like in caves. Must have had scaffolding
> > back then.
> Hmmm... that's a good point. Perhaps caves were deliberate burial
> sites. If so, then it's easy to see reasons why the social sorting may
> have been preserved there as well.
Caves were living sites. We find remains of meals there, food preparation and tool-making. Sorted by depth, more-primitive on the bottom.
> One remote possibility is that the
> caves were allowed to be used by the lower classes for a time, but
> that the higher classes got the privilege of being buried atop the
> lower classes. More likely, perhaps an analogy can be made with the
> pyramids in which an entire family, servants and all, were buried upon
> the death of the family's leader, preserving their social status in
> their order of burial.
You're right, that is a stretch. It sounds like your total time- scale here is on the order of generations. Cave deposits indicate occupation, on and off, for hundreds of thousands of years, from such indications as flowstone formation, bat guano, animal droppings and rock fall.
> Our ancestors were certainly less careful about burial in caves than
> they were about inhumation in pyramids, but burial hasn't always been
> a careful process. Besides, the lower classes wouldn't have been
> buried with the ritual and care that the upper classes were.
You're assuming that most or all of the "upper class" were found buried with any ceremony whatsoever. Do a little reading about how most human fossils are found, and what burial goods, if any are found with them.
Look, you get points for imagination, but almost zero for knowledge of the real world. Human fossil remains do not come in the categories you think they do, nor do their artifacts. The differences in skeleton, skull and teeth are way beyond social variation - especially such differences as cranial capacity and hip geometry. Your scheme for burial does not match the actual distribution of human ancestral remains, nor does it match even present-day remains in most of the world. Finally, you don't explain where the rest of the sediments come from and how they got there, which is 99.9% of the physical evidence for an old earth and the impossibility of the Biblical scenario. I'm sorry to have to spell all this out, but your idea is sorely missing in the basic knowledge of the world which you should have had to judge it in the first place.
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