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Author Topic:   Nested Biological Hierarchies
Modulous
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Posts: 7801
From: Manchester, UK
Joined: 05-01-2005


Message 61 of 87 (322332)
06-16-2006 2:40 PM
Reply to: Message 52 by Scrutinizer
06-16-2006 12:41 PM


sequence comparisons
The same sort of pattern is observed when comparing cytochrome C of the invertebrate silkmoth with the vertebrates lamprey, carp, turtle, pigeon, and horse. All the vertebrates are equally divergent from the silkmoth (27-30%). Yet again, comparing globins of a lamprey (a ”primitive’ cyclostome or jawless fish) with a carp, frog, chicken, kangaroo, and human, they are all about equidistant (73-81%). Cytochrome C’s compared between a carp and a bullfrog, turtle, chicken, rabbit, and horse yield a constant difference of 13-14%. There is no trace of any transitional series of cyclostome ’ fish ’ amphibian ’ reptile ’ mammal or bird.
It takes a while to do sequence comparisons, but here are the sequences:
silkworm
lamprey
turtle
Pigeon
Horse
and the result of the comparison:
Sequence 1: silkworm 107 aa
Sequence 2: lamprey 103 aa
Sequence 3: turtle 104 aa
Sequence 4: pigeon 104 aa
Sequence 5: horse 104 aa
Sequences (1:2) Aligned. Score: 70.8738
Sequences (1:3) Aligned. Score: 76.9231
Sequences (1:4) Aligned. Score: 77.8846
Sequences (1:5) Aligned. Score: 75.9615
Sequences (2:2) Aligned. Score: 100
Sequences (2:3) Aligned. Score: 79.6117
Sequences (2:4) Aligned. Score: 80.5825
Sequences (2:5) Aligned. Score: 82.5243
Sequences (3:2) Aligned. Score: 79.6117
Sequences (3:3) Aligned. Score: 100
Sequences (3:4) Aligned. Score: 92.3077
Sequences (3:5) Aligned. Score: 89.4231
Sequences (4:2) Aligned. Score: 80.5825
Sequences (4:3) Aligned. Score: 92.3077
Sequences (4:4) Aligned. Score: 100
Sequences (4:5) Aligned. Score: 89.4231
Sequences (5:2) Aligned. Score: 82.5243
Sequences (5:3) Aligned. Score: 89.4231
Sequences (5:4) Aligned. Score: 89.4231
Sequences (5:5) Aligned. Score: 100
Not easy to read, so I can make a N-J tree:
This is the way we should do these things. The interesting thing here is that the pigeon and turtle are grouped together, as per the hierarchy. You will note that it isn't perfect, which leads to my other point:
Just testing one protein is dangerous and firm conclusions cannot be drawn, but general tendencies are useful (and such a small number of organisms doesn't help, I don't have the time now, but might later to expand on this). One thing to bare in mind is that different techniques need to be applied with non-vertebrates, so a straight comparison between vertebrates and non-vertebrates is also fraught with potential error. There are some interesting resources out there, but they are a topic in themselves, if you are interested let me know.

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RAZD
Member (Idle past 1482 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 62 of 87 (322425)
06-16-2006 9:58 PM
Reply to: Message 57 by Scrutinizer
06-16-2006 2:17 PM


Re: Greetings
This may be off-topic, but I just thought I had to say something.
We can keep it on topic by talking about the nested hierarchies of the different eye mechanisms, and how they match the common descent pattern of the taxonomies derived from other characteristics. In no cases does a retina flip from one side to the other along a branch of evolution.
We can also keep it on topic by noting that there is no reason for a design process to show a nested hierarchy (unless it is derivative "bad" design -- good design doesn't), because good design takes features that work and combines them to make better designs.
According to good design procedures the taxonomic tree should be inverted as designs are refined and selected to end up at a final "good" design. There are several examples of this in objects that we know are designed (because they were designed by humans).
The human retina is by no means "inside-out" or a "bad" design. First of all, the neurons connected to the photoreceptors must run in front for the opaque retinal pigment epithelium (RPE) to make contact with all the rods and cones from behind to provide nutrients ...
This works no matter which way the retina faces, so it is not an argument that backwards is better, or even that it is "good" - just that it works (wow). One would expect any evolved eye to work or it would not be selected for, thus how the eye works is not an argument that the design of the eye is as functional as it could be if it were designed.
Notice that in evolution there is no "good" or "bad" there is only {more\less\dis} "functional" features, but once we introduce the concept of design - an intentional arrangement of the features - now we do have a basis to evaluate whether the design is "good" or "bad" by how well it fills the design requirements: either the eye is well designed or it isn't.
... and keep them from wearing out. . If I remember correctly, the neurons "in the way" of the light actually are virtually transparent and have the same index of refraction as the surrounding vitreous humor.
Which is completely and utterly negated as a concept by the fact that there are retinas facing outwards that don't need to have transparent linkages or any other adjustments to make the eye work. As there are retinas facing different ways in different organisms, and one way causes less interference with vision you can make the design argument that it is bad design.
You must like playing catch by standing with your back to the other person and then grabbing at the balls that just miss your head. Wear a padded helmet eh?
It doesn't matter that the system works -- that is not surprising given evolution's ability to refine features through mutation and selection, and the eye design we have has been around for a long time -- what matters is how well the system is designed.
As it sits right now there are better designs readily available -- if there is a designer then they have the patents and can apply them at will eh?
As for the inherent blind spot, it's no impediment since it is off to the side, and the other eye makes up for the lost information, anyway. We could discuss this in another thread if you wish.
Especially for people with only one eye, or for those "survival moments" where some object is only seen in one eye. When you only look with one eye the mind "invents" what the blind spot covers.
This "argument" of yours is a post hoc ergo propter hoc logical fallacy, basically arguing that it is a "good" design because it is what it is, and that it isn't a total failure as a design because it gets by. Not much to go on.
Conversely I can look at the design and see several ways to improve it using "current technology" employed in other organisms. I don't need to justify a blind spot -- it just isn't necessary, and if it isn't necessary then there is no good design reason for it being there.
If you want to discuss it further you can try {Silly Design Institute}{Investigator: Eye's Silly Design}
http://EvC Forum: Silly Design Institute: Let's discuss BOTH sides of the Design Controversy... -->EvC Forum: Silly Design Institute: Let's discuss BOTH sides of the Design Controversy...
Anyway, there actually is a restriction to updating the design, at least assuming one God. If designs were constantly changing or there were no consistency, it would make it look like multiple gods were competing; God would have to be consistent to show He is the only Designer. Besides, there is no real need for any modification to the human eye; it is all we need for survival, and our intelligence more than makes up for any deficiencies it may have (i.e., we can make glasses or contact lenses to correct near- or far-sightedness, and we can invent microscopes and telescopes if we ever need to see anything small or far away).
ROFLOL. Don't trip over your apologizing for bad design there. Yep, better to not update that design or they'll know the designer was incompetent. Thank you for absolutely making my point -- if it were a good design you wouldn't NEED to justify it like that. It is never too soon to stop going down the wrong road, and it is never to soon to stop using a bad design. Any design that needs "after market" fixes IS A BAD DESIGN.
Creationism gets a "bye" on bad design because they can claim all has been "corrupted" since the "fall" as an explanation. ID does NOT get a "bye" because it claims that design can be determined from the evidence we see.
Evolution -- the eye is what was available, evolved and adapted as necessary, it has a lineage that matches the nested hierarchy of other features and elements of the organisms.
Design -- the eye is slap-dash, assembled in haste, with corrective measures taken to "fix" errors that then cause other problems that need more fixes, and the designer is ignorant of other systems that handle the same process more efficiently AND that there are systems that could be combined to make an even better eye than any existing in any organism today.
If the eye were a good design it would NOT show the nested hierarchy of other features.
Actually, both concepts are entirely compatible. Any theory of intelligent design implies some supernatural intervention sometime in the past ...
LOL. It amuses me whenever creationists try to show that it is compatible by claiming that what it really is amounts to creationism in disguise. ID is either {religion} or it is {philosophy devoid of religion}. The whole political argument is that it is the latter, every person who professes it confirms that it is the former.
Once again you are mistaking SOME places where creationism and "intelligent" design don't actively cross swords as being evidence that it is compatible.
This is the logical fallacy of "some {A} is {C} and some {B} is {C} therefore {A} = {B}"
This is contradicted by "some {A} is {D} and no {B} is {D}" -- and vice versa.
The question is not whether ID concepts can "allow" creationism, but whether it allows anything that is NOT creationism: it does. ID concepts allow anything from evolved aliens to a Deist unconcerned god to a Hindu pantheon, and none of these are creationism, and none of these are even remotely (to say nothing of) "entirely compatible" with creationism.
The question is not whether creationism can "allow" ID concepts, but whether it allows things that are NOT compatible with ID concepts: it does. Creationism explains bad design by corruption, sin, fall, etcetera, and in creationism humans need to be the highest creation. There is no room in looking for evidence of design for finding elements of bad design. You ran into this very problem when you needed to make excuses for how bad the design of the human eye was, especially when (according to creationism) humans are the pinnacle of creation and should have the best of everything.
I'm sorry if I wasn't clear. I was talking about the biblical story of creation and just assumed you knew that that story involves an intelligent designer. Hence life is an intelligent design according to creation.
Explain the bad design of the eye to me again?
Enjoy.

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fallacycop
Member (Idle past 5598 days)
Posts: 692
From: Fortaleza-CE Brazil
Joined: 02-18-2006


Message 63 of 87 (322441)
06-16-2006 10:51 PM
Reply to: Message 57 by Scrutinizer
06-16-2006 2:17 PM


Re: Greetings
Scrutinizer writes:
As for the inherent blind spot, it's no impediment since it is off to the side, and the other eye makes up for the lost information, anyway.
the other eye may make up for the lost information in animals that have both eyes pointing toward the same direction (like us). But that is not the case for animals that have the eyes pointing in oposite directions (like most preys). By your logic then those animal should not have the inside out retina. But they do.

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Hyroglyphx
Inactive Member


Message 64 of 87 (322881)
06-18-2006 11:33 AM
Reply to: Message 46 by fallacycop
06-16-2006 12:35 AM


The evolutionists argument of incredulity
What about saying that a creator made both humans and chimps with a broken gene for vitamine-C production with which not to produce vitamine-C? Now, that's an asinine statement if I ever saw one. Explain that away if you can.
For starters, there is nearly fifty million bases in humans that are nowhere to be found in the chimp genome. That in itself is required of nearly 40 million potential mutations in order to arrive to a human being from a chimpanzee. That means that there is a total number of DNA differences at about 125 million. And because any given insertion can be more than one nucleotide long, that brings the figure to about 40 million separate mutations in order to distinguish the two species. This brings up the question of how 40 million separate mutations, whether neutral, harmful, or beneficial could transmit through any given population in 250,000 generations. How must the geneticist maintain an obvious lineage between human and simians and still overcome this anamole?
In another context, lets assume that in every generation of every organism, one male and one female received a beneficial mutation so advantageous that all the others in that group that do not possess the deletion or insertion perish. The new populace is replaced in a single generation from the progeny of the beneficial mutation. For ToE to reconcile this, we would have to assume that evolution was proliferated in this sequence of events repeatedly, generation after generation, for billions and millions of years. The question is, how many possible beneficial mutations were substituted at nearly the same pace for all ancestors in order for us to arrive to a human from a far distant relative, such as the nematode? What are the odds that evolution follows this sequence per population, per 500,000 nucleotides, when 500,000 nucleotides doesn't comprise even 0.1% of the genome?
ToE explains that the supplanting of antiquated traits with new and rare traits via natural selection and beneficial mutations as its delivery method; none of which can be verified with any empiricism, because I think we'd all agree that if beneficial mutations exist, they are so rare that they'd be virtually non-existent.
So lets break it down. What are the odds that even in millions of years that so many substitutions could act beneficially, especialy in light of those who favor the theory of punctuated equilibrium? If most of the biological population experiences a stasis this means that all these transitions had an even less amount of time to come to fruition.
Now, how would this occur in your Vitamin C argument? We know that most mammals synthesize their own Vit-C, but humans have to seek it in order to ward off scurvy. For people who scoff at arguments of incredulity, I can't help but notice the glaring contradiction. So, because the claim is that remnants of once functional genes have been abandoned in a non-coding sequence, the fact that humans and chimps share it means nothing, especially if there is no compelling evidence to marry all mammals together in the first place. In other words, this is only an argument that 'wows' an evolutionist because it presumes that all copies of genes originated from an ancestral gene. So, to you any corresponding genes must then be indicative of ancestry. Sorry, but as i said earlier, out of billions of species, the fact that many would have similarities is obvious. In fact, the more phenotypes that one organism shares with another, the greater the genotype will correspond as well. That in no way determines lineage. That simply determines that laws governing DNA is well established.

“Always be ready to give a defense to
everyone who asks you a reason for the
hope that is in you.”
-1st Peter 3:15

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kuresu
Member (Idle past 2590 days)
Posts: 2544
From: boulder, colorado
Joined: 03-24-2006


Message 65 of 87 (322885)
06-18-2006 11:49 AM
Reply to: Message 64 by Hyroglyphx
06-18-2006 11:33 AM


Re: The evolutionists argument of incredulity
I may be wrong in what fallacycop was trying to say, but if we were intelligently designed, why the heck would there be a non-functioning gene? And why would the creator make the break in the exact same point? There's no rhyme or reason then, no pattern that can be predicted. But, if evolution is true, which it is (scientifically true, that is), then it makes sense to say that chimps and us share an ancestor. And looking at this broken gene and making a cladistics chart with it leads to a similar chart as the one based off of other characteristics. Also, the broken gene isn't responsible for any phenotype. Again, you can't answer why the creator chose to make the exact same break in the exact same gene for two different species, but evolution has an answer to the problem.
Also, those however million base pairs that aren't found on the chimp genome, you have to remember, we've one (or is it two?) chromosomes more than them. And chromosomes have a huge number of genes (particularly ours, seeing as how they are so long).

All a man's knowledge comes from his experiences

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AdminNosy
Administrator
Posts: 4754
From: Vancouver, BC, Canada
Joined: 11-11-2003


Message 66 of 87 (322888)
06-18-2006 11:58 AM
Reply to: Message 65 by kuresu
06-18-2006 11:49 AM


Watching the topic.
The topic is the "Nested Biological Hierarchy". Please refer to the pseudogenes in that context only.
You are wrong Kuresu: We have a pair fewer chromosomes than the chimps. You should also not take numbers like those given without checking them first.
Also the topic here is NOT how many mutations it takes between any pair of existing species. It is about the nested biological hierarchy and an explanation for it only.
Edited by AdminNosy, : Correct author, correct spelling

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kuresu
Member (Idle past 2590 days)
Posts: 2544
From: boulder, colorado
Joined: 03-24-2006


Message 67 of 87 (322896)
06-18-2006 12:32 PM
Reply to: Message 66 by AdminNosy
06-18-2006 11:58 AM


Re: Watching the topic.
I stand corrected. Now once yo've said it, it makes sense, because two chimp genes fused into one of ours (or, rather, chromosomes)
And I wasn't the one who brought up the number of mutations necessary--that was NJ. Sorry for the diversion, though.

All a man's knowledge comes from his experiences

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Chiroptera
Inactive Member


Message 68 of 87 (322907)
06-18-2006 1:00 PM
Reply to: Message 64 by Hyroglyphx
06-18-2006 11:33 AM


Marrying genes to nested hierarchies.
quote:
So, because the claim is that remnants of once functional genes have been abandoned in a non-coding sequence, the fact that humans and chimps share it means nothing, especially if there is no compelling evidence to marry all mammals together in the first place.
Fortunately, there is a reason to link all mammals together, namely the nested hierarchical classification. In fact, the same classification links all primates together, and links humans, chimps, and gorillas even closer. It is a significant fact that after the nested hierarchies have been determined, this pattern of broken genes conforms to it, verifying that the observed pattern is, in fact, real, not subjective.
Edited by Chiroptera, : original post was badly written

"These monkeys are at once the ugliest and the most beautiful creatures on the planet./ And the monkeys don't want to be monkeys; they want to be something else./ But they're not."
-- Ernie Cline

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NosyNed
Member
Posts: 9006
From: Canada
Joined: 04-04-2003


Message 69 of 87 (322916)
06-18-2006 2:19 PM
Reply to: Message 64 by Hyroglyphx
06-18-2006 11:33 AM


Fitting into the NBH
You seem to be suggesting that there are too many mutations between humans and chimps. Since we are discussing the NBH (nested biological heirarchy) here perhaps you could show how it ties in?
You seem to be simply showing some degree of incredulity regarding the numbers. If you wish to show that the human - chimp transition is not credible perhaps you'd like to open a thread on it.
Your next paragraph is also, apparently, totally off topic as well.
ToE explains that the supplanting of antiquated traits with new and rare traits via natural selection and beneficial mutations as its delivery method; none of which can be verified with any empiricism, because I think we'd all agree that if beneficial mutations exist, they are so rare that they'd be virtually non-existent.
This is also off topic. Please stick to the NBH and then support what you are saying.
So, to you any corresponding genes must then be indicative of ancestry. Sorry, but as i said earlier, out of billions of species, the fact that many would have similarities is obvious
There is no reason for there to be any similarities for an all powerful God who can build things from dust any way he wants.
It seems from the last paragraphs that you accept the existance of the NBH but conclude that it is a huge coincidence. That is your explanation?
You have yet to say why it is not support for the idea of one or a few common ancestors. It isn't a final "proof" of course but it is something you have to expect if the idea is correct. You do see that don't you? If not explain why it would NOT appear if the ToE is correct.

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fallacycop
Member (Idle past 5598 days)
Posts: 692
From: Fortaleza-CE Brazil
Joined: 02-18-2006


Message 70 of 87 (322932)
06-18-2006 3:28 PM
Reply to: Message 64 by Hyroglyphx
06-18-2006 11:33 AM


what argument of incredulity?
Most of your post is completely irrelevant to the matter at hand.
I think we'd all agree that if beneficial mutations exist, they are so rare that they'd be virtually non-existent.
you assume to much.
Now, how would this occur in your Vitamin C argument? We know that most mammals synthesize their own Vit-C, but humans have to seek it in order to ward off scurvy. For people who scoff at arguments of incredulity, I can't help but notice the glaring contradiction. So, because the claim is that remnants of once functional genes have been abandoned in a non-coding sequence, the fact that humans and chimps share it means nothing
In order for you to acuse me of incredulity, you have to first give me some sort of explanation.(Then if I say "I don't believe it" you could say I'm being incredulous). In your post you gave me nothing , just handwaving. That's not surprising since the standard ID argument that A common creator explains common genetic material is completely inadecuate (Almost crazy really) when you are dealing with broken genetic materia. Just to make it clear:
the fact that humans and chimps share it means nothing
You got to be kidding!!! When I'm grading my students homework and there is a shared piece of information between two papers, If the Info is correct, I usually assume they both hapened to know it and give them credit for it. But if the information is incorrect, I take it as safe to assume that they have been copying from each other. Should I stop doing that now that you straightened me towards the truth that common broken information means nothing? I don't think so. You will have to do way much better than that if you expect anybody to even consider your point of view as vaguely viable. Connecting now with the point of the thread: The real punchline here is the fact that the animals that share this broken gene are exactly the ones that belong to one of the hierarchical groups previously stablished by other means. That way it not only confirms that group, but also is confirmed by it. The conclusion is: Unless ID proponents can come up with somethig much better then the handwaving non-argument that you atempted, ID is prety much a dead in the water still born theory.

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Chiroptera
Inactive Member


Message 71 of 87 (323255)
06-19-2006 12:22 PM
Reply to: Message 69 by NosyNed
06-18-2006 2:19 PM


Re: Fitting into the NBH
quote:
So, to you any corresponding genes must then be indicative of ancestry. Sorry, but as i said earlier, out of billions of species, the fact that many would have similarities is obvious
There is no reason for there to be any similarities for an all powerful God who can build things from dust any way he wants.
He's also missing the point here; the important idea here is not that similarities exist, but that there is a specific, detailed pattern to the similarities.

"These monkeys are at once the ugliest and the most beautiful creatures on the planet./ And the monkeys don't want to be monkeys; they want to be something else./ But they're not."
-- Ernie Cline

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happy_atheist
Member (Idle past 4991 days)
Posts: 326
Joined: 08-21-2004


Message 72 of 87 (323327)
06-19-2006 2:39 PM


I think we're losing NJ because he doesn't accept the objectivity of the observed hierarchy. When NJ says that mere similarities don't prove relatedness he's correct. There are similarities between all cars, but no "common descent", and there are similarities between all computers, but no "common descent".
Until we convince NJ that the specific pattern of similarities is completely objective and will be arrived at no matter which characteristics are used then this thread is just going to go around in circles of "Is Not's" and "Is So's".
NJ, what would you expect an objective hierarchy to look like? In what way do you think the observed hierarchy is not objective? Do you think the statistical analysis involved in the cladistics is flawed, and if so why?

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EZscience
Member (Idle past 5231 days)
Posts: 961
From: A wheatfield in Kansas
Joined: 04-14-2005


Message 73 of 87 (323615)
06-19-2006 10:27 PM


Perhaps we could point out that the 'objectivity' of phylogenetics is supported by the fact that very many independent lines of evidence give rise to remarkably similar 'trees'. These include paleotological evidence, molecular genetics evidence, and morphological evidence. The fact that all these different sources of evidence converge on extremely similar cladograms is strongly indicative of their veracity.

  
RAZD
Member (Idle past 1482 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 74 of 87 (323642)
06-19-2006 11:31 PM
Reply to: Message 72 by happy_atheist
06-19-2006 2:39 PM


color coded card analogy
Until we convince NJ that the specific pattern of similarities is completely objective and will be arrived at no matter which characteristics are used ...
This is the crux of the matter, for otherwise anyone could make their own nested pattern and call it valid.
The issue is not just patterns of inclusion -- all organisms in {Group A} have {Set A} characteristics, and all organisms in {Group B} have {Group B} characteristics -- but one of exclusion as well, there are characteristics that are unique to certain groups.
As an example, take a box of 2^10 index cards, and 67 different color markers. This is generation 0 (generation 0 has one group -- all the cards). Take one color marker and make a spot on each card.
Divide the cards in half (2^9 in each group), and using a different color marker for each group make a spot on each card in the group. This is generation 1 (generation 1 has 2 groups, each card has 2 colors marked on it and there are a total of 3 colors used so far).
Take one group from generation 1 and divide it in half (2^8 in each group), and using different color markers for each subgroup make a spot on each card in the group. This is half of generation 2 ...
Take the other group from generaton 1 and divide it in half (2^8 in each group), and using two more different color markers for each subgroup make a spot on each card in the group. This is the other half of generation 2 (generation 2 has 2^2=4 groups of 2^8=256 cards in each group, each card has 3 colors marked on it and there are a total of 7 colors used so far)
Keep dividing and marking in a similar pattern - each group from one generation gets its own distinctive color spot:
Generation 3 has 2^3=8 groups of 2^7=128 cards in each group, each card has 4 colors marked on it and there are a total of 11 colors used so far
Generation 4 has 2^4=16 groups of 2^6=64 cards in each group, each card has 5 colors marked on it and there are a total of 16 colors used so far
Generation 5 has 2^5=32 groups of 2^5=32 cards in each group, each card has 6 colors marked on it and there are a total of 22 colors used so far
Generation 6 has 2^6=64 groups of 2^4=16 cards in each group, each card has 7 colors marked on it and there are a total of 29 colors used so far
Generation 7 has 2^7=128 groups of 2^3=8 cards in each group, each card has 8 colors marked on it and there are a total of 37 colors used so far
Generation 8 has 2^8=256 groups of 2^2=4 cards in each group, each card has 9 colors marked on it and there are a total of 46 colors used so far
Generation 9 has 2^9=512 groups of 2^1=2 cards in each group, each card has 10 colors marked on it and there are a total of 56 colors used so far
Generation 10 has 2^10=1024 groups of 2^0=1 card in each group, each card has 11 colors marked on it and there are a total of 67 colors used.
No matter HOW you sort the cards by color of the spots you will eventually sort them into the nested hierarchy that created them -- there are no matches of colors specific to one subgeneration with those of another different subgeneration, the only matches across subgroups are with their parent generation marks.
This may seem fairly tame, but now add another wrinkle -- each time you mark a spot in a subgroup you always mark it in the same spot on each card.
Now you can also sort the cards by where the spots are located. Result -- the same nested hierarchy.
Then you add yet another wrinkle -- each 'spot' you make is unique to the supgroup you are marking (say a unique number or a letter is used for each subgroup).
Now you can also sort the cards by the kind of spot on the card. Result -- the same nested hierarchy.
color
location
kind
ALL give the same nested hierarchy, there are no false matches between them.
You could have successive sorting done by different people without instructing what to use for sorting and eventually they would end up with the generating nested hierarchy.
Enjoy.

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This message is a reply to:
 Message 72 by happy_atheist, posted 06-19-2006 2:39 PM happy_atheist has not replied

Replies to this message:
 Message 75 by kuresu, posted 06-19-2006 11:36 PM RAZD has replied

  
kuresu
Member (Idle past 2590 days)
Posts: 2544
From: boulder, colorado
Joined: 03-24-2006


Message 75 of 87 (323646)
06-19-2006 11:36 PM
Reply to: Message 74 by RAZD
06-19-2006 11:31 PM


Re: color coded card analogy
isn't math great. it allows one to prove logic and things like the nested heirarchy (that IS objective) beyond a shadow of a doubt. And all your opponent can do is say "but. . . but . . .but". I'm glad I was able to understand the math behind your argument RAZD. I often find myself unable to understand the more advanced concepts (because my foundation is kinda weak, which is why I'm beefing it up this summer)

All a man's knowledge comes from his experiences

This message is a reply to:
 Message 74 by RAZD, posted 06-19-2006 11:31 PM RAZD has replied

Replies to this message:
 Message 76 by RAZD, posted 06-20-2006 9:17 PM kuresu has replied

  
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