Uncommon Descent Serving The Intelligent Design Community

Antibody affinity maturation as an engineering process (and other things)

Share
Facebook
Twitter
LinkedIn
Flipboard
Print
Email

In Kairosfocus’ very good thread about functional complexity, I posted about antibody affinity maturation as an example of a very complex engineering process embedded in biological beings. Both Kairosfocus and Dionisio suggested that I could open a new thread to discuss the issue. When such good friends ask, I can only comply.  🙂

For lack of time, I will try to be very simple.

First of all, I paste here my original post (#6 in the original thread):

KF:

Thank you for the very good summary. Among many other certainly interesting discussions, we may tend to forget sometimes that functionally specified complex information is the central point in ID theory. You are very good at reminding that to all here.

I would like to suggest a very good example of multilevel functional complexity in biology, which is often overlooked. It is an old favourite of mine, the maturation of antibody affinity after the initial immunological response.

Dionisio has recently linked an article about a very recent paper. The paper is not free, but I invite all those interested to look at the figures and legends, which can be viewed here:

http://www.nature.com/nri/jour…..28_ft.html

The interesting point is that the whole process has been defined as “darwinian”, while it is the best known example of functional protein engineering embedded in a complex biological system.

In brief, the specific B cells which respond to the epitope (antigen) at the beginning of the process undergo a sequence of targeted mutations and specific selection, so that new cells with more efficient antibody DNA sequences can be selected and become memory cells or plasma cells.

The whole process takes place in the Germinative Center of lymph nodes, and involves (at least):

1) Specific B cells with a BCR (B cell receptor) which reacts to the external epitope.

2) Specific T helper cells

3) Antigen presenting cells (Follicular dendritic cell) which retain the original epitope (the external information) during the whole process, for specific intelligent selection of the results

4) Specific, controlled somatic hypermutation of the Variable region of the Ig genes, implemented by the following molecules (at least):

a) Activation-Induced (Cytidine) Deaminase (AID): a cytosine:guanine pair is directly mutated to a uracil:guanine mismatch.

b) DNA mismatch repair proteins: the uracil bases are removed by the repair enzyme, uracil-DNA glycosylase.

c) Error-prone DNA polymerases: they fill in the gap and create mutations.

5) The mutated clones are then “measured” by interaction with the epitope presented by the Follicular DC. The process is probably repeated in multiple steps, although it could also happen in one step.

6) New clones with reduced or lost affinity are directed to apoptosis.

7) New clones with higher affinity are selected and sustained by specific T helper cells.

In a few weeks, the process yields high affinity antibody producing B cells, in the form of plasma cells and memory cells.

You have it all here: molecular complexity, high control, multiple cellular interactions, irreducible complexity in tons, spacial and temporal organization, extremely efficient engineering. The process is so delicate that errors in it are probably the cause of many human lymphomas.

Now, that’s absolute evidence for Intelligent Design, if ever I saw it. :)

The most interesting answers came from Aurelio Smith and sparc. I have already answered AS’s comment in the original thread. Spark’s comments were more specific, so I paste them here  (#58 and 59):

You haven’t looked up evolution of AID, did you?

and

BTW, you let out the part of the B-cell development that occurs without any antigen. Lots of mutations, rearragements and selection. Where and how does ID interfere in these processes. Especially, in cases of man made synthetic artificial antigens that were not present 50 years ago?

OK, I will make just a couple of comments on these two points here, and let the rest to the discussion:

a) My point was not specifically about the evolution of the individual proteins in the system, but about the amazing complexity of the whole system. So, I have not done any detailed analysis of the individual proteins I quote. However, I will look at that aspect. As sparc seems aware of specific information about the evolution of AID, I invite him ot provide some references, and we can certainly go on from there.

b) I did not “let out” the part of the B-cell development. I simply focused on affinity maturation. However, the part sparc alludes to is extremely interesting too, so I will mention here in very general lines how it works, and why it is another wonderful example of intelligent engineering. And we can obviously discuss this second aspect too.

In brief, the adaptive immune system must solve the problem of reacting t a great number of potential antigens/epitope, which are not known in advance (I will use “epitope” from now on, because that is the immulogically active part of an antigen).

So, the two branches of the adaptive immune system (B system and T system) must be “prepared” to recognized possible epitopes coming from the outer world. They do that by a “sensor” which is the B cel receptor (BCR) in the B system, and the T cell receptor (TCR) in the T system.

Let’s focus the discussion on the B system.

To recognize the greatest number of possible epitopes (IOWs, of possible small biochemical configurations, mainly of proteins but also of other molecules), the B immune system builds what is usually known as the “basic repertoire”.Very simply, B cells underso a process of somatic genetic differentiation, essentially based on the recombination of VDJ genes, which generates a basic repertoire of different B clones with specific variable genes for the heavy and light chain, IOWs a specific BCR. In that sense, immune cells are different from other somatic cells, because they have a specific genetic recombination of the variable chains of the BCR (and therefore of the antibody that they will produce.

No one knows exactly how big that repertoire is in each individual, but new techniques are helping much in studying it quantitatively. From what I have read, I would say that the size is probably somewhere between 10^6 and 10^9 (more or less the total number of B cells in an organism).

Now, what is the purpose of this basic BCR (antibody) repertoire? We can consider it as a “network” of lower affinity antibodies covering in a loose way the space of possible epitope configurations. That repertoire is generated blindly (IOWs, without any information about specific antigens) by a process of sophisticated genetic engineering (VDJ recombination and other factors), which again uses random variation in a controlled way to generate diversity.

So, to sum up. two different complex algorithms act to ensure efficient immune responses.

1) The first one generates a “blind” repertoire of lower affinity antibodies covering as well as possible the whole space of configurations of possible epitopes.

2) The second one (affinity maturation) refines the affinity of the B cells selected in the primary response (from the basic repertoire) so that they become high affinity, specialized memory cells. This is the process I described in the beginning, in my post.

Both processes are wonderful examples of sophisticated engineering and irreducibly complex systems, and they are completely different one from the other. Both processes work together in sequence in a sophisticated and irreducibly complex meta-system.

Both use controlled random variation to generate diversity. The second process also uses intelligent selection based on existing information from the environment (the epitope conserved in the Follicular GC cell).

All that is very brief, and in no way covers the whole complexity of what is known. So, let’s open the discussion.

Comments
Box: come to think of it…. “a few small steps” sounds good, however in this hypothetical 5,000-dimensional space there are so many small steps that one wonders if the search is indeed reduced. What it means is that the probability of disconnected islands is vanishingly small. It also means there are many dimensional directions that can lead to increased fitness, many 'ways' to climb.Zachriel
February 19, 2015
February
02
Feb
19
19
2015
06:00 AM
6
06
00
AM
PDT
Gpuccio, Reading Wagner is like wading through a swamp of complete confusion. About your question, the hypothetical 5,000-dimensional space connects everything in a few steps. So that 'solves' the search problem.
Wagner: You can walk from each metabolic text in five thousand different directions, to find one of its five thousand neighbors in a single step. (…) Evolving organisms are like visitors to the metabolic library. Gene deletions and gene transfer allow them to walk through the library, to step from one metabolic text to another, often an immediate neighbor. (…) Evolution can reach them in a few small steps, minor edits in a genotype.
Yes ... it is indeed very "imaginative". edit: come to think of it.... "a few small steps" sounds good, however in this hypothetical 5,000-dimensional space there are so many small steps that one wonders if the search is indeed reduced.Box
February 19, 2015
February
02
Feb
19
19
2015
05:47 AM
5
05
47
AM
PDT
Box: Thank you for trying to help. I must say that I am not any nearer to understand, but certainly it's not your fault. :) What I would like to know is: what is Wagner's "big idea" which explains how extremely unlikely things can be found by random search? Maybe Me_Think can help. After all, he is a fan of the guy. :)gpuccio
February 19, 2015
February
02
Feb
19
19
2015
05:33 AM
5
05
33
AM
PDT
Gpuccio,
GP: And so? After we have discovered that 2^5000 is a big number, and that one can do a silly thing like representing complex biochemical sets of reactions with a 0 or a 1, how does the argument go on?
Excellent question. I think I have uncovered some of Wagner's line of thought. One can say a lot about Wagner as a writer, but one cannot say that his writing style is crisp ... Starting from the quote provided by Me_Think in #489 Wagner focusses on bacteria, because multicellular animals cannot effectively “explore the metabolic library”.
Wagner: the real geniuses of innovation are the smallest organisms on the planet: bacteria.
He goes on listing reasons why: faster reproduction, horizontal gene transfer, absorption of DNA from other cells and so forth
Wagner: (…) bacteria are masters of metabolic innovation. (…) the shelves of life’s universal library contain a virtually infinite number of masterpieces waiting to be found. (…) Everywhere on this planet, a relentless shuffling and mixing and recombining of genes takes place. Wherever microbial life occurs, in the depth of the oceans and on arid mountaintops, in scalding hot springs and on frigid glaciers, in fertile soils and desiccated deserts, inside and around our bodies, life is experimenting with every conceivable combination of new genes, rereading, editing, and rejuggling its metabolic texts without pause, yielding an enormous and still growing diversity of metabolisms.
Here comes Wagner’s first big idea: Because of all this gene transfers between bacteria and other organisms the ENTIRE “library” of all possible metabolic texts is available to every bacterium.
Wagner (commenting on his computer model of E.coli): New genes—acquired through gene transfer or otherwise—can change the genotype that brings forth this phenotype. If this change allows the mutant to metabolize ethanol, we replace the “0” next to ethanol with a “1.” Because every conceivable metabolic innovation can be written like this, by replacing a “0” with a “1” in a metabolic phenotype, there are about as many possible metabolic innovations as there are phenotypes.36
After that Wagner goes on housing the library - which contains the metabolic information of more than two thousand different organisms - in 5,000-dimensional space thereby ‘solving’ the search problem – after he notices that the library is too big to find anything ; see Wagner post # 468. Let's call this Wagner's second big idea. - Is Wagner restricted to explaining bacterial life – since they are the only ones with access to the 'hyperastronomical' library? Wagner himself doesn’t seem to think so and points to various connections between multicellular organisms and bacteria. He seems to hold that the innovations by bacteria explain the innovations of multicellular life:
Wagner: We think of a phenotype as something we can see, and many metabolic phenotypes are plain as daylight. They include the melanins that protect our skin against radiation, that camouflage a lion’s fur, and that color the ink of an octopus. All of them are molecules synthesized by metabolism. And so are the various pigments that dye tree leaves, lobsters, flowers, and chameleons, whether for defense, courtship, or sometimes for no good reason at all.31 But metabolic phenotypes do not end at this visible surface. They extend to depths that are hidden from our eyes yet visible to chemical instruments—and to natural selection. Their most important role is to ensure viability itself, which boils down to the ability to synthesize sixty-odd molecules very different from those pretty pigments—they are the essential biomass molecules I mentioned in chapter 2.
// Summing up: there seems to be some grounding in reality for the availability of the entire library to bacteria – the gene transfer stuff. However I have still no clue what could possibly ground 5,000-dimensional space. //Box
February 19, 2015
February
02
Feb
19
19
2015
05:07 AM
5
05
07
AM
PDT
gpuccio Your expresion "new avalanche of data" @487 is very accurate. I've been selectively looking at what has appeared about very specific topics just recently and it's simply overwhelming. Without the zotero tools I'd be completely disoriented. But even with those tools it's very difficult for me to keep up with what's coming out of research. Even considering that papers have to go through peer-review 'delay' before they get published. How can they analyze all that information accurately? It's beyond fascinating. :)Dionisio
February 19, 2015
February
02
Feb
19
19
2015
02:35 AM
2
02
35
AM
PDT
gpuccio Recent references starting @295 here: https://uncommondescent.com/intelligent-design/mystery-at-the-heart-of-life/#comment-549208Dionisio
February 19, 2015
February
02
Feb
19
19
2015
02:13 AM
2
02
13
AM
PDT
gpuccio Do you consider the subjects of these two recent references (@293-294) interesting too? https://uncommondescent.com/intelligent-design/mystery-at-the-heart-of-life/#comment-549122Dionisio
February 19, 2015
February
02
Feb
19
19
2015
01:15 AM
1
01
15
AM
PDT
Me_Think: By the way, I have dealt with a scenario strongly related to the Library of Babel issue in this OP: "An attempt at computing dFSCI for English language" https://uncommondescent.com/intelligent-design/an-attempt-at-computing-dfsci-for-english-language/ You may have a look at it, if you like. Combinatorial search spaces are the essence of ID theory.gpuccio
February 18, 2015
February
02
Feb
18
18
2015
11:29 PM
11
11
29
PM
PDT
Me_Think: And so? After we have discovered that 2^5000 is a big number, and that one can do a silly thing like representing complex biochemical sets of reactions with a 0 or a 1, how does the argument go on? Just for curiosity. And where are the "5000 dimensions"? Up to now, we have only defined a very abstract set of 5000 "metabolic reactions", and then the set of all their possible combinations, considering each reaction as binary (present or absent). The first set has cardinality 5000. The second set has cardinality 2^5000. OK, that is rather trivial. How does the argument go on? Please, explain.gpuccio
February 18, 2015
February
02
Feb
18
18
2015
09:34 PM
9
09
34
PM
PDT
Box @ 471
I’m not talking about metabolic pathways. I’m talking about the hypothesized “hyperastronomical metabolic library” and multidimensional space. Are you saying that these are empirical facts?
Of course it is based on facts. Why don't you read the book?:
thanks to twentieth-century biochemistry and to the technological revolutions of the early twenty-first century. They gave us access to a mountain of metabolic information on more than two thousand different organisms, stored in giant online repositories, such as the Kyoto Encyclopedia of Genes and Genomes, or the BioCyc database, and accessible in split seconds from any computer with an Internet connection.2 Figure 4 shows how we can organize this information. The left side of the figure stands for a list of five thousand reactions—written as chemical equations. To avoid clutter I wrote out the molecules in only one of them—the sucrose-splitting reaction—but simplified all others to a single letter. Let’s consider one organism, such as E. coli or a human, and mark a “1” next to a reaction if our organism can catalyze this reaction—it has a gene making an enzyme for it. Otherwise we’ll mark a “0.” The result is a long list of ones and zeroes like that in the figure, a compact way to specify a metabolism. Bacteria such as E. coli can make all twenty amino acids in proteins, whereas metabolic cripples like us humans can make only twelve of them. We lack the necessary enzymes and reactions for the remaining eight. The figure’s shorthand way of describing a metabolism is ideal for expressing differences like this: Because we lack some reactions, our list of reactions contains some zeroes where that of E. coli contains ones. A list like this is also an extremely compact way to write an organism’s metabolic genotype—the part of the genome encoding its metabolism—because an organism’s list of reactions is ultimately encoded in its DNA. You can also think of the list as a text written in an alphabet with only two letters, and without spaces or punctuation marks, like this: “1001 . . . 0110 . . . 0010.” The first letter in such a text might correspond to the sucrose-splitting reaction, which is present (“1”) in this example, whereas the second reaction might be one of those needed to synthesize an essential amino acid—it is absent (“0”) in this example text but could be present (“1”) in another organism’s genotype—and so on. It is a text in a library vast beyond imagination, the library of all possible metabolisms. The number of texts in that library can be calculated with the same arithmetic that computed the size of the universal library of books. Because each reaction in the known universe of reactions can be either present or absent in a metabolism, there are two possibilities (present or absent) for the first reaction, two for the second reaction, and so on, for each reaction in the universe. To calculate the total number of texts, we multiply the number 2 by itself as many times as there are reactions in our universe. For a universe of 5,000 reactions, there are 2^5000 possible metabolisms, 2^5000 texts written in the alphabet of zero and one, each of them standing for a different metabolism. This number is greater than 10^1500,( MT: actually it's 1.4 x10^1505. If we take 5,500 as lsited in BioCyc, we have a 'library' of 4.62x10^1655) or a 1 with 1,500 trailing zeroes. While not quite as large as the number of texts in the universal library of human books, it is still much larger than the number of hydrogen atoms in the universe. The metabolic library is also hyperastronomical.
Similarly, for proteins of say 150 amino acids, each genotype will have 150 x 19 (20-1) = 2850 neighbors in the genotype network. He even gives the reason for the library analogy (in Chapter Three Notes)
This analogy is inspired by a famous short story of the Argentine author Jorge Luis Borges entitled “The Library of Babel” (Spanish original: “La biblioteca de Babel”), published in English translation in Borges (1962). The idea behind this short story, however, predates Borges. It has been used by many other authors, including Umberto Eco and Daniel Dennett
Me_Think
February 18, 2015
February
02
Feb
18
18
2015
06:08 PM
6
06
08
PM
PDT
gpuccio
Great stuff on Nature from the NIH Roadmap Epigenomics Consortium! Now, let’s absorb this new avalanche of data. :)
Yes, that's exactly right!Dionisio
February 18, 2015
February
02
Feb
18
18
2015
05:46 PM
5
05
46
PM
PDT
Dionisio: Great stuff on Nature from the NIH Roadmap Epigenomics Consortium! Now, let's absorb this new avalanche of data. :)gpuccio
February 18, 2015
February
02
Feb
18
18
2015
01:47 PM
1
01
47
PM
PDT
Dionisio: You ask: "Maybe that has been done already? Is it documented somewhere?" I will answer quoting Me_Think's words (hardly an accomplice of mine): "However evolution of a system which has not been studied (search throws up very few papers, some paywalled) widely can be answered by specialists only, and there aren’t any visiting UD." The simple answer is: it has not been done; it is not documented anywhere. Like many other things...gpuccio
February 18, 2015
February
02
Feb
18
18
2015
12:16 PM
12
12
16
PM
PDT
Aurelio Smith: "We should not confuse maps and territories." Absolutely! That's one of my strongest principles. (Have you ever read about NLP?) :)gpuccio
February 18, 2015
February
02
Feb
18
18
2015
12:09 PM
12
12
09
PM
PDT
#480 addendum Perhaps a more practical approach, instead of trying to resolve abstract probability problems, would be to try to describe in details how our best scientists and engineers would have built the known biological systems, but in a way that could have also occurred 'naturally' without their intervention? Maybe that has been done already? Is it documented somewhere? However, most probably the majority of the researchers are busy trying to figure out how the biological systems function, hence they don't have time to squander on senseless OOL research. :)Dionisio
February 18, 2015
February
02
Feb
18
18
2015
11:40 AM
11
11
40
AM
PDT
Aurelio #482, Thank you. I gather now that your posting #474 was in fact not responsive to what I said - “hyperastronomical metabolic library” and "multidimensional space" are terms used by Wagner and are not equal to RM and NS.Box
February 18, 2015
February
02
Feb
18
18
2015
11:19 AM
11
11
19
AM
PDT
finding the needles in the haystacks won't resolve the problems: #436 gpuccio
let’s think abstractly and assume for a moment that all those challenges are ‘somehow’ (borrowing a term commonly seen in some ‘scientific’ literature these days) overcome and that all the required proteins can be ‘somehow’ produced, through genetic expression or another way. Does that get us the amazingly complex interwoven mechanisms that researchers see in the biological systems?
No, it doesn’t.
IOW, the protein availability is a necessary condition, but is it sufficient, in order to have those elaborate cellular and molecular choreographies orchestrated within the biological systems?
No, it is not.
Are there other factors to consider?
yes, there are. Let’s say that we are in front of an amazing multilayered irreducible complexity. :)
Dionisio
February 18, 2015
February
02
Feb
18
18
2015
10:30 AM
10
10
30
AM
PDT
gpuccio Several new references to recent papers on very important subjects (posts #288-291) in this thread: https://uncommondescent.com/intelligent-design/mystery-at-the-heart-of-life/#comment-549082Dionisio
February 18, 2015
February
02
Feb
18
18
2015
10:11 AM
10
10
11
AM
PDT
Aurelio Smith: It’s an analogy for the multi-dimensional nature of the niche environment.
Reference please. I have Wagner's book in front of me. A search for "niche" produces just one unrelated hit: 'But because waters of all temperature mix around a vent, a suitable temperature niche exists for any one of proto-life’s chemical transformations'Box
February 18, 2015
February
02
Feb
18
18
2015
09:55 AM
9
09
55
AM
PDT
Aurelio Smith: That is a discussion I have had many times, probably even with you. No reason to repeat all the details here. My simple point is that nobody has ever said that there is only one needle. The number and probability of needles is an integral part of ID theory. That's why I am really amazed that Wagner and you are so excited by the idea that there is more than one needle. That's all.gpuccio
February 18, 2015
February
02
Feb
18
18
2015
09:54 AM
9
09
54
AM
PDT
Aurelio Smith:
You could say the environment is the designer of evolutionary change.
You can say anything, however you still need the evidence to support it.Joe
February 18, 2015
February
02
Feb
18
18
2015
09:38 AM
9
09
38
AM
PDT
Me_Think: Yous arguments still look silly. First of all, define what you mean by "dimensions". OK, there are a number of metabolisms. And a number of functional proteins. But those are not dimensions. They are occurrences. The search space is the combinatorial space of sequences. There is no other search space, because random variation is random variation of nucleotide sequences. The only correct question is: how many of the possible combinatorial sequences are functional? How many are selectable? What is the sequence relationship between functional islands? (That we know well: none, at the superfamily level). These are the questions. The rest is (how was it, DNA_Jock?): bafflegab.gpuccio
February 18, 2015
February
02
Feb
18
18
2015
09:26 AM
9
09
26
AM
PDT
Aurelio Smith: No need to shout. Everybody knows that. And most needles are so small, that the probability of finding one of those needles is so low that it will never happen. Shout that, if you like.gpuccio
February 18, 2015
February
02
Feb
18
18
2015
09:19 AM
9
09
19
AM
PDT
Me_Think, I'm not talking about metabolic pathways. I'm talking about the hypothesized "hyperastronomical metabolic library" and multidimensional space. Are you saying that these are empirical facts?Box
February 18, 2015
February
02
Feb
18
18
2015
09:17 AM
9
09
17
AM
PDT
Box, 5000 is the metabolic pathways number - it is not a fantasy. The library is hypothetical in the same sense that landscape in search landscape is (Axe, Dembski et al). Wagner shows how searching the genotype network at hyper dimension (which is structural dimension) reduces search space. I think if you read the book for comprehension instead of for scoring points, you would understand.Me_Think
February 18, 2015
February
02
Feb
18
18
2015
08:51 AM
8
08
51
AM
PDT
Me_think #466, You seem to suggest that Wagner's reduction of search space has to do with known biologic structures.
Me_Think: When you take biological structural dimension into account, the search space reduces.
This is not the case at all - it's all fantasy stuff. Wagner hypothesizes a huge (hyperastronomical) "metabolic library" and then looks for an environment / organization that solves the search problem that follows from such a huge library. He comes up with follow-up hypothesis: 5,000-dimensional space. Search problem solved, since the hypothesized multidimensional space connects everything in the hypothesized library by just a few steps. IOW this is all just pure fantasy stuff and there is no connection whatsoever with biological structures as we know them.
But although it is hopeless to imagine higher-dimensional spaces, they follow the same laws as our three-dimensional space: The edges of a hypercube are equally long, adjacent edges are at right angles to one another, and each corner corresponds to a possible metabolism. And such cubes in high-dimensional space turn out to have curious properties well suited to house the metabolic library. The number of corners in a square is four, in a cube it doubles to eight, and in a four-dimensional hypercube it doubles again to sixteen. With every added dimension, it doubles, and by the time you have reached 5,000 dimensions, this number has become the hyperastronomical 2^5000, the size of the metabolic library. In other words, we can arrange the library’s metabolic texts on the corners of a hypercube in a 5,000-dimensional space. This is why off-the-shelf shelving would not work. You cannot cram the metabolic library into three puny dimensions. It needs thousands of dimensions to breathe. [Wagner, Chapter 3]
Box
February 18, 2015
February
02
Feb
18
18
2015
08:40 AM
8
08
40
AM
PDT
....continued from comment #437
A more appropriate argument would be if you claim network search cannot be equated to landscape search and so volume search doesn’t apply -only surface area of the search sphere should be used. May be I would be stumped ,or not – I would have to work that out
Ok. the math works out as below: The surface area of the network over the search sphere can be given by 2 Pi^(d/2)/ Gamma (d/2) Derivative with respect to d gives Pi^d/2 [Log(Pi)- Ploy Gamma (0, d/2)]/ Gamma (d/2) Solving for d and Finding root gives the Maximum surface Area at dimension 7.26, so the maximum surface area is reached at 7th structural dimension. Since bio-structures are all above 7 dimension we can safely say even if we take search space as a surface area and not volume, above 7 dimensions, the area will keep decreasing. As an Example for a unit sphere and dimensions from 1 to 10 will give :
2, 2 (Pi), 4 (Pi), 2 (Pi)^2, (8 (Pi)^2)/3, (Pi)^3, (16 /(Pi)^3)/15, (Pi)^4/3,(32 (Pi)^4)/105, (Pi)^5/12
which gives:
2, 6.28319, 12.5664, 19.7392, 26.3189, 31.0063, 33.0734, 32.4697, 29.6866, 25.5016
Note that area falls off after dimension 7. At 100th dimension, the value is just Pi^50/304140932017133780436126081660647688443776415689605120000000000 = 2.3682*10^-38Me_Think
February 18, 2015
February
02
Feb
18
18
2015
08:37 AM
8
08
37
AM
PDT
SA and Box, If you understand Axe's landscape search with minima and maxima hills and landscapes, you should have no problem understanding Wagner's hyper-dimension search Both Axe and Dembski's search is a white noise landscape search. When you take biological structural dimension into account, the search space reduces. As commented earlier in this thread:
Imagine a solution circle (the circle within which solution exists) of 10 cm inside a 100 cm square search space. The area which needs to be searched for solution is pi x 10 ^2 = 314.15 The total Search area is 100 x 100 = 10000. The % area to be searched is (314.15/10000) x 100 = 3.14% In 3 dimensions,the search area will be 4/3 x pi x 10^3 Area to search is now cube (because of 3 dimensions) = 100^3. Thus the % of area to be searched falls to just 4188.79/100^3 = 0.41 % only. Hypervolume of sphere with dimension d and radius r is: (Pi^d/2 x r^d)/r*(d/2+1) r* = Gamma function - when will UD enable LaTeX ? HyperVolume of Cube = r^d At 10 dimensions, the volume to search reduces to just: 0.000015608 % In the number of dimensions where our circuit library exists—get ready for this—the sphere contains neither 0.1 percent, 0.01 percent, nor 0.001 percent. It contains less than one 10^ -100th of the library
Me_Think
February 18, 2015
February
02
Feb
18
18
2015
08:00 AM
8
08
00
AM
PDT
As far as I understand Wagner he holds that the old RM+NS is incompetent as a search. IOW his book confirms the ID critique on Neo-Darwinism. How does he 'solve' the search problem? By hypothesizing things like hyperastronomical libraries in multidimensional space, genotype networks and other undetectable fantasy stuff. Okay admittedly that would speed up the search. However the law of conservation of information teaches us that you cannot beat a blind search. So where does the information in the libraries and the networks come from? This question Wagner attempts to answer by "self-organization".Box
February 18, 2015
February
02
Feb
18
18
2015
07:49 AM
7
07
49
AM
PDT
And the same holds for regulation circuits—we already heard about a circuit in the bacterium Escherichia coli that can be rewired in the laboratory without ill effects (chapter 5).
Regulatory circuits that can be re-wired without ill effects are far more evidence for design than of an unguided process. Robustness is a quality for the preservation of life - or survival, as the author says. But this apparent need for survival is also unexplained in a blind, chemical process. What it says, instead, is that life is something entirely different than chemical combinations alone. Robustness, preservation, stability, regulation and defense of the organism, self-organizing networks and the centrality of survival -- all point to life as something important, or intended.Silver Asiatic
February 18, 2015
February
02
Feb
18
18
2015
07:43 AM
7
07
43
AM
PDT
1 2 3 4 18

Leave a Reply