[...] Let us step back and consider another interesting analogy that can be established between the double Möbius strip, its principle of unity through perpetual duality, and the DNA (discovered by Watson, Crick and Wilkins): the model of the double helix is composed of two serpent-like intertwining spirals, representing a biological reflection of the archetypal idea of time as a spiral, creating a reunion of the linear and the cyclical aspects of time as a perpetual flow [...]
[...] One way in which DNA -- which, as everyone knows, takes the form of a double-helix (which looks like a twisted ladder) -- can replicate is by splitting the double helix up the middle into two pieces. Cut the rungs of the 'ladder', and the posts fall apart. But if the DNA is in the form of a closed circle, something interesting happens. When it is split down the middle, it will fall -- unlike our BILATERAL ribbon did --into TWO separate closed circular ribbons. You can see how that works by making a bilateral ribbon (with one "full" twist of 360 degrees). If you cut it up the middle, the two bilateral pieces it falls into will be linked like the two links of a paper chain -- with one "cross over." Furthermore, as the number of full twists in the bilateral ribbon that you start with increases, the more times the two resulting ribbons will cross over each other. When you split a bilateral ribbon with 7 full twists, you get 7 "crossovers" in the two offspring ribbons -- which will look like the figure above [...]
These interesting characteristics do not only indicate the non-Euclidean nature of the double Möbius strip, thus making it an ideal polygon for formal and conceptual research in post-Cartesian architecture, they also refer to a possibility of reversing and even uniting archetypal binary notions of surface/volume, space/time, inside/outside, matter/media etc. Let us step back and consider another interesting analogy that can be established between the double Möbius strip, its principle of unity through perpetual duality, and the DNA (discovered by Watson, Crick and Wilkins): the model of the double helix is composed of two serpent-like intertwining spirals
Your mentioning of the binary notion and DNA reminded me of a very interesting discovery I read about some time ago:Calculating that 0 + 0 = 0, 1 + 0 = 1, and 0 + 1 = 1 is normally no big deal. When the calculations are done in the lab using DNA molecules, however, these elementary manipulations look considerably more interesting. Researchers at the Mount Sinai School of Medicine in New York City reported some years back that they have developed an algorithm that permits the use of single-stranded DNA reactions to add binary numbers. More impressively, they had the experimental evidence to back their scheme. Since 1994, when computer scientist Leonard M. Adleman of the University of Southern California first demonstrated the feasibility of a molecular approach to solving mathematical problems, researchers focused on finding ways to link mathematics and biochemistry to perform different kinds of computations. Their long-term hope is that DNA-based computers will eventually prove superior in speed, memory capacity, and energy efficiency over electronic computers for solving certain kinds of problems. Most research efforts have tried to take advantage of the enormous number of DNA molecules that can be packed into a small volume. Adleman, for example, solved a combinatorial problem by generating all the possible combinations as different strands of DNA, then searching for, isolating, and identifying the one strand representing the correct solution. In contrast, Mount Sinai's Frank Guarnieri and Carter Bancroft have concentrated on developing a DNA-based addition algorithm, which demands only that the correct output be produced in response to specific inputs. Consequently, the addition operation requires a quite different model for the use of DNA in computing than that used previously for search procedures. A single strand of DNA consists of a chain of simpler molecules called bases, which protrude from a sugar-phosphate backbone. The four varieties of bases are known as adenine (A), thymine (T), guanine (G), and cytosine (C). Any strand of DNA will adhere tightly to its complementary strand, in which T substitutes for A, G for C, and vice versa. For example, a single-stranded DNA segment consisting of the base sequence TAGCC will stick to a section of another strand made up of the complementary sequence ATCGG. The links between pairs of bases are responsible for binding together two strands to form the characteristic double helix of a DNA molecule.The researchers first assigned 3-base units to letters of the alphabet, numerals, and punctuation marks. Adding binary numbers, represented as strings of 1s and 0s, requires keeping track of the position of each digit and of any "carries" that come up when 1 is added to 1 to give the result 10. For example, adding 11 to 01 means starting with the digits farthest to the right of each number: 1 + 1 = 10, so 0 goes in the first place from the right, and 1 is carried over to the next column. When the carried digit is added to the two digits in the second position from the right (1 + 1 + 0), the result is 10, with 0 in the second position from the right and 1 in the third position to give the final answer 100. 1 1+ 0 1-------1 0 0Converting this procedure into manipulations of DNA molecules demands the use of DNA sequences that not only represent strings of 0s and 1s but also allow for carries and the extension of DNA strands to represent the answers. In their DNA addition algorithm, Guarnieri and Bancroft use special sequences that encode the number in a given position (0 or 1) and its position from the right. For example, the first digit in the first position is given by two DNA strands, each consisting of a short sequence representing a "position transfer operator" (which carries information to the adjacent position), a short sequence representing the value of the digit (0 or 1), and a short sequence representing a "position operator." In their Science paper, Guarnieri, Bancroft, and Makiko Fliss supply DNA representations of all possible two-digit binary integers (00, 01, 10, 11), which can then be added in pairs. Adding such a pair involves four steps, in which the appropriate complementary sequences link up and strands are successively extended to make new, longer strands, finally yielding the correct output. The researchers term this set of steps a horizontal chain reaction. Input DNA sequences serve as successive templates for constructing an extended result strand. Like a tape recording, the final strand encodes the outcomes of successive operations, yielding the digits of the answer in the correct order. The growing strand is also an active participant in the addition algorithm because the output strand for each operation (reaction) serves as the operator (primer) for the succeeding operation. Thus, the resulting DNA strand serves both as an operator that transfers information during the addition algorithm and as a tape that records the outcome of the algorithm. What they've done with the horizontal chain reaction is to start getting DNA molecules to communicate with each other. To test their algorithm in the lab, the team combined in a test tube the DNA strands representing the two numbers to be added, along with the chemicals needed for the strand extension reactions. In this way, they successfully determined the sums 0 + 0, 0 + 1, 1 + 0, and 1 + 1 in the form of DNA strands of the appropriate molecular size. The necessary biochemical procedures took about 1 or 2 days of lab work for each calculation.
I read that the blueprint stored in DNA, an organism's genome, is, in effect, the program that describes how an organism builds itself and functions throughout its life. This information is subdivided into many discrete packages of instructions (genes). Each gene is typically associated with a particular function or trait (such as the instructions for producing the hemoglobin molecule used by red blood cells). An organism's DNA program is not read in its entirety from start to finish, but is broken down into many smaller units, each of which can be accessed as needed. An igene, like a gene, is a set of computer instructions that can be incorporated into other, more complex programs. Just as the gene for hemoglobin doesn't describe how to build an entire blood cell, an igene that describes how to calculate the sine of a number is a component that deals with a small part of a larger task. This modular approach for packaging instructions allows us to create symbols that are shorthand for an otherwise complicated set of instructions, and to combine these symbols to describe complex processes in shorthand form. The key difference between an igene and a gene is the igene contains computation instructions whereas a gene describes how to build a protein that is used by an organism. When an alien civilization first encounters our hypothetical radio message (or we detect a similar message ourselves), all they will see is an apparently endless stream of binary numbers. At first, the message will appear to be hopelessly jumbled and devoid of meaning. If it is not formatted so that it contains clues about its structure, the party on the receiving end may never figure out how it is organized, and will never be able to get beyond receiving the signal. The first step on the path to comprehension is to figure out how the series of numbers is organized into the equivalent of words, groups of words, groups of groups of words, and so on. A good metaphor to use is the general format of the information encoded in DNA. Learning the format of DNA is not the same thing as learning the meaning of the instructions encoded in DNA. The first step is to figure out how the information encoded in a genome is broken down into smaller subunits of information. Knowing how genetic information is organized doesn't mean that we understand what every gene does, but merely that we know how to parse this data into the equivalent of words and sentences.
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