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(human-centric def: what passes between us when we communicate) the removal of uncertainty or suppression of randomness |
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map associating symbols with what they represent- any isomorphism can encode any meaning, key is in construction/maintenance of map. this is the basis of coding. |
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choice of symbol/physical representation for an idea; the need to invent new symbols or symbols that take time/space; hand #s, roman numerals grow in proportion to # |
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1) should not need to invent new symbols to encode new things 1a) should be a fixed alphabet 2) should be efficient- size doesn't grow with thing encoded- many things encoded in small space- length(d) about= its info content |
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the # of combinations that can be made out of a set # of things. N symbols, code of length d, N^d combinations |
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# of items that can be encoded explodes as length of code increases- efficient code |
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combinatorial code that uses #s- (#, #) <#, #, #>. length of vector corresponds to dimension in space |
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the more improbable an event.. |
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the more information provided when it occurs (claude shannon) |
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identifies one object out of a set |
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shannon's measurement of info content |
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how many y/n questions does it take to identify? pres approval has 7 questions, or 7 bits |
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evolution defined through information theory |
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accumulation of useful information- to create an improbable event like the organization of atoms into an organism |
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evolution defined through information theory |
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accumulation of useful information- to create an improbable event like the organization of atoms into an organism. not possible w/out some kind of info storage |
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improbable event of weaving complex pattern into cloth- info not in loom, but punched cards-->1st computers |
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encoding in some medium, transforming the encoding via rules. any time info transformed in precisely determined way, computation takes place |
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the body is a machine, the mind is not separate from the body |
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arithmetic can be performed by machine- invented one, based on pedometer |
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logical reasoning can be performed by a machine (boolean arithmetic) |
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babbage's analytical engine, born of difference engine- key was to separate sequence of operations from machines (create a program). store (storage) + mill (arithmetic) + program |
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1) set out in finite terms exact instructions 2) produce desire result in finite steps 3) could be carried out by human and pencil 4) demands no insight/ingenuity on part of human |
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any mechanically computable function can be completed on turing machine |
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has a fixed set of states and can simulate any TM. reads the description of the encoded TM, acts like the encoded TM operating on the input |
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what it means to be universal |
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means to store fixed set of symbols (tape, means to perform simple operations on those symbols (execution unit), means to follow precisely defined set of instructions |
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has universality, can store a set of #s or symbols, perform operatiosn on them, and follow arbitrary set of instructions |
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set of instructions that solves particular problem (a recipe) crucial elements: specified set of inputs, set of steps w/ clear beginning end, appropriately specific and feasible, eventually stops, must be executed by machine, work for all inputs. fastest algorithm is the best |
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relationship bt size of text of a program and time it takes to run |
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there is no simple relationship |
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expression describing # of steps needed as function of problem size |
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# steps grows more slowly;faster;much faster;in proportion to input size |
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logarithmic;polynomial;exponential;linear complexity |
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Travelling Salesperson Problem |
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there are n! paths, which makes complexity even worse than exponential. like the knapsack problem this is the best we've got. |
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computationally unfeasible, currently. if we could solve one we could solve them all |
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the self-reference of the halting problem |
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if P halts, B doesn't, if P doesn't, B does- if B doesn't, B does |
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noncomputable problems reveal deep truths about computation |
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can be self-referential, can resist analysis |
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continuous, infinite inputs, no separation from noise & entropy; finite, discrete set of inputs- put into binary, easy to identify noise |
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the addition of error in copying info; the tendency for things to become disordered |
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information pattern that is relatively permanent or common. digital copying allows stable information patterns |
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one of the simplest forms of computing |
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rules of the utm ecosystem |
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utms move randomly from tape to tape, can read or write more than one tape, fixed amount of tape, error sometimes occur |
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write program R on a tape- a self-replicating program |
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write x on each of two tapes (fecundity); write y on a tape, then check to make sure it was written correctly (copy-fidelity); if tape has z, re-write to refresh it (longevity) |
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selfishness in UTM ecology |
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hoarding tapes, outcompeting neighbors for tapes |
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separate copies of pattern are |
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indistinguishable- not the tape itself that matters, but the pattern on it |
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machine that can only copy itself in the absence of mutations |
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array of cels that have two states + simple set of rules for updating cell states over time. 2^8 (256) possible rule sets- 256 ways ca might evolve in time |
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four classes of CA rule behavior |
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uniformity (all black/white/simple patterns); structure (nested patterns of considerable complexity); chaos (no predictable patterns); local structure (mixture of things happening locally with background simple patterns) |
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fundamental fact of nature |
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simple computations can yield unexpected, surprising results |
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pattern that emerges when molecules move randomly- can't observe by looking at one molecule |
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nested- interesting bc contains itself- portion is rescaled version of whole thing |
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game of life as ex of emergence |
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existence of gliders/shooters shows properties not built in- high level properties can't be predicted from low-level ones |
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emergence defines disciplinary boundaries |
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physics-> chem, chem->bio, bio->anthro, antro->philosophy/lit/art |
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emergence's relationship to noncomputability |
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cannot tell by looking at rules whether interesting properties will emerge. also the only way to find out for all programs p "does p do x" is to run program p. computation is inscrutable! |
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what underlies the wave/particle level of physics? the universe is a computer |
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key to emergence of life on earth |
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discovery by nature of how to extract and efficiently encode information- had only atoms/molecules to work with |
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life= metabolism;reproduction |
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obtaining energy from environment to break dwon raw materials into building blocks and construct/repair body & structure; make approximate copies of one's self |
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constructive, copying and control machines creates self-replicating machine+blueprint. gets corrupted and carries corruption |
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collisions of molecules, leading to rearrangement of atoms into new molecules- depends on molecule shape |
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molecule whose presence accelerates reaction without being changed |
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molecule made by stringing many small units from fixed set. long chains, define molecules shape and can carry info. sugar, amino acid, nucleotide- 3 polymers imp in life |
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how self-replicating info could arise. molecule that catalyzes own reaction. was probably rna |
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consist of backbone+base, always read 5->3, bases can bond to each other (A to U or G to C) |
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AUGC- elaborate structure, carry info, self-replication possible |
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rna templated polymerization |
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catalyst that causes copying of any other rna molecule- a tape copying turing machine |
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interacts w/ environment, resists entropy |
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evidence for rna world in prebiotic world- put methane, ammonia, hydrogen, water + electric current, found organic compounds |
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Catalytic and autocatalytic RNA can be produced in lab, Key cellular reactions are still catalyzed by RNA in nature, Even simpler replicators could have predated RNA |
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collection of molec that together are capable of more efficient replication- ex ribozymes that catalyze nucleotide production- beginnings of the cell |
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no machine needed, as in membranes |
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polymers with 20 possible subunits- much greater variety of molecule shapes available with their existence |
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improves longevity, much more stable, thymine instead of cytosine allows error correction |
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bacteria, archaea, eucaryotes- different ribosome, energy production different |
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information processing machinery |
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bacteria (unshielded chromosomes) and archaea & eucaryotes (histones, promoters) |
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alternate definitions of life |
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nasa- information first: self-sustained chemical capable of darwinian evolution. sagan- metabolism first: localized region increases in order through cycles driven by energy flow |
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first protein we learned a lot about- transports oxygen in lower animals (we use hemoglobin) |
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digestion. digests whatever contacts- deactivated while in cell until stomach |
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myosin and actin, bathed in ATP |
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myosin flexes- millions of molecules together make a muscle fiber |
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doesn't repeat- high information content. as in, chromosomes |
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eukaryotes->prokaryotes->viruses->proteins->small molecules->atoms |
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defense. several flexible arms-adaptive. 2 to 10 binding sites, 10^15 in our blood |
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communication. describes amount of sugar in blood, tells organs what to do. small distinctive shape, difficult folding problem |
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structure- triple helix. tendons, skin, organs |
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protein folding is a problem for cells- misfolding->alzheimers, sickle cell disease. folding environments chaperone folding |
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darwin said inherited traits are fluid, children get mixtures. mendel said at least some are discrete- traits inherited in numerical ratios, each parent passes half. genetic info is digital. |
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shows pneumonia's virulence changed by altering dna- implicates dna as material of heredity |
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dna replication is obvious |
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because of the structure- two strands with paired bases |
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part of dna where unzipping starts |
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shows where replication should start from by creating tags |
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protein structure of dna inherited in egg cell |
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dna transcribed to rna, rna translated to proteins (takes place in ribosome outside nucleus) |
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code for a single protein. many genes on each dna strand. specific markers show start/stop of genes |
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code embodied in tRNA. amino acid on one end, anticodon on other. 20 kinds, one for each amino acid |
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two parts lock together with mRNA in between. decoding happens here |
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remarkable separation of information and machinery |
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responsible for info flow. finds mRNA, matches codons with anticodons. |
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error resistance of gene encoding |
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many more codes than amino acids |
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process of making two things similar. allows single evolutionary advance to be used over and over. transformation of repeating structures can be basis for emergence of new species. |
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how embryo forms. timing and place of gene expression is a control problem |
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start at first instruction, proceed in order unless instructed otherwise. tedium fixed with subroutines |
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instruction that presumes certain level of knowledge-packaged set of instructions that can be used in mult. programs/places/times |
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gene where "run subroutine" command is found. every multicellular animal has this 180 base pair sequence in common. part of transcription factor |
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tells homeotic genes whether to turn other genes on |
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a repressor, as with fluorescence of squid |
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