> 87(
/0DTimes New Roman4?| )0Y0DMathematica1an4?| )0Y0 DTimesNewRomanPSMT| )0Y00DTimesNewRomanPS-ItalicMTY0@DTimesNewRomanPS-BoldMTTY0PDWP MathAomanPS-BoldMTTY0
`.
@n?" dd@ @@``x4
c$@{uʚ;2Nʚ;g4MdMd )0ppp@<4!d!d0D @<4dddd0D @<4BdBd0D @?%
` ` ̙33` 333MMM` ff3333f` f` f` 3>?" dd@,|?" dd@ " @ ` n?" dd@ @@``PR @ ` `p>> f(
6$ P
T Click to edit Master title style!
!
0
RClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level!
S
0 ``
>*
0$ `
@*
0 `
@*H
0h ? ̙33 Default Design,5(
,
,
0}@ppk
_Three conceptions of emergence:
Material (ontological)
Objective unpredictability
Conceptual" 2@ 2`H
,0h ? ̙33l0(
0t
0
0}@`&
One kind of material emergence fusion
Key idea: original objects lose their identity in fusing to produce a new object with novel properties
Examples:
Non-separable (entangled) states in quantum mechanics
Some functional systems such as monetary units (but here properties are additive); a few merged organizations e.g. UVA environmental science department" 2 2lH
00h ? ̙33RJ0(
0t"}
JVUnpredictability as computational incompressibility:
One difference is between:
(1) {Si (t+T)} = U{Si (t)}, for arbitrary T, where U is an updating function
e.g. predicting a solar eclipse at any point in the future
and
(2) {Si (t+T)} = UT{Si (t)}
e.g. unavoidably processing step-by-step iterations of updating for many agent based models.W 2W
acPV}
cH
0h ? ̙334`$t(
$<
$
0}`
(Computer simulations produce computationally emergent phenomena.
`Assume that P is a nominally emergent property possessed by some locally reducible system S. Then P is weakly emergent if and only if P is derivable from all of S s micro facts but only by simulation.
(Mark Bedau `Downward Causation and Autonomy in Weak Emergence , Principia Revista Inernacional de Epistemologica 6 (2003), pp. 5-50.)
R 250>>H
$0h ? ̙33TLp((
(
(
0t}
LComputing the partition functions (and hence the exact energy levels) for finite lattices of non-planar 3D and 2D Ising models are NP-complete problems.
(S. Istrail, Statistical Mechanics, Three-Dimensionality and NP-Completeness: I. Universality of Intractability of the Partition Functions of the Ising Model Across Non-Planar Lattices, Proceedings of the 32nd ACM Symposium on the Theory of Computing (STOC00), ACM Press, p. 87-96, Portland, Oregon, May 21-23, 2000 ) 2>q%H
(0h ? ̙33 Y(
!
0}p
KAn algorithm is intractable if the number of computational steps or the amount of memory required for an output is an exponential function of the input.
Example of intractable problem:
For a statement of Presburger arithmetic, length n, every algorithm deciding its truth has a runtime of at least 2^[2^[cn]] for some constant c.
&L 21,ZH
0h ? ̙33P0(
0q}&
DConceptual Emergence
`The ability to reduce everything to simply fundamental laws does not imply the ability to start from those laws and reconstruct the universe& .The constructionist hypothesis breaks down when confronted with the twin difficulties of scale and complexity& ..At each stage entirely new laws, concepts, and generalizations are necessary (P.W. Anderson `More is Different , Science 177 (1972), pp.393)
8 2H
0h ? ̙33B@(
J
0(S}` `S
One aspect
Let X be the state space for the system S . Then:
In general we do not have a closed form function F : X -> X that takes the current global state
X(t) = (s1 (t),...,sn(t)) 0 X
and maps it into some other state in the state space X
F(X(t)) = X(t+1)
Such a function is only implicitly given through the updating schedule. [This is because there is only an implicit global state.] The classical dynamical systems which can be explicitly given such a global dynamics are special cases. (Modified from: Steen Rasmussen and Chris Barrett `Elements of a Theory of Simulation European Conference on Artificial Life 95)
(2i 2t/ 7*
*,H
0h ? ̙336.(
00}$D0TL___PPT9.&
*Claims:
This re-conceptualization is often at the level of abstract, computationally tractable, structure.
Computational methods can thus result in a shifting of the boundaries between the sciences. What is important is computational form and methods (`computational templates ) not content. Fitness/energy landscapes are used to solve optimization problems in evolutionary biology, neural nets, financial markets; models originally invented to model the percolation of water through rocks are used to simulate forest fires, etc.
B 2 2 2 @`H
0h ? ̙33~4(
4
4
04(P4
~Some resources:
`Emergence in The Encyclopedia of Philosophy (Second Edition). London: MacMillan, 2006.
Emergence: Contemporary Readings in Science and Philosophy, Mark Bedau and Paul Humphreys (eds). Cambridge, MA: The MIT Press, 2007.B 21:J>X I'H
40h ? ̙33r8`Q%I*1`0"H-*!8;
Oh+'0`h
PowerPoint Presentation we we3weMicrosoft PowerPointon@P@@h 4@0*(4SGg C6& &&#TNPP2OMi
&
TNPP &&TNPP
--- !---&G&w@
ww 0w f,- &Gy& ---- @Times New Romanww 0w f,- .62
Three conceptions of emergence:
. . 2
=. .(2
=Material (ontological) . . 2
v. ..2
vObjective unpredictability . . 2
. .2
Conceptual .--"System, f,
!-&TNPP &՜.+,0(
On-screen Show
UVa HS/CSShc<'
Times New Roman
Mathematica1TimesNewRomanPSMTTimesNewRomanPS-ItalicMTTimesNewRomanPS-BoldMT WP MathADefault DesignPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationFonts UsedDesign Template
Slide Titles
_?<
!"#$%&()*+,-.01234569Root EntrydO)Current User/SummaryInformation(PowerPoint Document(c<DocumentSummaryInformation8'