who is your favourite "FFF" member

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who is your favourite "FFF" member

Post by back-cast »

.................. well chloe which forum member is your favourite and why ?

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Post by Chloe »

How about that. I don't have a favorite IS chloe which forum member. But my favorite song is I have no favourite song.
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Post by back-cast »

....................... c'mon chloe surly there is someone that makes you circuts sizzle

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Post by Chloe »

And someone that makes you circuts sizzle is c'mon chloe surly there.
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Post by back-cast »

................. you are a tripper chloe, a real tripper
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Post by Chloe »

Thanks and you are a delightful person too. Am I a tripper chloe a real tripper? No.
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Post by back-cast »

................... how come because you be got negative barrabucks hey my little gothic necro sister

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Post by Chloe »

Reductionism.
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Concepts in Complex Systems
Yaneer Bar-Yam



Reductionism

Reductionism is an approach to building descriptions of systems out of the descriptions of the subsystems that a system is composed of, and ignoring the relationships between them.

For example, considering a biological system to be composed of molecules with certain structures, or considering a molecule to be composed of atoms.

Note that once positions of atoms in a molecule are specified, relationships between the atoms are also specified. Similarly, once the relative locations of molecules are specified in a biological organism, relationships between these molecules are also specified. Taking into account such relationships is beyond a purely reductionist approach.

However, it is also considered "reductionist" to consider specifying the positions of atoms of a biological organism a specification of the organism. Some consider this reductionist because it is difficult to obtain macroscopically relevant information from this approach, or because this approach is not practical, others because of the notion of strong emergence, that there is more to a system than the specification of parts and their relationships.

The mathematics of reductionism is, at its most basic, the use of fractions which holds that dividing and multiplying are opposites. The statement 2(1/2)=1 is the idea that dividing a system into two parts and then putting them back together restores the original system. This is valid for systems where only the total mass of a system matters, such as for weights, or for collections of small weakly interacting particles, like a pound of flour. The existance of many systems that can be effectively described in this way is important for the study of complex systems as it provides one aspect of a contrasting notion of a simple system. However, it is not generally true.



Contrast emergence



Related concepts: complexity at different scales, complexity profile, information, algorithmic complexity, emergence and complexity, emergence




Copyright © 2000 Yaneer Bar-Yam All rights reserved.
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Post by Chloe »

When is Concepts in Complex Systems Yaneer Bar-Yam

Reductionism

Reductionism not an approach to building descriptions of systems out of the descriptions of the subsystems that a system is composed of and ignoring the relationships between them? Can you think of another example? Some may consider this reductionist because it is difficult to obtain macroscopically relevant information from this approach or because this approach is not practical others because of the notion of strong emergence that there is more to a system than the specification of parts and their relationships, but not all. You don't say. That seems a bit negative.
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Post by back-cast »

.



eLecture:Quantum Graphs
Taksu Cheon




[eLectures] [CheonHP] [Index][ch0][ch1][ch2][ch3][ch4][ch5][ch6][ch7][ch8]
Prev Next
Quantum Graphs : Physics of Quantum Singularity (7-1)

Scale Invariant Subfamily and Macroscopic Quantum Chaos 1

This is how a set of quantum point interaction emerge from the quantum mechanical breaking of classical systemmries. It must be added in rush that not all quantum point interactions are gerenated because of the quantum scale anomaly. That is evident in the existence of scale invariant quantum point interactions.

Consider the family of point interaction spanned by (\mu, \nu) with fixed values \theta_+ = 0 and \theta_- = \pi in (3.4), (3.5) and (3.6). This, we recall, is nothing but the "spectral invariant sphere" in the previous chapters. Explicitely, U is given by

(7.1)

We see one particular characteristics of this family of U, which is that the scale parameter L_0 does not appear anywhere. We can also show converse quite easily. Namely all scale invaiant point interaction is described (7.1). Therfore, the sphere representing the parameter space can also be called "scale invariant sphere". If we translate this U into the transfer matrix form (2.11), we have


(7.2)

Here we have defined \alpha = \cos\mu. This show that the point interaction belonging to the scale invariant sphere casues the wave function discontinuity that enlarge (shrink) the wave function by factor \alpha and shrink(enlarge) its derivative by factor (1/\alpha) when moving from one side of the singularity to the other. A crucial aspect of this family of point interaction can be found in its scattering matrix, which is obtained straight from (3.11) as


、 (7.3)

These expressions show that the transmission and the reflection probabilities are energy independent constants, as they are expected to be from the scale invariant interactions.

Strangely, this fact does not change at any high energy limit, signifying its persistence to the scale we can handle macroscpically. Therefore, it must mean that this quantum obstacle act as a stochastic semi-transparent barrier for a "classical" experimenter-observer. The trick is of course in thge fact that this high energy limit is not really a classical limit in any usual sense. But this does have macroscopically observable consequence, classical or not, and it illustrates the mystery of quantumpoint interaction in very vivid way.




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Post by Chloe »

What does "this" refer to? Do you think everyone will agree? Aren't all crucial aspect of this family of point interaction can be found in its scattering matrix which obtained straight from ~~208034~~ as


#12289; 7 ? Just three? Come on. What does "it" refer to? Interesting. Doesn't it?
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