Quantum mechanics appears to work. The equations predict things we can test and these check out. But numerous anomalies and paradoxes appear if we try and scale them up to the real world. There are two classic problems 1) Put a cat in a box with a radioactive pellet. If the pellet decays, release a poison capsule. After one half life of the pellet, the cat has 50% probability of being dead. The equations predict that the cat is both alive and dead until we open the box. Not either alive and dead but both alive and dead. 2) There are lots of atomic actions that generate a matched pair of particles with opposite values of some parameter. Like polarization of light photons. Now before we measure one of them we don't know their state. But after measuring one we know the state of the other. Now let them move light years apart. When we measure one we now know the state of the other instantaneously. So something (information perhaps) has traveled across the gap faster than the speed of light.

There are a bunch of major views on all this.

- The Copenhagen interpretation. The equations don't reflect reality. They reflect a reality we need to create in order to think about what's happening. They're nothing but maths, although they are useful maths

- Bell's Theorem. Particles that have been in touch continue to influence each other. They can only do this if the communication employs no known form of energy since it violates Relativity. Which leads to.

- Everett-Wheeler-Graham. Everything that can happen does but in another universe. When we open the box and discover a live cat we choose which universe to live in and it's the one with a live cat. Next door there is a universe where we found a dead cat.

- Hidden variable. There is an invisible hand below the quantum level that is manipulating reality to appear the way it does. Some people think this is consciousness

- Non-objectivity. The universe has no reality aside from observation. If the tree falls in the wood and nobody hears it, there is no sound.

Now Reed's law suggests that that the utility of large networks, particularly social networks, can scale exponentially with the size of the network. The reason for this is that the number of possible sub-groups of network participants is 2^N - N - 1 , where N is the number of participants. This grows much more rapidly than either

* the number of participants, N, or
* the number of possible pair connections, N (N - 1) / 2, (which follows Metcalfe's law)

But this requires that every entity in the network is in touch with every other entity, and all possible combinations of entities simultaneously. This violates several social relativity laws such as the number of people any one person can "know" and track. And as this is all happening in time rather than as a snapshot it assumes simultaneous communication across time and space at faster than light speed. So while the reality of the value of large networks does appear to be somewhere between Metcalfe and Reed, we can draw some parallels with the Quantum Physics paradoxes and theorems. :)

- Reed and Metcalfe are just mathematical formalisms. We don't actually know what they mean by value. But they seem to be handy when predicting the success of various networks.

- Two people who meet at an Social Networking meeting continue to influence each other across space and time (limited only by their ability to use email)

- Every possible combination of people at Social Networking meetings does in fact happen. Just not all in the same room.

- The network owners are actually manipulating all their members. They just don't all notice this.

- If you don't keep your eyes open at Social Networking meetings, you'll miss the details. If you're asleep in the corner and don't observe it, it's as if the meeting never happened.

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[ 04-Dec-05 4:26pm ] [ , ]