Mathematics of Local Optimism

Mathematics of Local Optimism

 

The theory of Local Optimism assumes that there are many possible worlds; most are virtual, not lasting long enough to be observed; a few last long enough to be observed, and are called real.

          Local optimism states that any real world is a local optimum; it is the best of all sufficiently similar possible worlds. Call such a possibility-neighborhood the “circumstances”; meaning “that which stands around”; then local optimism says that this is the best possible world, under the circumstances.

          This resembles Leibnitzian Optimism, which states that this is the best possible world of all. Leibnitz says that this world is a global optimum; whereas Local Optimism says that this is a local optimum.

According to local optimism, there may be many local optima, some better than ours, some worse. This leaves open the question of what is being optimized. Call any system of world-evaluation a “value field”. Real worlds exist at peaks in the value field.

          Local optimization is a proven principle in physics and biology. Biological systems naturally evolve to maximize reproductive fitness; and physical systems obey the law of least action; so optimization can be a maximization or a minimization.

Local optimism has these mathematical consequences:

          Let the rate of change of value be called ‘progress’, and the rate of change of progress be called ‘uplift’. Then at any local optimum, in every direction, progress is zero, and uplift is negative. That is the “Frown at the Peak”.

Any path from one local optimum to another must at first decline.

          Any path from one local optimum to another must meet a Path Pessimum; the worst of all possible worlds along the path.

At any path pessimum, progress is zero, and uplift is positive. That is the “Smile in the Valley”.

          A world ceases to be a local optimum when an ascending path appears, leading to a sufficiently different world. Such paths can appear or disappear when the value-field changes. Therefore revaluation can create and destroy local optima.

 

Local Optimism

Local Optimism

Voltaire mocked Leibnitz (in the guise of Dr. Pangloss) for proposing that this is the ‘best of all possible worlds’. But Leibnitz, co-inventor of the calculus, knew the difference between local and global maxima. A global maximum is the largest value that a function reaches, for any input; whereas a local maximum is the largest value that a function reaches, in some neighborhood of the locally-maximizing input.

I therefore propose this modification of Panglossian optimism; Local Optimism, which states that this is the best of all sufficiently similar possible worlds. Any stable world locally optimizes; it’s the best of all nearby possibilities.

          Local optimism suggests that there may be many stable worlds, some better than ours. There may also be inherently unstable worlds, that are the worst of all sufficiently similar possible worlds.

          Any continuous path from one stable world to another must begin by getting worse.

          Any continuous path from one stable world to a better one must, in between, pass through the worst world on the path.

          A path from one stable world to a better one that never gets worse must be discontinuous.

          Analogs of local optimism are confirmed - and fundamental - in biology and physics; Darwinian evolution for biology and the Law of Least Action for physics. Local Optimism has sufficient scientific support to appeal to the likes of Leibnitz; yet also sufficient satiric undertones to appeal to the likes of Voltaire.

          For why does the universe minimize action? Is it lazy?

The Information Society

     The Information Society

 

Information is important economically, given cybernetics, robotics, parallel processing, telecommunications, data bases, networks, etc. In the new economy, a nation’s wealth equals the nation’s knowledge.

The new technology makes information both more valuable and more easily copied, transmitted, and transformed. Word will spread quickly and easily through the network.

If laws are enacted against spreading information cheaply then people will disobey the laws. If technical measures make information hard to copy, technical countermeasures will be taken; and in any case, the technological trends is towards easier transmission.

Once text is released into the network, it becomes independent of its creator and can proliferate on its own. The network is a meme pool. All information tends to spread. Information tends to become common property.

Therefore most forms of information will be unownable. Some forms will not; there will remain uses for secrecy; but most data of productive value will be in plaintext, easily copied.

This presents a radical problem. If information can’t be owned, then how to encourage its production? The better the work is, the more people will copy it, and therefore the less the inventor can make money out of it. The best work will be available to all, and not give its inventor one zinc cent.

Information is not very good to keep, but it’s very good to give away, for you can give it away yet still have it. It self-replicates, so you won’t have to work to spread it.

Information is common wealth that works best when it flows freely; as such it undermines both capitalism and communism. The nations that adapt best to the information age will be those which value both free speech and cooperation.

Knowledge is common wealth, which needs freedom to thrive. Therefore freedom is essential to the nation’s wealth. Knowledge is common wealth, and what is held in common requires justice. Therefore justice is essential to the nation’s wealth.

Free speech will be free in both senses of the word. The danger of this is that the creative will not be paid. The opportunity of this is that they will have their say.

Capitalism and communism both depend on the ownership of information. Neither fit the economic realities of the information age. Both must change. Modern prosperity requires political rights, economic rights, the sharing of knowledge, and the sharing of wealth.

There already exists a world community well adapted to the information age; scholars. Scholarship has coped with cheap text ever since Gutenberg; the solution arrived at has been to encourage research and publication with subsidies and incentives. Personal accomplishments are to be acknowledged and accredited.

However, the reality is that science is mostly a collective enterprise; only the rare genius ever gets to make a personal imprint on a field. Genius is rarely rewarded fully, unless you count the joy of creation to be worth the hardships involved.

In science, knowledge is held in common. It is supposed to be held in common; the best thing you can do with it is to give it away. Science and scholarship share the values necessary for the information age.