http://esr.ibiblio.org/?p=4757&cpage=1#comment-394401
CoinCube, indeed the only known algorithm for global maximization (of an entirely unpredictable solution space) is a repeating cycle of random jumps followed or preceded by some gradient method, such as gradient descent or Newton's method. It is generally impossible to always find the global minima without the random jumps because the gradient method can get stuck in a higher valley (of the N dimensional solution space). Also in real life the solution space is dynamic and there are a plurality of simultaneous minima searches which are interacting with and modifying the solution space for others. Indeed there must be some order (i.e. not infinite entropy) otherwise there are no reference points from which to form any judgment of quality of position (c.f. my blog article The Universe). In my universal theory (which is partially elucidated in my blog article The Universe and spread out over numerous forum posts else where), a black hole is matter disordered (high entropy) than can be perceived by our judgments, i.e. I haphazardly posited more disordered than Planck's constant. I have not formed an understanding whether black holes must have infinite entropy. I need to study (the math of) them more. I expect the math to point out that only a lonely, unprovably existent God could have infinite entropy, but then he would be all alone with no recognizable patterns to join such an omniscient God.
http://esr.ibiblio.org/?p=4757&cpage=1#comment-393293
> Then we could talk contingent existence.
Indeed it would be impossible to construct an INSTANCE that is simultaneously all good, all powerful, and all knowing, because nothing imperfect could be constructed. Perfection would require infinite degrees-of-freedom, thus a dynamic, competitive world could not exist– the Second Law of Thermodynamics could not exist.
In type theory, top is the inductive bound and bottom is the coinductive bound. Top is the intersection of all types and bottom is the union of all types. Thus bottom can never be constructed as an instance, yet it exists as type bound.
Shift your frame-of-reference into the type of types domain of the universe to find the existence you claim is impossible.
Note that the operations (e.g. methods of a class) of an inductive type are a coinductive type and dually vice versa, e.g. the top class type contains the union of all methods of all types in the universe, thus can not be constructed. And dually, the bottom class type contains the intersection of all methods of all types, thus can be constructed.
I understood your tripartite impossibility claim to be that a good God would not be powerless to make good all that is in the universe.
The claim is illogical in several orthogonal ways.
1. Good does not exist without evil. Perception requires contrast.
2. Good is evil, and vice versa, from different perspectives.
3. Some cases of global or greater good require local or lesser evil.
Essentially by implication you claimed that infinity (infinite degrees-of-freedom to attain good at all possible perspectives) must be observable, else it is impossible. Or by implication you claimed that we can prove the universe is finite, thus the necessary degrees-of-freedom would be observed and achieved by such a God.
Some theories of the universe posit that infinity exists as an unreachable bound in some domain, e.g. entropy, space, time, or precision. True or not, we can not prove that infinity does not exist as unreachable bound. Your claim of impossibility is too strong. Such a God can not provably exist, because we can’t observe for infinite time, precision, etc..
A possible interpretation of your linked essay on math, is that an infinite universe can not be completely described by any finite set of theories or axioms.
Infinity can not constructed inductively from a starting point, because infinity (final unreachable bound) can not be observed.
Whether it exists or not, infinity or the finite bound is decomposed co-inductively as observations directed towards its final unreachable or finite bound that we can not prove is final.
How sad a finite universe would be, where the scientific method could be shelved and knowledge would cease to expand at some finite bound. The scientific method requires that we never trust a bound (e.g. Planck’s constant precision) as final and continue searching and testing forever.
Induction is the construction of expressible structure, e.g. defining the natural numbers with an iterative function. Co-induction is the decomposition into parts from a structure that is unknown a priori and not until all parts have been enumerated, e.g. reading a stream:
http://tunes.org/wiki/algebra_20and_20coalgebra.html
There is a tradeoff between expedience and getting stuck in local valleys (which can in the power vacuum of democracy morph the solution space towards zero entropy if there are no independent movements) and directionless randomization that never converges on any recognizable qualities (i.e. order).
Anonymity is not infinite randomization. It in theory increases the degrees-of-freedom (options) for the individual human actors in the economy, but it doesn't eliminate (and rather stimulates since it discourages the collective backstop) the economic incentives the humans have to optimize their individual outcomes. Optimization of individual economic outcomes (as contrasted with group-wise optimization) is a form of local gradient method.
So what is the informational value of the collective (aka socialism) which appears to me to be chains on our individual ankles? What do we lose by discarding it so that individuals can optimize more freely?
The collective had high utility when we needed to apply large quantities of manual labor in the industrial revolution. It enabled us to find collective balances between slavery and unionized labor, so as to prevent the capitalists from the unoptimal outcome of squeezing blood from a turnip, which could possibly have stifled the individual creative development which provided for our current knowledge age. In other words, it was the necessity of stored capital because of the negative scaling law of physical economic processes, which required lower degrees-of-freedom (i.e. lower entropy). Technology has advanced and we can now eliminate much of this requirement for stored capital with the positive scaling law of for example computer programming (and other hitech that can be done more efficiently individually without capital requirements). In order words, the granularity of economic optimization has moved to the individual from the corporation. Study the Theory of the Firm[1] to see why the utility of the corporation is dying too.
But now the economic solution space has changed , c.f. my upthread (or in my archives) points about positive scaling law and the Mythical Man Month. Stored capital and manual labor are dying. We are now moving to a new freedom of the individual where capital is what is stored in one's brain, and money will be a more ephemeral unit-of-exchange.
Thus to move forward we must destroy the old order which has lost its utility and is standing in the way of progress.
This realization is not random, rather a reasoned judgement, so there is no infinite randomization involved here. Yet it is also derived from the high entropy that enables me to be unique, think of it, and freedom-of-speech to write it. Note the current dying top-down socialism is starting to outlaw freedom-of-speech. We will soon have the technology to tap directly into the brain's thoughts, so then a powerful totalitarian collective could outlaw freedom-of-thought!
[1] http://esr.ibiblio.org/?p=4867&cpage=1#comment-397546
http://esr.ibiblio.org/?p=3753&cpage=1#comment-328383
Bottom line is that paradigms which are decentralized are able to grow at exponential rates, because plurality of actors are not as retarded by top-down management bandwidth. The linear market-share growth of Google requires an exponential growth of nominal units, and this is possible because Google is not trying to doing everything top-down, but instead allowing network effects.
The analysis of any particular company’s or person’s strategy is not so interesting to me, because by definition of the Theory of the Firm, every company exists because there is some friction in the free market which enables the firm to arbitrage and take a rent on the active capital doing the work (e.g. $345 billion to Apple shareholders, only $3 billion developers market). In other words, I view management as necessary because of friction. One set of people sees the friction and attacks it with management and makes money doing so successfully. Another smaller set of people, sets off to create technology that eliminates the friction (i.e. democratization via technology, e.g. the personal computer). Those who battled the friction with brute-force eventually reach the natural limit of growth that coexists with the friction, and then those who created the technology to eliminate the friction take over to eliminate this limit. This is the cycle of life. The former is order directed, the latter is disorder directed. The thermodynamic (entropic) universe is on an overall perpetual trend towards eliminating friction, i.e. order. Along the way there, we build some temporal orders as stop-gap measures. Often we need these orders to get the work down to eliminate the friction that caused the order.
Google’s strategy is to increase as fast as possible, the number of people using the web, because their revenues are correlated. They are employing network effects to commoditize the web access devices, and marginalize the telcoms and others who might try to retard the exponential growth rate of the WAN participation. For me it is not a question of who is good or evil, because every person and every corporation is both. Every actor in the markets is playing their role.
Degrees-of-freedom is the number of points in the network that are free to interconnect (i.e. provide fitness), e.g. think of the links in a bicycle chain for bending fitness, and in general these can be communication pathways, open source code, etc. These utility of these potential groupings due to increased degrees-of-freedom, are not always possible due to various frictions that I mentioned in one of my earlier comments, e.g. resources, legal (patents), political, vested interests, etc.. The potential exponential permutations from degrees-of-freedom exist and although the utility can be constrained by a lack of degrees-of-freedom else where, this model still needs to be respected, because a paradigm shift is where a blocking order is removed and the blocked degrees-of-freedom are unleashed in a period of rapid change. Note that blocking order is some friction, and friction is the transactional cost in the Theory of the Firm. Corporations only exist because of friction. With an ideal world of no friction, every human being would be his own company. The world is headed that direction, even though we have peaking fascism and debt at the moment. To an increasing extent passive capital (shareholders, stored money, usury finance) is peaking and will decline, with active capital (knowledge) taking a greater proportion of the value created. This is why I think Apple’s $345 billion valuation with only a $3 billion app market is an unsustainable balloon.
http://esr.ibiblio.org/?p=3689&cpage=1#comment-321944
http://esr.ibiblio.org/?p=2839
http://esr.ibiblio.org/?p=4946&cpage=1#comment-401597
What I really want to maximize is my earnings in knowledge. Money is just one fungible way of representing that, but it is more important for me to have a repository of knowledge that I am maintaining and it is sending me food and other material needs every day. The stored wealth should be in the knowledge, not in money that sits there and is stupid extracting rents and (not only) retarding civilization (but also enabling gaming production by statism leading to horrific societal busts via delaying annealing to technological acceleration).
The point is cut out the parasites by eliminating the impedance mismatch that provides the Theory of the Firm (thanks again Winter for turning me on to that some years back). So all of us earn more, and civilization improves.
As for those designers who are afraid of losing revenue without total control freak gardens, you are actually giving (a portion of) your work to the stockholders instead and being controlled (or retarded) by a paradigm of collective retardation.
Agreed. The peaking statism is perhaps funding much of this. Much of this excess stupid monetary capital (including all insurance and retirement plans that invested in bonds) should be wiped out soon, since it is just an illusion of debt being propped up on the backs of the authors in the hitech space in the developed countries and the labor in the developing countries. Then the expectation of free could be replaced with a reality of not many able to fund free software (unless it is paid for in some ancillary way).