Thursday, December 04, 2003
The Impending Singularity can now be found here
http://www.fightlikeapes.com/fla/departments/the_impending_singularity/main.html
The Impending Singularity can now be found here
http://www.fightlikeapes.com/fla/departments/the_impending_singularity/main.html
Saturday, February 08, 2003
Three Roads to Hell
I've always respected the abilities in others to solve problems. I usually use it as a gauge to determine how intelligent I think someone is. Maybe that's just projection on my part, since I feel I'm a pretty good problem solver. Now, one of the things that I believe may be propelling the Impending Singularity is the lack of basic problem-solving skills. That along with people's laziness, which causes quick fix solutions to be implemented as opposed to long term thinking. The Three Roads to Hell show some fundamental flaws in many when it comes to solving problems.Lack of Bayesian Logic
In a nutshell, (and also incredibly over-simplified), Bayesian logic concerns the ability to better solve problems by taking in new information. Here's a quick overview of Bayesian logic:
Bayesian Logic from whatis.com
Named for Thomas Bayes, an English clergyman and mathematician, Bayesian logic is a branch of logic applied to decision making and inferential statistics that deals with probability inference: using the knowledge of prior events to predict future events. Bayes first proposed his theorem in his 1763 work (published two years after his death in 1761), An Essay Towards Solving a Problem in the Doctrine of Chances. Bayes' theorem provided, for the first time, a mathematical method that could be used to calculate, given occurrences in prior trials, the likelihood of a target occurrence in future trials. According to Bayesian logic, the only way to quantify a situation with an uncertain outcome is through determining its probability.
Bayes' Theorem is a means of quantifying uncertainty. Based on probability theory, the theorem defines a rule for refining an hypothesis by factoring in additional evidence and background information, and leads to a number representing the degree of probability that the hypothesis is true.
A great little example of Bayesian logic is the "Let's Make A Deal Problem." It goes like this: let's say you're on Let's Make A Deal, and Monty Hall gives you a choice of three doors. Behind one door is a vacation to Hawaii, and behind the two other doors are zonk (bad losing prizes). He asks you to pick a door, and for shits and giggles you pick door #1 (for this argument it doesn't matter what door you pick). Now, Monty knows what's behind all the doors, so after you've made your choice, he reveals to you one of the doors that has a zonk behind it (remember, whatever you picked, since there were two zonks, there has to be one remaining). So Monty shows you door #3, which has 300 turkeys behind it, and he asks you, "Would you like to keep door #1, or switch to door #2?" The Bayesian question is, statistically, are you better off sticking with your original choice, or switching? Think about it for a second. The answer is, you are statistically better off switching. I know, it's very counter-intuitive, but it's true.
For an explanation and a chance to play a java version, I suggest you go to this website:
The Let's Make a Deal AppletVapor Locking
vapor lock
n.
A pocket of vaporized gasoline in the fuel line of an internal-combustion engine that obstructs the normal flow of fuel.
vapor lock (as defined by me and my friends)
n.
When someone gets a thought in their head (often, but not exclusively, the first thing that pops into their head), and, FOOMP! that person is now locked into that idea or path and nothing can ever sway them.
Unless you happen to be brilliant or someone who guesses right on the first try, if you have a tendency to vapor lock, you're not going to get a lot of things done.Faulty Abductive Reasoning
Abductive reasoning, the bastard child of inductive and deductive reasoning, with its use of generalizations and sometimes outright leaps of faith can put you in a corner. I've decided to call it faulty abductive reasoning because many believe today that abductive reasoning is the root of medical diagnosis and scientific discovery. It's even being used as a way to develop artificial intelligence.
The following examples are taken for the excellent site Dictionary of Philosophy of
Mind.
induction - A method of reasoning by which one infers a generalization from a series of instances. See abduction, deduction.
Inductive syllogisms are of the following form:
These beans are from this bag. (and these beans..., and these beans..., etc.)
These beans are (all) white.
Therefore, all beans from this bag are white.
In a much broader sense, induction can be thought to include various other forms of reasoning including analogical reasoning, inference to cause form symptoms, and confirmation of laws and theories.
deduction - A method of reasoning by which one infers a conclusion from a set of sentences by employing the axioms and rules of inference for a given logical system. See abduction, induction.
Deductive syllogisms in quantificational predicate calculus are of the following form:
All beans from this bag are white
These beans are from this bag.
Therefore, these beans are white.
More formally, deduction can be characterized as (Cambridge Dictionary of Philosphy, p. 183):
For any sentence S, relative to a set of sentences K, a finite sequence of sentences whose last sentence is S (the one said to be deduced) and which is such that each sentence in the sequence is an axiom or an element of K, or follows from preceding sentences in the sequence by a rule of inference.
Deductions are relative to particular sets of axioms and rules of inference, as a given sequence of sentences may be a deduction relative to one set of axioms and rules and not to another.
Some use the term 'deduction' in a general sense to denote the fact that a conclusion follows necessarily from the premises.
abduction - A method of reasoning by which one infers to the best explanation.
This notion was first introduced by Peirce (CP 2.511, 623; 5.270) in an attempt to classify a certain form of syllogism. Abductive syllogisms are of the following form:
All beans from this bag are white
These beans are white.
Therefore, these beans are from this bag.
This inference results in an explanation of the observation in the second premise. Though this form of reasoning is logically unsound (as the beans may be from a different source), Peirce argues that scientists regularly engage in this sort of syllogistic reasoning. Though scientific hypotheses are not valid by virtue of how they are abduced, abductive reasoning was thought to constitute a "logic of discovery" in one of Peirce's four steps of scientific investigation. These steps are:
1. observation of an anomaly
2. abduction of hypotheses for the purposes of explaining the anomaly
3. inductive testing of the hypotheses in experiments
4. deductive confirmation that the selected hypothesis predicts the original anomaly
Abduction is not currently thought to be well understood and Peirce's formulation has been criticized as being restricted to language-like mediums (Shelley, 1996). It should be noted that for Peirce, abduction was restricted to the generation of explanatory hypotheses. The more general characterization of abduction as inference to the best explanation is a more recent interpretation.That Being Said
Like I said in the beginning, I've always respected the ability in others to solve problems. Of course these three flaws are not the only reasons that people don't solve problems well, nor are they mutually exclusive, they tend to overlap. I'm sure as time passes I'll find some other catchword or equation or logic system that I could plug in above, pave a new road, but after putting this together, I realize it's all talk. Could someone actually change if you pointed out any of the above to them? Maybe the real thing to discuss is are problem solvers born or made? How do we teach a society to think better? Are there courses they could take in school? Would therapy help? And if they're born, what if through mutation we lose all our problem solvers?
