In a paper that has won an award by the Αssociation for Computing Μachinery and titled “The Complexity of Computing a Nash Equilibrium“, Constantinos Daskalakis, Paul W. Goldberg and Christos H. Papadimitriou, provide evidence that there are games in which convergence to a mixed Nash equilibrium takes prohibitively long. The paper details are left out for the following reasons: (1) I am not familiar with this subject in depth and I cannot judge the work details and (b) the details are very technical and only those who have worked in this area can comment on the specifics.

What interests me from from the philosophy of science point of view is this statement made in the paper

“But there is a third important desideratum on equilibrium concepts, of a computational nature: An equilibrium concept should be efficiently computable if it is to be taken seriously as a prediction of what a group of agents will do. Because, if computing a particular kind of equilibrium is an intractable problem, of the kind that take lifetimes of the universe to solve on the world’s fastest computers, it is ludicrous to expect that it can be arrived at in real life.”

The above statement is ludicrous in at least two counts. Let us consider both: The first involves the first part of the statement:

“But there is a third important desideratum on equilibrium concepts, of a computational nature: An equilibrium concept should be efficiently computable if it is to be taken seriously as a prediction of what a group of agents will do.”

This first statement equates ability to model efficiently to what we should take seriously. This notion hides a constructivist view of reality, in which real is what we can model efficiently. This is ludicrous because even our planetary system, in the sense of a many-body problem in a gravity field, we cannot model efficiently because as it turns out it is a chaotic system but it is a concept that it is taken, of course, seriously.

The second statement is even more ludicrous:

 “Because, if computing a particular kind of equilibrium is an intractable problem, of the kind that take lifetimes of the universe to solve on the world’s fastest computers, it is ludicrous to expect that it can be arrived at in real life”

No, it is the statement that is ludicrous. The fact that we cannot compute efficiently a particular kind of equilibrium or that it turns out to be an intractable problem does not imply necessarily that the equilibrium state cannot be reached in real life. Unless, again, those constructivists think that real life is what we can model efficiently (Logical positivists claimed once that whatever cannot be described mathematically does not exist). Reality does not use any algorithm that computes equilibrium. Reality is the algorithm itself and this algorithm may be of a different kind than the ones derived based on our axiomatic math. Reality is what is. We know of many phenomena that we cannot compute and predict but happen in real life. For example, our best theories predict a huge cosmological constant whereas observations result in a very small value (Weinberg, S. 1999. The cosmological constant problem. Reviews of Modern Physics 61: 1-23.). Actually the difference is in the order of 10¹⁰⁰! Wouldn’t it be ludicrous for someone to claim that reality is wrong and our theories are correct?

 As far as equilibrium concepts and real life, those computer scientists should remember this one: “Now you see it, now you don’t”.  Many rational economic agents do not seek equilibrium nowadays and their actions in effect cause non-equilibrium because they cannot profit from mere equilibrium as margins are very small. For example, rational economic agents seek to create bubbles knowing that this is how they can make money. It is an interesting period in the history of mankind we live where meaning of terms and objectives have changed because of greed and fear. What is rational nowadays is not the same as with what was rational 30 years ago or when keynes lived or Nash developed his theory. What equilibrium means today, is not necessarily what equilibrium will mean tomorrow. Equilibrium states are as dynamic as the process that generates them and what appears to be chaos today may be the equilibrium of tomorrow. Never forget that we have transcended from pre-established harmony to chaos. This world is becoming chaos and no algorithm will be able to predict anything in the future. This is the slow death of algorithms and the beginning of a new era.

In his paper titled “Realism and Objectivism in Quantum Mechanics“, Karakostas argues that the classical conception of physical reality must be abandoned and replaced by contextual realism:

“It is pointed out, however, that a viable realist interpretation of quantum theory requires the abandonment or radical revision of the classical conception of physical reality and its traditional philosophical presuppositions. It is argued, in this direction, that the conceptualization of the nature of reality, as arising out of our most basic physical theory, calls for a kind of contextual realism.”

Right from the start, two hidden premises are used in the argument:

(1) QM is a true theory of physical reality
(2) There cannot be different conceptions of physical reality

Then, another premise that is used is presented as a principle:

(3) Quantum theory is our most basic physical theory

Based on the above three premises, two hidden and one unfounded, with (1) related to (3) Karakostas develops an elaborate argument in favor of contextual realism.  However:

(1) Before one even considers changing the conception of realism, one must justify the assertion that quantum theory is a true theory of physical reality and not just an instrument of science. Otherwise, reality is “fitted” to a theory rather than theory ”fitted” to reality, which is the ultimate goal of realism. For example, Lyre (2010) has argued that quantum theory is possibly wrong.  

(2) Can we tolerate different conceptions of reality based on different theories? For example, relativity theory makes completely different metaphysical commitments than quantum theory (Esfeld 2009). Can two different conceptions of reality be true at the same time? Karakostas does not answer this question but assumes we cannot.

(3) That quantum theory is our most basic physical theory is a premise used to support the argumentation by Karakostas with no proof. This claim is much too important to be considered an indubitable truth.

After an elaborate argument based on the two hidden assumptions and the principle that quantum theory is our most basic theory, Karakostas states in his concluding remarks:

“A consistent understanding of modern science and its practice requires that we give up the idea that science aims at the description of reality as it truly is in itself…Quantum mechanics reveals that the hunt of a universal perspective for describing physical reality is in vain.”

Obviously, these conclusions do not follow from any of the premises in Karakostas’ argument. There are numerous interpretations of quantum theory and that is an indication that the theory should be viewed in an instrumentalist sense and not as a foundation for an inquiry into the nature of reality or, even worse, for arguing that “we give up the idea that science aims at the description of reality as it truly is in itself”. Because a theory is plagued by interpretational underdetermination that does not mean we should give up aiming at a science that fully describes reality.

FInally Karakostas concludes:

“On the other hand, let the followers of the anti-realist camp avoid condemning any inclination to deal with reality as an idle metaphysical exercise. Physics is not confined to purely operational, descriptive accounts of things;”

After thinking about the above statements for a while I finally understood the confusion in the paper. Realism and anti-realism are about theories and the metaphysical commitments they make, not about reality apart from theories. A reality must unltimately exist and be real in a metaphysical sense. Philosophers and scientists are realists or anti-realists about theories. Theories do not necessarily describe reality and reality may not be sufficiently described by any theory or theories combined. Reality is, what is. Theories come and go, no need to invoke pessimistic meta-inducation here. However, when we talk about “Realism and Objectivism in Quantum Mechanics” we have no right to later divert the discussion to “Realism and Objectivism in Science”. Unless we literally believe that quantum theory is the only viable science. I hope the point is clear.

A recent paper against intelligent design uses straw man arguments to distort and misrepresent an opponent’s position. In  Intelligent Design and the Nature of Science, deposited in PhilSci-archive, Ingo Brigandt starts with a statement that is not compatible with unbiased unscientific inquiry: 

“In the United States, creationists and evangelical Christians have threatened high school instruction in evolutionary biology for decades, even in public schools (where religious views may not be taught due to the constitutional separation of state and church). Similar worrisome trends have more recently started in other Western countries, exacerbated by the promotion of the label ‘intelligent design theory’ (Numbers 2009).”

What are “worrisome trends”? Why does intelligent design cause some to worry? I, for example, do not worry about it. Neither the majority of people who, based on common sense, believe that man was created. Common sense is not always correct but at the same time an emotive appeal against intelligent design is just an informal fallacy.

Then, Brigandt writes: 

“One of the most prominent intelligent design proponents, the mathematically trained theologian William Dembski…”

Probably Brigandt thinks that calling someone a mathematically trained theologician takes aways from his authority. I guess he also thinks that although there exist mathematicians, those who also studied theology should be rather labeled mathematically trained theologians.

Well, I think I should have stopped right there and not read the rest but I continued, only to find out that Brigandt takes an extreme fanatic position and wants to resolve the issue by asking teachers to refrain from using machine and information metaphors when describing organismal features in order to prevent students from thinking that they were maybe designed. This reminds me of medieval years when one was not supposed to talk about things that raised questions about anything else but of the prevailing religious dogma(scholasticism):

“The main lesson for biology education to be derived from this section’s critique of Behe’s irreducible complexity claims is that teachers should, wherever possible, avoid describing organismal features using machine and information metaphors, as they prime the false inference that organisms were designed by an intelligent agent, and prevent a proper understanding of how organismal development works and why flexibility and robustness in development make morphological evolution possible.”

Up to this point in the paper, however, Brigandt has only demonstrated his emotive approach to the intelligent design hypothesis, i.e. his fanatic stand, but then he attempts to justify that by talking about probabilities and he resorts to straw man arguments. Below is his main straw man argument, when he distorts the position of intelligent design proponents into some type of a deductive inference he latter plans to attack:

“(1) The evolution of complex biological features (be it anatomical structures, be it genetic information) solely by means of Darwinian processes is extremely improbable.
(2) Therefore, Darwinian evolutionary theory is probably false (given that there are complex biological features).
(3) Therefore, intelligent design is probably true.”

To start with, the proponents of intelligent design assume their hypothesis to be true. They do not conclude the hypothesis is true from a naive syllogism like the above. What proponents of intelligent design claim is that the fact that certain features of living things could not exit at all without design. Although evolution theory may be true in some cases, it does not apply to certain features of living organisms. This is very different from the naive syllogism Brigandt uses to set up a straw man. But let us see why the straw man is false. He writes:

“In mathematical terms:
(1) P(complex structures|Darwinian evolution) ≈ 0
However, what intelligent design proponents want to conclude, and must argue, is
that the truth of evolutionary theory is very unlikely given that we have evidence
about the presence of complex biological structures. That is:
(2) P(Darwinian evolution|complex structures) ≈ 0″

Brigandt then goes ahead to claim that by using Bayes’s formula he can show that (1)does not entail (2):

“Yet the conditional probabilities P(O|H) and P(H|O) are very different probabilities.
Moreover, they can have completely different values. According to Bayes’s
formula, P(H|O) = P(O|H)·P(H) / P(O). Thus, even if, as asserted by premise (1),
P(O|H) is extremely small and close to 0, P(H|O) can be close to 1, depending on
P(H) and P(O). As a result, (1) does not entail (2), and the small probability argument
is fallacious based on the confusion of two conditional probabilities.”

I think the only confused is the one(s) who came up with the above statement in a delibarate attempt of setting up a straw man. Actually,  intelligent design proponents claim that P(O), the probability of getting complex (living) structures, through inert particle mutations is approximately zero. [Edit: please note that particle mutations is a probability experiment like the tossing of a coin and NOT an event of a probability experiment. This can be confusing especially to first year students of probability who tend to confuse experiments, events and their probabilities] It takes the effort of a designer to come up with complex structures they claim. Thus, only the event O is involved here and its probability, which was estimated based on the number of particles in the universe. In other words, intelligent design proponents claim that if an experiment is set up that involves random mutations of inert particles, the probability of getting complex organic structures is near zero. The above Bayesian inference would make sense if the prior involved was about evolution theory, or P(H). In that case, some new evidence P(O), i.e. the complex structure argument, would affect the posterior probability P(H|O). But this is not what is involved here and what was attempted was not related to Intelligent design proponents’ arguments, which do not make claims about the probability of evolution theory but instead make claims about the probability of complex structures. These are two completely different probabilities and the Bayesian inference setup was about the former, not the latter. As a matter of fact, for intelligent design proponents evolution theory may apply in many cases but not in all. Or even, it can be part of the design process.

It is amazing to me how some, who are otherwise are regarded authorities in some fields, either misunderstand Bayesian inference or use it intentionally to set up a strawman. In both vases, it shows the degree of fanaticism in science.

 Therefore, I have shown how the straw man argument set up by Brigandt does not pass a sanity check. But then Brigandt strikes back in an attempt to reinforce his straw man and he writes:

“Very small probabilities mean little, as such events can be easily generated. Assume that a given coin is fair, and that our hypothesis H is that the coin is fair.”

He then asserts that for a given sequence of 500 tosses the probability of a random sequence is 1 in 2⁵⁰⁰, which is smaller than Dembski’s universal probability bound of 1 in 10¹⁵⁰.

But then Brigandt sets up another fallacy when he writes:

“Inferring the falsity of the hypothesis ‘coin is fair’ because of this extremely small probability would be fallacious; we cannot even infer that the hypothesis is probably false, as by assumption it is true.”

Why would anyone use a small probability of a random sequence of coin tosses to infer that the hypothesis that the coin is not fair is false? And how is that related to complexity argument? Brigandt attempts to make the analogy as follows:

“Both a true hypothesis (coin is fair) and a false hypothesis (coin is biased with P(h)=¾) can assign a very small probability to one and the same event (500 tosses of the coin), which makes plain that nothing can be inferred about the probable truth or probable falsity of the hypothesis asserting the small probability.”

Obviously, the above example is a false analogy. The low probability of complex living organisms is not used to decide whether a certain experiment has a bias towards a certain event in the limit of the law of large numbers, as in the case of a biased coin that favors a certain side, but to rule out one of two mutually exclusive events, those of evolution and design. Thus, another fallacious argument was involved here.

Conclusion

It seems that papers about intelligent design cannot get published in peer-reviewed journals but those journals are often eager to publish naive straw man arguments against intelligent design. This is because, in my opinion, being anti-intelligent design nowadays is a declaration of conformity to some rules of educational establishment the same way that being against empirical science showed conformity to a theocratic state in medieval years.

Nevertheless, intelligent design is just a bold non-falsifiable hypothesis at this point but it is evolution theory which has the problem because it is falsifiable. If this theory is falsified for some reason one day, the only viable alternative would be intelligent design or even creationism. Knowing that much at least, fanatical proponents of evolution theory are playing their last card by trying to even ban the terms used by proponents of intelligent design.

I am agnostic about intelligent design [edit: but I maintain a sympathetic position towards it because I believe in the wisdom of crowds]. In my opinion evolution theory describes a process but offers no explanatory context about the origins of human life. Evolution may as well be an epiphenomenon. But I will not get fanatic neither set up straw man arguments to prove a point and more importantly, I will not write another paper against intelligent design just to be accepted in the “club” and get published. I prefer to have my papers get rejected by main stream journals. As Arthur Schopenhauer said once:

“Every truth passes through three stages before it is recognized. In the first it is ridiculed; in the second it is opposed; in the third it is regarded as self-evident” –

In the paper “Nonconservation of Energy and Loss of Determinism. II. Colliding with an open set“, by Atkinson, David and Johnson, Porter, which remarkably enough was published in a peer reviewed journal, the following statement is made (Section 2):

“An infinite number of identical, stationary point masses (Zeno balls) are placed at the Zeno points 1, 1/2, 1/4, 1/8…on a straight line.”

Let us think about this: what is a point mass? How small is a point mass? Where can one find a point mass in this universe? Why the authors do not understand that the notion of a ball and a point mass are contradictory?

If philosophy of physics cannot comply to the reality of this world, then it is only a straw man generating process. In the mentioned paper, the authors had to invent point masses because for any finite radius R > 0, such that R is smaller than a every small number M, there is a pair of adjacent Zeno points Zn and Zn+1 such than |Zn – Zn+1| < 2M, with n being an index that depends on M. As a result, after a certain point, nature does not allow the existence of infinite balls of equal finite radius at Zeno points, no matter how small the radius is, and the number of balls is finite, it cannot be infinite.

If the ball radius decreases according to some function, the same will happen. The only way to have infinite balls on infinite Zeno points is to distort the very essence of reality, which is that matter has extension. But what purpose could such distortion serve?  It is clear that one of the purposes is the creation of a straw man argument to serve as the basis for the publication of a paper in a “peer” reviewed journal, which applies laws of nature to absurd distortions of reality.

Some philosophers should understand that nature insures that the law of the conservation of energy is never violated and prevents any potential violations by establishing bounds on the existence of systems that intend doing that.

Another shock from a paper in the junk `archive, a place full of epistemological and physical straw man arguments.

In the paper “AN ENDLESS HIERARCHY OF PROBABILITIES“ the authors only show that if a quantity υ is known then P(q0), i.e. the probability that the probability of q is υ_o  can be calculated at the limit. This means that the probability exists but it cannot be determined in general unless υ is known . This does not resolve the issue whether P(q0) can be known at all. 

In the paper the authors violated the condition set by Rescher that “After all, without a categorically established factual basis of some sort, there is no way of assessing probabilities.” by. in a sense. turning a general statement about mathematical convergence of series into a claim about specific values of probabilities. 

The authors further claimed that
 
“In this paper it is shown that the arguments of Rescher, Savage and Hume, plausible and persuasive as they may seem at first sight, are actually misleading. Not only can an endless hierarchy of probabilities be given a clear interpretation, it can also ascertain what the probability value for the original proposition q is.”
 
Although they carefully selected the wording, the claim is false because I do not believe that Rescher cares so much about “clear interpretations” as everything is fairly clear from start but whether the probability value for the original proposition q can be known at all since there are infinite choices between 0 and 1 for the value of õ.
 
Going one step further, I think everyone who are talking about “an endless hierarchy of probabilities” is at least three quarters-wrong. Such endless hierarchies make sense only in one of the four definitions of probability, i.e. when probability is a measure of belief of the occurrence of single events and not of averages of mass phenomena, like in physical sciences. (See Papoulis, A., Probability, Random Variables and Stochastic Processes, p. 14). Only then the concept of probability is a form of inductive reasoning. It is well-known in that case that prior estimates have negligible effects on posterior probabilities.
 
In general, it doesn’t even make sense to talk about the probability that P(q) =  υ_o
 
is true or false. It is either true or false. But if one wants to talk like that for some reason, then Nicholas Rescher is correct and the authors haven’t proved even remotely that he is wrong. All they have shown is that the probability has some unknown value at the limit.

Another epistemological shock from a paper disposed in the junk archive.

The fact of the matter is that anti-realism commits to the know ability thesis. Thus, anti-realists accounts of truth commit to the thesis that all truths are knowable:

∀p(p → ◊Kp)

Fitch’s paradox has been used to attack anti-realism by attacking the the knowability thesis, in my view quite unsuccessfully. For more details see the relevant post.

It doesn’t make any sense to talk about the need of “an account of novel predictions of unexpected phenomena” when nothing is really unexpected in anti-realism.

It also makes no sense to talk about John’s car when one needs to talk only about cars. Involving John is an obvious attempt to link the concept of car to John rather than to talk about cars.This is a technique used for indirect advertising and promotion rather than for science advancement.

Another epistemological shock by the junk archive.

The more incomprehensible is a talk in a science conference, the less the audience understands, the louder the applause at the end. This is because incomprehensibility is considered intelligence. But is it, or it is related to deception or even to Asperger Syndrome, a form of autism?

If a scientist cannot explain in simple language what he wants to say so that a college student with basic background on the subject can understand, then he is either hiding incompetence using incomprehensible code or has Asperger Syndrome.

Society should give an end to rewarding incomprehensibility and the people who promote it. Science, especially when funded by taxpayer’s money, should serve society rather than trying to attract its admiration.

If you, the reader of this blog, is not familiar with what I am saying, trying visiting a few science websites and read the posted papers. There are often contests of who is going to produce the most incomprehensible paper using the most incomprehensible code possible.

This post was motivated by an article by Sascha Vongehr here:

http://www.science20.com/alpha_meme/future_influence_quantum_physics_precognition_or_pseudoscience-84265

Precognition occurs when the calculated probability about a future event is very close to 1, i.e. it is almost the certain event. Obviously, some of the times the future will not turn out to comply with the calculated certainty and as a result, precognition has a statistical success rate.

Under this hypothesis, the highest the brain capacity of a person, the better the precognition ability that is exhibited and the highest the success rate. This is a falsifiable hypothesis as both brain activity and precognition ability can be tested and correlated.

 As a matter of fact I argue that precognition may be simulated in a computer.

“Consider, for example, a city council that has to make a decision on whether to build a new harbor site (represented by a proposition D, the resulting decision). This project is eligible for public funding if and only if two premises are satisfied: first, there is sufficient request for new harbor sites that cannot be met by existing harbor sites (represented by proposition A1), and second, the nearby marine reserve is not badly affected (represented by proposition A2). The decision rule can be formally expressed as the formula (A1 ^ A2) <-> D. Each member of the council expresses her judgment on A1, A2 and D such that the rule (A1 ^ A2) <-> D is satisfied.”.

Someone could spot the straw man argument in the above paragraph of the mentioned paper immediately but I will skip that for now because I am more interesting in the common sense defeat issue.

The following table (Table 1) is then presented in the paper for the city council voting results:

The authors then make the following claim:

“How shall we derive a group judgment given the individuals’ opinions on premises and conclusion? It is assumed that each individual expresses judgments on the propositions while respecting the logical constraints. If we define the group opinion as the majority view on the issues (premises and conclusion), it turns out that the group may take an inconsistent position, as shown in Table 1. The city council may face a situation where the majority thinks that the new harbor site should not be built. However, it will not be possible to provide reasons for this judgment as a majority of the members agrees that there is sufficient request for further harbor sites and another majority agrees that the nearby marine reserve is not badly affected. The literature on judgment aggregation refers to such a problem as the discursive dilemma.”

I see no dilemma here. Anyone with some basic common sense will see no dilemma. I wonder why modern epistemology does see one.

The dilemma arises because a straw man argument was setup. Let us think of a similar situation as in Table 1 where in the first row instead of 3 voters we had 1,000 with the other rows remaining the same. Would epistemologists still insist that there is a dilemma when 1,000 people would have voted for the project and only 4 against it? Common sense and simple algebra of counting votes says no. Epistemology says yes. Epistemology is wrong and common sense is correct. This is because Table 1 was setup up deliberately to ignore majority opinion and instead group individual votes according to premises and conclusions rather than getting conclusions based on groupings of individual premises. Let me be more specific.

In voting, at least in democratic places, what counts is majority opinion. Grouping of results in the way presented in the mentioned paper can lead to a defeat of majority opinion. For example, let us consider a country with three political parties in the parliament and a total of 100 members, the first party is the ruling majority of 96 members and the other two parties have only two members each. According to the straw man argument in Table 1, one could setup a voting procedure such that the two political parties with the four members could overrule the will of the majority of 96 members. Common sense dictates that such procedure is unacceptable and results should be weighted by the member count in each group rather than just counting group results. Alternatively, the members vote on individual premises and their aggregate results could be used to get the conclusions. This is straightforward and really common sense but the issue here is why it is ignored by epistemology, which instead proposes very complex resolutions of a non-existing paradox?

My answer is that nowadays people will do anything to push an already exhausted science to its limits and along the way of trying to discover paradoxes that can earn then a few publications, a permanent position and maybe some recognition, they will make mistakes. Others will, in subconscious ways, rely on their assumed authority and never question their ideas. It is a heard behavior and maybe this video offers some explanation of what is really happening nowadays in epistemology, in philosophy and even in science in general. I keep technology out of this because its results are scrutinized by the free market and not by closed circles of peer-review.

A example I have mentioned before is the so called Fitch’s Paradox of Knowability. A scholastic argument in my opinion that has attracted attention it did not really worth. This attention has generated hundreds of papers and has probably secured positions in Universities without providing society with any value at all. Money thrown out of the window at the expense of the taxpayer who takes scientific authority for granted because it is presented as such by scientists themselves. Here is another straw man example.

To make a long story short what those 117 scientists measured was some speed that came close to the speed of light within some experimental error. They did not measure a FTL (faster than light) speed.

What is interesting is the elaborate setup, the complicated statistics and the assumptions of accurate baseline measurements. All that noise for a 60 nanosecond difference between the measured time and the expected time or a 0.0025% difference. When the known systematic uncertainty sources generate 7.4 nanoseconds of error.

Well, this is too boring. I will wait for an experiment which will produce something like 1.01X the speed of light. In this case any unknown sources of systematic uncertainty will not matter and Relativity can be pronounced dead. Until then, please save the hype people…