Slashdot Mirror

"Somebody had to create the computer too. So that's just bringing more into the equation. This whole computer simulation thing is the same as everything else - it's just another religion, no matter how you twist it around."

The universe is not simulated, YOU are. That statement is not religious, it is simply the result of carefull observation and ruthless logic. The only magic* computer required is the universe itself and the algorithm it runs is infinitely recursive - your mind simulates the universe that simulated your mind with your brain.

A mind is a mathematical entity that emerges from the interactions of organised matter, you could say it's the byproduct of the universe observing itself. Human minds create a 3D repesentation of the universe and call it "commonly percieved reality".

The bottom line of all this is our minds are incomplete. We will never fully understand ourselves, let alone reality.

magic* - the universe "just is".

As Godel elegantly demonstrated we cannot compute everything.

Sorry but I think the GP is spot on.

What you are doing in your post is investigating the data until you UNDERSTAND what is usefull and then presenting (visualising) it for you're boss, who probably adds another layer of "visualization" for his boss, etc. (ie: You are acting as human visualisation tool that the boss can use to visualise the output of silicon visualisation tools)

To scale up you're simple X/Y plot of two variables to corporate size you propose using a visualization tool that UNDERSTANDS database structures and UNDERSTANDS the fact that to plot strings against integers you need a default transform, etc, etc. You are handed a bunch of DB's with hundereds of tables, thousands of columns and countless transaction transforms ferrying data from one DB to the other.

So you start with all possible pairs to see if there is a nice easy curve that can relate them. You get 10,000 statistically significant relationships - the problem posed in TFS is how do you now visualize all those graphs to find the relevant relationships without UNDERSTANDING the data.

As to TFS, visualization relies on data minning which will never be "solved" because given enough data you can always add one more level of UNDERSTANDING (see: Godel). This is not to say that trying to solve it is pointless. On the contrary, google news is excellent and accessible example of how far things have progressed in the last couple of decades.

Simply presenting multiple known facts/relationships in an easily accessible format takes a deep UNDERSTANDING of the data. Even if you do UNDERSTAND the facts/relationships, creating the format is an art that has few masters.

"Goedel already proved that axiomatic systems contain errors, especially the error of excluding inconceivable axioms, from which we can conclude that "scientific method" is a) provisional, and b) political."

Not sure who this 'Goedel' fella is but Kurt Godel did nothing of the sort. Godel's incompleteness theorm had nothing to do with errors, what it shows is that provability is a weaker notion than truth.

So lets be scientific and revise your provisional conclusion in light of new information....

a) Yes it's true that all science is provisional, that is by design and history shows that provisional does not mean useless. Many people like to belive there are "other ways of knowing" but those "other ways" have always revolved around wishfull thinking, none of them come close to the track record of utility seen in science.

b) Politics has nothing to do with science, politicians and others just like to see it that way because it's easier than practicing skepticisim on their own assumptions and assertions.

BTW: My dear old dad can bite his own forehead - science made this possible by providing him with false teeth.

"Unfortunately it's been proven that dogmatism is the ONLY non-self-delusional behavior. You see there is no rational basis for the universe...Any "true" theory therefore will be dogmatic...The problem is that it's entirely unclear WHICH dogmatism is "the one" (probably an entirely new one). "

I don't think it's unclear at all, most of the clues are right there in your post. Science is a rational method that attempts to throw out as many "truths" as possible and replace them with the most useful model.

I agree with the interesting mods you are getting but I don't know why you would pick Godel to support dogmatisim? Philosophically speaking his work in logic shows we can never fully understand ourselves. I take that to mean we can continue to understand more if we use the right methods, you seem to take it as a signal to throw the proverbial baby out with the bathwater.

"AGW for example, we make models and then "oops" the sun's corona, out of the blue, cools 20%. Trust me, it's going to be a f*cking cold winter"

Trust me, science rationalized that dogma away years ago. ;)

"One would hope people would read history and use that to decide which ideologies held out longest and most stably. That sort of thing is very thorougly frowned upon on slashdot however, probably because the answer would certainly not be "democracy", but probably a kingdom with a state religion."

Yeah, I've noticed the Ben Franklin fanboys! /sarcasm

GEB is a modern classic, the significance of Godel is nicely summed up here.

From the link:

In 1931, the Czech-born mathematician Kurt Gödel demonstrated that within any given branch of mathematics, there would always be some propositions that couldn't be proven either true or false using the rules and axioms ... of that mathematical branch itself. You might be able to prove every conceivable statement about numbers within a system by going outside the system in order to come up with new rules and axioms, but by doing so you'll only create a larger system with its own unprovable statements. The implication is that all logical system of any complexity are, by definition, incomplete; each of them contains, at any given time, more true statements than it can possibly prove according to its own defining set of rules.

Gödel's Theorem has been used to argue that a computer can never be as smart as a human being because the extent of its knowledge is limited by a fixed set of axioms, whereas people can discover unexpected truths ... It plays a part in modern linguistic theories, which emphasize the power of language to come up with new ways to express ideas. And it has been taken to imply that you'll never entirely understand yourself, since your mind, like any other closed system, can only be sure of what it knows about itself by relying on what it knows about itself.

[snip]

Although this theorem can be stated and proved in a rigorously mathematical way, what it seems to say is that rational thought can never penetrate to the final ultimate truth ... But, paradoxically, to understand Gödel's proof is to find a sort of liberation. For many logic students, the final breakthrough to full understanding of the Incompleteness Theorem is practically a conversion experience. This is partly a by-product of the potent mystique Gödel's name carries. But, more profoundly, to understand the essentially labyrinthine nature of the castle is, somehow, to be free of it. [ My emphasis, It reminds me of religious people who describe "seeing the light". ]

And if they're not fully knowable, then we should recognize the point at which we can learn no more and stop wasting our time. We're nowhere near that point, of course. But the idea that there will always be some new rule of the universe we don't know defeats the purpose of science entirely.

All consistent axiomatic formulations of number theory include undecidable propositions ...

Gödel showed that provability is a weaker notion than truth, no matter what axiom system is involved ...

How can you figure out if you are sane? ... Once you begin to question your own sanity, you get trapped in an ever-tighter vortex of self-fulfilling prophecies, though the process is by no means inevitable. Everyone knows that the insane interpret the world via their own peculiarly consistent logic; how can you tell if your own logic is "peculiar' or not, given that you have only your own logic to judge itself? I don't see any answer. I am reminded of Gödel's second theorem, which implies that the only versions of formal number theory which assert their own consistency are inconsistent.

The other metaphorical analogue to Gödel's Theorem which I find provocative suggests that ultimately, we cannot understand our own mind/brains ... Just as we cannot see our faces with our own eyes, is it not inconceivable to expect that we cannot mirror our complete mental structures in the symbols which carry them out? All the limitative theorems of mathematics and the theory of computation suggest that once the ability to represent your own structure has reached a certain critical point, that is the kiss of death: it guarantees that you can never represent yourself totally.

"The 'skills' you learn as part of philosophy, however, are related to developing internally consistent complex logical 'systems' (for lack of a better word) by carefully designing/choosing a few axioms."

Godel put a stop to that nonsense along time ago. :)

Turing was an heroic genius betrayed by society. He stood on the shoulders of another underrated genius of the 20th century, Godel

I like this quote from Hofstadter, talking about Gödel's Incompleteness Theorem

"Just as we cannot see our faces with our own eyes, is it not inconceivable to expect that we cannot mirror our complete mental structures in the symbols which carry them out? All the limitative theorems of mathematics and the theory of computation suggest that once the ability to represent your own structure has reached a certain critical point, that is the kiss of death: it guarantees that you can never represent yourself totally."

Personally I belive mathematics is so stunningly successfull because the mind is a mathematical artifact that emerges from the rythmic interactions inside our brain and nervous system. ( It also explains why humans have a universal love of music. ) But no matter how firmly my "internal dialoge" tells me that death will bring nothingness, my mind still considers itself seperate from my body and belives it is imune to the second law of thermodynamics. My mind long ago dismissed the idea of a God that "just is" as logically redundant, I prefer the notion that I "just am" because I emerged from a universe that "just is".

As for TFA: If someone can't find deep philosophical questions in computer science, they either have no "soul" or they don't understand it.

When I did my BSc in computer science as a 30yr old in the late 80's, there was hardly a mention of philosophy. The AI component completely ignored the basic questions of what is "consiousness" and "intelligence", just as the physics component avoided the metaphysical aspects of quantum theory.

OTOH: They did teach us the names behind the concepts and made attempts to give historical context to people like Ada Lovelace.( The "Pacal" language is also a tribute to a mathematician). Philosopical "clues" are scattered everywhere in the IT world, an educated person should have no problems following them, iff they are interested! And isn't that what a degree is all about: To give the student a "body of knowlage" in the form of facts and concepts so they can go on to ponder or research their own questions, even in "unrelated" displinces like science and philosophy?

"A market that is supposed to operate efficiently needs government regulation."

I don't have mod points so I will offer a supporting rant.

It could be argued that "regulating the market" is the main reason we have modern democracy. The Magna Carta took absolute power from the king and handed it to a group of merchants and bankers calling themselves "parliment", they claimed to be representative of "freemen" since members of parliment would be selected by a vote. They were able to take this power because together they financed the kingdom, without parliment the king would go broke and a more plyable king would be installed by force. The king did not dare take their money by force, the cream of merchants and bankers spread their risk by operating in competing kingdoms as they do to this day. Any king that took them on as a group was doomed to have waves of well financed invasions launced against him.

Not everybody got a vote, it was only for "freemen" (basically white-male landowners), but it was an improvement over an omnipotent king since power devolved from one weathy family to many wealthy individuals. Parliment made up rules that kept it's members reasonably peacefull with each other, everyone else was fair game and many rules were made by parliment to maintain the power/social divide between freemen and "others" who worked their land for food and and a place to sleep (ie:"others" = economic and traditional style slaves).

Other documents since the Magna Carta have attempted to devolve power to "the people", the US constitution is the best known example. Over the years power has devolved so that most of the population now gets an opportunity to vote. Problem is, we are still voting for "merchants and bankers" and (mostly) they still make rules that benifit themselves at the expense of everyone else.

I think it is admirable to be skeptical of government regulations, but to reject any and all regulation as "interference" is so stupid it has a name, anarchy. This particular rule appears to be an example of "the people" setting a rule that can be shown to benifit all. In this case the "benifit to all" is the attempt to maintain the status-quo of a global infrastruture against an artificial toll that benifits members of a key cartel at the expense of all other parties. If that is not "what government is about", then now is a good time to grab a pitchfork and change it.

The only exceptions I can think of for not making "rules that benifit all" are: rules that create "victims" where none existed (eg: adult drug use) and rules that are inherently uneforcable (eg: adult drug use).

Having said all that, anyone who belives a non-trivial set of rules can be made consistent must first answer to Godel.

"could it be the case that we might not even be able to understand and explain some phonemena simply because our brain power is not adequate."

Godel has already shown that no system of description is adequate, this is independant of of the amount of brain power on hand (or in head). People often wonder why maths is so good at describing the Universe, I belive it is because it is actually describing the model used by the brain to create the illusion of "I". ie: The simulated Universe containing the simulated self we all carry around in our heads. The "physical universe we live in" is an illusion.

A favourite quote from the above link: Although this theorem can be stated and proved in a rigorously mathematical way, what it seems to say is that rational thought can never penetrate to the final ultimate truth ... But, paradoxically, to understand Gödel's proof is to find a sort of liberation. For many logic students, the final breakthrough to full understanding of the Incompleteness Theorem is practically a conversion experience. This is partly a by-product of the potent mystique Gödel's name carries. But, more profoundly, to understand the essentially labyrinthine nature of the castle is, somehow, to be free of it.

I find the quote interesting because it relates a similar experience to religious conversion, ie: acceptance of the unknowable.

"...the goal of the Theory of Everything, to have a model that explains and can predict everything."

Pysicists in the 20th centry thought if you smash things together hard enough it is possible to deduce a TOE, Godel did not agree.

"The idea that we are not all knowing and will not know all is pretty painful to accept"

As the other poster pointed out science does not pove things, maths does within the confines of it's own axioms. You may be depressed to hear that maths has shown that the Universe is "unkowable".

Q2: Science is very ceratain about the fact we are all made from "star stuff", it is also very ceratin that the "star stuff" self orgainsed sufficiently to discuss philosophy. One day we may work out the complete sequence of steps from hydrogen to human but I doubt if it would be much use by itself. We will never know where or how often life has arisen in the Universe but the question answer is only useful as historical triva.

Q1: Now where did the hydrogen for the stars come from, "big bang" is the leading contender. Big bang is reasonably strong because of it's predictive power, I have not yet heard anyone propose a practical experiment to test string theory, for now it's just a mathematical curiosity.

Like God, the big bang "just is". However the big bang does a lot less moralising and there is always the possibility it can be explained with something deeper (infinite spacetime seems obvious but it cannot be "proven").

"If you get talking about potential universes, well, each of those has the same likelyhood of happening. If there are an infinite amount of "universes" (either spatial or throughout "time") every potential universe will/has/does exist infinite times."

This is more logical than extra layers of existance, after all the edges of my visable universe are unique to me and I have no reason to suspect that the universe does not go on forever. Also (to the other post) "just is" does not imply random, there may be rules that "just are" underlying the randomness. But it need not be that way, "laws of nature" may just be the collection of emergent properties coming from pure randomness, refer to the "mindless intelligence" of an ants nest.

We are part of the Universe and what I percive is my simulated universe, the three dimentional space around me is a simulation generated by me. Unfortunately this also leads to endless recursion as it can be said that I am really just an overly optomistic simulation of myself (thus the dissapointment when I use the mirror in the morning). The alternative to endless recursion is the replacement of free will with a inifinte number of simulated universes residing within a common infinite reality. Because we are part of the universe, it would seem that the universe is inherintely unknowable. An infinite unkowable Universe is more logical but could be seen as grim, I prefer to think of "free will" as an emergent property of life, it "just is", I cannot will what I will what I will what I will....there is not enough time!!!

Finding hidden parts of the Universe that we can all percive (eg:X-rays) expands our common understanding of it, finding extra philosophical layers just leads to more layers until an omni-potent being/thing/design/simulation "just is".

I read "The Emperor's New Mind", what he is basically saying is that the "magical" quality of the human mind is burried somewhere in quantum physics, he doesn't point out where. The book asks alot of questions but doesn't really answer anything. For an understanding of why the human mind will never understand itself I point you to Godel.

The first novel proofs by a computer occurred around 8-10 years ago if I recall correctly. At the time comments were made to this same effect. Recent philosophical work in mathematics from cambridge, as well as not-so-recent work (Godel) suggests that mechanically generated proofs will be by definition incomplete. Because, as shown by Goedel's incompleteness theorem, any sufficiently-complex logical system (all of mathematics) will contain truths not proveable within the system. Therefore any mechanical means of generating proofs will be limited to a small subset of the searchable space.

Note, this is not proof that humans can a-priori map out the unprovable space. Rather it is a limitation on what purely formal computational proof systems can do.

I must say I'm a bit skeptical of the article. Firstly, as I stated above, and they noted the idea of computer proofs is not new. Nor is the idea of "proof witnesses" although it is usually just considered to be a trace of the logical process. I am also surprised that they didn't mention Godel's work since it does bear directly on the distinction between formal logic a-la Bertrand Russell and the "informal logic" used by "working mathematicians".

Lest we forget this sort of rigour is fairly new (basically post 1920's) so the great mass of mathematics doesn't actually fit this rigorous paradigm.

Fun fun fun.

For a good introduction to incompleteness of mathematical systems people should really check out Godel, Escher, Bach: An eternal golden braid.
This book basically describes Godel's incompleteness theorem in an entertaining way for a general audience.

uhm, wouldn't this have some bearing on your plan for a formally complete system ?- Godel's Incompleteness theorem

Not sure what you mean by that, agnostic?

The reasoning of an agnostic is, I don't know all the details so maybe "God did it". Dig deeper, who created God?

All faiths have the same answer God "just is", so why can't the Universe "just be"?

You are spot on with the "fundamental problem". Probably the #1 mathematical breakthrough of the 20th century was Godel's incompletness theorem, "proof" that the "fundamental problem" will never go away.

I think it's based on dynamic equilibrium, note that the "environment which is not in equilibrium" is the Sun. The broader chaos theory. states that even chaotic systems are deterministic, so in principle are predictive. Without some sort of "model" you would be unable to get out of bed, as for the validity of any model refer to the genius of Godel.

Gödel notwithstanding, Slashdot itself is proof that humans will use *any* language to say stupid things about *anything*. People will even code Java sandbox VMs which crash the OS when processing harmless JPGs. Or moderate informative posts as Trolls. We are unstoppable!

Nagel and Newman, GÃdel's Proof

He proved it impossible to establish the internal logical consistency of a very large class of deductive systems - elementary arithmetic, for example - unless one adopts principles of reasoning so complex that their internal consistency is as open to doubt as that of the systems themselves ... Second main conclusion is ... GÃdel showed that Principia, or any other system within which arithmetic can be developed, is essentially incomplete. In other words, given any consistent set of arithmetical axioms, there are true mathematical statements that cannot be derived from the set... Even if the axioms of arithmetic are augmented by an indefinite number of other true ones, there will always be further mathematical truths that are not formally derivable from the augmented set.

The Heisenberg uncertainty principle states that there will always be true statements within a system that cannot be proved within that system.

Um, no. That would be Goedel's Incompleteness Theorem. Not that it's any more applicable to the issue at hand.