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Hawking: No 'Theory of Everything'
Flash Modin writes "In a Scientific American essay based on their new book A Grand Design, Stephen Hawking and Leonard Mlodinow are now claiming physicists may never find a theory of everything. Instead, they propose a 'family of interconnected theories' might emerge, with each describing a certain reality under specific conditions. The claim is a reversal for Hawking, who claimed in 1980 that there would be a unified theory by the turn of the century."
sounds an awful lot like what Buddha said 2500+ years ago
Godel proved that all formal systems are either incomplete or inconsistent. Perhaps that's what we're dealing with here.
Give me Classic Slashdot or give me death!
Saying that there is not a TOE is against my religion. Saying that we can't achieve a TOE because of our own limitations is, I guess, OK.
What a flip-flopper! This guy would make an awful president. Bush/Cheney 2004!
"Tell the bastards to shut the fuck up and get back to work until they actually generate some *real* results. "
This is what I tell the Space Nutters. 40 years of paintings, posters, bad sci-fi, crappy movies and not a single ant has colonized anything more than a tin can in LEO.
There is no first post, just a family of interconnected posts
xkcd
"The claim is a reversal for Hawking, who claimed in 1980 that there would be a unified theory by the turn of the century."
I think the turn of the century reversed his claim for him.
He's a theoretical physicist. Theories ARE his results.
My postings are informational and does not constitute legal advice. Act on it at your risk.
What sort of people do you think predict the as yet unobserved particles that Fermi and LHC people are looking for? Though I doubt Hawking is right on this one, not many besides you would say he was on the sidelines anyway.
They already reached Leo? :-)
The Tao of math: The numbers you can count are not the real numbers.
Tell the bastards to shut the fuck up and get back to work until they actually generate some *real* results.
Thou shalt not brute-force the universe. All Fermi and LHC is good for is inventing a new particle to explain the unexpected behavior of the month.
Seven puppies were harmed during the making of this post.
I certainly hate to say it. And I certainly don't think I'm any smarter. But, Hawking is past his prime. It seems like he's been saying stuff recently just to say stuff. Maybe it's for attention, maybe it's because he knows extraordinary claims will sell headlines and his books/documentaries, or maybe it's because he actually believes in them. However, after his comments on active SETI being dangerous and now this... I don't know, it's like watching an amazing baseball player, past his prime, coaching a crappy minor league team. It's hard to criticize because I was never as good as he, and even now I couldn't manage a Denny's, but I don't really want to watch him either.
We always knew Comcast was corrupt, here's the proof: http://tech.slashdot.org/comments.pl?sid=1909890&cid=34545432
Feh, the next thing you are going to tell me is that Linux won't work with 48 or more cores!
... There are theories around that he probably didn't read, because of scientific prejudice towards the material.. I read a few, that are considered by scientific community as garbage, without them reading it and keeping an open mind / being skeptical.
The book is called My Big Toe, a physicist. Written by Thomas Campbell. So if someone is interested in this kind of stuff, I suggest you read it, not because of my recommendation, but because you would have one more concept/idea to keep an eye for, and try to prove or disprove what is written there, therefore help the 'movement' evolve.. make room for new ideas and concepts that will push us forward.
Being closed minded and full of prejudice doesn't help, never did.
I'm reminded of a scene from DS9. Sure it's fiction, but it always held some sway with me:
Bashir: "Trevean was right. There is no cure. The Dominion made sure of that. But I was so arrogant, I thought I could find one in a week!"
Jadzia: "Maybe it was arrogant to think that. But it's even more arrogant to think there isn't a cure just because you couldn't find it."
Hawking a smart guy, but he by no means knows everything. Throwing in the towel and declaring that there is no right answer simply because he hasn't found it just doesn't hold much water with me. We might not figure it out for 100 years. We might figure it out tomorrow. We might NEVER figure it out, but simple logic says that there is a unified equation. It might not be simple or pretty, but if the universe operates on a consistent set of physical laws, it's out there.
"People who think they know everything are very annoying to those of us who do."-Mark Twain
Instead, they propose a "family of interconnected theories" might emerge
Which, if you read them all at the same sitting and follow all the connections, just might read like one big...unified theory.
This seems very, very close to a distinction without a difference.
> You don't see the guys at Fermi or LHC spewing these nonsense.
Those guys are technicians, aren't they? They get to prove or disprove the really smart guys work, right? ie is there Hawking radiation or not. And get that copper shielding clean - they big guys are coming round later.
I don't actually mind if this is the case. What it means then, is that new properties of aggregated matter emerge as you go up, and up in scope and scale, and that there does not have to be a set relationship on what rules must emerge.
Other than aesthetics, those emergent rules don't have to carry a thread of logic visible at all scopes. Rather, you just need to have the large number of interactions actually occur in relationship to eachother to see the combined effect, with many aspects unforeseeable by only observing the elements many magnitudes smaller.
Whether this might make the universe a more or less beautiful puzzle to figure out is open to interpretation.
Ryan Fenton
More importantly, who dropped a tin can there... and is there a string attached leading to another galaxy?
I'm right here. I promise I do exist. Really.
Science would die without the people that popularize it; Hawking, Dawkins, Sagan, Asimov, etc. Normal people don't really care that the LHC might find the Higgs Boson, especially younger people who might be just starting to take an interest in science and technology. Without good science fiction, good popular science books, and lots of media attention there would be next to no new scientists and engineers in a generation. Besides, it's not like Hawking hasn't ever published new research, just to name a few.
As scientists age they become somewhat jaded, it happens to a lot of people. Hawking has seen a problem he thought was about to be solved get ever more complex while little new progress has been made. I don't blame him for changing his stance. I had a professor during my undergrad who had been a part of some of the first fusion research, and he would occasionally bring up that he didn't think it was possible. According to him, "the kids today are trying what we tried and couldn't get to work back then" (Paraphrased). Maybe doubting there is a solution to the problems you have struggled with all your life is the best way to find peace as your life winds down?
Oh, on a personal opinion note, I doubt we will ever find a *provable* theory of everything. Eventually someone will put together something that relates a lot of complex fields, but I suspect it will be something ad hoc and beyond the practical limits of humanity to test. (*cough* string theory variant *cough*)
It's about time they rethink this artificial theoretical/experimental barrier if all the "theories" being cooked up are so far out of the realm of verification that they might as well move to philosophy department.
Fuck systemd. Fuck Redhat. Fuck Soylent, too. Wait, scratch the last one.
You forget important addition to Goedel's theorem. Namely: "all philosophical consequences of Godel's theorem are bunk" (including this one).
Regarding your comment: there ARE complete and consistent formal systems. For example, real number theory is complete.
You can't have consistent, complete system if it's _complex_ _enough_ to describe integers.
I just ordered a copy of Hawkins' 'A Grand Design', and now you're telling me that it's already outdated ? Before I even got the chance to actually read it ?
String Theory says there is.
I don't believe in time. It's a grand conspiracy designed to sell watches.
That's just not true. What teenage boys, and even more girls, wouldn't dream of working with gigantic hard-on busters?
Fuck systemd. Fuck Redhat. Fuck Soylent, too. Wait, scratch the last one.
"Without good science fiction, good popular science books, and lots of media attention there would be next to no new scientists and engineers in a generation."
When did sci-di start as a genre? Were there any engineers or physicists or scientists before? Now I've heard it all; we only have technology because of sci-fi? That's retarded. We got sci-fi because we got technology.
does that imply a limitation of the human mind? A problem with one or more of our theories? Or just a result of the incredible complexity of our universe?
the theory that there is "no theory of everything" is in itself a theory of everything.
It's about time they rethink this artificial theoretical/experimental barrier if all the "theories" being cooked up are so far out of the realm of verification that they might as well move to philosophy department.
Maybe they should call themselves theoretical metaphysicists....
Taking guns away from the 99% gives the 1% 100% of the power.
Can't move it there. According to Hawking, philosophy is obsolete(I forget what term he exactly used, but it was in his recent book.)
Everyone should read RyanFenton's post. This is a beautiful and deep analysis and, while it may be true or false, is a reasonable way to reconcile the current state of art.
Nicely done sir. I will ponder your words for weeks to come. A post like this can lift my entire assessment of humanity.
There's no "they" who created the barrier. Everyone does what they want - different talents are required to be a good experimental physicist and the same is true for the theoretical physicists.
How would you rather have it?
Gogol Bordello has the good doctor beat then: http://www.youtube.com/watch?v=jFBTmclJrto
"I'm not a quack, I'm a mad scientist! There's a difference." - Dr. Cockroach
Does this sort of negate his accomplishment of predicting Hawking Radiation 30 some years ago which was recently observed in a lab, thereby eliminating his chance of winning a Nobel Prize?
I mean, my physics teacher would have given me a pretty bad grade for getting 1 out of 2 questions right.
It's always these guys on the sideline talking up bullshit. You don't see the guys at Fermi or LHC spewing these nonsense. Tell the bastards to shut the fuck up and get back to work until they actually generate some *real* results.
Science isn't just "we got these results, and it means this." It's important to hypothesize out loud with peers sometimes, to get input, at very preliminary stages. For one thing, proving that there may be no theory that explains everything strikes me as very difficult to prove, though I have no concept of the math involved. Having more people make suggestions might better help him prove it? If it can't actually be proven, Hawkings saying it might cause some researchers to not waste as much effort going after a theory of everything, maybe now they're absolutely convinced it's just around the corner. If you're a physicist starting your career, you might not want to invest everything into finding a theory of everything. Realigning the field is something only a prominent scientist like Hawkings can do.
The guys at Fermi or LHC might be too focused on what they're doing at the moment to think in depth about larger issues like this. In many biological labs, the major theories that are mostly or completely unproven are usually thought up by the PIs, the more senior scientists with years of experience who write grants but don't do much lab work, wheras the postdocs and grad students are the ones doing the labwork, who haven't been in the field for as long and haven't had as long to make those big predictions.
There are plenty of exceptions to that of course. But it's not too surprising to me that the physicists who are "on the sidelines" are the ones who are coaching and calling plays.
Er, just to clarify, that wasn't to say that the scientists at LHC or Fermi are less senior or long-term thinkers than Hawkins. Maybe some of them were saying there's no theory of everything, but were too busy working on getting the LHC running to make a press release.
Saying that we may never find a TOE no more means that everyone should stop looking for one than saying we would find one before the turn of the century means everyone who wasn't looking one should stop what they were doing.
Both of Hawkings' statements were based on where he saw physics heading at the time. He was confident that we would find a TOE, and now he thinks that we may not.
Either way, physicists are going to continue to make theories, predictions, and observations and try to match them. They will go where the evidence directs them. If the universe is amenable to a TOE, then great. If it isn't, the it isn't, and so be it.
It might not be simple or pretty, but if the universe operates on a consistent set of physical laws, it's out there.
You're making a lot more assumptions about the universe than that it is merely consistent. How do you know the universe isn't best described by "a family of interconnected theories.. with each describing a certain reality under specific conditions"? Maybe gravity at the quantum scale really is different than gravity at other scales. Maybe these interactions can't be described by a single set of equations.
The enemies of Democracy are
-Stephen Colbert
...Theory of Everything held a press conference today, stating "There is no Stephen Hawking."
When asked what the implications were as to whether or not there could ever be a Stephen Hawking, ToE replied "The door is open for a Stephen Hawking in the future, but it can only be a possibility if graphene birds fly out of my lily white butt..."
What are you talking about ? :)
"all philosophical consequences of Godel's theorem are bunk" sounds fair but as you state probably falls in the undecidable set of assertions
but "real number theory is complete" ? are you confusing the "Gödel completeness" with the "Set completeness" (in the way that all Cauchy sequences are convergent in the same Set (unlike, say, rational numbers)) ?
I mean, it wouldn't it be surprising if they were given advanced degrees like "Doctor of Philosophy" or something like that?
Faster! Faster! Faster would be better!
The problem with many science celebrities is that they gloss over the actual work that makes for science: experimentation and heavy mathematics. Too many physics celebrities make cosmology sound like some vacuous daydreaming. If you want to sincerely speak of science to the public, you've got to give how it really is -- not showing the actual calculations, but speaking of the arduous effort and self-examination that leads to discoveries.
I always figured that when they found the theory to everything, they would find God. But since the don't believe in Him, they'll never find the theory to everything. At some point, science requires faith. On the religious side, God said the laws are irrevocable and He cannot break them - he knows the science and we are just trying to catch up. (In other words, science and religion/philosophy aren't necessarily at odds.)
Theories WERE his hand. Hawking has entered the realm of elder statesman, which means he can say any old bullshit he once and, well, he's Stephen Fucking Hawking, and it will get printed. Bemused physicists who all grew up admiring him as one of the gods of theoretical physics will let him have his say, and the rest of us will all fall back and get on our knees, for the Space Pope has spoken!
I'm only being a little sarcastic here. It's not uncommon for guys who reach Hawking's position to start saying these sorts of controversial things. They've earned the right.
The world's burning. Moped Jesus spotted on I50. Details at 11.
At some point, science requires faith.
Let me be the first to tell you that you don't understand science or the scientific method. At all.
"the simplest explanation is : believe what he says, or Occam slits your throat"
No. I mean _theory_ of real numbers. I.e. any statement that you can make using axioms of real numbers will be decidable.
Counterintuitive, but true.
It's about time they rethink this artificial theoretical/experimental barrier if all the "theories" being cooked up are so far out of the realm of verification that they might as well move to philosophy department. ...Said the blowhard in the 60s about the theoretical prediction of the W and Z boson twenty years before a device capable of detecting them was built.
It's not an artificial barrier, by the way, it's a practical arrangement. Both coming up with theories, and conducting and executing experiments, take substantial amounts of time that don't leave much left for the other. You might as well say we should eliminate the artificial barrier between academic computer architecture research and production circuit design. It don't work that way.
The enemies of Democracy are
What if Hawking figures it out but has lost the ability to communicate the discovery with the world?
http://www.scribd.com/doc/19550880/GUT-The-Grand-Unified-Theory-A-oneact-play-with-seven-blackouts
If Slashdot were chemistry it would look like this:Cadaverine
How the fuck would he know? its just guesswork relating to the current theories we have, and their incompatability.
But just because it comes from some supposedly smart dude its like the word of god or something.
Sci-fi started as a genre at least 1800 years ago, with Lucian's True History.
“There is a theory which states that if ever for any reason anyone discovers what exactly the Universe is for and why it is here it will instantly disappear and be replaced by something even more bizarre and inexplicable. There is another that states that this has already happened.”
1) He is getting old, losing his edge and is grumpy that he failed to find the holy grail. If he failed, everyone else will, too.
2) It's nice to see that some people have the balls to admit they might have been wrong.
Pick whichever you prefer.
We've got the answer, I googled it myself... 42.
Now we just need to build a bigger computer to understand the question!
If telephones are outlawed, then only outlaws will have telephones.
I always figured that when they found the theory to everything, they would find God. But since the don't believe in Him, they'll never find the theory to everything. At some point, science requires faith. On the religious side, God said the laws are irrevocable and He cannot break them - he knows the science and we are just trying to catch up. (In other words, science and religion/philosophy aren't necessarily at odds.)
I can't say my own views are too far off but there's a critical distinction that needs to be made. "Science" does not require faith (though the scientific COMMUNITY usually does...any non-physicists here test every law of thermodynamics lately?). "Science" is observation and experimentation. If you cannot experiment, you cannot demonstrably repeat it, it's usually not science. This isn't a Bad Thing because there are most likely some things we will never be able to classify under science.
I DO agree that science/religion aren't at odds...but only because when done properly the two have nothing to do with each other. One's about the How of the world working and the other's about the Why.
It's important to understand the difference between Religion/Philosophy and Science. The communities and people may have issues (kinda like our "faith" in Open Source...I haven't personally inspected the Linux kernel, but I believe that others have and what they tell me about it. Until I test it for myself I can't claim I'm doing science with it) but they are very, very distinct.
"Just a fox, a whisper."
It's about time they rethink this artificial theoretical/experimental barrier if all the "theories" being cooked up are so far out of the realm of verification that they might as well move to philosophy department.
In some alternate universes they already have...
The problem is that most young people who think they care about science are merely infatuated with the latest gadgets. Any venture that doesn't result in shiny toys to ogle and possess is a wasted endeavor.
'If we discover a complete theory, it would be the ultimate triumph of human reason - for then we should know the mind of God.' Hawkins - 1988
Thanks to file sharing, I purchase more CDs
Thanks to the RIAA, I buy them used...
[Citation Needed]
Sheldon Cooper now has his chance to change the world and be recognized for the genius he is!
I predict a lot of episodes written about this revelation!
If telephones are outlawed, then only outlaws will have telephones.
-Don't contact ET. On the one hand, what are the odds that we will do so? On the other hand, oops, you're about 100 years too late if we count radio signals alone, ignoring the big thrust that took place in the 70s and 80s.
-No need for God, gravity made everything. Creation versus evolution aside, doesn't gravity describe the attraction between particles based on their mass? So, if you have no particles, how could gravity make something ex nihilo?
-No Grand Unified Theory. Seems like a bit of hubris taking its course here. "If I can't find it, no one will!"
--Chag
Good one. I pissed myself laughing.
“If you can't explain it simply, you don't understand it well enough” -- Albert Einstein
Have YOU ever been to space? Have YOU ever personally visited Antarctica? Then you cannot tell me definitively that those places exist. You rely on someone else's experiences and results. There are people who have claimed to see God. There are a lot more people who believe those people are telling the truth. In both cases, there exists a method of proving both. One is relatively easy... get on a boat and go to Antarctica. One is relatively difficult... live as just a life as possible, believing in God, and He will show Himself to you.
I hate to say it, but as people get older and become disappointed that certain things didn't get accomplished in their lifetimes, they tend to deny the possibility that it will ever be accomplished.
I don't think we should take Hawking's change of heart too seriously.
No.
Long answer: FUCK no.
I've never been to space, but I can look up. And I trust the fine people at NASA that say they have launched numerous probes into space.
As for Antarctica I've actually been there, once. But I've never been to Australia so your argument is valid for that place.
I'm not buying into your superstitious crap about a god that only shows itself to deluded people that are mentally unstable. I'm sorry, but the notion is absurd.
Doug
http://bit.ly/GEMtshirt
http://visualphysics.org/preprints qmn:1009.9466
Working on new views of old physics at http://VisualPhysics.org
... The One Electronic?
Gah, my brain's jumping tracks a lot lately. Enjoy the link.
Cheers,
"What in the name of Fats Waller is that?"
"A four-foot prune."
You are correct mathematically, but this is not really counterintuitive. This boils down to the fact that are fewer constraints on real numbers than on integer numbers. A Diophantine equation can be unsolvable, but the same equation involving real numbers can be trivial. Same thing with mathematical optimization: real number linear programming is a polynomial complexity problem, whereas integer programming is NP-hard.
I've been watching documentaries about Dr Sheldon Cooper's work out at Caltech and I'm lead to believe that he's very close to proving String Theory as a Grand Unified Theory.
Surely, Professor Hawking is aware of this research?
"Karma can only be portioned out by the cosmos." -- Homer Simpson
This is just the words of cognitive dissonance coming from a dying man who does not have the intellect to make advancements in this complex area of Physics. Nothing to see here, move along.
Hawking, if you will note, has not really made any great discoveries, or at least not as many nor of great significance as his fame would make one believe. He is basically an average Physicist, who has been getting this much attention because of his physical condition.
When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is very probably wrong
what if they do find 'theory of everything'? Would that mean destiny exists? If so, I hope they fail. It seems to me the worst thing would be knowing precisely what will happen.
i don't agree with the last line of this, "The claim is a reversal for Hawking, who claimed in 1980 that there would be a unified theory by the turn of the century." He did NOT claim that physicists would discover a theory of everything, he simply asked what the chances were that physicists would find a complete unified theory of everything by the end of the century. It appears that there is a difference! Once again someone decided to skim read an article, or went off what they thought they remembered. way to go slashdot! rabble rabble rabble.
Too bad there are several people who claim to have done that, and they frequently report different 'gods' if any at all. Quite frankly I'd sooner believe accounts of Sikhist Waheguru than all the moral bankruptcy of Yahweh. However the universe works well enough without any gods, so I'll stick to believing only in things I could reasonably expect to prove to myself if I so chose.
I support the Slashcott and will not be reading or commenting from 2/10/14 to 2/17/14. Beta is steaming pile of dog shit
lol. Best. Troll. EVER!
All the non-sadistic ones?
You make perfect sense, this is exactly why recruitment for the armed forces is done with grisly carnage instead of half-fictitious visions of grandiose self-empowerment. /sarcasm
No really, you don't attract people with tedium or horror. You attract them with glossy simplifications and broad-minded, hopeful intangibles.
I support the Slashcott and will not be reading or commenting from 2/10/14 to 2/17/14. Beta is steaming pile of dog shit
Not to dismiss Lucian of Samosata (of whom I am exceedingly fond, his Hermotimus dialogue was catalytic in my teenage apostasy), but he was an outlying exception. While his True History was the first work of fiction that could be called science fiction, there would be none others like it until the modern era.
I support the Slashcott and will not be reading or commenting from 2/10/14 to 2/17/14. Beta is steaming pile of dog shit
Hawking is full of shit, always has been. Time will wipe away all he has said, and replace it with actual science.
FAITH is belief despite a lack of proof. Science is belief in things that have proof. No I haven't been to space, but those that have can provide proof that they have.
Way to go to fail to understand both Religion and Science. Is there anything left to the world that you actually _do_ understand?
I hate it when a human, smart as he/she is, claims to know something that is the absolute.
We're human. We understand things, but we don't know shit. Travel around the universe first, then we'll talk.
Gravity isn't really the attraction between things, no. Theoretically It's the curvature of space-time, it just happens that all matter is "downhill" from other matter due to the particular fashion in which it causes space time to curve. As you can imagine, the shape and nature of the fundamental space in which we live can change quite a lot of things about the universe, not least what exists within it.
One of the world's foremost experts: "There is no TOE, here is my reasoning".
/. posters: "You are old and bitter, and therefore must be wrong. And that is final."
Need I explain more?
Thus saith the LORD, thy redeemer, and he that formed thee from the womb, I [am] the LORD that maketh all [things]; that stretcheth forth the heavens alone; that spreadeth abroad the earth by myself;That frustrateth the tokens of the liars, and maketh diviners mad; that turneth wise [men] backward, and maketh their knowledge foolish; Isaiah 44:24-25 If you are interested in finding out more, please visit the following sites: http://www.thebereancall.org/ http://www.understandthetimes.org/ http://www.crossroad.to/
None that survived. We don't really know what else was written that didn't last, beyond a small subset that we know of because they are mentioned in other works.
That also dismisses the very distinct possibility that there were oral works never transcribed, or whose transcriptions never survived. The general characteristics of science fiction don't require a long format to be expressed, despite longer formats lending themselves to the explanations usually associated with the genre.
I mean, we are talking about an era when there were a few working machines that resembled robots, operated by pulleys.
I'd be willing to make a pretty large wager that the vast majority of "physics celebrities" do actually know how much math and experimental work go into physics. The problem comes in with scientific journalism. The population at large is at best bored with math, and a significant portion are actively afraid of doing math. Any equation more complicated than E=MC^2 is almost always the scientist writing on a chalkboard, markerboard or vertical piece of glass at a really sharp angle with a tight depth of field so you can't see what's going on. And any show, article or blog that goes much further into the math will be ignored by the population at large, the journalists aren't to blame.
And that "vacuous daydreaming" is extremely important. Without it, mathematicians wouldn't have anything to model. What value would experiment hold if the results are not confirming or disproving theory? Theory is necessary, but not sufficient, for good science to happen.
Although the topic is esoteric and almost never considered this is the edge of a really disturbing issue. Science does not describe reality. Science is coherent or consistent with itself. It is also always shifting as supposedly better evidence and proofs are absorbed. But the fact remains that science is actually presenting beliefs. The absolute or factual nature of science is vapor ware. Science is still very, very useful. But it does not reflect truth and by its nature can never reflect truth. And the sick part is that there are freaks out there who will jump on this and declare that that makes their magical belief systems every bit as valid as science. There are really off the wall believers attached to some of the better religions.
Next people will probably catch on to this and perhaps move to mathematics as the ultimate in non shifting sands. But math is now advanced enough to face similar issues as science. Even mathematics is not absolute. People do not want to deal with the notion that mankind is essentially deaf, dumb, blind and stupid, that we hurtle through space in directions that we can't even define towards endings that we can not know. The human mind will never understand even 1% of the serious issues and laws that surround us. When compared to the complexity of what is around us we are as intelligent as a red wiggler at the bottom of a kids fishing worm collection.
Hmm, sorry I don't know what is this theory, I'm sure there is one describing things you can do with things that will be called real numbers that happen not to be incomplete :)) 'theories' :)
There are many complete (or not incomplete
But at some point, when you have created your theory that alllows you to express statements, results, etc. you want your theory to be expressive enough to actually solve meaningful problems
This _theory_ of real numbers you are talking about will among other things fail to assert useful things about natural numbers (like their primality, and, I suspect, worse, their being actually natural or rational (I don't know, just guessing)), which are a part of the numbers it 'supports'.
Not to say that this makes it a useless theory, it is probably extremely useful if it allows you to establish some calculus or algebra results for instance, but whatever you have in mind with this theory of real numbers being complete despite arithmetic's incompleteness is not really a 'way to show hos goedel's proof is quickly limited' (which is how I understood why you were saying it)
But then again, I was also agreeing with your main point I was just puzzled by this particular example
I can prove to myself that space or antarctica exist without having to rely on someone else's experience. The difference between space and Antarctica, on the one hand, and God, on the other, are that, at least according to people who have been there, space and antarctica are physical, tangible things with discernible properties. God is not. I can watch a rocket taking off. I can not watch a person experiencing God. That experience is entirely subjective, and exists only in the person having it. Space and Antarctica are things that can be seen directly or videotaped. Sure, someone may be faking those videos, but that is stretching the definition of faith. Do you have to have faith to walk? According to you, you do. You need to have faith that the ground is solid, because you have not experienced the solidity of this piece of ground at this time. But don't you see that defining "faith" that way destroys any meaning the word has?
Science is not based on faith, because science does not even claim to tell us what is "true." If you think science tells us what is true and what is false, you drastically and fundamentally misunderstand what science is and how it works. True and false aren't part of it. It doesn't matter if a theory is true or not. We still use theories we absolutely know to be false, like Newton's theory of gravity. We use that instead of Einstein's theory in almost all engineering, because it is useful, that is to say, it makes accurate predictions in known circumstances. And it is much simpler to calculate. As long as your building is not traveling at light speed, Newton's theories are close enough to be useful. And that is all science tries to do, find theories that are useful, that make accurate and important predictions in given circumstances.
The thing about theories, you can test them. Science works because anyone can look at a theory, see what it predicts, and look at the real world, and see if it matches the theory. Personally, I have tested a great many theories of God, and none of them work as purported for me. I've lived as just a life as possible, believing in God. I've opened my heart. I've prayed. I've fasted. I've meditated. You know what I got for my troubles?
Nothing. Do you understand? I have done everything that the people who claim to have personally experienced God told me would work, and it didn't. That is the cold hard truth for most people. But I bet they said they did, because who wants to look impious? Now, science has given us other tools for looking at this dilemma. I could, with the help of science, personally experience God. Just shoot a beam at the right spot on a person's head, and they will experience everything the saints and mystics do, direct personal experience of God. Even knowing it came from a beam of electrons, most people who have experienced it still believe it was real, because it "felt real." But it wasn't really God, it was a particular region of the brain getting triggered by electricity.
Now, I have two possible explanations for this God thing. One is, he exists but is hiding from me personally. The other, everyone who had a direct experience of God just had a particular region of the brain triggered by some event.
And just to be clear, I do not want your advice on how to find God. Whatever you have to say, I've tried it already and it didn't work. No God for me. But that is really okay, I do not need a God. I do not need an external reason for this. This exists, and that is enough. All else is fantasy. There is no ultimate meaning or purpose to life or the universe, and that is a good thing, because it means we are free to create any meaning or purpose we like. I know that kind of freedom scares some small minded people, which is why they invented a God that, according to their books, is far, far less awe inspiring than the real universe.
I'll take reality, you can keep your useless schizophrenic God. You want to know who created reality? I did. Everything I see, I have given it all the meaning it
- None can love freedom heartily, but good men; the rest love not freedom, but license. -- John Milton
>
> For one thing, proving that there may be no theory that explains everything strikes me as very difficult to prove.
>
Well, according to Hawkings, a theory can *never* be proven. Rather, observation either agree with the predictions that the theory made, and the belief in the theory increases, or observation disagrees with the theory, causing belief in the theory to decrease.
And the same goes for the universe itself; it has a bounded number of observable states.
That is not clear. A free electron has no quantized energy and, since current evidence points to the universe expanding for ever, there is no limit to the accuracy with which we can measure that energy (as boring as that measurement may be). Hence a single free electron has an infinite set of states as long as the universe's lifetime is unbounded.
"The problem of induction is the philosophical question of whether inductive reasoning leads to knowledge. That is, what is the justification for either:
generalizing about the properties of a class of objects based on some number of observations of particular instances of that class (for example, the inference that "all swans we have seen are white, and therefore all swans are white," before the discovery of black swans) or
presupposing that a sequence of events in the future will occur as it always has in the past (for example, that the laws of physics will hold as they have always been observed to hold). Hume called this the Principle of Uniformity of Nature."
Like the greeks said we're standing on a raft on the river looking backwards and this in a universe that's bound to be significantly influenced by complete randomness. After all it was created by random quantum fluctuations.
How could you hope to capture in an equation a universe with random events based on so limited past observations as we can perform?
If all else fails, immortality can always be assured by spectacular error.
Is it the theory that there is no theory of everything, a theory of everything?
everything is true or not true depending on the context. Both claims are arrogant in that it tries to "cover it all".
i'm tolerably certain that our RF, EMP, and light emanations over the past century or so will be noticeable by the time they arrive at each star. I think it behooves us to start looking for whoever might be in the neighborhood before they come around and beat our asses for making too much noise. Kinda like an interstellar keger. no one said that once we suspected or confirmed existence of aliens that we had to make contact intentionally...
Marconi's first transatlantic broadcasts alone probably had enough power and covered enough of the spectrum to be detectable quite a long ways off. is it likely given the multiplication of probabilities involved? no. but neither is listening for neighbors likely to do more to attract them than our history and current emanations.
http://en.wikipedia.org/wiki/Spark-gap_transmitter
"If still these truths be held to be
Self evident."
-Edna St. Vincent Millay
"But at some point, when you have created your theory that alllows you to express statements, results, etc. you want your theory to be expressive enough to actually solve meaningful problems"
Theory of real numbers solves quite a lot of meaningful problems. As does Euclidian geometry (it's also Goedel-complete).
"This _theory_ of real numbers you are talking about will among other things fail to assert useful things about natural numbers (like their primality, and, I suspect, worse, their being actually natural or rational (I don't know, just guessing)), which are a part of the numbers it 'supports'."
Nope. Theory of real numbers works with _real_ numbers, not with integers. To define integers you need to introduce more axioms which will make the resulting theory more powerful (and incomplete).
Hawking isn't saying anything new. Robert Anton Wilson in the classic book "Cosmic Trigger The Final Secret of Illuminati" made the same point. Reality isn't limited by any theory. Different theories work in different situations, but none of them are truly 100% real even if they work.
Here's a link to the classic:
http://www.amazon.com/Cosmic-Trigger-Final-Secret-Illuminati/dp/B000GRHMNU
Here's the latest printing:
http://www.amazon.com/Cosmic-Trigger-Final-Secret-Illuminati/dp/1561840033/
It might be the best, most important book you every read, if your not afraid of a book scrambling your mind in the process.
It's time to come home, son.
But the halting problem is not in U. In fact, U cannot contain neither semi decidable nor undecidable problems (which was our base assumption).
This sounds like it would be a great setup for a Charlie Stross novel. Protagonist stumbles upon a conspiracy centered around an ancient alien text allegedly detailing knowledge of the state machine upon which reality executes -- and an artifact, which if activated, may place the universe into a halting state! Amazon review: "A hyperkinetic, Meme-filled trip with an explosive plot twist!"
I thought that was the entire axiomatic contradiction Godel pointed out. In any system of logic you use, there must necessarily be true statements that you cannot prove. You could say that it's decidable because it's true, but then you can't prove it - which would mean your system is inconsistent.
No, in any system of arithmetic that's at least as powerful as a particular axiomatization called Peano arithmetic.
Fun fact that most people haven't heard about Gödel: he's also the guy who proved the completeness of first-order logic. I.e., if a statement is logically valid in the semantics of first-order logic, then the axioms of first-order logic can prove it.
Are you adequate?
Not to put too fine a point on it, but the number of people who are convinced of a thing, have absolutely no effect upon the reality of that thing. It's either real, or it isn't. Your beliefs, or the unified the beliefs of the entire human population, won't change whichever is the actual case. At all.
For instance, at one time, it was believed by the intellectual elite that the sun orbited the earth. Yet this was wrong, and further, failed to change the situation from earth orbiting sun to the opposite, because: Incorrect belief has no power to affect reality. All it does is foul up decision making, and usually quite thoroughly. Which brings us right back around to your assertions about space and Antarctica.
I've fallen off your lawn, and I can't get up.
I believe you're making a mistake here by talking about "integers" instead of naturals. Gödel's theorem is about Peano arithmetic, which defines the natural numbers starting from zero, addition and multiplication.
Anyway, the real point here is that Peano Arithmetic is a very different theory than real closed fields. Read the pages and you'll see, at the very least, that understanding one does little to help you understand the other.
I kinda suspect it comes down to something like this: the theory of real closed fields doesn't allow you prove that, for example, 2 + 3 = 5 or that 2 x 3 = 6, and that the ability to prove this sort of fact is the really critical element. The theory simply assumes that the addition and multiplication operators have certain algebraic properties, and it doesn't concern itself with proving that two specific numbers add up to a specific third one.
Are you adequate?
There is no possible way to have a theory of everything. Hawking is correct this time. The reason is that the math gets so utterly complex to try to describe "everything" that it is impossible. Both to capture the "everything" and to describe it in a "simple" formula. There are only local systems that people are familiar with that encapsulate *their* "everything". Beyond that the universe is crazy and utterly indescribable. I'll take my honorary phd now and my life back... thanks!
That's how science works. The "laws" are the predictions made by the hypothesis, and as long as the predictions are experimentally borne out, we have a theory which remains credible. The whole point of science is that any part of it can be replaced by a better theory, at any time, as long as those very simple ideas pertain. Sometimes it turns out that a theory has a more limited domain than we initially thought.
Science is not a collection of absolute proofs. Science is a method of fussing with what we perceive in order to construct working metaphor. Which is not to say we can't find better metaphors.
I've fallen off your lawn, and I can't get up.
No, a finite number of is not required. For example, Hilbert-style proof systems for first-order logic have infinitely many axioms, but these all are instances of six axiom schema. IIRC, the real requirement is that it be decidable whether a proposition is an axiom.
Are you adequate?
Imagine a world with walls and divide by zero situations. The speed of light, black holes, singularity, the big bang, absolute zero, quantum levels, differences between quarks and quasars. Tons of stuff.
It is quite possible, that the laws of the universe are different on one side of the wall than the other. And better, you can't predict the behavior on one side, based on what you know about the laws on the other side, always.
This precludes a universal answer for all our understandings of the universe, because of the difference in laws and behaviors on one side of the wall and the other.
This means finding the walls (situations), and then discovering the rules for each area.
For example, real number theory is complete.
You can't have consistent, complete system if it's _complex_ _enough_ to describe integers.
So you're saying real numbers aren't complex enough to describe integers?
Hawking famously lost a bet regarding information loss in black holes.
I'm willing to bet that he's wrong on this too. In fact, I'll bet him that we'll have an accepted ToE within 5 years. I'll stake my reputation on it. It won't be complete, but it will unify relativity and quantum mechanics.
I say this because 1. I've seen glimpses of it, and 2. as far as I know, Hawking has a flawless record of losing bets.
From Gleick's "Genius: The Life and Science of Richard Feynman"...
"'People say to me, "Are you looking for the ultimate laws of physics?" No, I'm not...If it turns out there is a simple ultimate law which explains everything, so be it--that would be very nice to discover. If it turns out it's like an onion with millions of layers...then that's the way it is.' He believed that his colleagues were claiming more success at unification than they had achived--that disparate theories had been pasted together tenuously. When Hawking said, 'We may now be near the end of the search for the ultimate laws of nature,' many particle physicists agreed. But Feynman did not. 'I've had a lifetime of that,' he said on another occasion. 'I've had a lifetime of people who believe that the answer is just around the corner.... But again and again it's been a failure. Eddington, who thought that with the theory of electrons and quantum mechanics everything was going to be simple...Einstein, who thought that he had a unified thoeiry just around the corner but didn't know anything about nuclei and was unable of course to guess it...People think the're very close to the answer, but I don't think so....
Whether or not nature has an ultimate, simple, unified, beautiful form is an open question, and I don't want to say either way.'"
(From the epilogue of the book, pp. 432-433, emph. added.)
Hawking: God don't know.
The laws of physics are complex enough. Moreover, not just Godel but even Turing's limit applies to all physical thinking artifacts (including brains) because of the Bekenstein bound guaranteeing that information density is finite, i.e. makes things in essence discrete. You cannot have arbitrary precision real numbers etc. which might have allowed you to escape Turing. Uncountable infinities are a mathematical fantasy and have no real-world analogue.
"Politicians and diapers must be changed often, and for the same reason."
It's difficult to tell how much of the content and prose style is down to Mlodinow, but the book fell between two stools - trying to be light and fun to attract non-specialists and then being close to incomprehensible (and sloppy) in some of the deep-dive sections. The Standard Model is better explained in Wikipedia!
It felt as though the two were indeed grasping at straws and I was left unconvinced about M-theory. The idea that "any universe is possible with any set of laws" seems a little trite without more meat to their argument and smacks of an anything-goes cultural relativism (no pun intended), however sincere their commitment to, and explanation of, the strong anthropic principle: "the laws we have are that way because they are the laws of the universe that we are in". I really did expect better than that.
Tarski proved that the first-order theory of real numbers under addition and multiplication is decidable. However, the "usual" theory of the real numbers includes an axiom that every nonempty set of real numbers that is bounded above has a least upper bound. As that axiom is not first order (it talks about sets of real numbers), Tarski's proof does not apply to systems that contain such an axiom.
Within the first-order theory of the real numbers, how would you distinguish between the integers and nonintegers?
Physics is an attempt to describe the universe based upon mathematical principles and predict how it will change with time. Physics can't put requirements on the universe. For example, there may be no overlying principle that predicts the elementary unit of charge. It may just be an unexplainable property of the universe or maybe it's a random value. If that's true, then there's no "Theory of Everything" because the "Theory of Everything" can't tell you what the charge of an electron would be. It's a pretty obvious statement, but when Stephen Hawking says it, it gets press.
So I'll go one further, and blow your mind like the weed Stephen doesn't have the lung capacity to smoke. There may not be any physical laws at all. Everything that has occurred thus far in the Universe could have been random chance occurring in a way that makes it look like there are physical laws controlling how matter and energy behave. Even better, perhaps there is an infinite number of universes in superposition, but we can only observe the ones in which particles have behaved as if there were physical laws. Every instant an infinite number of those universes go random, instantly destroying an infinite number of copies of each of us. Fortunately an infinite number have followed the incredibly improbable course of behaving as if the universe made sense. Extremely unlikely, damn straight. Impossible, no.
Well, that's what you get when you stray from physics into philosophy. But remember, when Stephen Hawking says "Physicists may never find a Theory of Everything" it's logically equivalent to "Physicists may find a Theory of Everything". That's why politicians invented the word "may".
Support SETI@home
You know there are religions that describe everything we experience as our own creation, right?
No obligatory Douglas Adams quote?
For what it's worth, I think they're spot on to something. The next stage of this debate will probably happen when an apparently viable Theory of Everything appears. At that point, enough real work will go into analysis to prove that said Theory isn't valid within all possible valid frames of reference.
The real beauty of this assertion is that nothing of value is lost. It will only mean that some strong egos will have to deal with the philosophical outcome.
WHAT?
The answer is NOT 42?
Next, you're probably going to try to convince me that Elvis is dead.
Whatever. Keep babbling. I can't hear you :p
which means he can say any old bullshit he once and, well, he's Stephen Fucking Hawking
That's a seriously amazing typo in a how-the-brain-works kind of way. "once" == "wants"
Want to improve your Karma? Instead of "Post Anonymously", try the "Post Humously" option.
I would submit that one will not experience a universe in which someone else discovers a theory of everything. The act of experiencing the universe, the singleness of the consciousness, and the determination of how reality unfolds are all properties that only the mind experiencing the universe will be able to examine. So, it is very likely that these properties are pivotal in developing an all consuming theory. There could be a paradox in which only the person experiencing the universe could develop a theory of everything, having access to all the information both physical and beyond physical. While the mind might observe people theorizing and coming close to developing a theory, it would be impossible for them to actually succeed.
Theorists in this universe may have very different notions of what a 'mind' is. Most people look at other people and theorize that there must be a hidden metaphysical consciousness that goes along with each physical body, a soul. However, if something is metaphysical is it even possible to hide it? Hidden things and hidden information is a physical world concept that most likely doesn't apply to things like minds or souls. That is, if you experience the universe with one mind, you must experience the universe with all minds or those other minds don't exist. So there is evidence that there is no such thing as other minds or souls. People are just physical objects, and thus their concept of a mind is that of a computer, able to take input, process, and form output but they are strictly of the physical universe. So other people, being strictly physical objects, could never understand what a true mind is, and thus not be able to complete the broader puzzle of what gives the universe form. It's telling that most people are willing to attribute a mind to a physical human, but not to other animals, bugs, plants, etc.
If you believe in a multiverse or multiple minds, then the paradox allows that the person can experience themselves having a Eureka moment but will never experience another person, animal, or thing solving the puzzle.
I have seen Elephants personally, so I have very high confidence that Elephants exist. On the other hand, if someone tells me there are about 12,000 African elephants worldwide, I don't know offhand how reliable such a figure is. It's not just the really unlikely cases, i.e. that elephants have gone extinct since the last time I actually verified one's existence and there's a massive conspiracy to hide that fact, that affect that reliability, but the other, much more probable cases, such as people doing elephant surveys maybe missing some, or someone accidentally adding or dropping a zero while writing a newspaper article, or someone misremembering old information. (Hint, I just pulled that figure from my posterior, deliberately without looking it up, to make an example).
I'd be a fool to think the two facts were equally reliable. If I carefully specify that at least 3 elephants existed the last time I went to the local zoo, I can approach 100% confidence, but as soon as I get outside that carefully selected area, it is actually the more reasonable thing to do to assume that there is some significant uncertainty. For some propositions, the amount of uncertainty that is likely is very great indeed.
Now consider this proposition: "The scientific method is the most reliable means of determining the truth that can possibly exist". Can that be proved? Either there is a proof within science of that claim, which means the proof is only as reliable as science itself is, and science still could have any level of reliability including a very poor one, or there's a proof outside of science, which means there is some superior method to proving things and so the claim is actually false by counterexample.
If I put in in terms of reliability, I would have to, reasonably, claim that it seems more reliable to say that the scientific method is the most reliable method yet developed than to claim nothing better can possibly be discovered. I'd think it very unreliable indeed to declare that there are not even any minor improvements to the scientific method even remotely possible. So yes, in that sense, science requires faith. I have faith that I should continue using the scientific method on many problems, I have both a logical opinion that, where science does not yield ready answers, I should try various forms of logical or philosophical reasoning and a rule of thumb that is derived only from my own experience that says much the same thing. I may even hold the same opinion as a matter of cultural condition as well. Note that I did not say I have a scientific opinion that I should use logic where science doesn't yield immediate results, as that too makes no sense. How can science tell me what to do when science isn't producing results (at least yet)?
Who is John Cabal?
That's according to Sir Karl Popper, not Steven Hawking. (And why are several posters in this thread putting an 's' on Hawking's name?).
Who is John Cabal?
"I believe you're making a mistake here by talking about "integers" instead of naturals. Gödel's theorem is about Peano arithmetic [wikipedia.org], which defines the natural numbers starting from zero, addition and multiplication. "
This changes exactly nothing.
"The laws of physics are complex enough"
Are they?
Theory of Everything ( 696787 )
My mind would have been blown if his UUID was 42...
You may be onto something – adding each digit in his UUID (6 + 9 + 6 + 7 + 8 + 7) yields 43...
Of course, maybe it only equals 43 to us because of approximations in our generalised equations, but for him using his localised maths it's actually 42?
Hmmm maybe I am making a mistake but I don't see it, as far as I understand your post we must be agreeing because this is exactly what I meant :) (I am talking about the last part of your post)
What we are talking about here is about giving ourselves a certain level of confidence to say 'this is true', 'here is a proof of it'
Thanks to goedel we know we are limited in how far we can go this way as any formal system 'strong enough' as to support peano's arithmetic (not the oepration themselves, but as you say better than me, their 'truth assertion power') will necessarily be incomplete, you will need to add axioms to support some things you will have to or want to consider true when they are undecidable, that will give you a bigger system with its own limits and s on and so on
So anyway I was not disagreeing with Cyberax, I was just curious about what he meant with real numbers theory being complete
I believe it is misleading to present this fact as a way to show how much goedel's theorem is not all that relevant after all
What I do agree with in Cyberax's post is that goedel's theorem is shamelelly thrown at anything where some sort of science limitation is talked about
Careful there. Your argument only holds true for certain physical things. That is what a philosopher would call ontologically objective facts - they indeed exist regardless of belief in them. There is, however, a whole category of facts that are ontologically subjective - they only exist, because we believe in them. "Obama is the President of America" is such a fact. If the majority of Americans stop to believe in that fact, it ceases to be true.
Ubi solitudinem faciunt, pacem appellant.
(to the tune of Anarchy in the UK)
Right now!
Ha, ha, ha, ha, ha, ha.
I am a scientist.
I am a physicist.
I know what I want, and I know how to get it,
I want to unlock the universe.
Yes, I want a unified field theory.
It's the only one for me.
A unified field theory,
it's coming some day wait and see.
A theory to combine electromagnetivity,
with the weak and strong forces and gravity.
Yes, I want a unified field theory.
Not Newtonian gravity.
Einstein tried, but he couldn't see,
the random state of the galaxies.
But quantum theory will be key,
to a unified field theory.
Yes, I want a unified field theory.
Not relativity.
Right now the best bet seems to be,
the work being done in M-Theory.
Time will tell but I guarantee,
they ain't gonna find it at MIT.
The institute won't beat me.
Ain't gonna happen G.
Cause, I want a unified field theory.
Yes, I want a unified field theory.
You know what I mean?
Yes, I want a unified field theory.
And a Nobel prize for me.
O yeah!
Uhh!
Utilizing the synergization of benchmark e-solutions to pre-workaround action items!
So what do we do about Brian May (Scientist/Rock Star)?
Envy him...
Some privacy policy Slashdot.
That which cannot or can no longer be known becomes effectively immaterial as a contribution to humanity and can have no meaningful interaction with its development. You might as well argue about a million different things that somebody *might* have written or said but were similarly lost or not transcribed. Why stop there? What about all the ideas never given voice? The potential thoughts left unthought? Your position reduces to absurdity rather quickly. Unless there is some yet hidden treasure trove of ancient science fiction on clay tablets buried somewhere, what is unknown about that part of literary history is in fact unknowable to people in the present time, and therefore irrelevant.
(Ironically you undermine your original reference, as if we're supposed to wonder about things lost or untranscribed, then for all we know there was some unknown work by some unknown person created at some unknown time before Lucian's True History.)
I support the Slashcott and will not be reading or commenting from 2/10/14 to 2/17/14. Beta is steaming pile of dog shit
I don't know, compared to the EMF that comes from the sun, anything we transmit will be probably drowned out. OTOH, we can still latch on to the Voyager signals, and they've gone past the heliosphere. But that's a long was shorter than say, Alpha Proxima.
But if there's an alien species that has the capability to even get to their nearest neighbor star, if they want to kick our asses there's absolutely nothing we could do about it; we'd be toast. For someone advanced enough to travel even at half lightspeed, lobbing a big meteor at us would be trivial.
Free Martian Whores!
Yes, that must be so. You are obviously correct.
But those are more technically philosophies rather than religions. "You create your own reality" does not mean we are creator-Gods. It means that nothing means anything unless someone says it means something. Our minds create meaning out of raw experience.
- None can love freedom heartily, but good men; the rest love not freedom, but license. -- John Milton
Psychologists think they're experimental psychologists.
Experimental psychologists think they're biologists.
Biologists think they're biochemists.
Biochemists think they're chemists.
Chemists think they're physical chemists.
Physical chemists think they're physicists.
Physicists think they're theoretical physicists.
Theoretical physicists think they're mathematicians.
Mathematicians think they're metamathematicians.
Metamathematicians think they're philosophers.
Philosophers think they're gods.
Bingo Dictionary - Pragmatist, n. A myopic idealist.
I didn't undermine my original reference, as I said "at least" 1800 years ago. Hence, it could be more. There's definite proof of 1800 years, which is far longer than the post I originally responded to wanted to believe.
Also, the methods for constructing the pyramids, the contents of the Library of Alexandria, and the all of the details of the first human settlement are all currently unknown, but definitively had meaningful interactions with humanity while they existed, and may in the future have more.
I'm also not talking about potential things that may or may not have happened. I'm talking about the things that did happen, that we don't know about. There's a very distinct difference between the two. Their existence is definite; all of history is not recorded exactly, to be played back on a gigantic hologram. There's a possibility that within that definite existence, a portion had been science fiction. If it existed then, it had a definitive impact on humanity, as there is nothing that has ever been observed by humanity that hasn't affected the species in some way, minor or major.
The way I'm seeing your logic play out: I get into a car crash on the way to work; you don't know about the crash. It doesn't exist.
Any time I see a scientist (or any other 'pundit') predicting the future, I automatically assume the opposite of what they say will be true. The only guaranteed way to be wrong in life is to specify something about the future. Bill Gates saying 64k is all anyone will ever need in RAM or whatever, for instance.
Worse, and akin to what some people are arguing above...this sounds old and tired, to me. Someone giving up on a lifelong dream. Hawking has done a lot of great things in his life, but, to me, one of the greatest has always been inspiring other people with his love of science and his passion for knowledge. To say that humanity will never do something, given the practical infinity of time seems defeatist and...sad to me.
I think the theory of everything is one of the most important pursuits in science. Whether or not it is possible, rational, logical or what...it's already spurred massive amounts of research (LHC, etc) that has/will pay dividends in commercial, medical, or merely cool ways. It's the same argument I always have about the space program. Yes, it'll never be cool as Star Trek, at least not for a couple thousand years, but our need to explore, to climb, to name, to learn might be the thing that keeps us alive as a species. When we lose that...then I would expect extinction to be a natural outcome.
K.
A line from the article: "Of course, Hawking has become rather well known for jumping way out on a limb..."
I seem to have missed out on the news recently about Hawking. So when did he get a (cybernetic) limb that jumps way out?
Hawking's 2002 paper made a similar claim with reference to Godel's Theorem. This particular position was originally proposed by a Benedictine Professor Priest, Stanley Jaki, back in the 60s.
"all through my house i set up traps, it seems like the rats have a map, so now i feed the rats crack" - Donald D
>
> And why are several posters in this thread putting an 's' on Hawking's name?
>
Because they can't figure out the difference between Hawkings and Hawking's...
What do you mean it changes nothing? Peano arithmetic is a completely different logical theory than real closed fields, and neither of them is about integers; one is about naturals, the other is about reals. If you know that there is no complete algebraic of the integers (I don't), well, just say so.
Are you adequate?
God. That's my theory. Proven.
What those who want activist courts fear is rule by the people.
Integers can be bijectively mapped to natural numbers and integer operations can be expressed using first-order predicates and axioms of Peano arithmetic.
So for the purpose of my argument replacing "natural number" with "integer" changes exactly nothing.
You're looking at it from the wrong direction. There is a theory about the real numbers that is "weaker" than Peano arithmetic, despite the fact that the real numbers properly contain the naturals. How can this be so? Because that theory does not entail every fact about the natural numbers that Peano arithmetic does. It's axioms are about algebraic properties of the operators (associativity, commutativity, closure, order), not about proving specifically that 2+3=5 or 2x3=6.
Is there an analogous complete theory for the integers? I really do not recall, but I think there might.
Another way of going about this: if I read your reply correctly, you're saying that Peano arithmetic can encode the proof theory of a first-order theory of the integers. That is true, of course, but Peano arithmetic can likewise encode the proof theory of the real numbers. (The fact that the naturals can't be mapped bijectively into the reals is a moot point, because we're talking first-order theories here, and thus, Löwenheim-Skolem applies.) But the relationship can't be inverted--the theory of real closed fields can't encode Peano arithmetic. It's this second direction that I have in mind when I insist equivocating over the integers and the naturals might be a mistake.
And again, I must stress: think of the axioms, not of the domains. The relative cardinality of the naturals and the integers tells us nothing about the completeness of different logical theories--Löwenheim-Skolem is relevant here, again.
Are you adequate?
It got me to check 404 though, which actually displays a 404, given 403 and 405 do point to actual comics leads me to believe is actually intentional, geeze this guy is committed.
403 was posted on Monday, March 31, and 405 on Wednesday, April 2. Do the math...
In general, it is safe and legal to kill your children. -- POSIX Programmer's Guide