Can scientists know that they do not know?

Feb 17, 2014

Imagine you knew everything about the current universe – the state of every single particle – and all the laws governing the universe's evolution. Endowed with such knowledge, you could then predict the future, right? French mathematician Pierre-Simon Laplace thought so.

Not so, according to an analysis by SFI Professor David Wolpert – not even for the non-chaotic, non-quantum-mechanical that Laplace assumed.

This unknowability, says Wolpert, is the true nature of reality. With the help of a grant from the Foundational Questions Institute, an organization that funds research on physics, cosmology, and the underpinnings of reality, he hopes to extend his ideas from the realm of theory to allow them to be validated experimentally.

To understand Wolpert's claim, start with a philosophy classic: "this sentence is not true." If that's true, then it's false. If it's false, then it's true. Whether it's true is a question without an answer: a mathematical chicken-or-egg problem. Early last century, Alan Turing showed that such unanswerable questions are inevitable in any sufficiently powerful computer.

Wolpert says he's always been dissatisfied with attempts to use Turing's result to analyze the universe – to do so requires an assumption that the elaborate structure Turing created is the foundation for the laws of the universe. Instead Wolpert uses mathematical analysis of what it means for an experimental apparatus to observe a physical system in his effort to understand how a scientist can accurately know something about the external universe, whether by observing the universe's present, predicting its future, or remembering its past.

Wolpert's approach requires no assumptions about the laws of the universe. But it leads to an even wilder conclusion than Turing's: simply for there to be a physical reality that contains scientists observing, predicting, and recollecting, there must be unanswerable questions.

He has already used the approach to derive results with tantalizing connections to the uncertainty principle of quantum mechanics. He says he plans to investigate other possible connections.

"It would be drop-dead totally cool if the laws of popped out," he says, though he concedes that's a long shot. At a minimum, he expects the work to further our understanding of the fundamental limitations on what we can know about .

Explore further: 'Spooky action' builds a wormhole between 'entangled' quantum particles

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Protoplasmix
not rated yet Feb 17, 2014
I think if the first principles are correct then the natural expectation would be for the laws of QM to indeed 'pop out' in some recognizable way. I'm glad, upon encountering things like division by zero or the square root of negative one, that the mathematicians didn't throw up their arms in despair stating, "This stuff is unknowable."
TechnoCreed
3 / 5 (2) Feb 17, 2014
"The more you know, the more you know you don't know." ­ -Aristotle

And it is also a good way to evaluate commentators on Phys.org. When I comment on science issues here, I do it only when I have a good knowledge base on the subject; I would not defend a scientific position on biology for example because it is not in my field. If I take a stand to defend a thesis it is because I have a good scientific background of it, based on universally accepted science that has been empirically verified. Those who try to refute science do not even deserve a reply. But those who have a good scientific arguments to question my positions often help me to go forward in my knowledge base.

Also, everybody should be allowed to have their own philosophical position on different subjects and should be respected for that. Sometime discussions here turn to acrimonious bickering. One should accept divergence because, in these situations, we can only agree to disagree.
Eikka
5 / 5 (2) Feb 17, 2014
To understand Wolpert's claim, start with a philosophy classic: "this sentence is not true." If that's true, then it's false. If it's false, then it's true. Whether it's true is a question without an answer: a mathematical chicken-or-egg problem.


No it isnt.

If you propose that P equals not P, you haven't made any new insight - you've just made a logical contradiction akin to saying that 1=0. Trying to ask whether a contradiction is true or false is meaningless: there is no answer because the question is nonsensical. There is no question.

If you still insist in asking if P is true, the answer can be yes and no, because the original definition of P makes both answers equal by definition. In order to meaningfully say "This sentence is false.", you have to define that true=false.

And this has nothing to do with Alan Turing, who worked on the halting problem.
Eikka
5 / 5 (1) Feb 17, 2014
upon encountering things like division by zero or the square root of negative one, that the mathematicians didn't throw up their arms in despair stating, "This stuff is unknowable."


Yep. What they did instead was to pull a rabbit out of their hats and conjure up a new set of numbers for which there is a root for negative one.

Which is why they called them imaginary numbers.

And division by zero still is mathematically undefined. It just has a limit in infinity.
antialias_physorg
not rated yet Feb 17, 2014
If you propose that P equals not P, you haven't made any new insight

If you propose that if you know x (e.g. momentum) for certain then you don't know Y (position) and vice versa then I'd argue you do have a new insight based on mutually exclusive states.

"The more you know, the more you know you don't know." ­ -Aristotle

Many people get disheartened, scared or fatalistic based on this statement - as it never leads to 'full knowledge'. But getting an ever more complete picture is an interesting journey in itself. And Aristotle may be wrong: There may be a maximum of attainable (systemic) knowledge - i.e. a minimum of simple laws beyond which it just gets more complicated again.
antialias_physorg
not rated yet Feb 17, 2014
And division by zero still is mathematically undefined.

Which isn't really a problem in physics as you'll not find a representation of the concept(!) of zero in nature. Because that's all it is: a concept to express a limit.
You may get a problem with division by zero in physical laws - but you have to remember that physical laws are only ever approximations, and that the case where you divide by zero doesn't happen in reality.

As for imaginary numbers: Just a convenience for writing stuff in multiple dimensions on one line (e.g. using 3 hypercomplex numbers as an easier way to write 3D matrices...The concept of complex numbers can be extended to n dimensions. It isn't confined to square root of -1).
julianpenrod
1 / 5 (1) Feb 17, 2014
Among other things, the primary design of computers is either to carry out calculations, the introduction of cybernetics has added automatic control of peripherals, but they are not designed to produce questions.
And, here, the second error occurs. The unknowability issue, actually, undecidability, was proved by Kurt Godel. He demonstrated that any sufficiently involved philosophical system supposedly should have facets about itself that are true, but not decidable using the tenets of that system. Incidentally, a confirmation can either be a proof using deductive logic or a disproof using a single false example. But, being undecidable means no false example can be found, which means the statement is true by default. The trick, then, would be to find the statements that are undecidable.
It can display a deterioration of basic understanding that PhysOrg fails to frame this as originally presented and, instead, resort to the gimmick of computers.
Eikka
not rated yet Feb 17, 2014
If you propose that if you know x (e.g. momentum) for certain then you don't know Y (position) and vice versa then I'd argue you do have a new insight based on mutually exclusive states.


That's not the same thing. Mutually exclusive states are not a contradiction in terms. They simply describe a relationship, like XY = 1 so that Y = 1/X. The more X you have, the less Y you get, and vice versa.

"This sentence is not true" defines a statement that simplifies to the form P = -P which is contradictory, therefore meaningless, unless we re-define what negation means, and if we re-define what negation means to make the statement meaningful and not contradictory, then we are simply asserting that true means false and false means true.

ryggesogn2
not rated yet Feb 17, 2014
It just has a limit in infinity.

But it is not a real limit.
Looking at it from the other direction, given two points a and b, there is always a point that is between a and b that is not a or b as b gets closer to a.
I know there is a more precise definition, (epsilon-kappa?) but I think this captures the essence.
Nestle
3.7 / 5 (3) Feb 17, 2014
Can scientists know that they do not know?
Of course, we will tell them.
TheGhostofOtto1923
4 / 5 (4) Feb 17, 2014
Also, everybody should be allowed to have their own philosophical position on different subjects and should be respected for that. Sometime discussions here turn to acrimonious bickering. One should accept divergence because, in these situations, we can only agree to disagree
Well most people agree that cross-posting is frowned upon here. And there are certain philosophies which should be, and are, illegal such as overt bigotry and misogyny which incidentally are inextricable from most religious philosophies.

As to the article, it is refreshing and reassuring to see a physicist rightly tackling a question that philos might think they could offer some insight into... and of course they would be wrong.
Trying to ask whether a contradiction is true or false is meaningless: there is no answer because the question is nonsensical. There is no question
This has never stopped philos from trying to answer such questions, or from pretending that they, and only they, could.
TechnoCreed
5 / 5 (1) Feb 18, 2014
Otto,
Do not even dare to think that I am one who downgraded your last comment.

As far as philosophy is concerned, at 52 my values are pretty much settled and I feel very comfortable with them.

When there are exchanges of ideas about general knowledge, I am pretty much open, and can easily tip my hat when it is deserved. But when my values are putted in question I feel confronted, and I am pretty sure you feel that way too. When I post a philosophical comment on a subject, it is only good for those who want to receive them; Phys.org is an open forum.

Anyway, I just want you to know that some of your values are not so very far from mines. You have just showed that in the comment above.

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