Negative knowledge (or more precisely negative information)
August 8, 2005 10:40 PM   Subscribe

Know less than nothing!? What could negative knowledge possibly mean? In short, after I tell you negative information, you will know less... "In this week's issue of Nature, however, Michal Horodecki and colleagues present a fresh approach to understanding quantum phenomena that cannot be grasped simply by considering their classical counterparts." [via slashdot :]
posted by kliuless (26 comments total)
Is this WolfDaddy's celebrity link again?
posted by Rothko at 10:44 PM on August 8, 2005

Once in an engineering class, a professor explained something that I had figured out from the reading - I'd even done homework problems with it.

After he explained it, I no longer understood it - and I could never figure it out again.

Now I have an explanation.
posted by flaterik at 10:57 PM on August 8, 2005 [1 favorite]

I so thought this was advertising to get more people submitting answers for AskMe.
posted by dreamsign at 11:21 PM on August 8, 2005

I haven't read the paper yet and may comment again later but ... isn't this just a restatement of Feynman's proposition with regards to negative probabilities in the Wigner function? (I think he came up with that in the 80's)
posted by vacapinta at 11:28 PM on August 8, 2005

If you know less than nothing, do you remember when you forget?
posted by weapons-grade pandemonium at 12:40 AM on August 9, 2005

If you know less than nothing, do you remember when you forget?

You'll remember in the future, when Jane tells you what you were missing in your future's past.
posted by Rothko at 1:03 AM on August 9, 2005

From the first link: "Information was first defined rigorously by this dude Claude Shannon..."

Uh-oh. Inauspicious beginning. I hope I can make it through the rest of this one before heading straight to the arXiv link.
posted by gramschmidt at 1:17 AM on August 9, 2005

What you get from this article are a couple of clumsy metaphors (which the author acknowledges as such) and a pointer to the equation. The Feynman quote is on the money "You don't understand quantum mechanics, you just get used to it". In the end there's nothing in here to understand, just a forest of mathematics which must be the truth because it works. The fact that it produces such bizzare constructs as 'negative information' is just one illustration of the fact that the discipline is at war with common sense.

Time to dispose of our common sense concepts then. Well perhaps. I'm just curious to know .... are people (the ubiquitous Bob and Alice) actually sending real messages through the quantum states of particles? Has anyone actually built a quantum computer? Does it work? What can it do?

In my alternative universe the Ptolomaic system has survived into the 21st Century, reinforced by sophisticated mathematical tools which allow seemingly infinite epicycles to be calculated with compelling precision. No science has ever produced such precise predictions of future planetary alignments, but as psuedoFeynman suggests "you don't ever understand the system of epicycles, you just get used to them".
posted by grahamwell at 3:25 AM on August 9, 2005

The fact that it produces such bizzare constructs as 'negative information' is just one illustration of the fact that the discipline is at war with common sense.

From the paper:

"We can say that the ignorance of Bob—the conditional entropy—if it is negative, precisely cancels the amount by which he knows too much; the negative conditional entropy is just the potential future communication gained. [emph. mine]

"This solves the well-known puzzle of how to interpret the quantum conditional entropy, which has persisted despite interesting attemptsto understand it. Because there are no conditional probabilities for quantum states, S(A|B) is not an entropy as in the classical case. But by going back to the definition of information in terms of storage space needed to hold a message or state, we can make operational sense of this quantity."
posted by Rothko at 4:04 AM on August 9, 2005

I remember reading about a study which looked at medical school admissions - half of the students were assessed by their academic transcripts and face-to-face interviews, and half were assessed using their transcripts alone. The assessors were then asked to rank the candidates in terms of their expected academic performance. After the students graduated, the gap between the predictions and results for the two groups were compared, with the result that the assessors were significantly more accurate predictors of the performance of the students they had not interviewed. So you could say that the interviews provided negative information about the students - after the interview the assessors knew less about them than they previously had.

I can't find any information about it (and I can't remember the name of the book - dumb negative information). I think it was in the context of some stuff by Kahneman and Tversky, but I'm not sure that it was their research.
posted by wilberforce at 4:35 AM on August 9, 2005

Wilberforce is hinting at something that I have suspected for a long time: that experts are an important source of negative information.
posted by ZenMasterThis at 5:32 AM on August 9, 2005

I don't buy it. There's signal and there's noise. In the case of the befuddled professors, the noise overcame the signal and they made a bad judgement. They didn't know less though, they had more information, it just wasn't useful. I don't think noise can be considered 'negative information', which is a concept rather like 'negative color' ie: a composite term without everyday application (or obvious meaning). I repeat my challenge - does anyone understand this, can it be made to do anything useful? A quantum computer that worked and actually did stuff would shut me right up.
posted by grahamwell at 6:08 AM on August 9, 2005

A number of shamefully bad literary theory/cultural studies papers are going to be written about this.
posted by Prospero at 6:32 AM on August 9, 2005

Has anyone actually built a quantum computer? Does it work? What can it do?

Quantum computing has been successfully demonstrated in the lab. In 2001, IBM researchers managed to factor the number 15 using a quantum computer. This may sound terribly unimpressive (the factors turned out to be 3 and 5), but it's actually quite cool in what it represents: a real world demonstration of a computing system with the potential to solve problems too complex to ever solve with classical computers.
posted by justkevin at 6:42 AM on August 9, 2005

the factors turned out to be 3 and 5
Gosh, really?

(Just kidding)
posted by Goedel at 6:47 AM on August 9, 2005

I'm impressed, I'll shut up. Thanks Kevin.
posted by grahamwell at 6:55 AM on August 9, 2005

Prospero: haha!

Negative information doesn't seem that weird an idea to me. Imagine you have a tristate memory bank with a couple different inputs, a negative and positive. The positive one can assign bits and the negative one can erase them to the undef state.
posted by sonofsamiam at 7:08 AM on August 9, 2005

grahamwell, I totally agree with you. My guess is that quantum physics has no good way of comparing their notion of information to the information that electrical engineers (and Shannon) deal with everyday. This bit of the slashdot discussion illustrates the problem a tiny little bit. I would like to understand the issue better, but I am not about to become a quantum physicist to do it.

In the end I think it is a philosophical debate more than a scientific one. Personally, I have come to think that events can actually be random, in the pure sense - not the unknowable but still somehow deterministic result of myriad other things happening in the universe, but actual capital-r random. Belief in pure randomness seems to correlate with post-modern thinkers and electrical engineers. Belief in unknowable determinism seems to correlate with modernist thinking and computer engineers.
posted by Chuckles at 8:56 AM on August 9, 2005

Perhaps surprisingly, the question of whether or not our actual universe is fundamentally deterministic or not is almost certainly undecidable.
posted by sonofsamiam at 11:31 AM on August 9, 2005

Even the people at Slashdot couldn't grok this news in proper context. Dost Metafilter reckon itself comfortably versed in quantum mechanics?
posted by VulcanMike at 11:52 AM on August 9, 2005

More than most folks at slashdot, thanks.
posted by sonofsamiam at 11:53 AM on August 9, 2005

posted by zouhair at 12:56 PM on August 9, 2005

I am constantly astonished at people's willingness to surrender their own intelligence and abilities at the alter of credentialism.

Anyway, thanks for the link sonofsamiam. Interesting, but it assumes that the universe is infinite... Still, the argument does seem to contribute evidence that the question is more about philosophy than science.
posted by Chuckles at 5:41 PM on August 9, 2005

the 'third link' tries to address the "feynman problem" :D
As Feynman et al. say,
One might still like to ask: "How does it work? What is the machinery behind the law?" No one has found any machinery behind the law. No one can "explain" any more than we have just "explained". No one will give you any deeper representation of the situation. We have no ideas about a more basic mechanism from which these results can be deduced...
I will call the problem of explaining [QM rules] the "Feynman Problem". It seems frustrating that something as simple and basic as these rules cannot be explained. This uncomfortable fact implies that we still do not understand the deepest principles of physics, despite the considerable power and sophistication that our physical science has already attained.
so maybe it is a philosophical debate, for example, about what probability is, much less its interpretation [more here... also note there may be different types of entropies, not just shannon/boltzmann-gibbs! (cf:)] and the universe really is based on capital-r random truths! (or not?) but i think it's neat that as cosmology increasingly bumps into metaphysical constraints -- i.e. of interpretation/meaning/explanation or falsifiability/testing/empiricism, not to mention wrt discreteness, background independence, many-worlds, dimensionality, measurement, etc. and indeed as sonofsamiam implies whether or not at all reality is even amenable to description, either by equation or computation (at least apprehended by the human mind :) -- it still sometimes yields novel solutions! (altho predictive results must of course conform with reality :)

posted by kliuless at 8:01 PM on August 9, 2005

kliuless, thanks for the links!

I don't know weather I should be delighted or embarrassed that I couldn't make heads or tails of the 'a philosophical debate' article... I found the abstract of the 'what probability is' article completely inscrutable, but I clicked through to see the introduction anyway, and it looks like a must read.

The 'capital-r random truths' page contained the following gem near the top:
... And I learned that physics says that the ultimate nature of reality is mathematical, that math is more real than the world of everyday appearances. But then I was surprised to learn of an amazing, mysterious piece of work by Kurt Gödel that pulled the rug out from under mathematical reality! ...
Ugh! I'm not sure that demands a complete read. I suppose you have recommended it for a reason though...

On the other hand, Cosma Rohilla Shalizi seems like a very interesting person indeed. I definitely think I will spend a lot of time there!

So anyway, thanks again.
posted by Chuckles at 10:57 PM on August 9, 2005

I've been reading crshalizi's blog for a while now — really interesting stuff, when I understand it.
posted by hattifattener at 11:25 PM on August 9, 2005

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