I don't really think it matters if we can fully understand a theory, as long as that theory makes predictions that can be verified. For example, if a computer-generated theory gives the ability to build a radio that is a million times more efficient at spectrum utilization, and products can be built from it, that theory is still useful even if it is uncomprehensible.
I very much agree that you don't have to understand the details of how something works for it to be useful. Whether that's a theory, a car or a computer, the world is full of things that are too complex for me to understand _fully_.
But if you don't truly understand something, I think you've given up control of that thing to someone else. Someone else has to do the thinking for you.
Once that happens, you'll have a hard time doing something new in that area, or even applying whatever it is you're supposed to know to new areas.
Understanding isn't the only thing that matters, but it still matters.
Nobody (well except for Chomsky maybe[0]:)) is arguing that incomprehensible is useless. This article is about a deeper question of whether or not we have reached our cognitive limits in terms of understanding the surrounding world, however we may have developed an incredibly powerful theory that can describe some aspects of this incomprehensible world to us.
Very good article. It makes the point that science is heading in an unprecedented direction where the complexity of what is happening is too difficult for a single human mind to understand. In fact, I would say it's almost arrogant to assume that our 1100 grams of processing power is capable of understanding the incredibly complex interactions that build and build upon themselves.
This is the reason for computational science. Imagine trying to render a photorealistic scene analytically. There's just no way you could do that. Exactly integrate the rendering equation over complex geometries? It's unfathomable. There's a reason the Schrodinger equation has only been solved analytically for systems of just a few particles (not to be confused with exactly, which is possible with numerical methods).
Eventually science experiments will be conducted by setting up your initial system, plugging in the relatively simple laws of physics, and letting it go (well... if we solve the n-body problem).
I don't think biology will ever be "understood" in the same way that derivatives or diffusion or gravity is understood. There's so many levels of nested complexity that it is totally mind-boggling, and I'm surprised more biologists aren't impressed by the sheer fact that any of it works at all.
I don't think what your describing is science. At it's core science is a question of experimentation and running complex simulations can't truly provide new information, just validation. That said, there is a great temptation to call many things science because it lends credibility even if you go though the motions and ignore why honest experementwtion has value in the first place.
>Running complex simulations can't truly provide new information, just validation.
This is entirely and absolutely false.
I think you may want to read up on simulation (FEM, molecular dynamics, etc.). It's my research field. For instance, Quantum Monte Carlo has been used to calculate energy levels to a ridiculous level of agreement with experimentally measured values. There's plenty that can be learned about reality that can't currently be studied through experimentation because it's either 1) too expensive or 2) impossible to study with current technology.
Also, I wouldn't say science is "about" experimentation. It's about prediction. Any theory that can more accurately predict a system's future state than another theory is the better science. And simulations can do this better in many cases than experiment.
A simulation is just a way of finding out what the current model predicts (maybe... assuming things like roundoff and truncation error didn't mess things up).
What if the current model is wrong?
An experiment in the real/natural world is the only way to find out if a model (or its simulation) is wrong. You have to ask nature.
Quantum mechanics (or QFT) isn't likely to be found wrong anytime soon. And if it is, it will be to such a degree that it has almost no day-to-day consequences (much as how GR is only considered for particle physics and satellite synchronization).
What I mean by this is that the whole nature of chemistry and biology is already rooted on a very secure foundation. So as simulation capabilities increase, you can be sure that these have a very high probability of modeling the "higher-order" phenomena correctly. Even superconductors and superfluids can be modeled correctly. The only things that may not be correct would be the high energy limit of quantum gravity models. But simulation in this area is almost (and may be?) nonexistent.
Now... having stated that we have an almost perfect description of the underlying reality for any practical phenomena we would be interested in, it is true that this model is currently mostly unamenable to calculation. The amount of computation required to reach chemical accuracy is very high and we may not have that capability for quite a while. So we make concessions and approximate things. For example, wavefunctions are modeled as Slater determinants which satisfy the wavefunction's antisymmetry but do not take into effect all the correlative effects (like electron-electron interactions).
It is a scientific and mathematical challenge to characterize exactly how much these models are off from the "true" solution. Most of the time, you have a good idea if the approximation you are using will work for your domain. If I want to fold proteins, I don't need anything more accurate than CHARMM (describes pairwise interactions; it's a non-reactive potential). But if I want to study Cooper Pairs (in superconductors) I'm going to need to make many less approximations, and it will be a much more expensive model computationally.
QM says nothing about the validity of your simulation. Worse we are incapable of simulating something as complex as a single helium molicule using the full QM model for 1 second using 1 days computing power on any current supercomputer. Even protean folding is forced to greatly simplify what's going on to the point it's often wrong. ( Proteans are not folded in a vacuum.)
Want to simulate a cell? Even with hardware 10^100 times faster you can't use QM, it's all models of models. None of which are 100% accurate, but that's no reason you can't Kidd yourself.
From a practical standpoint Chemistry is not based on QM. You basically said QM > Chemistry > more complex things, my counter argument is even fairly simple. Chemistry is way to complex to model from pure QM. So, even at your first step your model is making simplifications. And 10^100 times the processing power does not get you to the point where you can model even the simplest cell for a meaningful time-frame.
Even at the timescales of atomic explosions and the best hardware / software around those models are vary simplified.
PS: That's not to say you can't make useful simulations, but trusting them to be accurate without testing is not science.
> I don't think biology will ever be "understood" in the same way that derivatives or diffusion or gravity is understood. There's so many levels of nested complexity that it is totally mind-boggling, and I'm surprised more biologists aren't impressed by the sheer fact that any of it works at all.
...yet at the same time biology and medicine will probably be the hardest fields for computers to "make discoveries in" for quite some time, except low level molecular biology things like low scale protein interaction or selecting from dug-candidate molecules. There's so much data so "badly formatted" and full of ambiguity that I can't even imagine when an AI will be able to read medical research papers and make sense of them - it's hard even for humans. Otoh there will be tons of data where computers will be able to search for patterns, but the actual knowledge necessary to transform "patterns" into "discoveries" is in the icky ambiguous format of papers and books that are impossible to make sense of for any less-than-human-level-AI.
Who would possibly want to hear what it has to say?
Television executives.
Everything has an application, and many fewer of those applications are useless than you'd think. Plus there are higher-order effects to consider, mostly related to the tools people develop to attack interesting problems. The classic example is the space race: how useful is it to be able to fire four-hundred-foot-tall fuel tanks into space?
I would. An electronic intelligence with a profound understanding of anything would be interesting.
If I said that, in the next room, there was a computer with a profound understanding of TV shows - wouldn't you be interested? That would be fascinating.
We know that the mind is Turing complete. What the author is suggesting is that it's possible for there to be some science or mathematics that is beyond the capability of our mind to comprehend. (and that it's possible that there's science or mathematics that may be derived by computers that we may not fundamentally be able to understand)
However, any attempt to compute or derive new science/mathematics outside the theoretical capabilities of our (Turing complete) minds on merely Turing complete computers is doomed to failure (at least, until we get some computers better than Turing complete ones).
Turing complete is really only meaningful for a computer with infinite time and storage; humans are limited in both. Just as a smarter human can understand something a less smart human can't, computers will eventually understand many things we can't wrap our heads around.
True, but assuming in this future humans have developed brain enhancements, the issue of storage space and computing power becomes less relevant. Though I suppose the whole idea of brain enhancements would render the author's point null anyways...
> and that it's possible that there's science or mathematics that may be derived by computers that we may not fundamentally be able to understand
I think what the author meant is that us understanding this "new science" would be like trying to run StarCraft II on 386. It's not that it is not fundamentally possible, it's just that our wetware has nowhere near the required computational power.
Science is not an agglomeration of random observations and facts - it should not get more complicated as more is discovered - if the theories and tools like maths we have do not explain the theories then we are doing something wrong with the fundamental tools (maths stats)
I accept there is more and more unknown or unexplained - but that is not to say the theories we have are not explained with the same set of "unreasonably effective" tools
> it should not get more complicated as more is discovered
But it does for the simple reason, that you need to read more and more papers just to know whether or not someone didn't already do your research, or if there isn't already a growing body of evidence against the theory you're trying to develop.
Scientific progress is about to hit a self-complexity boundary due to the amount of knowledge we amassed - we have a huge overhead on adding any single new piece to a puzzle. Our brains are not good enough for handling it anymore, we need computers to help.
EDIT
And also because of that, I believe there's a huge amount of undiscovered facts lurking in all the discoveries we already had described, that no one noticed before because it requires correlating different papers from different disciplines (think about the more messy fields, like biology/medicine). Finding a way for computers to effectively do that work for us will likely result in some amazing progress.
If so one should force the release of copyright papers from the publishers at gunpoint tomorrow. And make google dedicate half it's employees to indexing it
I suspect though that there are so few scientists working on most areas that the research is old or outdated across the majority of fields.
And it rather indicates a lack of fundamental tools - for example studying insect species - it's well know that there are millions of species to every insectologist(?) - yet Linnaeus classification is three centuries old - one could imagine a production line of genome mapping - put insec into machine out comes its genome - oh look that is not the species we were thinking of
The tools (mechanical) and the tools (mental) need to integrate large branches if science are what is needed - not a fear over the vast number of facts we have acquired
Interesting article, but I think that the humans will probaly evolve in ways that will extend their capacity of understanding.
It may start by people living longer and then someday they will have memory implants and maybe even processing power implants.
It doesn't help that most research papers are behind paywalls, or in forgotten books long out of print but still in copyright (and owned by the publisher, not the author), buried and not scanned theses, or technically published in patents but then also unusable by anyone interested.
24 comments
[ 4.3 ms ] story [ 70.6 ms ] threadBut if you don't truly understand something, I think you've given up control of that thing to someone else. Someone else has to do the thinking for you.
Once that happens, you'll have a hard time doing something new in that area, or even applying whatever it is you're supposed to know to new areas.
Understanding isn't the only thing that matters, but it still matters.
[0]I actually don't know what I'm talking about.
This is the reason for computational science. Imagine trying to render a photorealistic scene analytically. There's just no way you could do that. Exactly integrate the rendering equation over complex geometries? It's unfathomable. There's a reason the Schrodinger equation has only been solved analytically for systems of just a few particles (not to be confused with exactly, which is possible with numerical methods).
Eventually science experiments will be conducted by setting up your initial system, plugging in the relatively simple laws of physics, and letting it go (well... if we solve the n-body problem).
I don't think biology will ever be "understood" in the same way that derivatives or diffusion or gravity is understood. There's so many levels of nested complexity that it is totally mind-boggling, and I'm surprised more biologists aren't impressed by the sheer fact that any of it works at all.
>Running complex simulations can't truly provide new information, just validation.
This is entirely and absolutely false.
I think you may want to read up on simulation (FEM, molecular dynamics, etc.). It's my research field. For instance, Quantum Monte Carlo has been used to calculate energy levels to a ridiculous level of agreement with experimentally measured values. There's plenty that can be learned about reality that can't currently be studied through experimentation because it's either 1) too expensive or 2) impossible to study with current technology.
Also, I wouldn't say science is "about" experimentation. It's about prediction. Any theory that can more accurately predict a system's future state than another theory is the better science. And simulations can do this better in many cases than experiment.
What if the current model is wrong?
An experiment in the real/natural world is the only way to find out if a model (or its simulation) is wrong. You have to ask nature.
What I mean by this is that the whole nature of chemistry and biology is already rooted on a very secure foundation. So as simulation capabilities increase, you can be sure that these have a very high probability of modeling the "higher-order" phenomena correctly. Even superconductors and superfluids can be modeled correctly. The only things that may not be correct would be the high energy limit of quantum gravity models. But simulation in this area is almost (and may be?) nonexistent.
Now... having stated that we have an almost perfect description of the underlying reality for any practical phenomena we would be interested in, it is true that this model is currently mostly unamenable to calculation. The amount of computation required to reach chemical accuracy is very high and we may not have that capability for quite a while. So we make concessions and approximate things. For example, wavefunctions are modeled as Slater determinants which satisfy the wavefunction's antisymmetry but do not take into effect all the correlative effects (like electron-electron interactions).
It is a scientific and mathematical challenge to characterize exactly how much these models are off from the "true" solution. Most of the time, you have a good idea if the approximation you are using will work for your domain. If I want to fold proteins, I don't need anything more accurate than CHARMM (describes pairwise interactions; it's a non-reactive potential). But if I want to study Cooper Pairs (in superconductors) I'm going to need to make many less approximations, and it will be a much more expensive model computationally.
Want to simulate a cell? Even with hardware 10^100 times faster you can't use QM, it's all models of models. None of which are 100% accurate, but that's no reason you can't Kidd yourself.
Even at the timescales of atomic explosions and the best hardware / software around those models are vary simplified.
PS: That's not to say you can't make useful simulations, but trusting them to be accurate without testing is not science.
...yet at the same time biology and medicine will probably be the hardest fields for computers to "make discoveries in" for quite some time, except low level molecular biology things like low scale protein interaction or selecting from dug-candidate molecules. There's so much data so "badly formatted" and full of ambiguity that I can't even imagine when an AI will be able to read medical research papers and make sense of them - it's hard even for humans. Otoh there will be tons of data where computers will be able to search for patterns, but the actual knowledge necessary to transform "patterns" into "discoveries" is in the icky ambiguous format of papers and books that are impossible to make sense of for any less-than-human-level-AI.
Imagine an electronic intelligence with a profound understanding of TV shows. Who would possibly want to hear what it has to say?
Everything has an application, and many fewer of those applications are useless than you'd think. Plus there are higher-order effects to consider, mostly related to the tools people develop to attack interesting problems. The classic example is the space race: how useful is it to be able to fire four-hundred-foot-tall fuel tanks into space?
If I said that, in the next room, there was a computer with a profound understanding of TV shows - wouldn't you be interested? That would be fascinating.
However, any attempt to compute or derive new science/mathematics outside the theoretical capabilities of our (Turing complete) minds on merely Turing complete computers is doomed to failure (at least, until we get some computers better than Turing complete ones).
I think what the author meant is that us understanding this "new science" would be like trying to run StarCraft II on 386. It's not that it is not fundamentally possible, it's just that our wetware has nowhere near the required computational power.
I accept there is more and more unknown or unexplained - but that is not to say the theories we have are not explained with the same set of "unreasonably effective" tools
But it does for the simple reason, that you need to read more and more papers just to know whether or not someone didn't already do your research, or if there isn't already a growing body of evidence against the theory you're trying to develop.
http://lesswrong.com/lw/kj/no_one_knows_what_science_doesnt_...
Scientific progress is about to hit a self-complexity boundary due to the amount of knowledge we amassed - we have a huge overhead on adding any single new piece to a puzzle. Our brains are not good enough for handling it anymore, we need computers to help.
EDIT
And also because of that, I believe there's a huge amount of undiscovered facts lurking in all the discoveries we already had described, that no one noticed before because it requires correlating different papers from different disciplines (think about the more messy fields, like biology/medicine). Finding a way for computers to effectively do that work for us will likely result in some amazing progress.
If so one should force the release of copyright papers from the publishers at gunpoint tomorrow. And make google dedicate half it's employees to indexing it
I suspect though that there are so few scientists working on most areas that the research is old or outdated across the majority of fields.
And it rather indicates a lack of fundamental tools - for example studying insect species - it's well know that there are millions of species to every insectologist(?) - yet Linnaeus classification is three centuries old - one could imagine a production line of genome mapping - put insec into machine out comes its genome - oh look that is not the species we were thinking of
The tools (mechanical) and the tools (mental) need to integrate large branches if science are what is needed - not a fear over the vast number of facts we have acquired