The Shrodinger equation was able to produce pretty good results by simply ignoring the mathmatical "not defined"s.
What do you mean?
There is much written, way to much to go into here. It breaks a whole string of mathematical rules, yet it produces extremely powerful observable results. Conclusion: ether the the universe is wrong, or the whole of mathematics is.
@Fardragon I've done a course on quantum mechanics at uni and don't remember breaking maths. On the contrary, QM was born from ignoring conventional physical thinking and applying maths.
QM is definitely more math than science, it regularly describes things we cannot define in the macro world doing something we ALSO cannot define in certain ways. Guess what? We can't describe those ways either. QM is an exercise in accepting that math can be used to explore the framework of physics, which makes sense, since we define physics with math for some time. QM contradicts observed world, not math, that's why people find it so disturbing.
Philosophy and math are extremely closely related, always have been. Oddly enough, math is also the wing of science most strongly associated with faith and mysticism. Math is the common factor that ties all the various fields of science we've been creating together; without math, they cease to be science.
It's older than that, and the next step is logic, then philosophy. Philosophy is the foundation of science. Especially once you get into the big names, many were also scientists in their own era, and were famous mathematicians. Logic stems from examining thoughts and the world, which is something we train via philosophy, and math stems from logic, and I think you could say math evolves directly out of apply logic rigorously and finding patterns. Maybe geometry comes before math, many don't consider geometry proper maths.
Good summation though, and I do enjoy reading xkcd from time to time. Helps keep me up to date on general nerdery in fields I'm not following well enough! I like materials science best these days, and I doubt I'll be moving on any time soon; the addictive properties on chemistry may not be well documented, yet they must exist.
But there is a fundamental problem here. For something to be Science, it has to be possible to test it by experiment. Can you design an experiment to prove (or more precisely, fail to disprove) that "All Physics" is dictated by mathematics?
But there is a fundamental problem here. For something to be Science, it has to be possible to test it by experiment. Can you design an experiment to prove (or more precisely, fail to disprove) that "All Physics" is dictated by mathematics?
I can definitely design an experiment that will fail to disprove that all physics is dictated by mathematics. It might involve some bean sprouts or a Play-Doh volcano.
I would point out that everything prove-able by experimentation can by default also be proven by math. You might need enough working knowledge to do the experiments on paper, so not a perfect argument here.
Then again, for about a century all physics has been worked on in pure math first, then we've tried to explain wtf the math is telling us, because it's usually well beyond our ability to test experimentally.
By the way, I am still reading this thread and appreciate all of the contributions, insights, reflections, and digressions. I've been a little on the busier side lately, which has prevented me from sharing my own thoughts, but I also think they're not too dissimilar from @DreadKhan and @FinneousPJ. There are some divergences, but that's what makes dialogue entertaining. It's nice to see a place where there isn't excessive hostility to philosophy though, which makes me wonder about your backgrounds; it's encouraging. I teach both logic and philosophy, and I'm busy because papers are due and finals are around the corner. I try to balance the seriousness of my work with the silliness of my personality, the latter of which is mostly on display here in the forums.
But there is a fundamental problem here. For something to be Science, it has to be possible to test it by experiment. Can you design an experiment to prove (or more precisely, fail to disprove) that "All Physics" is dictated by mathematics?
Umm, there's a reason I referred to it as "a half-joking quote" rather than a scientific theory.
I would point out that everything prove-able by experimentation can by default also be proven by math. You might need enough working knowledge to do the experiments on paper, so not a perfect argument here.
Then again, for about a century all physics has been worked on in pure math first, then we've tried to explain wtf the math is telling us, because it's usually well beyond our ability to test experimentally.
You couldn't be more wrong. Yes, a vast quantity of theorising is done using pure maths. However, if it can't be tested experimentally (e.g. string theory), it isn't science, and therefore isn't physics. It is properly classed as philosophy. We have come full circle back to Aristotle.
@Fardragon: Ah yes, the universally accepted Definition of Science that unequivocally excludes string theory. Can you remind me of the exact text? I seem to have lost my pamphlet.
Of course, philosophers of science do argue about what does and does not constitute science, but they could save themselves the trouble if they would just read The Definition.
science ˈsʌɪəns noun the intellectual and practical activity encompassing the systematic study of the structure and behaviour of the physical and natural world through observation and experiment.
@Fardragon: A bit more seriously, that definition seems to downplay the role of prediction in science. I'm assuming you don't completely dismiss all theoretical science, though. String theory makes predictions, but the standard gripe is that they can't be experimentally checked. I think the most interesting philosophical question there hinges on that "can't," because they *could* be tested if we had vastly stronger devices. So is a prediction unscientific because we don't have the technology to test it right now? Would the answer be different if the necessary experimental apparatus was just *slightly* out of reach of current technology? It's fine if you have strong opinions on these, but I think they're valid (philosophical) questions.
There it is! Like I said, every philosopher of science who writes about the demarcation problem must be feeling pretty foolish right now.
I hope this is just being playful. For one, that definition is fairly general to the point of being trivial, but, for two, its generality also permits obvious counterexamples. You need only look at the laundry list of abandoned scientific theories that were experimentally and predictively useful. I can reference some here, but can also reference Larry Laudan's article, "A Confutation of Convergent Realism" as well for some of those. For that matter, ID theory with the right built-in hypotheses would qualify. There are far better, more accurate definitions as a result of that philosophical analysis. Philip Kitcher, for example, proposes that theories are bundles of hypotheses, and therefore, any scientific theory needs to be such that its hypotheses can be isolated and tested independently (which excludes ID now). In addition, he argues that it should promote unity either by compatibility with what we think we already know or by being able to explain better the domain of another theory. Finally, it should enhance our knowledge by being able to do more than just what it set out to do in the first place. These three criteria are testability, explanatory scope, and theoretical fruitfulness or fecundity. In light of that, I actually prefer this definition from the OED instead:
A branch of study that deals with a connected body of demonstrated truths or with observed facts systematically classified and more or less comprehended by general laws, and incorporating trustworthy methods (now esp. those involving the scientific method and which incorporate falsifiable hypotheses) for the discovery of new truth in its own domain.
It seems more accurate and informative, especially if we modify it appropriately to restrict it to the natural / physical world like the previously given definition.
@Fiendish_Warrior: Yep, just being playful. As I said near the beginning of this thread, blind adherence to a single "correct" definition is not consistent with how I look at things.
@Fardragon: A bit more seriously, that definition seems to downplay the role of prediction in science. I'm assuming you don't completely dismiss all theoretical science, though. String theory makes predictions, but the standard gripe is that they can't be experimentally checked. I think the most interesting philosophical question there hinges on that "can't," because they *could* be tested if we had vastly stronger devices. So is a prediction unscientific because we don't have the technology to test it right now? Would the answer be different if the necessary experimental apparatus was just *slightly* out of reach of current technology? It's fine if you have strong opinions on these, but I think they're valid (philosophical) questions.
I'm not, in any way, suggesting that string theory be dismissed, just pointing out (as most of those behind the theory would agree) it doesn't become science until it makes a testable prediction. That doesn't make it useless or wrong. It is science (and it's dependency on mathematics) that is limited. There is no reason to suppose, or any way to prove, that it is possible for science, maths, or the human brain to fully describe the universe. It's simply a process of creating and improving a model which we can understand, and use to make useful predictions.
@Fardragon: I'm deeply skeptical that most string theorists would say that string theory is not science. Also, my point was that there is some interesting nuance to the concept of a "testable prediction."
@Fardragon Uh, the problem with string theory as I understand things is that it doesn't have MATH to back it up. Meaning it has no real basis, it's just an idea atm. Quantum Mechanics couldn't be proven in the macro world, which shouldn't be a surprise since it defines the rules of the micro world. But, the math all worked, even if it wasn't directly testable back then. As we got the ability to test it further, we've found lots of things behave as predicted, even really disturbing things that completely violate macro physics.
If the math works, something can still be a 'math trick', which was what some said about QM when it was unveiled, but it ALSO explained some known mysteries, so it was given a pretty thorough examination.
BTW, science by definition has to include 'can be repeated by anyone, at any time and in any similar situation'. If nobody can reproduce your experimentation, its not science. Can't imagine a dictionary leaving out the importance of reproduceability.
BTW, science by definition has to include 'can be repeated by anyone, at any time and in any similar situation'. If nobody can reproduce your experimentation, its not science. Can't imagine a dictionary leaving out the importance of reproduceability.
I agree. Replication is very important, which is why I hate the media's coverage of scientific results. That is also why I liked the OED definition I used above as I believe replication falls indirectly within the scope of "trustworthy methods."
@Fardragon I've done a course on quantum mechanics at uni and don't remember breaking maths. On the contrary, QM was born from ignoring conventional physical thinking and applying maths.
Hmm, this reminds me of something fun: Measurements of the Casimir force (a force predicted by QM) proved that the sum of all positive number (1+2+3+4+...) = -1/12. On the surface it looks like QM did break math, until you apply renormalization theory. See: http://en.wikipedia.org/wiki/1_+_2_+_3_+_4_+_⋯ for more information on how that works.
I'm not, in any way, suggesting that string theory be dismissed, just pointing out (as most of those behind the theory would agree) it doesn't become science until it makes a testable prediction. That doesn't make it useless or wrong. It is science (and it's dependency on mathematics) that is limited.
There is no reason to suppose, or any way to prove, that it is possible for science, maths, or the human brain to fully describe the universe. It's simply a process of creating and improving a model which we can understand, and use to make useful predictions.
I cannot comment intelligently on the first as I am too ignorant of the details to make a meaningful contribution, but I do know that the truth-value of the second claim is independent of the first. Therefore, it shouldn't get lost in the crossfire and deserves a more thorough examination.
I actually agree with this second claim. I consider myself a kind of epistemological utilitarian in the vein of a kind of Kantian- / Sellarsian-inspired idealism. There are a host of serious problems associated with "knowing" the nature of the universe in part, let alone in whole. For one, there's no good way to explain correspondence in a meaningful way between ideas and objects, especially considering that classical representationalism has been more or less rejected.
This leaves one with a pragmatic view of knowledge, but at that point, it's conceded that we don't know anything concerning the *reality* of nature; we just know how to *manipulate* it to our benefit and advantage. Realists will contend that pragmatism guarantees a minimum of approximate truth, but I respond that approximation is a binary concept that only possesses meaning in light of that from which it is a deviation. We can't understand what it means to miss the mark unless we know what the mark *is*. Even if we grant that pragmatic effects are a hallmark of truth, the realist is still left with the burden of explaining how incompatible and mutually exclusive theories or models can each adequately account for the same phenomena or target-system.
All of these considerations lead me down the ultimate path of a mitigated anti-realism. This isn't to say "anything goes" because I do believe that pragmatic effects and observable phenomena act as *constraints* on what we can reasonably say and believe, but *as constraints* they're not restrictive enough to leave us with one and only one way to describe the world and its objects. And there is simply no objective way to privilege one functional description over and against another.
Knowability of the universe is a pain in the butt for science, because the 'Theory of Everything' is the goal, but it's also a mirage; the closer you get, the further away it seems to get (the more answers we find, ever more questions are created).
Most scientists are comfortable with viewing science as something that gives us working models rather than actual objective truth. Useful fictions are still useful, as long as nobody is crazy enough to cling to a theory that is no longer useful.
The problem with the term useful I note would be that people have a habit of using science to do evil, if they can get away with it, IE many 'learned men' tried to use science to corroborate their theory that non-whites were all stupid, or that people with squarer hands were all criminals. It wasn't science, but they CLAIMED it was... and people clung to those 'theories', as they were 'useful' (if you want to oppress non-whites). So, @Fiendish_Warrior mentioned, trustworthy methods/ethical standards are important, and Lord knows scientists have been known to falsify data when its handy. Look up some of the really big names that have committed scientific fraud, it's disappointing.
@Fardragon I've done a course on quantum mechanics at uni and don't remember breaking maths. On the contrary, QM was born from ignoring conventional physical thinking and applying maths.
Two independent friendly remarks:
Quantum mechanics was created to explain concrete experiments and observed behaviours, noticeably what happens when you disturb an atomic system (a way to try to understand why an atom can be stable). Even if they intensively use mathematics, those original theories are driven by physics as a science.
One of the most famous paper in quantum physics introduced a famous and non defined mathematical object. That was covered by a broader theory in mathematics a few years later. That was both dangerous and useful. I am quite sure you saw that thing in your course (or electrodynamics) but the underlying mathematical nature and issues were perhaps hidden.
Anyway I don't think it is fun to discuss those things on a game forum.
Comments
Philosophy and math are extremely closely related, always have been. Oddly enough, math is also the wing of science most strongly associated with faith and mysticism. Math is the common factor that ties all the various fields of science we've been creating together; without math, they cease to be science.
All biology is dictated by chemistry
All chemistry is dictated by physics
All physics is dictated by math
Ergo, everything is math
Edit: it looks like this quote might stem from an XKCD comic
https://xkcd.com/435/
Good summation though, and I do enjoy reading xkcd from time to time. Helps keep me up to date on general nerdery in fields I'm not following well enough! I like materials science best these days, and I doubt I'll be moving on any time soon; the addictive properties on chemistry may not be well documented, yet they must exist.
Then again, for about a century all physics has been worked on in pure math first, then we've tried to explain wtf the math is telling us, because it's usually well beyond our ability to test experimentally.
Werther or not it counts as philosophy or science fiction - that is philosophy.
Of course, philosophers of science do argue about what does and does not constitute science, but they could save themselves the trouble if they would just read The Definition.
ˈsʌɪəns
noun
the intellectual and practical activity encompassing the systematic study of the structure and behaviour of the physical and natural world through observation and experiment.
If the math works, something can still be a 'math trick', which was what some said about QM when it was unveiled, but it ALSO explained some known mysteries, so it was given a pretty thorough examination.
BTW, science by definition has to include 'can be repeated by anyone, at any time and in any similar situation'. If nobody can reproduce your experimentation, its not science. Can't imagine a dictionary leaving out the importance of reproduceability.
One is a claim about string theory: The other, an epistemological claim: I cannot comment intelligently on the first as I am too ignorant of the details to make a meaningful contribution, but I do know that the truth-value of the second claim is independent of the first. Therefore, it shouldn't get lost in the crossfire and deserves a more thorough examination.
I actually agree with this second claim. I consider myself a kind of epistemological utilitarian in the vein of a kind of Kantian- / Sellarsian-inspired idealism. There are a host of serious problems associated with "knowing" the nature of the universe in part, let alone in whole. For one, there's no good way to explain correspondence in a meaningful way between ideas and objects, especially considering that classical representationalism has been more or less rejected.
This leaves one with a pragmatic view of knowledge, but at that point, it's conceded that we don't know anything concerning the *reality* of nature; we just know how to *manipulate* it to our benefit and advantage. Realists will contend that pragmatism guarantees a minimum of approximate truth, but I respond that approximation is a binary concept that only possesses meaning in light of that from which it is a deviation. We can't understand what it means to miss the mark unless we know what the mark *is*. Even if we grant that pragmatic effects are a hallmark of truth, the realist is still left with the burden of explaining how incompatible and mutually exclusive theories or models can each adequately account for the same phenomena or target-system.
All of these considerations lead me down the ultimate path of a mitigated anti-realism. This isn't to say "anything goes" because I do believe that pragmatic effects and observable phenomena act as *constraints* on what we can reasonably say and believe, but *as constraints* they're not restrictive enough to leave us with one and only one way to describe the world and its objects. And there is simply no objective way to privilege one functional description over and against another.
Most scientists are comfortable with viewing science as something that gives us working models rather than actual objective truth. Useful fictions are still useful, as long as nobody is crazy enough to cling to a theory that is no longer useful.
The problem with the term useful I note would be that people have a habit of using science to do evil, if they can get away with it, IE many 'learned men' tried to use science to corroborate their theory that non-whites were all stupid, or that people with squarer hands were all criminals. It wasn't science, but they CLAIMED it was... and people clung to those 'theories', as they were 'useful' (if you want to oppress non-whites). So, @Fiendish_Warrior mentioned, trustworthy methods/ethical standards are important, and Lord knows scientists have been known to falsify data when its handy. Look up some of the really big names that have committed scientific fraud, it's disappointing.
Quantum mechanics was created to explain concrete experiments and observed behaviours, noticeably what happens when you disturb an atomic system (a way to try to understand why an atom can be stable). Even if they intensively use mathematics, those original theories are driven by physics as a science.
One of the most famous paper in quantum physics introduced a famous and non defined mathematical object. That was covered by a broader theory in mathematics a few years later. That was both dangerous and useful. I am quite sure you saw that thing in your course (or electrodynamics) but the underlying mathematical nature and issues were perhaps hidden.
Anyway I don't think it is fun to discuss those things on a game forum.