The Philosophic Corruption of Physics and Logical Leap

[Pepin]

That is going to take a little time for me to process, especially since that is closer to my personal ideas on the matter. Are there any resources on the topic that go into this? Something that explains the other side very well and points out all of the flaws in the opposing argument? I am rather sceptical, mostly because of my eagerness to accept what you are putting forward, and because the opposing arguments make sense to me. In other words: I am confused.

[RestoringGuy]

I can't find any authors that are close.  I am tempted to say there are traces of what I am saying from Penrose (the three worlds model) and additionally the so-called "Mathematical Universe Hypothesis" , but those are not quite what I suggest, because they seem to presuppose that mathematics is more extensive than the physical universe itself, or at the least there are parts of mathematics that apply to us and parts that do not.  Galileo is probably closest to my thinking.  I did find this article "The Sin of Galileo" with the interesting quote (related to quantum mechanics): "a successful mathematical theory does not enable us to understand what is going on in reality."

http://www.friesian.com/mumford.htm

I welcome skepticism because I am at a crossroads of studying this sort of stuff for more years than I care to admit.  There are a handful of paradoxes that I claim my theory solves.  I accept it is probably flawed.  But I feel compelled in this direction since I no longer can believe our objective reality lacks a real presence of mathematical prediction (it requires a presence much bigger than previous acknowleged anyway), nor do I care to go down the impossible road of subjectivists who suggest the universe emerges from our minds.

 

[Pepin]

Would the essential claim would be that all math has predictive value when applied to what it describes? If so, the idea would presume that any mathematical concept can be observed in objective reality given an appropriate situation in which the mathematical concept comes into play. If a mathematical concept is true, then the question would be, "where can this concept be observed?". Am I on or off base with what I am saying?

[Lians]

Back in secondary school I used to struggle with the conceptual understanding of mathematics and how it fits in our world. I was good at applying what I was taught, but in the back of my mind I was never quite satisfied. Later, when I started participating in competitions I was confronted with a very dysfunctional world. The level of dissociation in those math circles was quite frightening (even though I didn't know anything about dissociation at that time). I often heard people suggesting that mathematics is a science, that it was, in fact, a conceptual interpretation of the world around us (everything is mathematics!). Some people even suggested that we should all communicate in mathematics because it's much more rigorous and logical. Where was all this coming from? Well, giving people definitions and teaching them how to reason is not in the interest of the public school system. Definitions and critical thinking make for incredibly poor propaganda tools, so most teachers prefer to completely bypass the subject. Sadly, a severe lack of conceptual understanding allows people to easily project all their unconscious thoughts on the subject matter. You can probably find a link between the introduction of the public school system and the rise of "mathematical science".

Mathematics is a conceptual construct, and as such, it's built on a set of axioms. It's a language. Take your favourite fantasy novel as an example. It's probably inhabited by non-existing creatures living in a non-existing universe. However, the laws that govern their world are (ideally) internally consistent given a set of axioms that the author provides to the reader. That's what allows us to suspend our disbelief. We don't walk out the front door expecting to be assaulted by a wizard who's riding a dragon because the axioms in the context of which these entities exist don't apply to our universe. The predictive or descriptive value of a conceptual construct is proportional to the degree to which its governing axioms conform to the context of application. Any derivations of the axioms should, of course, be internally consistent.

This is why the scientific method is so successful in advancing our knowledge of the universe. It requires that the value of a conceptual construct be measured against empirical evidence. Mathematics, similar to philosophy, can be a wonderful tool if handled properly. As with all great tools, its misuse can have terrible consequences. Unfortunately, over the last couple of decades we've seen the rise of what some call "mathematical physics". Here's a common trick: take a complicated-looking equation (or make one up), set one of the fundamental quantities in physics to zero (mass seems to be the favourite one) and derive a formula. Apply said formula to cases where the quantity isn't zero. If someone questions your methodology you can claim that examining the limit can give you important insight. Naturally, the preferred approach is much more convoluted, but I think you get the picture. Unprovable statements (no null hypothesis) and abuse of notation are now the tools of the trade. How are theories tested? You convince enough people (usually in government) that your research is important. You're quite happy that no one seems to demand a null hypothesis before investing millions of dollars in your experiment. Measurements don't support your theory? No worries, you can simply claim that you need more accuracy and therefore more money for research. It's quite beautiful in terms of profit.

Few years ago I watched a National Geographic documentary about the origin of the universe and the context in which it exists (can't remember the name). They interviewed some of the world's "top" physicists that worked for an institute dedicated to this kind of research. Did they run any experiments? No. What did they do? They played around with equations. What's funny is that everyone had a completely different theory. The theories were derived through manipulation of existing laws of physics. Pick a set of physics laws, set a few of the constants or variables to zero, throw in a few extra dimensions and derive a theory explaining what you've done. Congratulations, you're a physicist with a six figure salary.

Long story short, you've got every reason to be skeptical about modern-day physics. If anyone wants to pursue the subject academically, I suggest they go for an engineering degree. Physics and mathematics are wonderful fields of study, but as with most things in our current society, they've got way too much "government" in them. I think most of you know what I'm talking about.

[ribuck]

Physics and mathematics are wonderful fields of study, but as with most things in our current society, they've got way too much "government" in them.

I agree with you, but most people just don't see it.

Here's an interesting TED Talk released two days ago:
[View:http://www.youtube.com/watch?v=jc_-Y9rDN2g:640:480]

by Laura Snyder who discusses the origin of the word "scientist", and the four principles that separated scientific inquiry from the scientific philosophy that preceded it.

Unfortunately, one of the four principles that she holds in high regard is "external funding of science". Later in her talk she laments that modern scientists direct their energy towards their funding
sources rather than towards the general public, but it seems she can't see why this is. He who pays the piper calls the tune.

An academic was complaining to me recently that when he applies for research funding, he is required to describe the "expected outcome" on the funding application form. His complaint was that he wanted to do research in fields where the expected outcome was completely unknown. My complaint would be that the funding masters will inevitably be selective: if the expected outcome isn't what they want to see, the work won't be funded.

[Pepin]

Lians, I am not really sure how to respond to your post. I could respond to it, but I would't enjoy it very much, and I don't feel like it would be a good use of my time. If you disagree, I urge you to pretend to be Richard Feynman and to dissect the argument you are making through his eyes and or brain.

[RestoringGuy]

 

Would the essential claim would be that all math has predictive value when applied to what it describes? If so, the idea would presume that any mathematical concept can be observed in objective reality given an appropriate situation in which the mathematical concept comes into play. If a mathematical concept is true, then the question would be, "where can this concept be observed?". Am I on or off base with what I am saying?

 

My idea is that all mathematics has predictive value, but that is only half of what I claim.  My perspective is that when a symbolic formula has predictive value and that value is objectively reproducible in a totally generalized way, that is what makes it mathematical truth.  There is a view that "true" mathematics does not exist until it is conceived (constructivism), and a view that mathematics is simply manipulation rules over symbols (formalism), but it says nothing about how those symbols must be embeddable into the real world.  I am closer to the view called Platonism (not the Idealist flavor, but the Realist flavor) which holds that mathematical truths exist, and by an act of proof we expose them to observation.  My main reason for this holding this view has to do with computer algorithms and the independent way certain results can be reproduced.

 

 

You can probably
find a link between the introduction of the public school system and the
rise of "mathematical science".

Mathematics is a conceptual construct, and as such, it's built on a
set of axioms. It's a language. Take your favourite fantasy novel as an
example. It's probably inhabited by non-existing creatures living in a
non-existing universe. However, the laws that govern their world are
(ideally) internally consistent given a set of axioms that the author
provides to the reader.

 

Certainly the fields of physics and mathematics have been damaged by government, and the evils of seeking funding take precedence over any real progress.  By connecting mathematics to the public school system, sure it is easy to argue mathematical science is bad.  There is certainly a large part of mathematical activity that is conceptual construct, including the axioms.  In that regard it is like you say, a fantasy novel.  But fantasy novels do not require proofs.  What I am talking about is the relationship between the axioms (which we may regard as fictional) and the conclusions (when isolated they may be regarded as fictional).  With the advent of automated deduction and automated proof checking, it has become easier and more empirically certain whether or not such a symbolic relationship exists.  We have dealt with this kind of thing in science for a long time.  In the classical physics equation F=ma the letter "F" is fictional and only a conceptual construct.  Only by connecting the letters to some apparatus (a spring scale or whatever) do these letters have meaning and the truth of the symbols "F=ma" are only true in the fictional realm where the letters mean what you have decided they mean.

In the same way, when I write a computer program to generate prime numbers, and my apparatus proves 3433 is prime, my claim "3433 is prime" is only true in the fictional realm where digits and symbols (what is "3",etc.) hold the meaning I have decided upon.  Despite all that fiction, I am able to make a prediction about what a physical system will do much like F=ma.  When a prime number generator is made of atoms, simply an apparatus, I predict it will generate 3433.  What about the fiction?  Well if the computer is built so that "3" and "4" are reversed, then 4344 will be produced, but 4344 is not prime.  But 4344 is prime in a fictional world where symbols are chosen differently (1,2,4,3,5,..).  The numeric value of the speed of light will also be "different" now that 3 and 4 are switched.  Nevertheless, I am able to predict 4344 in such a reversed-computer will be generated using the mathematics that I already know, because the reversal of the symbols is something I can learn about.  This kind of generalization is exactly the same as physics, where experiments are performed in a specialized environment (a laboratory).  When principles and predictions are made and proven, they can be applied to new situations in places and in other symbolic languages where those results have previously not been empirically verified.

 

[Lians]

 

 

You can probably
find a link between the introduction of the public school system and the
rise of "mathematical science".

Mathematics is a conceptual construct, and as such, it's built on a
set of axioms. It's a language. Take your favourite fantasy novel as an
example. It's probably inhabited by non-existing creatures living in a
non-existing universe. However, the laws that govern their world are
(ideally) internally consistent given a set of axioms that the author
provides to the reader.

 

Certainly the fields of physics and mathematics have been damaged by government, and the evils of seeking funding take precedence over any real progress.  By connecting mathematics to the public school system, sure it is easy to argue mathematical science is bad.  There is certainly a large part of mathematical activity that is conceptual construct, including the axioms.  In that regard it is like you say, a fantasy novel.  But fantasy novels do not require proofs.  What I am talking about is the relationship between the axioms (which we may regard as fictional) and the conclusions (when isolated they may be regarded as fictional).  With the advent of automated deduction and automated proof checking, it has become easier and more empirically certain whether or not such a symbolic relationship exists.  We have dealt with this kind of thing in science for a long time.  In the classical physics equation F=ma the letter "F" is fictional and only a conceptual construct.  Only by connecting the letters to some apparatus (a spring scale or whatever) do these letters have meaning and the truth of the symbols "F=ma" are only true in the fictional realm where the letters mean what you have decided they mean.

In the same way, when I write a computer program to generate prime numbers, and my apparatus proves 3433 is prime, my claim "3433 is prime" is only true in the fictional realm where digits and symbols (what is "3",etc.) hold the meaning I have decided upon.  Despite all that fiction, I am able to make a prediction about what a physical system will do much like F=ma.  When a prime number generator is made of atoms, simply an apparatus, I predict it will generate 3433.  What about the fiction?  Well if the computer is built so that "3" and "4" are reversed, then 4344 will be produced, but 4344 is not prime.  But 4344 is prime in a fictional world where symbols are chosen differently (1,2,4,3,5,..).  The numeric value of the speed of light will also be "different" now that 3 and 4 are switched.  Nevertheless, I am able to predict 4344 in such a reversed-computer will be generated using the mathematics that I already know, because the reversal of the symbols is something I can learn about.  This kind of generalization is exactly the same as physics, where experiments are performed in a specialized environment (a laboratory).  When principles and predictions are made and proven, they can be applied to new situations in places and in other symbolic languages where those results have previously not been empirically verified.

 

 

 

I'm not disputing the value of mathematics in physics. What I'm talking about is turning mathematics into what it's not. Using your example, evaluating the equation F=ma for m=0 has a meaning in mathematics, but not in physics. Physics has a built in validation mechanism (scientific method) that ensures its constructs are accurate relative to physical reality. Mathematics is geared towards high-level abstraction. Mathematics and physics are complementary, but one has to have a clear distinction of boundaries in order to utilize their facilities. These boundaries are incredibly important. However, they are often ignored because they're philosophical in nature (yikes!).

To give you another example, if you're programming in a high-level compiled language, your compiler is your bridge between physical reality (machine instructions) and abstraction (source code). A microprocessor has no idea what a class is, yet it's able to utilize the logic encoded with it. Your phys-gcc compiler is applying the scientific method to your mathematics source code, allowing you to manipulate physical hardware. There are obvious limitations with this example, but I think it gets the point across.

As for language and proof, if you think about it, mathematical proof is a method for checking internal consistency. We're doing the same with language, but it's hardware accelerated by our language centres to the point that we're not even conscious of it. It's what allows you to have a chuckle at a google translation.

[RestoringGuy]

 

I'm not disputing the value of mathematics in physics. What I'm talking about is turning mathematics into what it's not. Using your example, evaluating the equation F=ma for m=0 has a meaning in mathematics, but not in physics. Physics has a built in validation mechanism (scientific method) that ensures its constructs are accurate relative to physical reality. Mathematics is geared towards high-level abstraction. Mathematics and physics are complementary, but one has to have a clear distinction of boundaries in order to utilize their facilities. These boundaries are incredibly important. However, they are often ignored because they're philosophical in nature (yikes!).

To give you an example, if you're programming in a high-level compiled language, your compiler is your bridge between physical reality (machine instructions) and abstraction (source code). A microprocessor has no idea what a class is, yet it's able to utilize the logic encoded with it. Your phys-gcc compiler is applying the scientific method to your mathematics source code, allowing you to manipulate physical hardware. There are obvious limitations with this example, but I think it gets the point across.

As for language and proof, if you think about it, mathematical proof is a method for checking internal consistency. We're doing the same with language, but it's hardware accelerated by our language centres to the point that we're not even conscious of it. It's what allows you to have a chuckle at a google translation.

 

 

The validation methods of mathematics, while symbolic, have to be manifested in physical reality.  You have said mathematics is conceptual construct and a language.  But that is insufficient and I challenge that view.  If I say such a thing about physics, you would suggest it must be augmented by the scientific method in reality.  That is simply a physical action that verifies some physics symbolism.  But I have met no mathematician who claims something must be accepted as "true" without demanding a physical presentation (a proof as one example).  In those cases where mathematical proof is so complex only a computer can do the job, it seems to me totally illogical to say mental conceptualization is all that is required.  A physical artifact must be shown that demonstrates truth, even if the entire concept is too complex to simply be held inside our monkeylike brains.

Your point about boundaries is a good one.  But that only seems to be a valid argument many years ago when mathematicians could never prove things they cannot personally grasp.  At that time one could get away with arguing that mathematics is just conceptual.  Proof is not a method for checking internal consistency (that is model theory), but it only establishes that a particular state can be acheived given the axioms (same as initial conditions in a science experiment).  I don't believe internal consistency of axioms can ever be shown because of the incompleteness theorem.  Mathematicians have accepted this.  With all the conflicts with quantum mechanics and relativity, science in general does not mandate rigorous proof of consistency.  It should be no surprise that mathematics can never be proven to be consistent.   Proof is something mathematicians demand, and physical demonstration of proof is also required.  Even if we cannot comprehend the proof, it is still allowable as long as the methodology is valid.  To me it seems perfectly reasonable that mathematics should be equally as certain and physically relevant as any other science.  Your points in interpreting things incorrectly are good.   I am sure F=ma with m=0 is of little use in physics.  But I do not know what meaning it has in mathematics either.  Until somebody tells me what those letters mean and what predictions do they make (as far as provability of mathematical assertion), I doubt F=ma has any mathematical meaning.

 

[Lians]

 

The validation methods of mathematics, while symbolic, have to be manifested in physical reality.  You have said mathematics is conceptual construct and a language.  But that is insufficient and I challenge that view.

 

All acts of thinking are manifested in physical reality through electrochemical signals in the brain, but that doesn't mean that all products of thinking have a descriptive or predictive value in the context of said reality. You're conflating the medium of existence of a conceptual construct with its applications.

 

You have said mathematics is conceptual construct and a language.

 

I made no such claim. What I said (and implied) is that language is a conceptual construct with a very specific structure. You're implying that they're discrete entities.

 

If I say such a thing about physics, you would suggest it must be augmented by the scientific method in reality.  That is simply a physical action that verifies some physics symbolism.  But I have met no mathematician who claims something must be accepted as "true" without demanding a physical presentation (a proof as one example).  In those cases where mathematical proof is so complex only a computer can do the job, it seems to me totally illogical to say mental conceptualization is all that is required.  A physical artifact must be shown that demonstrates truth, even if the entire concept is too complex to simply be held inside our monkeylike brains.

 

It would be correct to say that a bear is an animal. It would also be correct to say that a bear is a mammal. The two claims are not contradictory because one is a subset of the other. Providing additional information doesn't invalidate the key argument. Physics is a conceptual construct whose structure contains the notion of the scientific method. What people accept as true and how you communicate truth is irrelevant to the topic of discussion.

Again, I never claimed that mental conceptualization is the sole requirement for proof.

 

A physical artifact must be shown that demonstrates truth, even if the entire concept is too complex to simply be held inside our monkeylike brains.

 

Physical artefacts have physical properties. Truth is a property of an abstraction (statement). A physical artefact can't be shown to demonstrate truth because truth is a measure of congruence between (physical) properties and knowledge statements. The level of complexity is of little importance in this discussion.

 

Your point about boundaries is a good one.  But that only seems to be a valid argument many years ago when mathematicians could never prove things they cannot personally grasp.  At that time one could get away with arguing that mathematics is just conceptual.

 

If mathematics is not just conceptual, what is it? Where can you find mathematics if humanity disappears from the face of the planet? The second sentence implies that proof can exist outside of human understanding. Where can you find "proof" in physical reality?

 

 

Proof is not a method for checking internal consistency (that is model theory), but it only establishes that a particular state can be acheived given the axioms (same as initial conditions in a science experiment).

 

I fail to see a difference between the two definitions. Internal consistency implies that a proposition or a state can be derived from the system's defining axioms and, if necessary, a set of initial conditions.

 

 

I don't believe internal consistency of axioms can ever be shown because of the incompleteness theorem.  Mathematicians have accepted this.

 

There's no notion of internal consistency when dealing with axioms. I believe you're talking about systems of axioms. Mathematicians have accepted that a system of axioms can't prove its own consistency and that there are unprovable statements within every such system. Moreover, direct applications of the incompleteness theorem are relevant only when you're dealing with formal systems. The two incompleteness theorems say nothing about any statement in particular. What's interesting is that the scientific method conforms to both even though it was developed centuries prior to Gödel's proofs. The requirement for a null hypothesis is due to the fact that certain statements are unprovable, and empirical testing is designed to push the boundaries of fixed theoretical models (and their respective systems of axioms).

 

 

 

With all the conflicts with quantum mechanics and relativity, science in general does not mandate rigorous proof of consistency.

 

This is why one of the fastest growing fields in theoretical physics is the pseudo-science of string theory. It piggybacks on the traditional notion of science while ignoring the scientific method.

It's funny you should mention incompleteness, because any physicist working on theoretical models "applicable" outside our universe should immediately quit his or her job if s/he is serious about the subject matter. The fact that none of them will actually do so tells you everything you need to know about the integrity of their research.

 

It should be no surprise that mathematics can never be proven to be consistent.   Proof is something mathematicians demand, and physical demonstration of proof is also required.  Even if we cannot comprehend the proof, it is still allowable as long as the methodology is valid.

 

I have no idea what you're talking about.

 

To me it seems perfectly reasonable that mathematics should be equally as certain and physically relevant as any other science.  Your points in interpreting things incorrectly are good.   I am sure F=ma with m=0 is of little use in physics.  But I do not know what meaning it has in mathematics either.  Until somebody tells me what those letters mean and what predictions do they make (as far as provability of mathematical assertion), I doubt F=ma has any mathematical meaning.

 

Mathematics is very old and so broadly used that over the years it's become saturated with concepts belonging outside of its domain (usually coming from the sciences). That doesn't make it a science any more than sticking feathers up your butt makes you a bird. The force equation can be analyzed mathematically without understanding what the variables (or the equation itself) describes. You can solve a system of equations without knowing what the variables mean. Whether these systems describe actual physical behaviour is a different matter altogether. Go to a mathematician and ask her to run experiments on her mathematical proofs. She's probably going to claim, "That's not my job," and rightly so.

Just to be clear, when I talk about "science", I talk about Baconian (now I'm hungry) science. Of course, definitions of science vary a lot. Why is that? A lot of people want to ride on the wave of success and respect that modern-day science has garnered. When people settle on definitions they inevitably put structural boundaries around the various fields of human knowledge. If you ask mathematicians studying chaos theory about how well the general public understands the subject matter, they'll inevitably start complaining about ridiculous publications claiming spectacular applications of the theory and how these authors give chaos theory a bad name. Part of the reason why this field is so open to exploitation is because most people aren't trained to analyze conceptual constructs. If they were, the greatest and most dangerous abstract construct of all, the government, will be revealed for the primitive superstition that it is in a matter of seconds. If you're in power, you definitely don't want that.

Since Feynman was brought up, how does this statement fit your philosophical frameworks: "If you think you understand quantum mechanics, you don't understand quantum mechanics"? A 4 year old can take apart the logical constitution of this statement and laugh at it. Those of us that couldn't do that prior to joining this philosophical conversation should weep.

This turned out to be longer than I anticipated. I hope you found it somewhat valuable.

[RestoringGuy]

 

Physical artefacts have physical properties. Truth is a property of an abstraction (statement). A physical artefact can't be shown to demonstrate truth because truth is a measure of congruence between (physical) properties and knowledge statements. The level of complexity is of little importance in this discussion.

If mathematics is not just conceptual, what is it? Where can you find mathematics if humanity disappears from the face of the planet? The second sentence implies that proof can exist outside of human understanding. Where can you find "proof" in physical reality?

 

That is not something I understand.  You strip away reality from mathematics in order to prove what you assume.

When the expression "2+2" is asked to be made shorter (simplified), and 4 is answered, the symbols and the human brain are together the system that I think in your view you might call "doing mathematics".  Sure without the human brain (and no other change), the mathematics would not be done in this particular case.

But if you substitute the brain with a computer and assume humanity is gone, are you now claiming this calculation "2+2=4" proven by computer no longer constitutes mathematics?  You are actually insisting that "mathematics" and "human" are words connected by definition?  In that case, by your words I am not even talking about mathematics, but mathematics-like-behavior and you can reinterpret all of my other sentences with that substitution.

The physical artifact of mathematics might be a human with paper-and-pencil.  It might be a computer.  It might be any number of physical systems which require mathematical calculation to make a prediction.  You will argue that the symbols are following laws that are not in fact physical laws, but concepts in the mind.  True.  But the mind itself is a physical thing that is itself part of the system.  When the mind is a computer, the same predictions are made and mathematics does not magically become false.

[RestoringGuy]

All acts of thinking are manifested in physical reality through electrochemical signals in the brain, but that doesn't mean that all products of thinking have a descriptive or predictive value in the context of said reality. You're conflating the medium of existence of a conceptual construct with its applications.

I did some more thinking.  Quite true what you describe, although I do not conflate.  Yes the thinking is conceptual, but mathematics is not just thinking.  I know you don't claim such a thing, but you'd have to say that if you maintain I was conflating.  Mathematics must make a proof, and I argue this constitutes external validation and that proves the predictive value.  The electrochemical signals (which make the same predictions as some external device) now have the same value.  Not all of the signals, just the mathematically proven ones! 

Physical artefacts have physical properties. Truth is a property of an abstraction (statement). A physical artefact can't be shown to demonstrate truth because truth is a measure of congruence between (physical) properties and knowledge statements. The level of complexity is of little importance in this discussion.

Knowledge statements cannot be physical?  The electrochemical signals are physical.

There's no notion of internal consistency when dealing with axioms. I believe you're talking about systems of axioms. Mathematicians have accepted that a system of axioms can't prove its own consistency and that there are unprovable statements within every such system. Moreover, direct applications of the incompleteness theorem are relevant only when you're dealing with formal systems. The two incompleteness theorems say nothing about any statement in particular. What's interesting is that the scientific method conforms to both even though it was developed centuries prior to Gödel's proofs. The requirement for a null hypothesis is due to the fact that certain statements are unprovable, and empirical testing is designed to push the boundaries of fixed theoretical models (and their respective systems of axioms).

Correct (well correct for every system more complex than arithmetic).  Yes of course incompleteness says nothing about whether an axiom is true or not.

It's funny you should mention incompleteness, because any physicist working on theoretical models "applicable" outside our universe should immediately quit his or her job if s/he is serious about the subject matter. The fact that none of them will actually do so tells you everything you need to know about the integrity of their research.

You are right, they should quit.  Not because it's applicable only outside our universe, but because it is applicable to physical objects inside our universe different than the ones physicists should be working on.

The force equation can be analyzed mathematically without understanding what the variables (or the equation itself) describes. You can solve a system of equations without knowing what the variables mean. Whether these systems describe actual physical behaviour is a different matter altogether. Go to a mathematician and ask her to run experiments on her mathematical proofs. She's probably going to claim, "That's not my job," and rightly so.

Let's say a system of equations is solved and the variables have no known meaning.  They still have predictive value.  If you encounter a physical system that matches those equations (and I guarantee you there is one, even if it's just a microchip), then you can predict what that physical system does.  The level of complexity matters, because the abstractions needed to make an accurate prediction will be totally unrecognized by the physicist.  The mathematician can make those physical predictions in cases where the physicist fails.

[Lians]

 

But if you substitute the brain with a computer and assume humanity is gone, are you now claiming this calculation "2+2=4" proven by computer no longer constitutes mathematics?

 

I believe this is where most of our disagreements stem from. A computer performing a mathematical operation has no notion of mathematics any more than a river understands fluid dynamics. The computer doesn't do mathematics. It simply runs electricity through an integrated circuit. You, as a human, can abstract out the physical process through a conceptual framework (such as mathematics) because you're capable of concept formation. This is why I asked you if mathematics exists outside the human mind. We've come back to conceptual boundaries and their importance yet again.

[Jake Danczyk]

 

[View:https://www.youtube.com/watch?v=Q185InpONK4]

Stephen Crothers destroying Einstein's relativity equations and various 'black hole' nonsense. (No particularly advanced understanding of math required).

It's all a load of gibberish! I'd go as far as saying criminal-level fraud.

 

I remember stumbling across a website this man had made several years ago. There was some physics content, but most of it was ranting against what he had perceive as academic censorship from professors who would not listen to his ideas.

His ideas are nonsense. Simple proof you have likely encountered: the GPS system is dependent on the theories of relativity being correct. Relativity has also endured long and rigorous inquiry from a large number of brilliant scientists, who certainly had flaws, but generally a clear and logical grasp of Mathematics and physical reality. Here is a list of some more well known experimental proofs: http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html

This might be more interesting to read though, http://www.leapsecond.com/great2005/, it is a guy who does a relativly simple proof of General Relativity by taking 3 atomic clocks up Mt Rainer for a weekend in his Van(with his kids). General relativity predicts that time runs slower in stronger gravity fields. The strength of Earth's gravity field weakens very gradually as altitude above the surface rises. After climbing a few thousand feet, the atomic clocks run faster than identical clocks in a lab at sea-level. But only by a tiny amount (they gain 22 nanoseconds on the lab clocks after about two full rotations of the earth(2days)).  

I am a college senior studying Physics. It is a public school and obviously there is a lot of corruption embedded in this system, but the great thing about Math is that it is impossible to corrupt and the great thing about Observation is that it is almost impossible to corrupt. I have seen and calculated the Quantum Mechanics equations which correctly predict the behaviour of PNP transistor junctions, and then I have built, operatated, and measured the behavior of an electrical circuit containing such a transistor. 

Quantum Mechanics is almost certainly correct. Particles do exist in a fundamentally probalistic nature. A uranium 238 nucleus is unstable. If it could lose an Alpha Particle (2 protons & 2 neutrons, same thing as normal Helium nucleus) its energy would be lower, and nature prefers lower energy states. However, for the alpha particle to escape the nucleus it has to first climb over a small "energy hill", and the there isn't enough kinetic energy in the nucleus for the particle to get over this little hill and ride down the loooong energy drop on the far side. The odds of the alpha particle getting over the hill in any given second are incredibly low, but as it bounces around inside the nucleus, everytime it approaches the barrier it has some non-zero chance of crossing over. It is in a superpostion of states where it is both already over the hill and inside the nucleus. Don't ask what a particle in superpostion looks like, it doesn't look like anything, but mathematics can describe its behaviour. On average, it takes over 4 billion years for the alpha particle to escape. But with U-235, where the hill is much smaller, the particle escape happens much faster and thus your can put a bunch of U-235 together and get a pretty light show. \

Sorry if this is too long, but its just the rigour and logic of QM and relativity should be something this community embraces. Of course, they aren't totally correct, because they cant explain all physical behaviour in the universe, but whatever replaces them will certainly continue along the same paths, extending them. Classical Physics is dead, but its still pretty useful for engineering

[ribuck]

Thanks Jake for your great post. I wanted to say similar things, but I couldn't find a way to express them eloquently.

... the great thing about Math is that it is impossible to corrupt ...

I think this is why there were so many great Soviet mathematicians during the communist area. It was one of the few fields of work where the Communist Party didn't (and couldn't) really interfere, and that would have attracted great minds.

[RestoringGuy]

 

 

But if you substitute the brain with a computer and assume humanity is gone, are you now claiming this calculation "2+2=4" proven by computer no longer constitutes mathematics?

 

I believe this is where most of our disagreements stem from. A computer performing a mathematical operation has no notion of mathematics any more than a river understands fluid dynamics. The computer doesn't do mathematics. It simply runs electricity through an integrated circuit. You, as a human, can abstract out the physical process through a conceptual framework (such as mathematics) because you're capable of concept formation. This is why I asked you if mathematics exists outside the human mind. We've come back to conceptual boundaries and their importance yet again.

 

That is possible.  I don't deny a modern computer has limitations a human does not.  But to establish what is and is not mathematics requires, in your view, invoking a conceptual framework which you admit is electrochemical (a physical process).  If a human is doing their taxes, adding numbers on a calculator, writing numbers, following a procedure, making simple decisions, you would say the human is not doing any mathematics because they might not have sufficient understanding of what they do?  I do not believe mathematics "exists outside the human mind" in the same way an idealist would.  Originally I thought it was a slightly sarcastic question to add some humor to the discussion.  It seems to me mathematics includes the mind as a component, and there are components outside the mind that are necessary.  The mind (a human one) is not a necessary component, because every decision and conclusion that is mathematically doable by human is doable by some type of computer.

True the river does not understand fluid dynamics, but only because fluid dynamics is far more general than the specific action the river takes.  The river can not give answers to questions different than its own particular behavior.  If we take the angle that human conceptualization is the only valid litmus test, then we are at a philosophical dead end and physics too does not exist outside the mind.  Same is true for the scientific method in general.  It is just a mental fiction like all subjective things.  But in an objective view, I argue there is no way define conceptualization outside of asking questions and seeing what conclusions are derivable by a physical system that is doing the conceiving.  If human is a requirement, then our words become very specific.  Birds can not eat, and computers cannot answer questions, because eating and answering are things humans do, if we choose to restrict verbs in that fashion.  If no such restriction is made, then what is an objective test to know when a conclusion is derived in a qualifying manner?

 

[feedmeliberty]

Just wanted to reference previous discussion on this topic: http://board.freedomainradio.com/topic/34478-nihilism-countering-its-physics-quantum-theorygeneral-relativity/

[Bastii]

Just wanted to reference previous discussion on this topic: http://board.freedomainradio.com/topic/34478-nihilism-countering-its-physics-quantum-theorygeneral-relativity/

I see what you did there