What qualifies as science?

[Yazata]

I was [using 'function' in its mathematical sense] but was told there is only physics and that's it!

One can certainly make an argument that physical reality has ontological primacy and that mathematical physics simply models physical reality. I believe that myself.

But... if mathematical physics is supposed to be true, or (for those who don't like truth) if it is supposed to model physical reality in such a way as to work successfully producing accurate predictions of experimental or observational results, then the form of the mathematics would seem to have to be isomorphic somehow with some important element of how reality behaves. It will have to correspond to reality somehow, by somehow capturing or mirroring its underlying form.

It's hard for me to understand what meaning is left in the phrase 'mathematical model' if we don't agree that there's some underlying similarity of form between the theoretical physicist's mathematics and the physical reality that the physicist is ostensibly talking about. Without that, any predictive success that science boasts about turns into little more than magic.

I agree, but the concept is not new and the ever increasing ability to make predictions based on mathematical behaviors of physical properties, argues in favor of a strong mathematical aspect to universal behaviors of physical objects.

I agree wholeheartedly.

Where we perhaps differ is that I'm very doubtful that physical reality can be reduced to mathematics without remainder. I (tentatively) think there's more to physical reality than mathematics. (That suggests that mathematical physics' ability to fully describe and explain physical reality is likewise limited. 'Theories of everything' will therefore be impossible.)

But... I am convinced that mathematics mirrors an exceedingly important element of physical reality. The kind of relationships (and they can correctly be called functions) on the theoretical physicist's chalkboard refer to and describe similar relationships that experiment and observation suggest hold true in reality.

We don't even know what mathematics is, or what kind of reality the objects of mathematical propositions have. I (again tentatively) lean towards the mathematical Platonism idea, the idea that mathematical objects have some kind of abstract extra-mental reality. That's what (it seems to me at least) accounts for mathematics being objective rather than subjective, for why mathematical facts are seemingly discovered rather than imaginatively invented and for why mathematics is arguably the same for mathematicians everywhere. (We would expect 'pi' to have the same value even for hugely biologically-dissimilar space aliens with profoundly alien psychologies.)

http://www.iep.utm.edu/mathplat/

So... IF (big 'if') mathematical objects really do have some kind of poorly-understood abstract existence, and if the mathematical term 'function' refers to one of the kinds of contents (in this case relational) of this abstract reality, I don't see a whole lot of problem with imagining that functions manifest not only on mathematicians chalkboards but in physical reality too. (I'm inclined to hypothesize that is precisely what makes applied mathematics possible.)

I assumed that in a science forum, we could dispense with having to explain function as necessarily being connected to an intentional watchmaker.

I agree again.

You are correct, I was too confident that my use of the word would be taken in context of my original expressions in support of Tegmark's mathematical universe. Clearly I was wrong.

I've never thought that there was anything wrong with your use of the word 'function'. If it wasn't possible to model physical realities with mathematical functions, how would applied mathematics even be possible?

https://www.math.uh.edu/~bekki/Function_Concept.pdf

What does the success of applied mathematics tell us about the nature of reality? How must reality be so that it can be mathematically modeled?

It seems to me that your critics would be on much stronger ground if they criticized the mathematical universe idea directly and not just your use of the word 'function', which seems fine to me. If they want to subvert that, then they need to address the deeper questions.

Certainly there are BIG questions revolving around the nature of what mathematics is, to say nothing of its applicability to physical reality, but those need to be intelligently addressed. Snark won't suffice.

I am not that easily intimidated and I knew they were speaking from their perspective in Physics.

'Function' is a perfectly good word and I'd suggest you keep using it as long as the kind of function you are referring to is reasonably clear.

 

[NotEinstein]

I've never thought that there was anything wrong with your use of the word 'function'. If it wasn't possible to model physical realities with mathematical functions, how would applied mathematics even be possible?

https://www.math.uh.edu/~bekki/Function_Concept.pdf

What does the success of applied mathematics tell us about the nature of reality? How must reality be so that it can be mathematically modeled?

It seems to me that your critics are arguing just to be arguing.

Yazata, you seem to understand Write4U better than I do. Perhaps you can explain the usage of the word "function" in this sentence:

The only point I am trying to make is that, no matter what physical phenomenon or structure we look at, there is always a certain Imperative, which is deterministic of how specific properties (input) and interactions (function) and results (output) become expressed in our reality, which relative to the point of observation.

Remember, Write4U has stated that (s)he always used the word "function" with its mathematical definition.​

 

[Yazata]

Yazata, you seem to understand Write4U better than I do. Perhaps you can explain the usage of the word "function" in this sentence:

The only point I am trying to make is that, no matter what physical phenomenon or structure we look at, there is always a certain Imperative, which is deterministic of how specific properties (input) and interactions (function) and results (output) become expressed in our reality, which relative to the point of observation.

Remember, Write4U has stated that (s)he always used the word "function" with its mathematical definition.

I'm not sure what he meant. But I think that he's talking about what's often called 'physical law'.

The mathematical function idea seems to be the idea that particular variables (the function's 'domain') map onto another set of variables (the 'range' of the function) in such a way that particular sets of variables in the domain determine particular variables in the range.

An example might be any equation taken from physics class. Specify all the independent 'input' variables, turn the mathematical crank, and you've specified a particular 'output' variable.

I read Write4U as suggesting that the same mathematical relationship between the variables on the chalkboard also hold true between physical quantities in physical reality. If that wasn't true, then it's hard to understand what the point of mathematical physics is or what accounts for its peculiar success.

The word "imperative" is a little mysterious. Maybe he's thinking in terms of physical determinism, the idea that if the precise state of the universe is completely and exhaustively specified for some particular time t and if all the laws of physics are correctly known, then the physical variables for the entire past and future are somehow compelled to take particular values. If we accept that kind of model, then the laws of physics along with particular values for physical quantities/variables would seem to impel reality to take the particular forms it displays.

Don't physicists assume something like that when they calculate various quantities and then expect physical reality to actually display those predicted values? (Physical reality isn't random.) Engineers certainly behave that way when they use physics to calculate things when designing aircraft.

Obviously we can argue with that if we like (I'm not sure that I'm really a believer in physical determinism) but it isn't a stupid idea and it isn't obviously unscientific. But I don't see how it could even be possible if we weren't identifying physical law not only with mathematical functions scrawled on chalkboards (our models) but with how physical reality behaves as well.

The phrase "become expressed in our reality" is a bit opaque too.

It might be a reference to mathematical Platonism, to some idea of a Platonic world of pure (mathematical) form from which our physical world is kind of a lesser projection. (Plato's analogy of the cave.) That seems to be what guys like Tegmark are perhaps suggesting. (I haven't read Tegmark's book.)

I'm not personally prepared to sign onto that one. I'm much more Aristotelian. I don't think of mathematical forms as constituting a separate higher mathematical world, but rather think of mathematical forms being fully immanent in this one world as the form of what we see happening around us.

Or perhaps "become expressed in our reality" might just mean something like 'come to our attention' or 'become known to us'.

​

 

[NotEinstein]

I'm not sure what he meant. But I think that he's talking about what's often called 'physical law'.

So when Write4U wrote "interactions", (s)he really meant "physical laws"? And related those "physical laws" to "(mathematical) functions"?

See, there may be critics here are arguing just to be arguing. But I'm not. I'm trying to understand what Write4U is actually saying. And I see you don't have the foggiest either.

​

The mathematical function idea seems to be the idea that particular variables (the function's 'domain') map onto another set of variables (the 'range' of the function) in such a way that particular sets of variables in the domain determine particular variables in the range.

An example might be any equation taken from physics class. Specify all the independent 'input' variables, turn the mathematical crank, and you've specified a particular 'output' variable.

I read Write4U as suggesting that the same mathematical relationship between the variables on the chalkboard also hold true between physical quantities in physical reality. If that wasn't true, then it's hard to understand what the point of mathematical physics is

The fact that you were typing this on a computer designed by the rigorous application of both science and mathematics, thus indicating its success, undermines this option.

or what accounts for its peculiar success.

I personally indeed find this hard to understand. It's easy to just say "maths are real" and be done with it, but nobody has even proven this. But I don't see the problem with this being hard to understand? There's all kinds of hard to understand assumptions in science. Why does Occam's Razor work so well? What about Hume's induction problem?

Yet, science seems to work. The pragmatist simple moves these hard to understand problems onto the "to figure out"-pile of a philosopher, and continues designing even better computers.

Maybe he's thinking in terms of physical determinism, the idea that if the complete state of the universe is completely and exhaustively specified for some particular time t and if all the laws of physics are correctly known, then the physical variables for the entire past and future are somehow compelled to take particular values. If we accept that kind of model, then the laws of physics along with particular values for physical quantities/variables would seem to impel reality to take the particular forms it displays.

Don't physicists assume something like that when they calculate various quantities and then expect physical reality to actually display those predicted values?

No, they test the predictions. If they assume them to be right, they are not doing science.

(Physical reality isn't random.) Engineers certainly behave that way when they use physics to calculate things when designing aircraft.

Right, because they tested the predictions.

Obviously we can argue with that if we like (I'm not sure that I'm really a believer in physical determinism) but it isn't a stupid idea and it isn't obviously unscientific.

It is if you don't test the predictions.

But I don't see how it could even be possible if we weren't identifying physical law not only with mathematical functions scrawled on chalkboards (our models) but with how physical reality behaves as well.

​

I have no alternative either, but I don't see how us not being able to come up with an alternative is somehow conclusive proof it must be. (That would be an argument from ignorance.) It's strongly suggested, yes, but not proven to be so (yet?).

 

[Write4U]

Is anyone prepared to argue this;

Laws being consequences of mathematical symmetries[edit]
Main article: Symmetry (physics)
Other laws reflect mathematical symmetries found in Nature (say, Pauli exclusion principle reflects identity of electrons, conservation laws reflect homogeneity of space, time, Lorentz transformations reflect rotational symmetry of space–time). Laws are constantly being checked experimentally to higher and higher degrees of precision. This is one of the main goals of science. Just because laws have never been observed to be violated does not preclude testing them at increased accuracy or in new kinds of conditions to confirm whether they continue to hold, or whether they break, and what can be discovered in the process. It is always possible for laws to be invalidated or proven to have limitations, by repeatable experimental evidence, should any be observed.
Well-established laws have indeed been invalidated in some special cases, but the new formulations created to explain the discrepancies can be said to generalize upon, rather than overthrow, the originals. That is, the invalidated laws have been found to be only close approximations (see below), to which other terms or factors must be added to cover previously unaccounted-for conditions, e.g. very large or very small scales of time or space, enormous speeds or masses, etc. Thus, rather than unchanging knowledge, physical laws are better viewed as a series of improving and more precise generalizations.
Many fundamental physical laws are mathematical consequences of various symmetries of space, time, or other aspects of nature. Specifically, Noether's theorem connects some conservation laws to certain symmetries. For example, conservation of energy is a consequence of the shift symmetry of time (no moment of time is different from any other), while conservation of momentum is a consequence of the symmetry (homogeneity) of space (no place in space is special, or different than any other). The indistinguishability of all particles of each fundamental type (say, electrons, or photons) results in the Dirac and Bose quantum statistics which in turn result in the Pauli exclusion principle for fermions and in Bose–Einstein condensation for bosons. The rotational symmetry between time and space coordinate axes (when one is taken as imaginary, another as real) results in Lorentz transformations which in turn result in special relativity theory. Symmetry between inertial and gravitational mass results in general relativity.
The inverse square law of interactions mediated by massless bosons is the mathematical consequence of the 3-dimensionality of space.
One strategy in the search for the most fundamental laws of nature is to search for the most general mathematical symmetry group that can be applied to the fundamental interactions.

https://en.wikipedia.org/wiki/Physical_law#Laws_as_definitions

I won't confuse this analysis by making any additional statements. I'll let this quote speak for itself

 

[NotEinstein]

Is anyone prepared to argue this;
https://en.wikipedia.org/wiki/Physical_law#Laws_as_definitions

I won't confuse this analysis by making any additional statements. I'll let this quote speak for itself

I am familiar with Noether's theorem, and I do accept it and thus the idea that the descriptive laws of nature that model reality are often based on mathematical symmetries. But I do not agree that there exist physical mathematical symmetries that give rise to the behavior of particles and waves that we observe in reality.

 

[river]

I am familiar with Noether's theorem, and I do accept it and thus the idea that the descriptive laws of nature that model reality are often based on mathematical symmetries. But I do not agree that there exist physical mathematical symmetries that give rise to the behavior of particles and waves that we observe in reality.

To your last sentence I agree . This nonsence is based on mathematical ego of theoretical physics .

Forgetting that even to have mathematics to exist in the first place , is all based on physical forms that manifest and their consequent dynamic interactions with the like forms and unlike forms .

Mathematics , physics , has no basis in empty space . Space devoid of objects , of any kind .

 

[NotEinstein]

To your last sentence I agree . This nonsence is based on mathematical ego of theoretical physics .

Please define what you mean by "mathematical ego".

Forgetting that even to have mathematics to exist in the first place , is all based on physical forms that manifest and their consequent dynamic interactions with the like forms and unlike forms .

What are "like forms" and "unlike forms"?

Mathematics , physics , has no basis in empty space . Space devoid of objects , of any kind .

Are you saying mathematics and physics cannot exist in empty space, or that mathematics and physics have no meaning in empty space, or something different? I don't understand what you are trying to say here.

 

[river]

↑
To your last sentence I agree . This nonsence is based on mathematical ego of theoretical physics .

Please define what you mean by "mathematical ego".

Meaning that mathematics is superior to the physical world . So that mathematics created the physical world . Rather than the physical world allowed mathematics to exist .

Mathematics originally was based on accounting in ancient times .

 

[river]

↑

Forgetting that even to have mathematics to exist in the first place , is all based on physical forms that manifest and their consequent dynamic interactions with the like forms and unlike forms .

What are "like forms" and "unlike forms"?

Like forms ; hydrogen , with hydrogen , oxygen with oxygen , carbon with carbon

Unlike forms ; hydrogen with oxygen

 

[river]

↑

Mathematics , physics , has no basis in empty space . Space devoid of objects , of any kind .

Are you saying mathematics and physics cannot exist in empty space, or that mathematics and physics have no meaning in empty space, or something different? I don't understand what you are trying to say here.

I'm saying exactly what I said in my above quote . Plain and simple .

 

[NotEinstein]

Meaning that mathematics is superior to the physical world . So that mathematics created the physical world . Rather than the physical world allowed mathematics to exist .

Mathematics originally was based on accounting in ancient times .

Then we indeed agree.

Like forms ; hydrogen , with hydrogen , oxygen with oxygen , carbon with carbon

Unlike forms ; hydrogen with oxygen

OK, understood.

I'm saying exactly what I said in my above quote . Plain and simple .

I just don't understand exactly what you mean with "has no basis". Does reality have a basis in empty space?

And back to:

Forgetting that even to have mathematics to exist in the first place , is all based on physical forms that manifest and their consequent dynamic interactions with the like forms and unlike forms .

I'm not 100% I agree with this. Mathematics isn't based on physical forms, it's based on abstract forms, such as numbers and functions.

 

[river]

Mathematics , physics , has no basis in empty space . Space devoid of objects , of any kind .

↑

I'm saying exactly what I said in my above quote . Plain and simple .

I just don't understand exactly what you mean with "has no basis". Does reality have a basis in empty space?

Inotherwords , without objects , mathematics and physics has no starting point to develope any theory.

No and thats my point .

 

[river]

↑

Forgetting that even to have mathematics to exist in the first place , is all based on physical forms that manifest and their consequent dynamic interactions with the like forms and unlike forms .

I'm not 100% I agree with this. Mathematics isn't based on physical forms, it's based on abstract forms, such as numbers and functions.

Both of which are based on a physical form , us . And the physical forms around us . At the Root of mathematics are physical forms .

 

[NotEinstein]

Inotherwords , without objects , mathematics and physics has no starting point to develope any theory.

No and thats my point .

Ah, so your point is that in empty space there is no one around to start developing the fields of physics and mathematics. I agree with that.

Both of which are based on a physical form , us . And the physical forms around us . At the Root of mathematics are physical forms .

I disagree. Numbers can be based on set theory, both of which don't need humans around to be properly defined. Mathematics is about abstract concepts, and has no physical forms as the root/basis of it. (Historically, of course it does, but not the way it's constructed in more modern times.)

 

[river]

Ah, so your point is that in empty space there is no one around to start developing the fields of physics and mathematics. I agree with that.


I disagree. Numbers can be based on set theory, both of which don't need humans around to be properly defined. Mathematics is about abstract concepts, and has no physical forms as the root/basis of it. (Historically, of course it does, but not the way it's constructed in more modern times.)

How did these numbers come to be ?

The abstract , is based on us . Or any thinking being .

Not defined brought into , manifested , in the first place .

 

[Write4U]

So when Write4U wrote "interactions", (s)he really meant "physical laws"? And related those "physical laws" to "(mathematical) functions"?

Reverse your sentence and you will understand what I'm saying. You may not agree.

IMO, mathematical functional constants are the (enfolded) imperatives on which physical laws are founded, which in turn determine how physical things must interact and become physically explicated (unfolded).

Like forms ; hydrogen , with hydrogen , oxygen with oxygen , carbon with carbon.
Unlike forms ; hydrogen with oxygen

I see "like" and "unlike" as mathematical equations, regardless of form or substance.
Things are symmetrical or asymmetrical in form or function.

p.s. the origin of the word Physics means "essence" or "natural", not "material stuff".

The change of the word "Physis"
Since Aristotle, the physical (the subject matter of physics, properly τὰ φυσικά "natural things") has often been contrasted with metaphysical (the subject of metaphysics).[23] "Physis, translated since the Third Century B.C. usually as "nature" and less frequently as "essence", means one thing for the presocratic philosophers and quite another thing for Plato."[24] Physis is a great example of a keyword that was very important in classical rhetoric and helped define Greek language, but over time was modified through culture changes into a related, but new word.

i.e. "physics".

 

[river]

↑

Like forms ; hydrogen , with hydrogen , oxygen with oxygen , carbon with carbon.
Unlike forms ; hydrogen with oxygen

I see "like" and "unlike" as mathematical equations, regardless of form or substance.
Things are symmetrical or asymmetrical in form or function.

The form and the substance of the form is the essence of physics and mathematics .

Equations cannot exist without the fundamental existence of material form .

 

[Write4U]

↑
The form and the substance of the form is the essence of physics and mathematics .
Equations cannot exist without the fundamental existence of material form .

I can think that 2 + 2 = 4 , as a (symbolic) equation which holds true in the abstract, and can be proved true in material form.

 

[river]

I can think that 2 + 2 = 4 , as an equation which holds true in the abstract, but can be proved true in material form.

It is the material that proves 2+2=4 . Not the abstract form .

The abstract form would have no idea or concept as to where , 2+2=4 could be drawn from . Or understood from .