Relying on faith of some other work

[MathematicalPhysicist]

Yes the title is a little bit ambiguous.

I wanted to know a few stuff in writing articles and doing research in maths and physics, assuming your work will depend somehow on others work, I guess not every researcher who relies on others work understand their work completely.

For example, a work in physics which relies on new machinery in maths, I guess that not all of the theoretical physicists understand the maths they are using, as in rigorously proving it for themselves.

What I am getting at I guess is that when you are relying on some established mathematical and physical results which do relate to your work but not directly, I mean your'e using them, but not necessarily need to know why they are correct? is this legitimate for a lot of researchers?

A concrete example is for example using random matrix theory in modelling something in quantum cosmology, though you don't necessarily a specialist in random matrix or cosmology (but at least in one of them you are), do you need to know a lot in the other branch?
Or the bare minimum? would you need to rely on faith on some results in cosmology if your'e not a cosmologist or results in random matrix if your'e not an expert in it?

It's kinda ruining the whole idea of people who try to understand if you need to rely on faith, understanding goes through the window...
I guess this is kinda of the bad side for specilization in science.

 

[sEsposito]

I'll preface my post by first stating that I am not a working professional (yet)... Just a student.

I think what you're saying is true in that many physicists are not as adept in proving the theorems that they use as mathematicians are; and of course the same can be said for mathematicians that may be working on an applied problem, perhaps even more so. I don't think there are a lot of mathematicians out there that actually understand the science of string theory, but I know that there are many mathematicians working on string theory indirectly.

Driving to the heart of the question: do scientists put a great deal of faith in other scientists? I would say absolutely. I think this is the beauty of an international scientific community. I think if there is anyone field of study here on Earth that is earnestly pushed forward by a global community, or humanity as a species if you will, it's science. And I think a lot of that is a testament to the faith that we have in one another.

There is also things like the peer-review process and other such fail safes. These are clearly in place to ensure credibility within the community.

 

[MathematicalPhysicist]

Yes, but not even peer review journals can be immune to mistakes.

I mean look for example on the french brothers who got Phds in physics and maths respectively from some university in Italy if I am not mistaken, and their work is rather untrsuted by most of the community, but nevertheless they got their Phds.

 

[arunma]

Yes the title is a little bit ambiguous.

I wanted to know a few stuff in writing articles and doing research in maths and physics, assuming your work will depend somehow on others work, I guess not every researcher who relies on others work understand their work completely.

For example, a work in physics which relies on new machinery in maths, I guess that not all of the theoretical physicists understand the maths they are using, as in rigorously proving it for themselves.

What I am getting at I guess is that when you are relying on some established mathematical and physical results which do relate to your work but not directly, I mean your'e using them, but not necessarily need to know why they are correct? is this legitimate for a lot of researchers?

A concrete example is for example using random matrix theory in modelling something in quantum cosmology, though you don't necessarily a specialist in random matrix or cosmology (but at least in one of them you are), do you need to know a lot in the other branch?
Or the bare minimum? would you need to rely on faith on some results in cosmology if your'e not a cosmologist or results in random matrix if your'e not an expert in it?

It's kinda ruining the whole idea of people who try to understand if you need to rely on faith, understanding goes through the window...
I guess this is kinda of the bad side for specilization in science.

Yeah...maybe it's bad. But if so, it's a necessary evil, because there's just too much stuff out there for one person to know. For example, I do particle astrophysics. When I make a detection, I've got a certain number of source counts and background counts in every part of the skymap. From this, I can calculate the significance and say "the significance of the detection is <number> sigma." There's a formula I use that came rom some paper written a couple decades ago. I know the formula, but I have no idea why it's true. I just use it because everyone else does. Should I try and figure this out? Yes. But is it shady? I don't think so.

 

[sEsposito]

Yes, but not even peer review journals can be immune to mistakes.

I mean look for example on the french brothers who got Phds in physics and maths respectively from some university in Italy if I am not mistaken, and their work is rather untrsuted by most of the community, but nevertheless they got their Phds.

There are untrustworthy people in every profession. Think about this: compared to other professions and fields of study a very small amount of the population of scientists is untrustworthy. And even so, these people that publish untrustworthy work are for the most part known to the rest of the group and most of the time expelled from many circles.

I think reliance on one another should not be though of as a detriment. The collaboration is, in my opinion, a good thing. Yes, it's true that it would be nice for everyone in science to be a generalist, and if that were the case we'd make progress at a faster rate (although, I can argue this if you provoke me), but in reality we need specialists. We're not omnipotent, all-knowing beings, we need to focus our attentions on special areas in order for us to fully understand the grand scheme of things. And this system of everyone taking a smaller piece of a very large, overwhelming pie only works if we trust one another to some degree. Even if once in a while we have to deal with some "bad seeds" and bumps in the road.

If you need an example, I'd say the Manhattan Project is a perfect one. Now, I won't get into the morality of the project, but for our purposes let's call the building of the bomb a greater good. Many different specialists from many fields came together to put their specialized expertise into something greater, and they made remarkable progress in a very short amount of time. One could say all these specialists came together for the greater good, instead of having one man try and figure everything out on his own.

 

[fasterthanjoao]

What I am getting at I guess is that when you are relying on some established mathematical and physical results which do relate to your work but not directly, I mean your'e using them, but not necessarily need to know why they are correct? is this legitimate for a lot of researchers?

Yes and no. It depends on the researcher and their field. For many fields, having a complete understanding of the machinery is perfectly reasonable. In things like data analysis and data-mining, the novelty might come from the application, rather than the technique. In this case, the technique must be understood to the level that it can be verified for a particular application, but not necessarily derived.

You'll be aware that citing the results of others is very normal in research, and in fact entirely necessary. The discussion on the peer-review process could be a very lengthy one, and is something that I shall avoid

 

[MathematicalPhysicist]

Folks, don't think that I don't agree with you, I just wanted to know if it's acceptable and seen.
As for the concrete example I gave, I guess I am inclining to go into this field of arithemtic chaos, and I have seen some papers which desrbie applications of it in cosmology, but obviously being an expert in both would be too much for me...

 

[twofish-quant]

What I am getting at I guess is that when you are relying on some established mathematical and physical results which do relate to your work but not directly, I mean your'e using them, but not necessarily need to know why they are correct?

All models are wrong. Some models are useful.

What's more important than knowing if a result is correct is knowing what happens if the result is wrong. For example, I don't know much about nuclear equations of state, so I just take Doug Swesty's tables. However what I *do* know is what happens if Swesty happens to be wrong and the EOS is stiffer or softer than his tables.

If you have a conclusion that doesn't depend much on the inputs, this is good. If you have a conclusion that depends critically on something being true, then this is a brittle result.

A concrete example is for example using random matrix theory in modelling something in quantum cosmology, though you don't necessarily a specialist in random matrix or cosmology (but at least in one of them you are), do you need to know a lot in the other branch?

You need to know enough to communicate which usually involves a lot of knowledge.

Or the bare minimum? would you need to rely on faith on some results in cosmology if your'e not a cosmologist or results in random matrix if your'e not an expert in it?

The thing about your model inputs is that most of them are wrong to some extend. So you deal with it by knowing what happens if an input happens to be wrong. If your model depends very critically on one result, then you focus on learning about that result. Also, if that result happens to be wrong, then GREAT. You have work to do. What makes physics different from mathematics is that mathematicians live in a Platonic world, whereas physicists live in the imperfect world where computer codes have bugs, data can be reduced incorrectly, etc. etc.

It's kinda ruining the whole idea of people who try to understand if you need to rely on faith, understanding goes through the window...

One of the most important things to know is to know what you do not know.

 

[MathematicalPhysicist]

TwoFish, I don't see why is it brittle (though I don't understand what the word means but from the context I guess it means bad or catastrophic)?

I mean all the work in science is infering from some known axioms, or in physics postulates (which may also be regarded as axioms in some respect), by logical rules...
so every conclusion should be depended on its antecedent otherwise the whole tower will be destroyed.

Unless you meant something else...

 

[twofish-quant]

TwoFish, I don't see why is it brittle (though I don't understand what the word means but from the context I guess it means bad or catastrophic)?

Brittle meaning that one mistake and it's destroyed. Brittle models are bad, because your model never completely reflects reality. If your model relies critically on one assumption, then you can get away with that, but if your model critically relies on a dozen things being true then it is useless.

I mean all the work in science is infering from some known axioms, or in physics postulates (which may also be regarded as axioms in some respect), by logical rules...

No it's not. You create a model which attempts to describe and predict some physical phenomenon. This model contains assumptions which are *known* to be incorrect, but by determining which assumptions are important and which ones are not, you gain insight as to the behavior of the phenomenon.

It's a very different game than mathematics.

So every conclusion should be depended on its antecedent otherwise the whole tower will be destroyed.

This is not true. It's true with math, but it's not true in physics at all.

The trouble is that the inputs to the model are *always* different from reality. Any model that depends critically on all of the assumptions being right is useless. When you write a computer code, you *know* that there will be bugs, but you can try to make sure that the bugs aren't critical. That's at the implementation level. At the specification level, you are making tons of simplifying assumptions that you know are false.

Also wrong models are sometimes good models. You assume X,Y,Z, this leads to conclusion B. B is wrong, so you look at which of X, Y and Z are incorrect. One good example of this is the Black-Scholes model of finance. You can mathematically show that give a set of axioms, then an option should be priced as X. However the cool thing is that the option is *never* priced at X, so but the model is useful because it tells you how wrong your assumptions are.

 

[MathematicalPhysicist]

Brittle meaning that one mistake and it's destroyed. Brittle models are bad, because your model never completely reflects reality. If your model relies critically on one assumption, then you can get away with that, but if your model critically relies on a dozen things being true then it is useless.

didn't you say that our models are always wrong either way?
so obviously they don't reflect reality, espceially if they are ad-hoc.

No it's not. You create a model which attempts to describe and predict some physical phenomenon. This model contains assumptions which are *known* to be incorrect, but by determining which assumptions are important and which ones are not, you gain insight as to the behavior of the phenomenon.

I agree but still under the assumptions that you make you use obviously logical inference, and some assumptions are called postulates which you take them on faith to be true in order to do the calculations or to derive a phenomena, obviously these postulates can be false as well, but nontheless, you have them.

 

[twofish-quant]

didn't you say that our models are always wrong either way?
so obviously they don't reflect reality, espceially if they are ad-hoc.

All models are wrong. Some models are useful. Models *never* perfectly reflect reality, but they can be useful in that they are good enough to do something useful. The problem with brittle models, is that you can't do anything useful with them.

I agree but still under the assumptions that you make you use obviously logical inference, and some assumptions are called postulates which you take them on faith to be true in order to do the calculations or to derive a phenomena, obviously these postulates can be false as well, but nontheless, you have them.

This is math-think and not physics-thinking.

In physics you can work inductively. I start with assumptions which I have no idea are true or not, I run the model. The model differs from observations. Try to figure out which assumption is wrong. Also, I hesitate to use the word "faith." I have assumptions. I *know* that some of my assumptions are wrong, but often I don't know which ones. Sometimes I know explicitly that my assumptions are wrong, but I want to see if it makes a different or I'm assuming that things are "good enough."

I have extremely problems with the term "faith" since it has religious and emotional connotations. Someone that has "faith" usually reacts badly if it turns out that they are wrong, whereas the whole point of making models is to break them.

One thing that I should point out here is that I think that there is a lot of scientific reasoning and philosophy that hasn't been codified. The way that I at least look at "scientific truth" is something rather different than what Kuhn or Popper describes, and there is a lot of interesting philosophy and logical reasoning here, that I haven't seen described.

At least for me "useful" is more important than "truth" or worse yet *TRUTH*. This opens the question of what is "useful" at which point my philosophy starts merging into ethics and economics. Also, it's possible that my philosophy of science is heavily Chinese, since "use" is a very important concept in Chinese philosophy (google for ti-yong) which is wildly anti-Platonic.