Theory(s) in the Natural Sciences

[Resha Caner]

I'd like to get a feel for how people view theories in the natural sciences.

So, suppose we have a phenomena P, and a theory T1 that explains P - written T1 : P. T1 is our theory of choice because it is the best known explanation of P - written R(T1 : P) > R(Tj : P), where R is some agreed upon correlation function and j = 2...k and k known hypotheses have been tried as an explanation of P. R = 1 would be perfect correlation, but currently
R(T1 : P) < 1.

Further suppose T1 is composed of multiple dictums (principles, laws, axioms, etc.) Dm, where m=1...n.

We shall say T1 augmented a previous theory, T0, if the dictums of T0 are a proper subset of D1...Dn.

We shall say T1 is a new theory if T1 removed at least one of the dictums of T0.

I could ask a battery of questions about the above conditions, but I'll start with this one: How would you respond to the claim, "There exists a new yet currently unknown theory Tk+1 such that R(Tk+1 : P) >= R(T1 : P)"?

 

[bhsmte]

.

 

[essentialsaltes]

"How would you respond..."

Maybe?

If I understand you, you're asking if a better theory exists for a given phenomenon (and given your explicit definition for 'new', this better theory discards some part of the old theory). I think the answer to your question is 'maybe'.

All scientific theories are subject to revision and improvement.

 

[Davian]

 

[Resha Caner]

If I understand you, you're asking if a better theory exists for a given phenomenon (and given your explicit definition for 'new', this better theory discards some part of the old theory). I think the answer to your question is 'maybe'.

All scientific theories are subject to revision and improvement.

OK. I would take your last statement to mean:
1. If R(T1 : P) < 1, then there exists a theory Tk+1 that is either augmented or new.
2. The set of all scientific theories, {Tj, j=1..infinity} has R(Tj : P) < 1.
3. Therefore, there will always exist a theory R(Tk+1 : P) > R(T1 : P).

The issue is whether that theory is augmented or new.

- - -

P.S. I responded to you in the "space" thread as well. Of course it's your prerogative whether you reply, but I thought my comments might have been lost in the (cough) other discussion.

http://www.christianforums.com/t7858512-5/#post66855846

 

[essentialsaltes]

OK. I would take your last statement to mean:
1. If R(T1 : P) < 1, then there exists a theory Tk+1 that is either augmented or new.
2. The set of all scientific theories, {Tj, j=1..infinity} has R(Tj : P) < 1.
3. Therefore, there will always exist a theory R(Tk+1 : P) > R(T1 : P).

#3 may be a bit strong. When I say "All scientific theories are subject to revision and improvement," I am not insisting that all theories can be improved. Just that science never stops and declares "This theory is now written in stone and immutable."

The issue is whether that theory is augmented or new.

Could be either. My bet would be either augmented, or augmented AND new/reduced.

P.S. I responded to you in the "space" thread as well.

Thanks, I missed it -- I'll take a look.

 

[Resha Caner]

#3 may be a bit strong. When I say "All scientific theories are subject to revision and improvement," I am not insisting that all theories can be improved. Just that science never stops and declares "This theory is now written in stone and immutable."

I would suggest your objection is actually with #2.

To say R < 1 but we can't improve T1 would be rather defeatist - something people don't like to say. To be honest, I was once at the point of saying that, but people always scolded me as being bitter and pessimistic, so now I paste on a smile and say, "Of course it's possible we could improve." After all, I can't prove T1 can't be improved.

Which leads to where you are more likely at. Even if R=1, we can't know it, can't prove it. So, we always have to keep an open mind that possibly R<1.

Could be either. My bet would be either augmented, or augmented AND new/reduced.

FYI, if you read closely, "new" includes the possibility of adding more dictums. It simply has the additional condition that it does not contain the complete subset of T0.

So, given we are working under the condition R(T1 : P) < 1 (and always will be as best we know), do we ever reach the point where |R| is good enough? |R| is the magnitude - the value of the correlation function.

 

[essentialsaltes]

I would suggest your objection is actually with #2.

To say R < 1 but we can't improve T1 would be rather defeatist - something people don't like to say.

I'm not so sure. Standard QM predicts that we can't know whether, say, the spin of that electron (in a 50-50 state) will be up or down when measured. So the theory, which may well be the best theory, does not fully describe the data. I'm not sure this is the same as your R function. I mean, if QM predicts it will either be up or down, and you measure it as down, that's a true prediction of the theory that correlates with the phenomenon. Another thing we look for in 'better' theories is that they explain more, which is separate from your R function.

[One could imagine a toy theory to explain the phenomena of measuring a particular group of 10 electrons. Quantum mechanics says nothing more than there's a 50-50 shot each time. But you could write up 2^10 toy theories that 'predict' all possible outcomes. One of them will be perfectly correlated with the eventual measurements. It's not a very useful theory going forward, but its correlation is perfect for this restricted phenomenon. Is it a better theory than quantum mechanics?]

do we ever reach the point where |R| is good enough?

Good enough for what?

"All scientific theories are subject to revision and improvement."

Nevertheless, the amount of money NASA should spend on rethinking heliocentric theory is zero.

 

[Resha Caner]

I'm not so sure. Standard QM predicts that we can't know whether, say, the spin of that electron (in a 50-50 state) will be up or down when measured. So the theory, which may well be the best theory, does not fully describe the data. I'm not sure this is the same as your R function. I mean, if QM predicts it will either be up or down, and you measure it as down, that's a true prediction of the theory that correlates with the phenomenon. Another thing we look for in 'better' theories is that they explain more, which is separate from your R function.

[One could imagine a toy theory to explain the phenomena of measuring a particular group of 10 electrons. Quantum mechanics says nothing more than there's a 50-50 shot each time. But you could write up 2^10 toy theories that 'predict' all possible outcomes. One of them will be perfectly correlated with the eventual measurements. It's not a very useful theory going forward, but its correlation is perfect for this restricted phenomenon. Is it a better theory than quantum mechanics?]

It becomes a semantic discussion from here, so I don't think it's worth debating it much. But I do think my OP covered these contingencies. I could argue the original question that drove QM was: What are the fundamental entities of matter and how do they behave? If so, adding something like electron spin (by adding dictums) merely improves the predictive power. At the same time, the inability to know which spin (up or down) it will be means R < 1.

I did, however, leave out the element of predictive power. So, per my OP your toy theories would be better (R would be larger) for the span of what they claim to predict ... but not interesting and with very low predictive power in regard to the original question.

Good enough for what?

"All scientific theories are subject to revision and improvement."

Nevertheless, the amount of money NASA should spend on rethinking heliocentric theory is zero.

Yes, so even though we could continue to improve predictions of earth's position relative to the sun, it's not a very interesting question anymore, and so not worth pursuing improvements. But I think there are 2 issues here:

1) Isn't the lack of interest because R ~= 0.99999? If R ~= 0.5, we might think differently. And isn't that what might lead one to question whether a new theory is needed? If R = 0.49, and we augment the theory to obtain R = 0.499, so we augment it again and obtain R = 0.4999, and then R = 0.49999 ... wouldn't we begin to suspect something is wrong? That is, supposing there is no uncertainty principle telling us R = 0.5 is the maximum we can ever achieve.

2) Even if R = 0.99999, I would find it very interesting if a completely new theory (one that throws out all - or at least a large number) of the dictums of T1 could also produce R = 0.99999. And isn't that a possibility as long as R < 1?

 

[RiemannZ]

I don't think a strict mathematical definition of correlation is very helpful in most cases (if any?) in the natural sciences

Let's take Newtonian mechanics for example, according to 18th century measurements the R value for classical mechanics was certainly very close to 1, they just couldn't have known that all the measurements themselves are affected by the relative velocities. When going from T0 to T1 you'll have to update not only the dictums but also the correlation function, making the OP essentially meaningless.

 

[Resha Caner]

I don't think a strict mathematical definition of correlation is very helpful in most cases (if any?) in the natural sciences

Let's take Newtonian mechanics for example, according to 18th century measurements the R value for classical mechanics was certainly very close to 1, they just couldn't have known that all the measurements themselves are affected by the relative velocities. When going from T0 to T1 you'll have to update not only the dictums but also the correlation function, making the OP essentially meaningless.

I think I'll have to give you that, though I don't see that it changes much of what I said. It would still be the case (as I said earlier) that we can't know if a theory is the most effective explanation possible. Therefore, I think the two issues in post #9 remain.

 

[essentialsaltes]

wouldn't we begin to suspect something is wrong? ... And isn't that a possibility as long as R < 1?

I really can't improve over what I originally wrote.

"All scientific theories are subject to revision and improvement."

 

[SkyWriting]

All scientific theories are subject to revision and improvement.

Lets assume that we "revise" a theory, not intending to make it suck.

So theories are created to be subjected to testing to prove them wrong.
That is the intention, by the way.

 

[SkyWriting]

I'd like to get a feel for how people view theories in the natural sciences.

They are written to be destroyed.
Provided they are not, then they live another (1) day.

People continue to test relativity all the time.
Those traveling at the speed of light,
do their testing relatively slowly.

 

[Loudmouth]

I think I'll have to give you that, though I don't see that it changes much of what I said. It would still be the case (as I said earlier) that we can't know if a theory is the most effective explanation possible. Therefore, I think the two issues in post #9 remain.

It depends on how you define "effective" as it applies to explanations. Is the most effective explanation the one that makes you the most money, gets the most converts, or fits the data.

Ultimately, the strength of a theory (IMHO) is the risks it takes, the variety of evidence it explains, and its independence from the data. A theory that makes very strong and specific predictions about data that is expected to be gathered in the near future is a theory that takes risks. That's why Relativity is a good example since it made quite a few testable predictions that ran counter to Newtonian physics. That is why the aether was (and I stress was) a good theory, because it made very specific predictions that could be tested, as Michelson and Morley did.

The problem that some people make is trying to defend a theory. What you need to do is test a theory. That is what scientists look for, a theory that dares you to test it, and continues to pass that test.

 

[[serious]]

OK. I would take your last statement to mean:
1. If R(T1 : P) < 1, then there exists a theory Tk+1 that is either augmented or new.
2. The set of all scientific theories, {Tj, j=1..infinity} has R(Tj : P) < 1.
3. Therefore, there will always exist a theory R(Tk+1 : P) > R(T1 : P).

The issue is whether that theory is augmented or new.

- - -

P.S. I responded to you in the "space" thread as well. Of course it's your prerogative whether you reply, but I thought my comments might have been lost in the (cough) other discussion.

http://www.christianforums.com/t7858512-5/#post66855846

"may" =/= "always"

All scientific theories MAY have a more accurate formulation (as per essentialsaltes, "you're asking if a better theory exists for a given phenomenon ... the answer to your question is 'maybe'") is not the same as all scientific theories DO have a more accurate formulation (as per you, "there will always exist a [better] theory")

 

[[serious]]

Let's try another approach. Let's distinguish between theories and models. Scientific models are "simplified reflections of reality" according to wikipedia, which is about as good of a definition as I can think of. By virtue of being simplified, there must be some more complex, fuller model which would more closely reflect reality. This can obviously continue right up until the entirety of reality is reflected, at which case it is no longer a model as it is no longer simplified. Assuming that the approach to that full complexity is continuous, that would mean for every model, there exists a more accurate model (if it's a discrete increase, there can be one or more models for which no more accurate model exists, but we can ignore that for now)

But is every theory a model? Let's say I have a theory that 1+1=2. Until we have some deviation from that in experimentation, we can't very well say that there is some more accurate value for the equation 1+1.

 

[chilehed]

...I could ask a battery of questions about the above conditions, but I'll start with this one: How would you respond to the claim, "There exists a new yet currently unknown theory Tk+1 such that R(Tk+1 : P) >= R(T1 : P)"?

"There's a new and better theory, but no one has any idea what it is?"

BWAAAAHAHAHAHA!!!!

 

[Resha Caner]

All scientific theories MAY have a more accurate formulation (as per essentialsaltes, "you're asking if a better theory exists for a given phenomenon ... the answer to your question is 'maybe'") is not the same as all scientific theories DO have a more accurate formulation (as per you, "there will always exist a [better] theory")

Sure, but if R < 1, neither is there a reason to say no better theory exists, and therefore no definitive reason to stop looking. One proceeds under the assumption a better theory exists. After all, why would one look if one didn't think a better theory existed?

Now, I said no definitive reason exists to stop looking. People will stop looking for "good enough" types of reasons.

Let's try another approach. Let's distinguish between theories and models. Scientific models are "simplified reflections of reality" according to wikipedia, which is about as good of a definition as I can think of. By virtue of being simplified, there must be some more complex, fuller model which would more closely reflect reality. This can obviously continue right up until the entirety of reality is reflected, at which case it is no longer a model as it is no longer simplified. Assuming that the approach to that full complexity is continuous, that would mean for every model, there exists a more accurate model (if it's a discrete increase, there can be one or more models for which no more accurate model exists, but we can ignore that for now)

But is every theory a model? Let's say I have a theory that 1+1=2. Until we have some deviation from that in experimentation, we can't very well say that there is some more accurate value for the equation 1+1.

It's a nice analogy, so I get your point. But it still boils down to a "success" argument - a "good enough" argument.

1 + 1 = 2 ultimately fails for several reasons (excepting you and I are both Platonists ... and I am not).

 

[[serious]]

It's a nice analogy, so I get your point. But it still boils down to a "success" argument - a "good enough" argument.

Could you expound on that? We are ruling out the possibility of definitively claiming success, I agree, but rather than good enough, we are calling it best so far. I feel like I may be missing a broader point though