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Underdetermination in Science


Zosimus

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On ‎18‎/‎11‎/‎2018 at 10:47 PM, Zosimus said:

As you can see, a simple straight line adequately expresses the data. Unfortunately, we can also generate other graphs. Two sine-wave-shaped graphs have also been provided, each with a different amplitude. Nor do our choices end there. Even if we just stick to sine waves, we could easily construct an infinite number of graphs to express those data points.

 

On ‎18‎/‎11‎/‎2018 at 11:26 PM, swansont said:

The missing argument here is that in many cases, you are not doing an arbitrary fit. Sure, you can fit a sinusoid, or a ploynomial. But why would the curve have those properties? 

....and of course - you can simply TEST the results against experimental reality.  If, for some reason, you suspect that your straight line of 10 measured [points could be 10 points where a sine curve is returning to its base... then you can test this by selecting points midway between those you have already measures to see if they fit on your curve, giving you y=mx+c, or if they do actually miss the line totally...  I mean - sometimes coincidences happen, sometimes there are mistakes...  but this is why we check and recheck results, rerun experiments, update curves with data taken from new experiments etc.. The kind of error you are describing with this underdetermination is one a schoolboy might make  -  but it shouldn't happen in professional science...  good thing is that if it DOES, then it can be checked and challenged if conflicting data is measured by someone else.

 

 

10 hours ago, Zosimus said:

You are ignoring the problem of unconceived alternatives. Simply because you cannot come up with an infinite number of alternatives does not mean that there are not an infinite number that simply have not been thought up yet.

As we said - you can test to see if this is the case or not by picking points on your graph between your current data points and checking them against experiment to see if you have fitted your curve accurately or not. 
 

 

 

8 hours ago, Reg Prescott said:

I've haven't the faintest idea what this undetermination is

He explained it in the OP.

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11 minutes ago, DrP said:

....and of course - you can simply TEST the results against experimental reality.  If, for some reason, you suspect that your straight line of 10 measured [points could be 10 points where a sine curve is returning to its base... then you can test this by selecting points midway between those you have already measures to see if they fit on your curve, giving you y=mx+c, or if they do actually miss the line totally...  I mean - sometimes coincidences happen, sometimes there are mistakes...  but this is why we check and recheck results, rerun experiments, update curves with data taken from new experiments etc.. The kind of error you are describing with this underdetermination is one a schoolboy might make  -  but it shouldn't happen in professional science...  good thing is that if it DOES, then it can be checked and challenged if conflicting data is measured by someone else.

I have already pointed out that no sine curve fits the data as drawn.

The simplest equation to produce the sketches is f(x) = {Ax + Bsin(x)}

This is not a sine curve for a numebr of reasons.

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I followed the discussion a little, but did not participate because of 2 reasons:

- one very practical: I am not very versed in the philosophy of language, and going into 'deep thought mode' when my daily business already needs that capacity also, it becomes a little bit too much. I simple do not have the time

- the discussion about these topics have shown (inductive reasoning?) that they become emotional very soon. Which maybe funny for people who both, in different ways, believe to be rational.

I have not very much hope to alleviate the tension a bit, but at least I can give it a try.

Reg clearly stated a few times that he does not question the results of science. What is discussed here, as far as I can see, is the self-understanding of science, not science itself. And that is a philosophical discussion, not a scientific one. But of course, one has to know what the daily praxis of science is. If one wants to reflect on 'how science works', or the even more philosophical question 'why science works' one needs to know when scientists accept new theories, why other theories are rejected, why and how scientists err, etc etc. Until now, I did not see that Reg is principally wrong in his philosophical musings. What I see is a lot of misunderstandings.

I am still not quite clear what Zosimus' position is: when he says that 'science is wrong' and scientific theories do not play an important role in the development of technology, I think he is clearly wrong. Just to conclude from that it happens that (technical useful) discoveries are made without any theory does not question the relationship between praxis and theory completely (e.g superconductivity was completely unexpected, and the theory came much later).

I just want to add that the problems of the relationship between language and reality are notoriously difficult, and a simple 'we know that science works' is not very clarifying in trying to understand how it is possible that science works.

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10 minutes ago, studiot said:

I have already pointed out that no sine curve fits the data as drawn.

That's not my point - The curve could be of the form y=mx^7+nx^4+fx^2+D...  it doesn't matter - it could be anything...  if all the points fit a straight line then it is trivial to check to see if it really is a straight line or not. That's the beauty of science - we can check the curve by testing it against the reality observed from experimentation.  The OP still seems concerned with us not knowing if the points that lie between the data points on our line will fit our line or not. My point is that it is simple to check this.

 

Just now, studiot said:

It doesn't help to chose the opening example from a discipline he has insufficient knowledge of.

That is clear. ;-)

 

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5 minutes ago, DrP said:

The OP still seems concerned with us not knowing if the points that lie between the data points on our line will fit our line or not. My point is that it is simple to check this.

The OP is right to be concerned about that.

It is very very important in Science, which is why such an extensive theory of interpolation and extrapolation has been developed.

In Physics we are lucky that in general the 'pathological' mathematical functions that make it difficult or even impossible to check this do not appear.

The only exceptions to this I know occur with cellular automata, fractals and Gibbs Phenomena.

Edited by studiot
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Just now, studiot said:

The OP is right to be concerned about that.

I thought his concern was going too far when he stated this - [Zosimus wrote: "You are ignoring the problem of unconceived alternatives. Simply because you cannot come up with an infinite number of alternatives does not mean that there are not an infinite number that simply have not been thought up yet. "]

 

You have to draw the line somewhere with these 'unconceived alternatives'.... you can continue to split your data points and run tests on every space between every data point over and over across ever increasing degrees of accuracy  -  eventually you can't do that anymore but long before this point comes  you can confidently conclude you are dealing with a straight line or close to or with a set of points that can be treated as such for practical purposes.

 

 

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29 minutes ago, DrP said:

You have to draw the line somewhere with these 'unconceived alternatives'.... you can continue to split your data points and run tests on every space between every data point over and over across ever increasing degrees of accuracy  -  eventually you can't do that anymore but long before this point comes  you can confidently conclude you are dealing with a straight line or close to or with a set of points that can be treated as such for practical purposes.

Yes, as I said there is a whole extensive and sophisticated theory so that you can find bounds for any error, which you can make as small as you like, consistent with the actual precision of the  data points.

This is one of the underlying principles that allows finite element analysis to be so successful.

 

BTW, it's nice to discuss the actual topic with someone.

Edited by studiot
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9 hours ago, Rob McEachern said:

Not anymore. In twenty-first century physics, they have become accepted without ANY experimental evidence:

"There is no more experimental evidence for some of the theories described in this book than there is for astrology, but we believe them because they are consistent with theories that have survived testing."  Stephan Hawking, "The Universe in a Nutshell", Bantam Books, 2001, pp 103-104.


“Sabine Hossenfelder argues, we have not seen a major breakthrough in the foundations of physics for more than four decades… The belief in beauty has become so dogmatic that it now conflicts with scientific objectivity… Worse, these "too good to not be true" theories are actually untestable…”  https://www.amazon.com/Lost-Math-Beauty-Physics-Astray/dp/0465094252

 

Without actual detail (you know, citing the theories in question, rather than providing quotes from other people) it's impossible to address this. Are these actual, accepted theories? Or are they works in progress? 

And this ignores all the examples where followup experiments did happen.

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11 hours ago, Zosimus said:

You are ignoring the problem of unconceived alternatives. Simply because you cannot come up with an infinite number of alternatives does not mean that there are not an infinite number that simply have not been thought up yet.

And by ignoring, I must assume you mean acknowledge, since that's precisely what I did in my post. I was contrasting what your recommended source says with what you say with regard to the magnitude. Not the issue of other possible theories.

At some level it doesn't matter. Whatever data we have, any new theory is going to have to predict precisely that. GR supplanting Newtonian gravity does not invalidate the results that Newtonian gravity gives under the conditions where it works, because they are identical (to reasonable precision) to GR. Our orbit about the sun did not change when people started accepting GR. At such time that a theory of quantum gravity succeeds, it will not change the results of GR (and by extension, Newton). These turtles go all the way down. 

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11 hours ago, Zosimus said:

 

Time index 2:42

"No matter how many data points you add, there will still be an infinite number of possible lines or theories that can be drawn through them."

You found someone who shares your misunderstanding. Congratulations.

A curve fit is not a theory.

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5 minutes ago, Reg Prescott said:

Well, concerned paren*s, for one, migh* be disturbed *o learn *ha* wha* *heir children are being *augh* in school science class is no* wor*hy of belief. Indeed, *o believe wha* is being *augh* would be an irra*ional ac*.

Surely they would be even more concerned if what they were being taught was KNOWN to be wrong, outdated, demonstrably false nonsense imagined up by superstitious people thousands of years back.  The most up to date best tested modals are preferred.

 

There is something wrong with your format here - all the T's and some of the R's are replaced with a '*'.  It makes it harder to read fluently.

 

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54 minutes ago, studiot said:

 Normally it is the other way round, the 'fit' is used to calibrate the curve.

This reminds me: a week or two ago a colleague was telling me about a paper he was reviewing (internal process, before it goes to submission to a journal) and he was critiquing their curve fit, because the authors had not justified why they chose that particular function as a fit.

The "let's pick any function that works" just isn't what science does. It's a caricature. It's apparently what some non-scientists guess that scientists do.

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2 minutes ago, swansont said:

The "let's pick any function that works" just isn't what science does. It's a caricature. It's apparently what some non-scientists guess that scientists do.

Isn't it usual to pick the simplest curve that fits the data? Of course if new data turns up then the curve can be refitted, but surely it makes sense to 'assume' the curve with the least inflections and least complexity when fitting? With the suggestion/knowledge that there could be an infinite number of possible orders to the equation of the curve I would have thought the most simple is taken unless proven to be otherwise in the light of further data points.

In other words - if your 10 points make a straight line then it probably is a straight line if you have taken data points at a decent spread. You don't assume a 20 order equation snaking between the 10 points - you draw a line through the lot. if there seems to be reason to suspect possible deviation at certain points or under certain conditions then this can be tested for and the data added to the curve.  You don't 'assume' or conclude the most complex situation if there is no evidence for it.

 

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17 minutes ago, DrP said:

Isn't it usual to pick the simplest curve that fits the data?

 

Not necessarily.

First there is the question of how one measures 'fit'.

for example MiniMax or Least Squares.

Then there is the question of curvature (and even perhaps higher order derivatives).

This is particularly true at the endpoints, where the curve may have to fit smoothly into something else.

Even straight lines, (and not everything is a straight line especially with 'end corrections')

Curvature fitpoints are also used to generate additional equations to solve Physics situations.

For example zero at the bottom of an elastic curve and a min or max in some energy consideration.

And what about pulse measurement? All the wobbles are at the corners. And even the sags and slants from a stright line are significant.

 

The schoolboy "I got a straight line through the origin sir" only works for Nigel Molesworth.

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On 11/18/2018 at 10:47 PM, Zosimus said:

On a forum such as this one, we often hear people claiming that science has proved theory X or Y. Later, the person may partially recant claiming that theory X isn’t completely proven, but it is 99.999999% certain. Because of the evidence, the theory has been so repeatedly confirmed that it would be wrong to withhold provisional assent.

However, philosophers disagree because of the problem of underdetermination.

Reminds me of the value of Pi. It's the concept of "tends towards". You can't nail it down, but it is still an obvious fact. As the number of verifications grows, the certainty grows. As your number of decimal points grows towards infinity, so you approach an absolute value for Pi.

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3 minutes ago, studiot said:

Even straight lines, (and not everything is a straight line especially with 'end corrections')

Curvature fitpoints are also used to generate additional equations to solve Physics situations.

For example zero at the bottom of an elastic curve and a min or max in some energy consideration.

And what about pulse measurement? All the wobbles are at the corners. And even the sags and slants from a stright line are significant.

 

The schoolboy "I got a straight line through the origin sir" only works for Nigel Molesworth.

What about a very shallow minimum....  that could look like a flat line if you are very close to the curve.  I am not talking about such situations though.  If you are measuring one variable against another and you have 20 points and they seem to be a straight line with gradient m then it probably is...  it probably isn't a 21st order rollercoaster which you have coincidently measures at every point along the track which has the same height. You 'assume' it is straight (putting fine structure aside from real life wobbles and wibbles). (Admittedly it would also depend on the context of the experiment and what it was that was being measured for sure).

I'll admit there are case where fine structure of a seemingly straight line could be a total roller coaster....  like the fine structure of an Infa Red spectrum...  it might look like a parabolic peak for a particular molecular stretch...  but the fine structure will show that 'smooth curve' with many wibbles on it from quantised rotational energy levels...   zoom in on any of those wibbles of fine structure and you have the same wibbles within the wibbles from the electronic fine structure..   Some things are way more complex still - but it can usually be detected or confirmed - we know about these things.  I don't like the thinking that we know absolutely nothing and cannot possibly ever know what we are talking about - which is the view I am seeing from some people - including the OP.

 

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40 minutes ago, mistermack said:

Reminds me of the value of Pi. It's the concept of "tends towards". You can't nail it down, but it is still an obvious fact. As the number of verifications grows, the certainty grows. As your number of decimal points grows towards infinity, so you approach an absolute value for Pi.

Yes a good thought. +1

But we should remember that our proposed curve between the points, straight or not is just a model.

I think this is also what swansont was indirectly alluding to.

 

26 minutes ago, DrP said:

If you are measuring one variable against another and you have 20 points and they seem to be a straight line with gradient m then it probably is..

Taking this model idea further, we should not say

These are the measured points, this curve or straight line  fits them so that is the correct reality.

but

These are the measured points. Whatever this curve measures does not deviate anywhere from the curve by more than X, which is an acceptable model between the points.

 Obviously straight lines, and therefore direct proportion, are generally the most preferable and often provably accurate enough.

But here is a straight line conundrum.

 

The height of a brick wall is given by the staight line function

H = cN

Where H is the height, N is the number of courses and c is the course size.

Given that the standard course size is 75mm how many courses are needed to build a 5m wall?

Well 67 courses will give you a wall that is one inch too tall and 66 courses will provide a wall that is two and a half inches too short.

So what's to do?

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50 minutes ago, studiot said:

Given that the standard course size is 75mm how many courses are needed to build a 5m wall?

Well 67 courses will give you a wall that is one inch too tall and 66 courses will provide a wall that is two and a half inches too short.

So what's to do?

Dig a 2 and a half inch foundation. ;-)

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