The Impossible

[Loudmouth]

It uses the word "uncertain" in that definition. As such, your statement comes across to me as "Science is uncertain because it is uncertain."

Hence I am asking why. Why is it tentative?

Because we do not have all empirical facts. We will always have a small subset of all facts, so we keep theories tentative and open to falsification. The best science can do is to state that all evidence on hand is consistent with a theory.

I wasn't saying I think math & science treat assumptions differently. I was asking if you thought that. To be honest, I can't make much of this. I asked about mathematical assumptions, not equations.

Those are the same thing. Mathematical assumptions are the equations.

Further, I'm not sure I understand your usage of "dogmatic", because I find mathematicians to be quite the opposite.

So 2+2 could equal 4 or 5 or 6?

So, let me ask, is science dependent upon mathematics?

No, science is dependent on evidence. Science uses math to build models, but the reality around us is not forced to conform to our equations. For example, if I wrote the equation c=500 mph the speed of light does not suddenly slow down to 500 mph. To the point of the topic, our measurement of the speed of light is also refined by new techniques, and the constancy of the speed of light is also checked on a regular basis in different experiments. Finding deviations in the speed of light would actually be a very exciting find.

OK. So it is possible to test all scientific assumptions and convert them to theories? There is a 100% certainty that they can all be tested?

Now we are to a problem of definition. Theories, by definition, must be testable. If it isn't testable, then it isn't a scientific theory. Hypotheses are given a little more leeway. These are considered questions that people are currently trying to figure out how to answer.

I don't think that's what your cited papers said. For example, the paper on nuclear constants said it was studying the effects of expansion of the universe.

Yes, studying the effects of expansion on physical constants through time here on Earth by studying naturally occuring nuclear reactors that fired up about 2 billion years ago in Oklo which is in modern Africa. These naturally occuring nuclear reactors allow scientists to study the interaction of the fundamental nuclear forces by studying the decay products in those reactors. If the constants had been different in the past then we should see deviations of specific isotopes from the ratios expected from actually constant laws.

I don't see that as saying time or location is the cause.

The nuclear reactors at Oklo test the time component. The masers test both time and location as the speed of light is tested as the Earth moves around the Sun (and around the galactic center).

For similar expansion, I would think the effect is the same regardless of when or where it happens. So this fits with what I said. Once the effect is known (be it expansion, gravity, or dark energy), the compensation is added to the measure.

IOW, constancy is not assumed.

Yet there still remains an assumption that those compensations which have not been added are not affecting the measurement.

How so? Be specific.

But suppose, for the sake of the discussion, a time effect were found. And? It gets added to the list of compensations, and we still have the assumption that effects not in the compensation list are not affecting the measurement.

That is also not assumed. Measurement methodologies are constantly under refinement.

And statistics never effect your measurement?

Statistics are used after the measurement.

It has no impact on sample size, and sample size has no impact on the measurement?

Let's say there are 20 tigers. One scientist weighs the tigers, weighing my favorite tiger "Monty" first. He finds that Monty weighs 200 lbs. Another scientist comes along and also weighs the 20 tigers, weighing Monty last. He finds that the other tigers have an average weight of 300 lbs. How does this average change the measurement of Monty's weight? Will Monty's weight be different because other tigers were weighed before him?

Does other signal processing ever effect the measurement?

Signal processing is done on the measurement.

Just to insure we're on the same page: Accelerometer - Wikipedia, the free encyclopedia

So, following up on my previous comment. What is the "measurement" in an accelerometer?

The article isn't very explicit, but it appears that the measurement is the induction of an electrical current caused by the movement of a magnet through a coil.

 

[Resha Caner]

Because we do not have all empirical facts.

Does this apply to measurements as well? Less than 100% confidence in a measurement means you don't have all the empirical facts?

Those are the same thing. Mathematical assumptions are the equations.

So 2+2 could equal 4 or 5 or 6?

You seem to be talking about arithmetic (or maybe algebra) rather than mathematics. I don't recall any equations in Euclidean geometry.

I also assume you mean standard arithmetic. In that case, yes, 2+2=4. But there is a theory of arithmetic (as well as number & set theory) that deals with "zero", "one" and other arithmetic properties as concepts. As such, in the general case, the answer for 2+2 depends on which form of arithmetic one is using. Are you familar with Frege, etc?

No, science is dependent on evidence.

Are you a nominalist then? Someone who would claim science can be done without mathematics? Are you familiar with Hartry Field?

Now we are to a problem of definition. Theories, by definition, must be testable.

Is that a yes? Theories are guaranteed to be 100% testable? And if they aren't, you would call them a hypothesis?

How so? Be specific.

I thought post #199 was specific enough. Or are you saying it is 100% guaranteed that all possible compensations for every measurement are known?

Statistics are used after the measurement.

Signal processing is done on the measurement.

OK. Your definition of measurement sounds less and less useful, but we'll go with it. In that vein, is any measurement used without some kind of processing? i.e. interpretation?

The article isn't very explicit, but it appears that the measurement is the induction of an electrical current caused by the movement of a magnet through a coil.

I can provide others if we need deeper detail on the workings of an accelerometer. Not to criticize, but just to clarify, their are other (and more common) types of accelerometers. The ones I've used are piezoelectric. Also, I had planned to focus on the phrase, "Conceptually, an accelerometer behaves as a damped mass on a spring." which is the opening sentence to the section called "Structure". But, based on your answer, we can probably skip it.

Rather, I'll ask this question: Are you saying the accelerometer does not directly measure acceleration? The measurement, rather, is electrical in nature?

 

[Loudmouth]

Does this apply to measurements as well? Less than 100% confidence in a measurement means you don't have all the empirical facts?

The measurement is the fact. To be more specific, those are the specific results of your experimental set up. In the case of our accelerometer, the measurement is the production of a current induced by the movement of a magnet through a coil or by the buildup of charge due to mechanical stress in the case of piezoelectric sensors. That is the measurement, and we could probably chop that down to an even more fundamental observation.

How that relates to an accurate representation of acceleration is actually theory. The reading on the screen of the accelerometer is not the actual measurement. It is an interpretation of the measurement that may or may not be fed through algorithms and filters.

So it is not the specific measurement that is in doubt. It is what the measurement represents that is considered tentative.

[qutoe]You seem to be talking about arithmetic (or maybe algebra) rather than mathematics. I don't recall any equations in Euclidean geometry.[/quote]

I do remember proofs where the premises were considered axioms. There is no tentativity in the proof that the angles of a triangle add up to 180 degrees. That is as dogmatic as any algebra equation.

I also assume you mean standard arithmetic. In that case, yes, 2+2=4. But there is a theory of arithmetic (as well as number & set theory) that deals with "zero", "one" and other arithmetic properties as concepts. As such, in the general case, the answer for 2+2 depends on which form of arithmetic one is using. Are you familar with Frege, etc?

I would actulally consider math more of a philosophy than a science. Math does not operate within the epistemology of the scientific method. It has its own epistemology, and I think it should be treated differently.

Are you a nominalist then? Someone who would claim science can be done without mathematics? Are you familiar with Hartry Field?

I would argue that mathematics are secondary to evidence. Like I said, you can write c=500 m/s but that doesn't make light slow down.

[quoet]Is that a yes? Theories are guaranteed to be 100% testable? And if they aren't, you would call them a hypothesis?[/quote]

Are circles guaranteed to be round? A squares guaranteed to have 4 sides?

I thought post #199 was specific enough. Or are you saying it is 100% guaranteed that all possible compensations for every measurement are known?

Of course not. Intepretation of experimental results are always going to be less that 100% accurate.

OK. Your definition of measurement sounds less and less useful, but we'll go with it. In that vein, is any measurement used without some kind of processing? i.e. interpretation?

For a useful definition that doesn't get too philosophical, yes there are measurements used without some kind of processing. I can remember sequencing DNA by reading the 4 lane gels myself. Of course, these were film exposures of a gel containing 32P, so there is one filter between you and the actual DNA bands, but that is pretty close to the direct measurement. Even then there is a point where you are not able to determine which band is lowest out of the 3 lanes, and also a point where even small changes in the consistency of the acrylamide gel will cause one band to be slightly lower than the other even though it has a higher molecular weight. That's the first example that comes to my mind. The gels would look something like this:

Rather, I'll ask this question: Are you saying the accelerometer does not directly measure acceleration? The measurement, rather, is electrical in nature?

That is correct. The output on the accelerometer is an interpretation of the actual measurement.

 

[Resha Caner]

The measurement is the fact. ...

So it is not the specific measurement that is in doubt. It is what the measurement represents that is considered tentative.

First of all, this statement makes it sound as if you are saying uncertainty in a theory comes only from measurements that have not been done: theories are tentative because facts are missing, and measurements are facts. Are you sure that's what you mean?

But, second, that's not what I'm getting at. There is uncertainity in a measurement, even as you've defined it, as you yourself said. Why is there uncertainty in measurement?

I do remember proofs where the premises were considered axioms. There is no tentativity in the proof that the angles of a triangle add up to 180 degrees. That is as dogmatic as any algebra equation.

You're taking trivial cases. Assuming planar geometry, angles in a triangle add up to 180. For the Riemannian geometry mentioned earlier (i.e. elliptic geometry), the sum is greater than 180. And, as I also mentioned, this comes from changing the parallel postulate. So, I don't see any dogma there.

I would argue that mathematics are secondary to evidence.

I don't see how this answers the question. You think mathematics is of secondary importance. OK. Am I to take that to mean you are saying it is necessary for science - though of secondary importance?

Are circles guaranteed to be round? A squares guaranteed to have 4 sides?

Same thing here. I don't see how this answers the question. Further, the question specifically referred to scientific theories, not mathematics. So, are scientific theories guaranteed to be 100% testable? And if they are not 100% testable, are they hypotheses?

For a useful definition that doesn't get too philosophical, yes there are measurements used without some kind of processing. I can remember sequencing DNA by reading the 4 lane gels myself. ...

I'm not familiar with "measuring" DNA, but I think there would be some processing. I can't see DNA, so how was the picture produced?

That is correct. The output on the accelerometer is an interpretation of the actual measurement.

OK. Let's take the piezoelectric case. I don't think even the voltage reading is the "measurement" according to your definition. It has to be run through a charge amplifier. So isn't the charge the measurement?

Well, actually, probably not even that. According to the wiki article, charge can be measured directly with an electrometer.
Electric charge - Wikipedia, the free encyclopedia

But even that doesn't seem to fit your definition.
Electrometer - Wikipedia, the free encyclopedia

What an electrometer actually measures is distance (movement in the leaf).

 

[Loudmouth]

First of all, this statement makes it sound as if you are saying uncertainty in a theory comes only from measurements that have not been done: theories are tentative because facts are missing, and measurements are facts. Are you sure that's what you mean?

Yes. No matter how many measurements we make we will never have all of the facts, just the facts that we have been able to collect.

But, second, that's not what I'm getting at. There is uncertainity in a measurement, even as you've defined it, as you yourself said. Why is there uncertainty in measurement?

Let me put this another way. There is the real world and there is the observer. The observer learns about the real world through instruments and through their senses. However, the observer must always be aware that the results produced by the instruments and senses are not the real world itself. They are only a representation of the real world.

You're taking trivial cases. Assuming planar geometry, angles in a triangle add up to 180. For the Riemannian geometry mentioned earlier (i.e. elliptic geometry), the sum is greater than 180. And, as I also mentioned, this comes from changing the parallel postulate. So, I don't see any dogma there.

All you are doing is changing the conditions. It is still dogmatic. Geometry, like math, is axiomic. That is why you have proofs in geometry and evidence in science.

I don't see how this answers the question. You think mathematics is of secondary importance. OK. Am I to take that to mean you are saying it is necessary for science - though of secondary importance?

It's not really a matter of importance. It's a matter of evidence.

Going back to the example of Newton's laws and Mercury's orbit. Newton's law predicted a specific orbit for Mercury, but Mercury followed a different orbit. So which is right? Are Newton's laws and equations right, or is Mercury right?

Same thing here. I don't see how this answers the question. Further, the question specifically referred to scientific theories, not mathematics. So, are scientific theories guaranteed to be 100% testable? And if they are not 100% testable, are they hypotheses?

It is a matter of semantics. If an idea is not testable then it can not be a theory, by definition.

I'm not familiar with "measuring" DNA, but I think there would be some processing. I can't see DNA, so how was the picture produced?

You use the Sanger method combined with radioactive isotopes(usually 32P):

Sanger sequencing - Wikipedia, the free encyclopedia

The mixture of different length PCR products are separated on a gel by electrophoresis, and then visualized by exposing the gel to photographic film. The decay of the radioactive isotope produces bands on the film.

OK. Let's take the piezoelectric case. I don't think even the voltage reading is the "measurement" according to your definition. It has to be run through a charge amplifier. So isn't the charge the measurement?

The amplifier does add a level of filtering, but that is pretty much it.

Well, actually, probably not even that. According to the wiki article, charge can be measured directly with an electrometer.
Electric charge - Wikipedia, the free encyclopedia

But even that doesn't seem to fit your definition.
Electrometer - Wikipedia, the free encyclopedia

What an electrometer actually measures is distance (movement in the leaf).

I think you are getting a sense for how this works.

 

[Resha Caner]

I think you are getting a sense for how this works.

And I think you are getting a sense of what I am saying. I could find quite a long list of people who take the position they are measuring acceleration. You would disagree, but to do so requires you take a position that makes the term "measurement" almost useless. As you said, it's become a matter of semantics.

According to dimensional analysis, the system of independent measures was set at 3 by Newton's second law (F = ma). Which 3 are chosen is arbitrary, but there are supposedly only 3. The typical ones used are length, time, and mass. Any other unit can supposedly be derived from these 3. IOW, it depends on a model.

For some time, however, I have had my own private hypothesis that really there is only one independent unit of measure: length (or, I prefer to say distance). Anything else depends on a model - hence my note that measuring charge is actually measuring distance. And further, beyond some very basic affine concepts, distance is dependent on the concept of number.

 

[Loudmouth]

And I think you are getting a sense of what I am saying. I could find quite a long list of people who take the position they are measuring acceleration. You would disagree, but to do so requires you take a position that makes the term "measurement" almost useless. As you said, it's become a matter of semantics.

I said the requirement that theories be testable is based on semantics, but no matter.

If you really pressed them and talked through it I think they would agree that they are not measuring acceleration directly. Instead, they are using an experiment that allows them to conclude what the acceleration probably is. This may sound like a subtle difference, but it isn't. Facts and conclusions are very, very different beasts.

For some time, however, I have had my own private hypothesis that really there is only one independent unit of measure: length (or, I prefer to say distance). Anything else depends on a model - hence my note that measuring charge is actually measuring distance. And further, beyond some very basic affine concepts, distance is dependent on the concept of number.

I would add entropy as another unit which also forces us to incorporate forward moving time. Entropy seems to be as much a fundamental part of our universe as length, IMHO.

 

[Mr Clean]

Interesting discussion. One thing I'd like to add:

"You're taking trivial cases. Assuming planar geometry, angles in a triangle add up to 180. For the Riemannian geometry mentioned earlier (i.e. elliptic geometry), the sum is greater than 180. And, as I also mentioned, this comes from changing the parallel postulate. So, I don't see any dogma there."

I think the term geometry is causing some confusion here. Riemann geometry is a differential geometry. It is a three dimensional geometry, which is why is uses calculus and differential equations. The other geomentry is 2D. Comparing 2D to 3D is like comparing apples to fire hydrants.

There is also a difference between 2D geometry with just straight lines and geometry with other types. such as curves or closed shapes (like a circle).

I think the issue is that you are trying to make all geometry the same when it's not...

 

[Resha Caner]

I think the term geometry is causing some confusion here. Riemann geometry is a differential geometry.

Yes, I realize Riemannian geometry has some special features to it. That is the reason why, at one point, I noted "elliptic geometry" is the more general name. Similar techniques can be applied to Euclidean geometry, and it is then sometimes called analytic geometry.

It is a three dimensional geometry, which is why is uses calculus and differential equations. The other geomentry is 2D. Comparing 2D to 3D is like comparing apples to fire hydrants.

Neither is restricted to a specific number of dimensions. I realize R3 is common for Riemannian geometry, but in general any n-dimension manifold could be used. I also realize that most people only get instruction in planar Euclidean geometry. However, it can also be applied to any n-space. My dad is a retired geometry teacher (and I had him for a class). We studied up to 4 dimensional Euclidean spaces.

I think the issue is that you are trying to make all geometry the same when it's not...

Yes and no. Euclidean geometry is definitely different than elliptic or hyperbolic geometry. But they all come from the same root. Conic sections are a good way to visualize how they are all connected ... at least it helps me. This stuff can be very difficult to grasp. As I said, my dad taught about 4-D spaces when I was in highschool, but I didn't honestly grasp it until just a few years ago. So, it took me almost 30 years. But then, there are several people here who claim I'm a bit slow, so maybe it's just me. I am, after all, the expert fool.

 

[SkyWriting]

What would science say is impossible?

The creation of matter and energy where there was none before.

The ability to prove or disprove "Spirit" or "Soul".

Life from nonllife.

Violations of Entropy Law.

That germs existed.

That DNA was more important than proteins.

That Atoms had smaller parts.

That a feather would accelerate as fast as a brick.

That Alchemy was not science.

 

[durangodawood]

...Violations of Entropy Law....

Do you agree with "science" that this^^^ is impossible?

 

[Davian]

The creation of matter and energy where there was none before.

The ability to prove or disprove "Spirit" or "Soul".

Life from nonllife.

Violations of Entropy Law.

That germs existed.

That DNA was more important than proteins.

That Atoms had smaller parts.

That a feather would accelerate as fast as a brick.

That Alchemy was not science.

This "Spirit" or "Soul" - are they subject to entropy?

What do you think, Resha?

 

[Mr Clean]

Neither is restricted to a specific number of dimensions. I realize R3 is common for Riemannian geometry, but in general any n-dimension manifold could be used. I also realize that most people only get instruction in planar Euclidean geometry. However, it can also be applied to any n-space. My dad is a retired geometry teacher (and I had him for a class). We studied up to 4 dimensional Euclidean spaces.

I don't think Riemann can drop below 3D. Euclidean can be taken to 3D. I've never heard of it going 4D because time is not a measurement (that I know of) in Euclidean gemoetry. Euclidean is based on angles and lengths only. Riemann geometry can have rotational variances in it which is why it can go to 4D. But I am not a teacher or have a mathematics degree either. I took all three calculus classes and differential equations in college, but that doesn't make me an expert. I don't deal with 3D and higher geometrics very often.

Yes and no. Euclidean geometry is definitely different than elliptic or hyperbolic geometry. But they all come from the same root. Conic sections are a good way to visualize how they are all connected ... at least it helps me. This stuff can be very difficult to grasp. As I said, my dad taught about 4-D spaces when I was in highschool, but I didn't honestly grasp it until just a few years ago. So, it took me almost 30 years. But then, there are several people here who claim I'm a bit slow, so maybe it's just me. I am, after all, the expert fool.

They do come from the same root, but they do have differences at the higer levels. The angles that were being discussed are one of those differences.

I wouldn't put yourself down. The fact you are discussing it comprehensively says a lot.

 

[Mr Clean]

The creation of matter and energy where there was none before.

The ability to prove or disprove "Spirit" or "Soul".

Life from nonllife.

Violations of Entropy Law.

That germs existed.

That DNA was more important than proteins.

That Atoms had smaller parts.

That a feather would accelerate as fast as a brick.

That Alchemy was not science.

That's the great thing about science. It doesn't hold rigidly fast to something just because it is old. When new information becomes available, things are updated. Science is a path, not a destination...

When we could make a vacuum, we could prove that a feather and a brick accelerate the same in that vacuum, for example.

"Disproving" a soul or spirit would be the exception in that list of course, because you can't prove that something does not exist. False logic. You can only prove something does exist. The logical conclusion to having no proof for something is to say that it does not exist.

 

[super animator]

The logical conclusion to having no proof for something is to say that it does not exist.

You know I could argue that this is an argument from ignorance, but I don't want to derail this thread.

 

[Mr Clean]

You know I could argue that this is an argument from ignorance, but I don't want to derail this thread.

It still doesn't change the logical ending to that scenario. If proof exists and it just hasn't been found yet, then obviously we are dealing from an ignorant position. But until that knowledge is discovered, there is no other logical conclusion that can be reached. Do you disagree?

 

[freezerman2000]

That's the great thing about science. It doesn't hold rigidly fast to something just because it is old. When new information becomes available, things are updated. Science is a path, not a destination...

When we could make a vacuum, we could prove that a feather and a brick accelerate the same in that vacuum, for example.

"Disproving" a soul or spirit would be the exception in that list of course, because you can't prove that something does not exist. False logic. You can only prove something does exist. The logical conclusion to having no proof for something is to say that it does not exist.

You brought up an answer to the OP in an indirect way..A perfect vacuum occurring naturally is impossible..The "vacuum of space",for instance, is not pure..it is full of matter,just no atmosphere between planets and some of the moons involved.
We can however, artificially create a perfect vacuum in the laboratory.