Problems with Measurement

[Imaginist]

Greetings!

I am troubled by some observations about measurement that someone more intelligent and/or educated might be able to help me resolve.

1. A point is defined as having location without dimension, and in this world we describe a point's location by its relationship to other points.

2. In describing the relationship between points, we use terms of distance, yet we say that there are an infinite number of points in any distance because we can regressively divide any fraction into yet smaller fractions.

How then can we ever precisely define where anything actually is?

Where does one inch end and the second inch begin?

Is everything just an approximation? If so, then is there really any objectivity in our perceptions?

 

[Dancing David]

Yowza!
These are paradoxes the greeks and others have struggles with.

The resolution lies in the fact that in the part of the universe we live in thier is a minimum size to the wavicles that make up of solid matter. So while there may be an infinite number of mathematical point in between two locations there is a finite space between those two locations. That space is commonly measured by the amount of time it takes for a photon to traverse it.

Now if we start to deal with distances that are really small really wierd things happen.

Peace
dancing david

 

[Tez]

Greetings!

I am troubled by some observations about measurement that someone more intelligent and/or educated might be able to help me resolve.

1. A point is defined as having location without dimension, and in this world we describe a point's location by its relationship to other points.

2. In describing the relationship between points, we use terms of distance, yet we say that there are an infinite number of points in any distance because we can regressively divide any fraction into yet smaller fractions.

How then can we ever precisely define where anything actually is?

Where does one inch end and the second inch begin?

Is everything just an approximation? If so, then is there really any objectivity in our perceptions?

Welcome - hope youre not a troll!

They are impressive questions.

Basically the answer is that we use the notion of convergence, which is defined in terms of a countable infinity of sequences (i.e maps to the integers which most people are ok with) to get around the paradoxes you mention.

This method allows us to talk about non-metric spaces - spaces of mathematical objects for which there is NO concept of distance...

As far as "real physical" measurements go - there is no such thing as infinte precision. Physics could be founded on finite precision for everything, if someone was pedantically inclined. Its just a pain in the bum...

 

[Skeptical Greg]

Is everything just an approximation?

Ultimately, yes!

But you shouldn't let it stand in the way of getting on with your life.

If everyone had (let it stand in the way of getting on with their life), we wouldn't have computers, airplanes or atom bombs, to name a few.. And, we wouldn't be having this conversation for an infinite number of reasons..


We went over this recently in a thread about Zeno's paradox.. I'll try to dig it up...

 

[Soapy Sam]

There is a subatomic particle named the Tossicle. Or there would be, in a rational universe.
It's about, oh, yeay long by this high and moves roughly that fast.
It's mass is a bit more than zero.
The Tossicle is the littlest thing worth worrying about.
There are twelve of them in a dozen.

 

[Imaginist]

Hi Folks,

Thanks for the responses.

First, I don't think I am a troll, but since I don't really know what one is supposed to be, then I guess it's possible! Anyway, my intentions are to explore these observations and questions with people who might have some useful insight about them.

I appreciate the sincerity and the humor of the various responses so far, but they leave me still questioning the objectivity of measurement, which is in many ways the very basis of most of the things we call "science." One of you was very clear about stating that all we have are useful approximations. I too think this is a sufficient basis for working with a great deal of conventional experience, but when we start pushing the limits of observation it appears that precision and certainty become rare commodities.

One of you mentioned Zeno's paradoxes, which I did not throw into the mix simply because so many have concluded it is really just a linguistic problem. I'm interested in a scientific perspective, not simply an exercise in metaphilosophy. I also haven't yet bothered to refer to the Uncertainty Principle, basically because I would expect many of the folks here to know more about it than I do.

Perhaps this is getting into material that would be best for the philosophy forum, but this problem brings to mind the Kantian position that we cannot really know things in themselves, but only the phenomenal approxmations that we derive through perception.

The thing that I find really interesting about all of this is that it chips away at the foundation of the conventional worldview, which seems to be based upon the idea that we can and do know things in themselves because we can quantify and qualify them with measurement. But with precision and certainty in measurement slipping through our intellectual fingers, where is the objective world that we are supposed to be working with in science?

 

[roger]

The thing that I find really interesting about all of this is that it chips away at the foundation of the conventional worldview, which seems to be based upon the idea that we can and do know things in themselves because we can quantify and qualify them with measurement. But with precision and certainty in measurement slipping through our intellectual fingers, where is the objective world that we are supposed to be working with in science?

I'm sure that you'll get better responses than mine, but the conventional scientific worldview is that all measurements of positions have an element of error in them.

We could discuss this philosophically, but let's take a concrete example. I pick up the ruler beside me, and measure an object to be 2.5 cm.

There are both approximations and errors in this measurement. Among them are:

* the ruler may not be marked accurately
* the ruler expands/contracts with heat
* the marks have non-zero width
* my eyes can only resolve details to x microns
* the wavelength of visible light restricts accuracy to y microns
* the alignment of my eye with the object and ruler will affect how i perceive the ruler markers lining up with the object.
* etc.

However, this does not destroy certainty, it just limits it. For example, I know that the object is not 1 km long, let alone 10^10 light years long. I also know the object is not 1 micron long. More precisely, I can certainly limit it's size to be between 2 and 3 cm with absolute certainty. In practice, my measurement is probably precise within .1 cm.

And it doesn't stop here. I have multiple ways of measuring the size of the object. I can use calipers with a digital readout. I can use lasers. etc. Given the assumption that the world exists (something I will not debate in this forum), we can keep refining our instruments and techiniques to get ever finer precision and accuracy (upto what the Heisenberg uncertainty principle will allow).

A common error in thinking about these things w/o doing the math is to imagine a measuring process that has error (which all do), then imagine another process, which also has error, etc, etc, and then sum those errors, and conclude that there is no measurement, no certainty, just a mass of confusion. Sometimes that is how errors work, they sum, but if you choose your measurements correctly they don't.

An example: GPS. GPS works by satellites orbiting earth. A receiver receives signals from the satellites, and can determine how far it is from the satellite.

If the receiver sees 1 satellites, it can only know that it is Da miles from the satellite with xa error, so that places your position within a huge sphere of xa thickness.

If the receiver sees 2 satellites, then it computes the sphere for satellite 1 and the sphere for satellite 2, and then computes their intersection. The result is some kind of torus shape.

If the receiver sees 3, the estimate gets better. With 4 satellites, you can pinpoint your position in 3D space, with of course some error. Furthermore, you can start doing error corrections. If one satellite is broken and sending bad signals, you can detect that because its sphere will not intersect with the other 3 satellites.

Of course the math is more complicated than I have described, but the point remains that by triangulating we are reducing the error, not increasing it. And with each measurement we are not getting incremental improvements, but orders of magnitude.

And that is how science works, by triangulating, metaphorically speaking, onto the truth. Given the assumption of a real world, then by multiple measurements we can improve our accuracy and precision. Proving that takes a lot of math, but the GPS example let's me present it qualitatively.

Interesting questions, thanks for the contribution to the board!


roger

 

[Imaginist]

Hi Roger,

Thanks for your response. What I get from your statements is that we can be certain about our uncertainty! Seriously, I understand that you are saying that we can be certain that what we are observing actually falls within a given range of measurement and error, but that perfection is not ultimately attainable.

To me, this implies that while science is pretty good at predicting phenomena and describing their relationships within predetermined parameters, science really can't say anything for certain about things in themselves.

This is really where the difference between sceince and scientism starts to become apparent. Just to clarify what I mean here - unlike science, scientism does not acknowledge that the ultimate nature of reality is really a philosophical question that refers to science but is not solved by it.

On that note, some of the folks reading this thread might be interested in the Materiaism thread in the Religion and Philosophy forum.

Thanks again!

 

[DrMatt]

Hi Folks,

{etc}

Measurement is accomplished by comparing one thing to another thing using light.

Where you don't have enough things, your data about the universe gets rather sparse.

Somewhere in his writings, Assimov wrote about some hypothetical universes... Let's see if I can recall them by memory.

In the first universe, you're alone on a planet and it's the only thing in the universe. You look out at the blackness--there's nothing there, so your concept of planetary motion ends right there.

In the second universe, you're on a planet, and there's one other body in the universe, and you can see it. After a while of observing it, you notice that it appears to grow and shrink periodically. If you're really sophisticated, you find ways to perform parallax experiments for observing it from different places on your planet, and discover that it's periodically getting closer to you and further away. Your concept of planetary motion ends there.

In the third universe, you're on a planet and there's two other bodies in the universe, and you can see them. With that difference, you suddenly have enough data from which to derive Newtonian universal gravitation--and, with a little bit more observation, General Relativity.

NB that for the inhabitants of the first two universes, General Relativity is consistent with their observations, but untestable and unnecessary for their gravitational physics.

NB that all three of these scenarios involve ruling out space travel, for the simple reason that as soon as you add space travel, you've converted the universe into the NEXT one in the series.

------------

Now let's try to observe really small things and get really precise measurements of them. What are you going to use as your rulers for comparison? The effort is tricky and fraught with philosophical pitfalls---and there's no guarantee that the universe will follow commonsense rules as size scales approach those of molecules, or atoms (in fact, it doesn't, and the exploitation of the ways in which it doesn't is key to the functioning of transistors and thus modern computers...).

 

[DrMatt]

Hi Roger,

Thanks for your response. What I get from your statements is that we can be certain about our uncertainty! Seriously, I understand that you are saying that we can be certain that what we are observing actually falls within a given range of measurement and error, but that perfection is not ultimately attainable.

Well, that too, but QM really implies that such perfection of measurement is not a real-but-hidden property of the universe even.

To me, this implies that while science is pretty good at predicting phenomena and describing their relationships within predetermined parameters, science really can't say anything for certain about things in themselves.

Science says things that are as certain as anything can be. The uncertainty implicit in science really forms a boundary case severely limiting the level of certainty and precision of all other forms of knowledge. This kind of certainty and precision is qualitatively different from the emotion of certainty.

This is really where the difference between sceince and scientism starts to become apparent. Just to clarify what I mean here - unlike science, scientism does not acknowledge that the ultimate nature of reality is really a philosophical question that refers to science but is not solved by it.

Hm. I follow along with this, so long as we can agree that science is the activity which comes closest to describing reality of any human activity.

On that note, some of the folks reading this thread might be interested in the Materiaism thread in the Religion and Philosophy forum.

Mmm, maybe. I personally tend to find just about anything in R&P Forum irritating and circular, but I could be pleasantly surprised.

Thanks again!

Enjoy!

 

[DrMatt]

Greetings!

I am troubled by some observations about measurement that someone more intelligent and/or educated might be able to help me resolve.

1. A point is defined as having location without dimension, and in this world we describe a point's location by its relationship to other points.

NB that this definition is derived from our way of THINKING, not from empirical observations of the universe. Whether the universe actually behaves in ways that resemble the points, lines, and planes of any particular axiomatic geometry is a hypothesis worthy of being tested. Such tests have been conducted, and the outcome is "so far, yes, within relatively narrow boundaries of uncertainty."

 

[Houngan]

Hi Roger,

Thanks for your response. What I get from your statements is that we can be certain about our uncertainty! Seriously, I understand that you are saying that we can be certain that what we are observing actually falls within a given range of measurement and error, but that perfection is not ultimately attainable.

To me, this implies that while science is pretty good at predicting phenomena and describing their relationships within predetermined parameters, science really can't say anything for certain about things in themselves.

This is really where the difference between sceince and scientism starts to become apparent. Just to clarify what I mean here - unlike science, scientism does not acknowledge that the ultimate nature of reality is really a philosophical question that refers to science but is not solved by it.

On that note, some of the folks reading this thread might be interested in the Materiaism thread in the Religion and Philosophy forum.

Thanks again!

Imaginist,

Hmmm. You're slipping into trolldom. It seems that you are trying to nicely rehash the old idea of "since nothing can be fully understood, we don't understand anything." But anyway:

On measurement. We have a way of expressing this idea mathematically, called Limit Theory, which is useful for determining the value of a function at a certain point, even when the actual computed value is 0. It's a subset of calculus, I recommend you pick it up.

Otherwise, we do measure things precisely, in the sense that counts are infinitely precise. While some level of uncertainty exists when you measure something by another thing, say a rabbit by a kilogram, there is no uncertainty that there is exactly one rabbit.

Now, the philosopher will say, "the idea of a rabbit is just a convention by man" and be correct. However, you can call it what you will, the little furry thing is still just one. Scientism is a reaction against those who would try to make everything up for opinion, so that ignorant people can feel good about there incorrect ideas. No scientist would ever submit a paper saying, "Hey, I've found out exactly, in every detail, what this is about." But when confronted by a dunderhead, sometimes you have to speak in certainties, otherwise the argument instantly degenerates into semantics.

And yes, science can say plenty about things themselves. Give me an instance of a quality of a thing, and I'll give you the scientific definition or measurement of that thing. Of course, you can bring in fuzzy anthropomorphic qualities, like "How much love does a rabbit have?" Which is both ridiculous and unanswerable, but it doesn't change the fact that the rabbit is mostly made of carbon, hydrogen, and oxygen.

H.

 

[jj]

And that is how science works, by triangulating, metaphorically speaking, onto the truth. Given the assumption of a real world, then by multiple measurements we can improve our accuracy and precision. Proving that takes a lot of math, but the GPS example let's me present it qualitatively.

Interesting questions, thanks for the contribution to the board!


roger

Well, I'd like to point out that you've confused several issues here.

The first is that of degrees of freedom in solution vs. number of data points.

That's why you need at least 3 sattellites (consider, you know you're on the surface of the earth. That's going to seriously eliminate one of the two solutions you have with 3 sattelites, yes? That's now providing the full solution via 4 inputs, now, but one of them is not a sattelite.) There's also issues to be raised by having sattelites at different altitudes, but as you may guess, this also introduces operational problems...

This, however, isn't measurement error, it's having a complete determination of the measurement system.

Now, let's talk about measurement error. Each sattelite distance has an inaccuracy in measurement. This inaccuracy manifests by the solutions from various sets of sattelites not matching, i.e. you don't get one answer, you get a set of contradictory answers.

Which gets us to the next point, that of REDUCING THE ERROR by taking multiple measurements.

When you take multiple measurements, you'll have, with some simplification, two components, a systematic error that will not disappear (something that is not terribly likely to manifest using different systems, etc, but that we must include for completeness because there are some classical examples of this mattering) and a noise component that will have some kind of a distribution, the mean (expected value) of which can be extracted with increasing accuracy with more measurements.

As we repeat measurements, then, we can reduce the error by the square root of 'n' where 'n' is the number of independent measurements (some care in independency matters here, but is secondary to the point I'm making) and reduce the error by making these multiple measurements, eliminating the noise component and winding up, slowly but surely, with a good approximation to the expected value. This leaves only the systematic error.

Now, for each sattelite (to use gps) we may have a small, different systematic error. When we can see 5 or 6 or 7 sattelites, which is often the case, we can even begin to discover the systematic errors to each sattelite, relative to the mean systematic error, and reduce even those to the extent that we can start to get close to the overall system's systematic error.

Now, this is all for MACROSCOPIC things. I'm talking human-sized scales here.

If you try to make a measurement on an atomic level something, the very photon you must use (well, particle, wave, something ) will MOVE whatever it is that you measured. The photon has a momentum. If it bounces, momentum has to be conserved, some momentum went somewhere else. (Have we found any primary violations of this sort of parity yet, Tez?)

There can be no multiple measurements. Ergo, there is an absolute limit of accuracy (Heisenburg Uncertainty) in such measurements.

Now, groups of particles, etc, are a different story, as Tez or some other guys can tell us, in things like superconductors, etc.

But that's at a different scale altogether than measuring our location on the planet, of course.

 

[Imaginist]

Hmmm. You're slipping into trolldom. It seems that you are trying to nicely rehash the old idea of "since nothing can be fully understood, we don't understand anything." H.

I appreciate concerns about people just looking to argue for arguement's sake, but let's not get too distracted on this troll stuff. Nobody is forcing anyone to read this thread or talk to me, and I'm not flaming anyone or butting into other people's conversations. If a troll is simply someone who continues to question when they perceive a lack of clarity or completeness in their own thought or that of someone else, then I'm guilty as charged and I better get kicked off the forum right now. Besides, I thought I just defined a skeptic. So far, you're being nice, I'm being nice, and we're having a civil debate on a matter at the foundation of science itself. So, please, let's not let this "troll snowball" roll any further.

As to that last part of your opening statement, this is not what I wish to say at all. I think we understand a lot, I just don't think we should confuse any understanding of something with the thing itself. Understandings can be very useful, but in time they tend to change, and often quite dramatically.

Otherwise, we do measure things precisely, in the sense that counts are infinitely precise. While some level of uncertainty exists when you measure something by another thing, say a rabbit by a kilogram, there is no uncertainty that there is exactly one rabbit. H. [/QUOTE]

That's true. There are times when we can be certain about the quantity of particular phenomena.

And yes, science can say plenty about things themselves. Give me an instance of a quality of a thing, and I'll give you the scientific definition or measurement of that thing. Of course, you can bring in fuzzy anthropomorphic qualities, like "How much love does a rabbit have?" H. [/QUOTE]

LOL That would be a silly case! The first thought that came to my mind is "beauty", to borrow a little from one of Socrates' threads. You can call beauty fuzzy and anthropomorhpic, but it is nonetheless something most of us experience and would call a quality. I'd be interested in a scientific definition or measurement for beauty.


H. [/B][/QUOTE]

 

[Houngan]

Sorry, but that falls under the fuzzy heading. How about something that isn't a product of human qualitative perception.

H.

 

[roger]

Well, I'd like to point out that you've confused several issues here.

Sure. In practical applications the 4th satellite is used to sync the receiver's time to universal time, as discarding the obviously wrong point from the 3 satellite solution will give you 1 position (which doesn't exactly converge). And I didn't account for ephemeris errors, atmospheric errors, multipath errors, high GDOP values, etc. It just seemed a bit too detailed for someone asking "Where does one inch end and the second inch begin?"

 

[Imaginist]

Originally posted by DrMatt


Science says things that are as certain as anything can be. The uncertainty implicit in science really forms a boundary case severely limiting the level of certainty and precision of all other forms of knowledge. This kind of certainty and precision is qualitatively different from the emotion of certainty.

I think I follow you here. However, I would argue that there are things we can be more certain about than those things which science can measure or quantify. Like Descartes, I would point out that I there are no phenomena in the same class of certainty as my perception of my own thinking. Perhaps I misunderstand your point, but I fail to see how either the strengths or the limitations of science have any effect at all upon that fact.

I follow along with this, so long as we can agree that science is the activity which comes closest to describing reality of any human activity.

That's pretty hard to disagree with! But I would reiterate that descriptions and explanations are not the things themselves, and that they have a tendency to change as new information is acquired, which it seems that you personally agree with.

I personally tend to find just about anything in R&P Forum irritating and circular, but I could be pleasantly surprised.

It has been argued that the philosophical bases of all worldviews include circular thinking in one way or another. This problem is just one of many that suggests the primacy of assumptions (and thus perception and other mental processes) in all human activity and understanding. This line of thinking leads deeper into phenomenology. I won't get into what phenomenology is at this time, and I suspect there are folks reading this that could do a better job at it than me anyway. But it raises further questions about the fundamental instrument of science, which is the mind.

 

[Imaginist]

Sorry, but that falls under the fuzzy heading. How about something that isn't a product of human qualitative perception.

H.

No offense, but this seems like an awefully convenient set of circumstances for defending your case. Two problems here:

1. You're assuming the prerogative to set up the criteria for what qualifies as a quality, or at least which qualities count and which do not.

2. In essence, it seems you are saying, "Show me a measureable quality that can't be measured."

Anyway, your last statement really draws us closer to the crux of the problem. What knowledge isn't "a product of human qualitative perception"? That bunny you were talking about might not be produced by such perception, but what can you say about that bunny without making reference to such perception? Even your knowledge that it exists is itself dependent upon perception, and I question how that perception can exclude "qualitativeness."

 

[jj]

The first thought that came to my mind is "beauty", to borrow a little from one of Socrates' threads. You can call beauty fuzzy and anthropomorhpic, but it is nonetheless something most of us experience and would call a quality. I'd be interested in a scientific definition or measurement for beauty.
H.

[/B][/QUOTE]

You need to distinguish between "objective" or "analytic" measures and "subjective" measures.

An objective measure is something like counting. An analytic expression of a count is exact. An analytic measure can also be something like a length, for which there must absolutely be some error, but for which an external definition exists (rejecting absolute solipcism here).

A subjective measure, like beauty, comes down eventually to individual preference. It is, or isn't. There is no external measure.

We can (that's what subjective testing, which UCE seems to reject, at least in part) measure, with error, people's internal opinions, so yes, one could run a LIMITED subjective test on "how beautiful is an 'x'" for some specific 'x' in some specific circumstances, but there is no absolute measure stick and no external verification beyond consistancy.

More often, subjective testing attempts to establish a relationship between an analytic measurement (what is the intensity of this tone) and a percept (subjective response) of "how loud does this tone sound".

Such work, which involves measuring intellect, the results of intellect, etc, despite some people's inane assertions here, is well known and long established. It works better for some things (intensity vs. loudness for instance) than other things (do you like nSync).

In general when dealing with subjective issues, one has to realize that it is possible that there will be different families of responses in different people, sometimes (but rarely) down to highly disparate reactions from each individual.

Please understand that I am rejecting ultimate solipcism here, and that that is the only belief involved. All other things can be confirmed by other individuals, who I stipulate exist by rejecting ultimate solipcism.

 

[Houngan]

No offense, but this seems like an awefully convenient set of circumstances for defending your case. Two problems here:

1. You're assuming the prerogative to set up the criteria for what qualifies as a quality, or at least which qualities count and which do not.

2. In essence, it seems you are saying, "Show me a measureable quality that can't be measured."

Anyway, your last statement really draws us closer to the crux of the problem. What knowledge isn't "a product of human qualitative perception"? That bunny you were talking about might not be produced by such perception, but what can you say about that bunny without making reference to such perception? Even your knowledge that it exists is itself dependent upon perception, and I question how that perception can exclude "qualitativeness."

All I'm saying is that there is plenty that can be objectively measured, one of your first points. We've already discussed Limit theory and infintesimal distances, so now we're on to other things. Also, note that "quantitative" and "qualitative" mean two different things.

Lastly, you can apply "everything is subject to human perception" to anything, which renders this point moot from the get go (all of us assumedly being human) I thought we were beyond that.

H.