# Man is the measure of all things.November 23, 2011 2:38 PM   Subscribe

What is the philosophy of measurement?

I'm interested in the act of measurement: of using a physical device to extract a number out of the universe, and assigning it some form of meaning which exists in some half-world between mathematics and reality (for example, when we say something weighs 56kg, we can use the number "56" to do calculations and the tag "kg" to interpret the further results)

What kind of work has been done about such questions, and where should I start?

Here are some points of interest for me:

Counting: another form of extracting numbers from the environment, does not seem to qualify as a "measurement" as above. Is counting fundamentally different than weighing, for example? I suppose one can count using physical means and thus the point may be moot. But can the type of the measurement (integer or real, say) be of interest?

How to define measurement, anyway? Using a scale, for instance, presupposes some use for the data extracted from it, and so the use we make of the data must to some extent reflect the physical laws generating the numbers. Measurements always have error -- how much error is tolerable until all one gets is "noise"?

I could keep going but I'll stop.

Also: I'd like to avoid any kind of confusion with what quantum mechanics calls "measurement" because to be honest I don't fully understand it.
posted by StoneSpace to Religion & Philosophy (27 answers total) 28 users marked this as a favorite

You might want to take a look at number theory - one of the first things you do is address the question "hey, what *is* a number anyway?!"
posted by b1tr0t at 2:45 PM on November 23, 2011

I am specifically interested in the relationship between mathematics (or, in general, the language constituting science, with is a subset of English + math, basically), and the real word. While I love pure math, I would be much more interested, say, in what could ground its axioms in the real world (some kind of "logical measurement", in a sense)
posted by StoneSpace at 2:48 PM on November 23, 2011

Right right homies the real word.

ahem, world.

posted by StoneSpace at 2:51 PM on November 23, 2011

You might be interested in some of the work done in anthropological mathematics (studying how different cultures "do" math, including the relationship between counting and measuring). There's a lot out there, but the one I particularly enjoy and unceasingly recommend is a foundational text, Science and an African Logic.
posted by muddgirl at 2:54 PM on November 23, 2011 [3 favorites]

The word you want is "isomorphism".
posted by Chocolate Pickle at 3:02 PM on November 23, 2011

I may be being thick, but I don't understand the question's premises. I don't think this has much to do with math, let alone sitting in some half-world. Suppose there is something you want to measure or count. You have to identify the relevant units of it -- kg, foot, degree, whatever. Some of these are more or less arbitrary and generated by history; some are more influenced by instrumentation, etc. I imagine there is a philosophy about this, but I don't see how it is math-driven.

Just as a shot in the dark, consider Sobel's Longitude as an interesting example.
posted by Clyde Mnestra at 3:04 PM on November 23, 2011

A descent starting point might be Wigner's short essay The Unreasonable Effectiveness of Mathematics in the Natural Sciences. It doesn't address measurement per se, but measurement falls fairly naturally out of broader theories in the natural sciences. For example, mass is, among other things, the same as the magnitude with which one body interacts with another gravitationally. Or, in this one case, a quantity that relates the force on a body with its acceleration. The measurement process itself is fairly simple, but the fact that there is a quantity to measure is a consequence of a deeper theory. The relationship between math and theory certainly has a lot written about it, but I can't say I know much of it. Wigner's essay and discussion of it by others should hopefully get you somewhere, though.
posted by Schismatic at 3:09 PM on November 23, 2011 [2 favorites]

You have to identify the relevant units of it -- kg, foot, degree, whatever. Some of these are more or less arbitrary and generated by history; some are more influenced by instrumentation, etc. I imagine there is a philosophy about this, but I don't see how it is math-driven.

How do you measure the strength of a magnetic field and how is it related to mass, distance and time? You have to figure out what your fundamental units are and how they related to other measurable quantities, and that's math.
posted by empath at 3:12 PM on November 23, 2011

"Measurement theory" is TOTALLY what you want. Would post links but am on my phone... Google should work.
posted by kestrel251 at 3:18 PM on November 23, 2011

empath: I think you are saying that I am, indeed, being thick. But how thick, precisely?

Joking aside, I admit I am probably just not getting it. I do not see the issue of measuring the strength of a magnetic field as at all involving a philosophy of math, unless we think that anything using numbers does. That seems to me to be a minimal threshold. I do grant that measurement involves a philosophy, and that an understand of the physical world and its properties (mass, distance, time) will be implicated.
posted by Clyde Mnestra at 3:19 PM on November 23, 2011

OK I have to explain myself again.

Just to make a quick point I can math pretty well and have a good grounding in physics...

The idea is that our usage of the results of measurements reflect what is the nature of that which we extract from the environment by measuring (erm, "meaning is use" I suppose). The meaning we ascribe -- and the meaning goes beyond simple units, it goes to the actual concepts of mass, or temperature , for example -- rests on both the mathematics of using "56kg" in a particular situation, and the metaphysics of mass itself, I suppose.
posted by StoneSpace at 3:43 PM on November 23, 2011

muddgirl: looks wonderful, thanks.

Schismatic: this essay is great but I feel it sidestepped the issue. Just a feeling of course...thanks for the reminder.
posted by StoneSpace at 3:44 PM on November 23, 2011

Agreed, the essay isn't about exactly what you asked. But I maintain that there's no sensible way to think about measurement as anything other than determining quantities already present in physical theories. The unit "kg" is arbitrary, but it reflects the ratio of how two properties, acceleration and force, should interact. The number and the exact choice of unit (not to be confused with dimension) are just there because we have to pick something. You say "the meaning goes beyond simple units, it goes to the actual concepts of mass," and these concepts are exactly what one gets from investigating the fundamental theories. This is why I suspect it'd be fruitful to take a step back and read more broadly on the philosophical relationship between physical theory and mathematics first and then look into the particular measurement angle with that background. I doubt you'll get much of the latter without the former, and I'm not convinced that they aren't much the same thing.
posted by Schismatic at 4:11 PM on November 23, 2011

I can't say I really understand "philosophy", but concepts I find interesting (and tricky to understand) that have probably heard of, but are relevant to the discussion of how measuring something in fact can affect that thing...

Heisenberg uncertainty principle - you can't know the both the position of and momentum of a particle at the same time.

Schrödinger's cat - the cat remains both alive and dead (to the universe outside the box) until the box is opened
posted by trialex at 4:43 PM on November 23, 2011

I don't know if this is relevant, but the kilogram has a standard - a physical object - that everyone agrees is a kilogram.

"The IPK and its six sister copies are stored at the International Bureau of Weights and Measures (known by its French-language initials BIPM) in an environmentally monitored safe in the lower vault located in the basement of the BIPM’s Pavillon de Breteuil in Sèvres on the outskirts of Paris (see External images, below, for photographs). Three independently controlled keys are required to open the vault. Official copies of the IPK were made available to other nations to serve as their national standards. These are compared to the IPK roughly every 50 years.
The IPK is one of three cylinders made in 1879. In 1883, its mass was found to be indistinguishable from that of the Kilogram of the Archives made eighty-four years prior, and was formally ratified as the kilogram by the 1st CGPM in 1889."
posted by abirdinthehand at 5:48 PM on November 23, 2011

It sounds to me as if you're in the process of becoming lost in a labyrinth of abstractions, and would benefit from a bit of grounding.
posted by flabdablet at 7:05 PM on November 23, 2011 [1 favorite]

I came back to link to this. Check out the syllabus and notes on measurement theory.
posted by kestrel251 at 7:35 PM on November 23, 2011

You might be interested to hear that the object abirdinthehand mentioned, the standard kilogram, is a lighter than it used to be.

But basically I think you're asking not just about quantitative measurements, but in general, what's the relationship of our scientific theories to the world that's out there? Are our theories True with a capital T, or are they just good-enough-to-match-the-evidence ("empirically adequate"), or are they just arbitrary social conventions, etc? These are questions in the philosophy of science.

Here's one place to start investigating:
Scientific realism is one of the main positions philosophers of science have taken on this question. That article describes and links to articles on some of the other main positions.

You might also be interested in a bit on Theory and Observation in Science.

These are both articles from the Stanford Encyclopedia of Philosophy; they're a bit dense as introductory reading but both have bibliographies and links to other articles, and should at least give you a sense of where to start.

Here's a recent paper that might be of interest. (I haven't read it and don't know whether it's any good; if you're at a college or university your library may subscribe to the journal.)
"The Logic of Measurement: A Realist Overview" by Joel Mitchell in the journal Measurement.
posted by LobsterMitten at 9:55 PM on November 23, 2011

You might be interested to hear that the object abirdinthehand mentioned, the standard kilogram, is a lighter than it used to be.

posted by flabdablet at 10:11 PM on November 23, 2011

Slightly tangentially, there was a pair of articles on Cosmic Variance in the past week about what exactly Quantum Mechanics experiments are measuring.
posted by empath at 10:15 PM on November 23, 2011

You might want to look into Error theory as well.

The major difference with Measurement and Counting is that there is no error in counting. (Well, there shouldn't be). There is always an error in measurement.
posted by kjs4 at 10:46 PM on November 23, 2011

Dammit, thank you flabdablet.

If it's really measurement per se that you're interested in, here is a useful article "Measurement", by Hasok Chang and Nancy Cartwright, which appears as chapter 34 in the Routledge Companion to the Philosophy of Science, Stathis Psillos, Martin Curd eds. 2008.

Here's the intro:
Measurement is one of the most distinctive and pervasive features of modern science, but it is not easy to say what measurement actually is. Philosophers commonly define measurement as the correct assignment of numbers to physical variables. there are many difficult philosophical and practical questions about whether a measurement is made correctly and how we can know that it is. Various philosophical views surrounding these questions are discussed next; in the final two sections, we highlight concrete questions concerning the practice of measurement in the physical and the social sciences.

And an excerpt from their recommendations for further reading:
Useful philosophical discussions about measurement in various sciences can be found in John Forge (ed), Measurement, Realism and Objectivity[(1987)...] Woolf (1961) gives very interesting historical views on quantification in the natural and the social sciences. [...] Broad surveys of measurements in a wide variety of fields can be found in David J Hand, Measurement Theory and Practice [(2004) ...] and Herbert Arthur Klein, The Science of Measurement [(1974) ...] Those interested in studying formal theories of measurement, introduced in [Patrick] Suppes (1998) [Suppes's article "Measurement, Theory of" which appears in E. Craig, ed. The Routledge Encyclopedia of Philosophy, vol 6, pp 243-49], can refer to David H Krantz et al., Foundations of Measurement, 3 vols (1971-90).
Here is what seems to be a PDF link to a draft of that chapter. The whole book would be useful and if you have access to a university library they might have it.
posted by LobsterMitten at 10:57 PM on November 23, 2011 [2 favorites]

Wonderful, thank you all for the answers and suggestions.
posted by StoneSpace at 5:29 AM on November 24, 2011

You might also get something out of reading about Benacerraf's dilemma, which tries to highlight the tension between the abstract mathematical concept of truth, and our feeling that it ought to be able to fit into a "real world" epistemology (of which measurement would be a part I think).
posted by crocomancer at 5:35 AM on November 24, 2011

Three related books from philosophy and sociology of science:

Thing Knowledge: A Philosophy of Scientific Instruments by Davis Baird.

How Experiments End by Peter Galison.

What Engineers Know and How They Know It: Analytical Studies from Aeronautical History by Walter Vincenti.

Someone mentioned error theory above. One of the core texts in that area is Taylor's Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements.
posted by ollyollyoxenfree at 10:01 PM on November 24, 2011

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