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Representing objects and properties in Physics

By adiffer in Technology
Tue May 07, 2002 at 10:00:32 AM EST
Tags: Science (all tags)

A student first learning physics usually faces two inter-related tasks that are difficult to unwind and see as separate fundamentals. Older students and practitioners rarely go back and address the assumptions they made at the very start, so the intuitive leaps they made rarely surface for examination.

Besides the early concepts of kinematics and Newton's forces, a student must also learn how to represent things of interest in the mathematical language they are expected to use. It is the issue of object representation that will be addressed by this paper. The objects to be represented are the typical concepts of physics. The reader is assumed to be knowledgeable about enough of them to follow the argument.

Early students are assumed to know the tools of algebra, geometry, calculus, and parts of linear algebra. After a time, the student usually picks up more knowledge concerning linear and matrix algebra, differential equations, complex numbers and various specialty functions and polynomials.

While each of the added mathematical tool sets greatly expands a student's capabilities for problem solving, they tend to get appended through the working of example problems to which they are powerfully adapted. It is rare for a student to face an unsolved problem to which they must find the appropriate tools until they are at the graduate level of their training. Even then, many never face this task.

This paper focuses upon how we use the mathematical tools we choose. It asks the questions 'How do we choose to represent that which we perceive?' and 'How do we know others are perceiving the same objects we are trying to address?' Which tools we use depends a great deal on our knowledge of them and the depth of our experience with them. This paper assumes the question of why we choose our tools has much to do with simplicity, power, and convention and pays it no further attention.


There is historical evidence of changes to the primary tool sets used for the oldest branches of physics. Newton crafted the contents of his Principia with geometry and his new calculus. Modern students use algebra, calculus, and vectors for the same material and usually find the Principia difficult to decode. Maxwell's description of Electric and Magnetic fields was radically different from what is taught today. With modern vectors and matrices, electromagnetism is hard to recognize for those who put forth the effort to read the older texts.

Whether Newton or the others would have used modern tools had they been available is not the question. The fact is, modern practitioners moved away from older approaches in favor of other means to represent much the same concepts. How they did so is worth some consideration because modern instructors rarely bother to teach or even mention the older approaches. Something important has occurred and the existence of these changes suggests it is worthwhile to consider the foundation of our approaches to object representation.

An Example

Imagine a sharp, straight stick on the ground. We wish to represent the length and orientation of the stick mathematically. There is more than one tool that can be used, but modern students will almost always reach for vectors once they have learned how to use them. Two will be shown here.

Vector Technique

  1. Choose a reference frame. Pick an origin for it and then write down some information about the directions of your basis vectors relative to each other. You have quite a bit of freedom, but most people pick right-handed systems and make the basis vectors have a length of one unit and stand at right angles to each other.
  2. Pick one of the basis vectors. Imagine a light bulb that projects a shadow of the sharp end of the stick onto a line that extends through your basis vector from the origin outward. Put a slit in front of the bulb. Arrange the slit so the light it allows out moves toward the stick parallel to the other basis vector you didn't choose. How long would your basis vector have to have been to be long enough to just reach the projected shadow? Write down that number.
  3. Do the light trick again swapping your basis vectors and write down that number.
  4. Multiply your first number by the first basis vector and add it to the product of the second number with the second basis vector. This vector points at the sharp end of the stick.
  5. If you didn't pick your origin at the blunt end of the stick, do both projections and the addition trick again for the blunt end. This vector points at the blunt end of the stick.
  6. The length and direction of the stick can be represented by the difference of the two vectors. Take the sharp end vector and subtract the blunt end vector and you are done.

Algebra Technique

  1. Choose a coordinate system. Pick an origin for it and then write down some information about the directions and scale of your coordinate axes. You have quite a bit of freedom, but most people pick right-handed systems and make the axes stand at right angles to each other.
  2. Draw out a coordinate grid using the axes you chose. Find the coordinates of both ends of your stick.
  3. Find the straight line equation that goes through both of the points you found earlier.
  4. The stick is represented by the straight line function over a domain and range limited to the span between the two coordinate points. The distance formula between two points gives the length while the domain and range spans start at the blunt end to give the orientation.

These two approaches may sound the same, but they are not. In the first, a vector represents the stick. In the second, a function represents the stick. Both of them have different descriptions for the reference frames used. There are some similarities, of course. This shouldn?t surprise anyone since both techniques are being used to try to describe the same properties of the stick

If the reader is still unsure that these two techniques and their supporting tools are different, imagine expanding the example in the following way. Suppose we also try to describe the size and orientation of the cross-sectional area of the same sharp stick. Vector proponents would be tempted to write another vector oriented normal to the cross-sectional area. Algebraic proponents might be tempted to do the same, but they could also represent the functional equivalent of the cylindrical or conical surface area surrounding the stick and use formulas to demonstrate the cross-sectional area. Both techniques work, so one cannot claim to be superior than the other.

The Postulates

For the purpose of further discussion, we propose three postulates to act as an abstraction of the representation techniques and intentions of the users. The postulates make no attempt to describe any physics. Instead, their purpose is to address how we recognize and represent physically interesting things for our physics theories to address. If the abstraction works, it should be possible for the reader to write examples similar to the one above and see their techniques described by the postulates.

1: Completion terms

Complete Objects are represented as a list of observables representing each of the independent properties of an Object.
2: Rendering of representations
Properties are rendered as observables through representations as combinations of components in a suitably complex mathematical tool.
3: Identity terms
Representations of an observable describe the same property of an Object if under an agreed upon family of passive transformations suitably defined for the mathematical tool, all Observers can passively transform their rendition into the renderings of the other Observers. This is not invariance.

Terminology Dictionary


An Object is a physically interesting thing. It is the subject of theory and experiment. It is a part of reality singled out for further attention.


A property is a part of an Object describing some definable portion we might observe and test through experimentation.


An observable is related to a property and is the direct result of a rendering of that property into an appropriate mathematical tool. The observable is what actually gets tested in experimentation because the experimenter must make assumptions about the property being tested. Those assumptions are embodied in the observable.


Independence is a concept useful for distinguishing properties of an Object from each other. An example of two properties that are not independent of each other might be color and the reflection coefficient as a function of energy for a body bathed in sunlight.


A component of a math tool is defined relative to that tool. In geometry of two dimensions, line segments, area segments and points make up some basic components. In algebra, polynomials of order N make up an unending list of components. In a geometric algebra, the generators of an algebra and their products make up the available components.


A combination is a sum and products of components scaled by elements from a field such as real or complex numbers. If this definition were limited to sums, it would be equivalent to the standard meaning used for 'linear combination.'


A representation is a particular rendering of an observable within the mathematical tool of choice. There are often many ways to represent the same observable.

Transformation (passive)

A passive transformation is one that alters the representation of an observable without doing anything to the observable itself. These transformations are usually more a measure of what the Observer is doing that changes the representation than anything else.


An Observer is someone or some thing that can definitively answer questions about their representations of observables. The typical observers are the experimenters trying to understand an object.

Postulate Support and Explanation

Postulate one is largely about knowing how to decompose an object to parts that may be rendered and tested separately, but it will most often be used in the other direction. It is possible and quite likely that observers will initially fail to understand the full scope of an object. Without this understanding, initial representations are likely to be partial. A strategy for completing a representation, therefore, is in order.

The completion strategy is to form a list of properties known to be associated with an object. This is what is done today. The length of the list depends on the experience of the observer and in what properties they are interested. The appearance of the list depends on the tool to be used. Most practitioners simply write a natural language list of the representations of the expected observables. To many, initially including this author, this postulate is assumed and goes by without thinking.

Postulate two addresses the issue of how properties are rendered as observables. Each mathematical tool is different enough to make a general discussion of representations quite generic and of little interest here. The proponents of the vector technique in our sharp stick example earlier rendered the length and orientation during steps two through four. The correctly sized components were found in the first two steps while the combination was created in the last one. The proponents of the algebraic technique rendered the length and orientation during step three. The components were suitably scaled monomials (order one and order zero) while the combination was the sum that created the straight line function.

Postulate three forms the basis of a strategy that may be used by multiple observers who wish to know if their renderings describe the same object. The strategy is not fully deterministic. Probabilistic knowledge, therefore, can enter into the concept of object identity long before it enters into the physical theories using the representations.

Consider our earlier example of the sharp stick. Imagine further that many observers create representations of the length and orientation and share them with each other. How does Observer A know that the representation offered by Observer B addresses the same properties of the same stick? Do they simply trust each other? Is there a method for creating identity in the representation that may eliminate the need for trust? In practice, trust is used, but it tends to undermine the purpose of experimentation in the scientific method.

The notion of identity can be added to the representation through an agreed upon family of passive transformations shared by all observers. Ask an observer to render the observable again and a different outcome may occur. After all, the observers were free to choose a reference frame before finding a suitable linear combination for their vector. Different representations would occur for each choice of reference frame. If one observer is asked to create many different representations of the same observable, another observer could discover the passive transformation family used by the first observer through a careful study of the renderings. If that family is found, and there exists a transformation in that family that turns the representation written by observer B into one written by observer A, observer B may be reasonably confident both renderings refer to the same object.

Postulate three does not lead to a bulletproof concept of identity. If one observer produces a representation that fails the test, the other observers can be certain that particular observer rendered a different property or object. If all representations pass, though, all the observers can say is they are pretty sure the renderings refer to the same object. The higher number of representations that pass, the higher the odds are that they do refer to the same properties of the same object.


Any observable that proves to be invariant under the family of passive transformations used by all observers obviously qualifies to represent an object seen by all observers. The only block to knowing absolutely that a given representation refers to an object is the possibility that the observer might have been looking at a similar object elsewhere. Are you and I looking at the same sharp stick? What if we were instead trying to describe an electron?

Issues of identity are rarely raised if each observer sticks to representations that are invariant under the agreed upon transformations. This suggests that invariance is a suitable stand-in for identity much of the time. It also suggests that observers will choose between two equally powerful tools in favor of the one where invariance is most easily found and demonstrated. This last statement depends largely on the desire of most practitioners to avoid unnecessary work.

Whether the identity of an object is fully agreed upon by all observers or not, the invariance of a representation can be determined with certainty by any one observer and then promised to the others. The mathematical tool offers this certainty, so no trust is needed.

This promise between observers is probably at the root of how we choose our representations. Any supporters of newly developed tools must be able to offer at least this much if they hope to have their work displace older techniques. To test this notion, we can ask if the newer tools offer an equally strong or stronger sense of identity to the objects Newton originally represented with geometry for Principia. If the answer is yes, this premise survives its first test and might be worth consideration by a larger audience.

Consider Proposition 36 of Book 1. (From Cajori's revision of Motte's translation)

To determine the times of the descent of a body falling from a given place A
Upon the diameter AS, the distance of the body from the centre at the beginning, describe the semicircle ADS, as likewise the semicircle OKH equal thereto, about the center S. From any place C of the body erect the ordinate CD. Join SD and make the sector OSK equal to the area ASD. It is evident (by Prop 35) that the body in falling will describe the space AC in the same time in which another body, uniformly revolving about the centre S, may describe the arc OK.
(Proposition 35 addresses the notion that equal areas are swept out in equal times on a gravitational orbit.)

Newton used proposition 36 in book 3 to show how the rate at which the Moon falls toward the Earth can be directly formulated from our knowledge of how masses accelerate here on the surface of the Earth.

Early physics students learn a similar lesson when they are taught about gravity. These students are taught to replace geometric line segments with distances calculated from a Cartesian or similar coordinate system. The areas swept out (sectors OSK and ASD) can be shown too, but often aren't. The algebraic formula for the force of gravity is used directly in modern texts and the approach is considered sufficient.

Each of the objects represented in Newton's proposition can be translated to modern renderings using algebra. In each case, care can be taken to use the typical coordinate systems taught in the texts and the identities of each object get preserved. The invariants are much the same as they were with the geometric description. Lengths and angles do not get altered between observers. Time ticks at the same rate for all, else proposition 35 would fail. Young students are taught not to violate those invariants whether they realize it or not. In their acceptance, then, the concept of object identity is likely to be preserved and different observers can be confident in their use of each other's renderings.

Anyone who knows special relativity well enough should be able to see the beginnings of how revolutionary the new concepts were. The two postulates of special relativity strike directly at the heart of the invariants used in Newton's work. The representations written in tools capable of supporting special relativity fundamentally alter what a property is, let alone how its observable behaves.


How we choose to represent our objects can be summarized by the creation of a trustable identity for the interesting properties. Invariance provides the root for trust between observers. The rest of the rules concerning representation are technique that varies from one tool to the other.

As long as the practitioner takes steps to represent complete properties for objects whose identity can be trusted by other observers, they have done what the community expects of them. Most everyone except the users of statistical mechanics and its related subjects largely ignore the probabilistic nature of the identification.


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Representing objects and properties in Physics | 39 comments (24 topical, 15 editorial, 1 hidden)
a couple of likes (3.00 / 1) (#2)
by khallow on Tue May 07, 2002 at 01:44:13 AM EST

I'll have to read the article again, but I like the layout. Clean and somewhat brisk. Also, it's nice to see the distinction between a property and what you actually observe.

Stating the obvious since 1969.

Description vs Explanation (4.00 / 1) (#11)
by SocratesGhost on Tue May 07, 2002 at 04:35:14 AM EST

Since this is a part of a larger work, I'm wondering if you give any thought to useful models of explanation? What you have here is an attempt at rigorous and exhaustive descriptiveness, but pure description falls short of a thorough explanation (and vice versa). To say that an object responds in a particular manner in a situation does not say what that object means at that time, and often times that meaning cannot be interchanged as easily as the description of the object itself. "Morning star" and the "evening star" may very well be the same planet Venus if the use of those phrases have the same referant, but the context of either of those aspects would be lost if expressed in purely mathematical terms. This is often expressed as the difference between an object's sense (or meaning, context, intention, connotation) versus its reference (or naming, description, extension, denotation).

Quine says it better: "The general terms 'creature with a heart' and 'creature with a kidney,' e.g., are perhaps alike in extension but unlike in meaning."

btw, brilliant work. +1FP, and I hope to read more about this.

I drank what?

explanations (4.00 / 1) (#13)
by adiffer on Tue May 07, 2002 at 05:14:30 AM EST

As a physicist, I tend to shy away from explanation and stick to descriptive representations that feed predictive theories.

Explanation is rarely approachable by the scientific method. How do I know when I'm right or wrong?

I know that explanation is needed, though, to build intuitions. I will occasionally stretch a bit and write analogies that can be used temporarily as explanations. Be ready to throw out the analogies at the drop of a hat, though. I may use them, but I don't BELIEVE any of them.

-Dream Big.
--Grow Up.
[ Parent ]

exactly (3.00 / 1) (#14)
by SocratesGhost on Tue May 07, 2002 at 05:23:11 AM EST

that's why i ask. They are such tricky things. And yet, in many ways, that is the whole point of description models. Formulae don't show relevance, importance, or purpose. It may answer, "Who, what, when, where, how" but it neglects "Why" and "So what?"

I drank what?

[ Parent ]
some first thoughts (5.00 / 4) (#15)
by martingale on Tue May 07, 2002 at 07:22:41 AM EST

OK, I read it once and here as some first thoughts, in no particular order. I found it a bit hard to follow to tell you the truth, mainly because it seems to me to jump around many topics, making allusions but not going sufficiently deeply into things. Of course, that's not surprising given that this is only a short article.

I found your terminology bothered me a bit. You mix computer science concepts (rendering, objects) with physics concepts (observable) and mathematics concepts (symmetry). Since I know a little bit about these subjects, I found I was fairly defensive towards the nontraditional use of these words. This probably accounted for some of the difficulties I had reading.

To elaborate a bit, you use the word component in its cs meaning (part of a system) to apply to the building blocks of mathematical representations, and later on your discussion of symmetries alludes to the mathematical meaning of components (of a vector) when introducing symmetries and invariance. So you've jumped from a very abstract and simplistic description of systems through a modern algebraic approach to maths/physics back into a simpler vector analysis problem, where the word component has a very concrete but imho different meaning.

Overall, it feels a bit like you're trying to write a computer algorithm for the thought processes of a modern physicist, who has to weed through his full conceptual framework to solve a simple problem (your illustrative example). But in doing so, the algorithm wastes a lot of effort in deciding what to throw away for this concrete problem. It also means that as a reader, I am constantly told about generalizations which reduce to nothing in the concrete example provided. That makes it difficult to follow I think.

I'll leave it at that for now. Good effort though.

thanks (none / 0) (#22)
by adiffer on Tue May 07, 2002 at 04:43:12 PM EST

I hear you on the terminology issues. I am straddling two or three camps and trying to pull good ideas from each one. The math and physics camps aren't all that far apart for those of us trained as theoretical types. The CS camp, though, is quite a reach.

The words I am using now aren't the ones I started using. I'm looking for a set that doesn't cause too much grief for anyone, so if you have suggestions, I'm all ears.

I like the CS terms quite a lot. They force me, as a physicist, to think about things I used to gloss over. Of course, that leads to algorithmic thinking which is counter to how I learned to solve physics problems. It's all useful for doing a bit of house cleaning and tidying, though. My problem solving approach has been shifting over the last couple years.

An algorithmic way to describe what a physicist does when setting up a problem may not be needed, but I think it will prove useful. I've seen some of the code that developers write for simulation applications. A lot of them write decent UI's and event models and then get bogged down in the physical model. The physics community isn't helping much with our basket of kludges and limited scope solution spaces. We can do better.

-Dream Big.
--Grow Up.
[ Parent ]

Physics, math, and CS (none / 0) (#25)
by phliar on Tue May 07, 2002 at 05:54:58 PM EST

The math and physics camps aren't all that far apart for those of us trained as theoretical types. The CS camp, though, is quite a reach. ... I like the CS terms quite a lot.
Ahem! My academic training is primarily math and CS with a little bit of physics thrown in. I wish [pedant warning!] people wouldn't use "CS" as a generic term for "things having to do with computers". CS comprises the formal underpinnings of the craft of "writing code". Words like "model" and "render" are part of that discipline. Concepts like the various complexity classes are the realm of CS. The confusion comes because, since it's quite a young field, there is a lot of overlap between the practitioners of the two. At various times I've been doing more of one than the other. (The "writing code" aspect certainly pays much better than the other, which is why these days that's what I do!)

Aside: I think it's because of the youth of the field that current literature (research) in CS is absurdly formal; the notation is far more obtuse than anything you'd find in, say, algebraic topology. It's like they are trying to out-notate and out-formal each other.

"Computer Science" has the further deadly drawback of using that S-word... any discipline that feels the need to tack it on is obviously not one! Cf. Political "Science". Instead of "CS" can we use something like "programming" or "engineering"?

I like this kind of article. Are you planning on discussing mathematical models: how they are constructed, what makes a good [effective] model, etc.? Talking to people I find that a lot of them think that "Science" is all about "absolute truth" and "reality". etc. I like to think that when a scientist says "this is how it works" what is really meant is "here's a very effective and useful model for that phenomenon". Perhaps this subject is not of general interest, but the good and deep articles never are. I look forward to reading more.

Faster, faster, until the thrill of...
[ Parent ]

horse hockey (none / 0) (#27)
by adequate nathan on Tue May 07, 2002 at 07:07:24 PM EST

CS comprises the formal underpinnings of the craft of "writing code". [sic] [1]

It's not like computers existed and then someone realised there needed also to exist a discipline studying coding, you know. Saying that CS is "formal writing code" is like saying that mechanical engineering is "formal plumbing" or "formal metal work." Technological fields are theoretically subsidiary to theoretical fields.

You are also slightly linguistically misninformed as to the association of the word science with academic disciplines such as CS or Poli Sci. Science refers to scientific methodology and as such is correctly applied to the methodical study of computers, politics, the physical properties of the earth, and many other things.

[1] Periods outside of quotation marks, please.

"For me -- ugghhh, arrgghh."
-Canadian Prime Minister Jean Chrétien, in Frank magazine, Jan. 20th 2003

Join the petition: Rusty! Make dumped stories & discussion public!
[ Parent ]

Horses play hockey? (none / 0) (#30)
by phliar on Wed May 08, 2002 at 02:05:49 AM EST

It's not like computers existed and then someone realised there needed also to exist a discipline studying coding, you know. Saying that CS is "formal writing code" is like saying that mechanical engineering is "formal plumbing" or "formal metal work."
I don't understand what you're trying to say here. My calling CS the "formal underpinnings of the craft of writing code" in no way implies any kind of temporal relationship about which came first. I could say that "statics is the formal underpinning of bridge-building". Does it imply that one came before the other? Does it imply that "statics" is "formal bridge-building"?

Methinks you should look in your own stable before naming my game.

Periods outside of quotation marks, please.
Is that a request or a scornful jibe? Is that a practice you object to? If so, why?
You are also slightly linguistically misninformed as to the association of the word science with academic disciplines such as CS or Poli Sci.
That was a joke, son.

Faster, faster, until the thrill of...
[ Parent ]

thank you (none / 0) (#32)
by adequate nathan on Wed May 08, 2002 at 02:13:46 PM EST

For clearing up some confusing statements that I misread as arguments. To wit:
  • CS comprises the formal underpinnings of the craft of "writing code". [sic]
  • Instead of "CS" can we use something like "programming" or "engineering"?

    The first reads as though CS is antecedent to writing code (see JonesBoy's post for a reading agreeing with mine.) The second reads as though you believe what the first implies.

    As for placing periods outside of quote marks, that is a usage error. It's like putting periods (outside of parentheses). This orthography is a g**k affectation rather than Standard Written English. Hope this helps.

    "For me -- ugghhh, arrgghh."
    -Canadian Prime Minister Jean Chrétien, in Frank magazine, Jan. 20th 2003

    Join the petition: Rusty! Make dumped stories & discussion public!
    [ Parent ]

  • Orthography and regional differences (none / 0) (#33)
    by phliar on Wed May 08, 2002 at 03:57:29 PM EST

    As for placing periods outside of quote marks, that is a usage error. It's like putting periods (outside of parentheses). This orthography is a g**k affectation rather than Standard Written English.
    I'm afraid I'd have to take exception to this. As a kid I was taught that fullstops [period? why period?] went inside quotation marks. In the US, though, common usage puts them outside. I find myself vacillating back and forth on this issue, not having decided which is "correct". (Or which is "correct.") I tend to put the fullstop outside when I'm quoting just a word or a phrase; it goes inside when I'm quoting someone."Man," he said, "your spelling is all screwed up."

    I have decided how to treat parentheses, though: the fullstop goes inside the parentheses if it's a complete sentence; it goes outside if the parenthetical clause is at the end of the sentence. I consider this correct: blah blah (foobar bar foo.). However it looks ugly enough that I'd rewrite it.

    Faster, faster, until the thrill of...
    [ Parent ]

    if that is how usage goes in the USA (none / 0) (#36)
    by adequate nathan on Wed May 08, 2002 at 06:54:10 PM EST

    Then it is the result of ignorance on the part of teachers of English.

    Accepted usage has always been within quotes and parentheses, as a quick look at any Elisabethan or later sources would tell you. Anything new is an unnecessary modern perversion.

    "For me -- ugghhh, arrgghh."
    -Canadian Prime Minister Jean Chrétien, in Frank magazine, Jan. 20th 2003

    Join the petition: Rusty! Make dumped stories & discussion public!
    [ Parent ]

    accepted usage is not very logical (none / 0) (#39)
    by ethereal on Mon Jul 22, 2002 at 10:49:55 AM EST

    I was taught to do it as you describe - period within enclosing quotes or parentheses. However, it makes it confusing as to what exactly is being quoted or parenthesized. Since computer people tend to be sensitive to minute details like this, there are a lot of people (myself included) who try to disambiguate this notation by only putting the period inside the quotes if you're quoting the period itself (for example, quoting a full sentence). I was unaware that others in the USA considered this to be standard usage; I knew that I was doing it differently and really didn't care, since I'm pretty sure I can justify my choice.


    Stand up for your right to not believe: Americans United for Separation of Church and State
    [ Parent ]

    CS != programming!!! (none / 0) (#31)
    by JonesBoy on Wed May 08, 2002 at 10:32:58 AM EST

    "CS comprises the formal underpinnings of the craft of 'writing code'".<GASP> I can't believe you even implied this.   Computer science is all about the algorithms, describability, solvability, etc.    Theory.   Programming is merely a side effect of this knowledge.   It is an implementation, but not the intent.   There are a lot of CS people out there that are horrible coders, or do not code at all.   Look at Alan Turing.   He was doing CS before computers existed!   There are also a lot of good CS programmers.   Thats 'cause theory usually doesn't put food on the table.

    Science is not necessarily about truth, but about abstraction.   Engineering is about the implementation of scientific abstractions.   Programmers that develop algorithms from theories may be classified as engineers, but most are merely technicians.   I mean, calling a front end programmer a software engineer is like calling a garbage man a sanitation engineer - P.C. feelgood bullshit.   Yes, far too many people lump Computer Science, Computer Engineering, Software Engineering, and Programming Technicians into CS, but martingale and adiffer were spot on.

    CS is not new either.   It has been a collegiate major for ~35 years, and the science it is teaching has been around even longer.

    Speeding never killed anyone. Stopping did.
    [ Parent ]

    blurred terminology (none / 0) (#35)
    by adiffer on Wed May 08, 2002 at 05:29:10 PM EST

    Sorry folks. My bad.

    The camp I am reaching out toward is the one filled with people who write code and the languages in which the source is written. These are the people dealing with day-to-day issues of representation. They are also the most easily understood by a large group because their work is so transparent. I did not mean to misuse the term 'Computer Science' no matter how much people may differ on their definition of it.

    Regarding future articles... yes. I am planning to write some more stuff and offer it here to K5 readers. It seems to pass the voting test even if it doesn't lead to a lot of discussion.

    I don't know how good I'll be writing up comparisons of the various representation techniques, though. I know a couple of them well enough to write confidently, but others here have already found my limits elsewhere. I think what I'll do is write up stuff for the ones I know and then ask others to fill in the gaps.

    Who knows... Maybe the book we were planning to write could contain a collection of articles along with it describing opposing systems.

    -Dream Big.
    --Grow Up.
    [ Parent ]

    Representation is an important issue (5.00 / 1) (#19)
    by sebpaquet on Tue May 07, 2002 at 12:36:59 PM EST

    Nice, original article, although I must admit I didn't understand all of it. It would be nice to see examples/applications of your framework.

    The way we represent things largely determines what we will be easy and hard to do with them. Most outstanding thinkers usually have several ways of seeing the same thing, and are able to shift from one to the other according to where they're trying to go. For instance, almost every problem in physics can be stated in several ways. If you use the right description the solution follows naturally; if you don't, you could be in for hard work.

    You made an important point in stating that practitioners are often not aware of there being this additional "layer" of representation between themselves and objects. And I'd be inclined to add that they can become entraped in the particular layer they grew up in and learned by example (rather than by specification). At times someone will begin representing an object in a way that is fundamentally different and not strictly equivalent to previous ways of seeing it. The implications of the new view are not the same as those associated with the old. An example is the shift from geocentrism to heliocentrism, or from Newtonian mechanics to relativity theory. When the new view better matches reality, and if this comes to be widely recognized, a paradigm shift occurs. I recommend the excellent book "The Structure of Scientific Revolutions" by T.S. Kuhn for an in-depth look at how such important events are lived by scientific communities.

    When you think about it, computer science is all about representations. The physicist or biologist typically thinks he's dealing with objects and so pays little attention to this issue. Knowledge about representations is somehow kept tacit. When the computer scientist comes into the picture, he is faced with the difficult task of unearthing tacit knowledge and making it explicit. And often has to make choices that the physicist never thought about.

    All this borders on philosophy - a fascinating topic if you ask me.
    Seb's Open Research - Pointers and thoughts on the evolution of knowledge sharing and scholarly communication.

    philosophy (4.00 / 1) (#24)
    by adiffer on Tue May 07, 2002 at 05:40:23 PM EST

    I usually get sour looks from other physicists when I bring this topic up because it is so close to philosphy. I think it is a shame we have distanced ourselves so much from our roots as natural philosophers.

    I also think a good house cleaning should be done by us regarding how we choose to represent stuff. The only physicist that interacts directly with the object is an experimentalist who then interprets their results in terms of the observables. The rest of us are playing games for which we should be able to write the rules. Rules lead to algorithmic thinking and suddenly (bang!) the theoreticians will have a powerful new tool to help them out.

    Fun stuff.

    -Dream Big.
    --Grow Up.
    [ Parent ]

    classic example (5.00 / 1) (#29)
    by martingale on Tue May 07, 2002 at 09:21:29 PM EST

    The way we represent things largely determines what we will be easy and hard to do with them.
    The classic example of this is the old Newton/Leibniz flamewar regarding derivatives. Newton wrote f', f" etc for the derivative of f, while Leibniz invented df/dx etc. Same concept, but Leibniz' notation was way more useful for hundreds of years. More geometric. You could write df/dy = (df/dx)(dx/dy) which is really intuitive. It had some problems with infinitesimals, but that's been solved. Newton's notation only became interesting/useful last century with the push into functional analysis.

    Most outstanding thinkers usually have several ways of seeing the same thing, and are able to shift from one to the other according to where they're trying to go.
    I agree completely with you on this one. This is perhaps the most important lesson, but unfortunately it takes years to assimilate, simply due to the sheer number of alternatives to be mastered. But fortunately, people can still contribute even if they are ignorant of some or most of the alternative viewpoints.

    [ Parent ]
    Bad examples (4.00 / 1) (#20)
    by KWillets on Tue May 07, 2002 at 02:34:51 PM EST

    I'm afraid the concepts presented are not very clear, and the examples are lacking in clarity and validity.

    The "vector" method describes the process of assigning coordinates by projection onto basis vectors, skipping the concept of a perpendicular space and ending up with (I hope) two points to describe a line segment.

    The "algebraic" method assigns coordinates in an equivalent space, which apparently doesn't require projection or much of any process to find coordinates. The result is a line segment which is claimed to be described by "a function", but is really the image of a closed interval under a function. This image is itself a line segment, consisting of endpoints and every point in between, unlike the "vector" method.

    Why these representations are different is more due to confusion than any real difference in representation.

    Likewise the concepts of symmetry, invariance, conservation laws, and the like have been studied in detail by Physicists and Mathematicians for centuries. If the claim is that mathematically unsophisticated students have difficulty understanding the different descriptions, I have no quarrel with that, but I would suggest a bit of guidance from, say, a Mathematical Physicist.

    thanks (none / 0) (#23)
    by adiffer on Tue May 07, 2002 at 05:29:44 PM EST

    My examples could use some improvement. I just made them up yesterday as a response to an earlier editorial comment. I'll bullet-proof them before anything goes in the book.

    To the physicists, these representations are different. They hard to grasp for the beginning students largely because we don't talk much about how we do it. We just provide some examples and expect the students to imitate them long enough to get it right. Even the more experienced physicists rarely think about representation. The biggest hurdle the string theory folks face in getting a successful theory adopted by the rest of us is getting us to not look too closely at the space they concoct to get testable hypotheses that survive experimentation. I know plenty of physicists who reject the string theory approach simply because they can't accept the solution space being offered.

    -Dream Big.
    --Grow Up.
    [ Parent ]

    From a Mathematical standpoint (none / 0) (#28)
    by KWillets on Tue May 07, 2002 at 08:36:52 PM EST

    Physicists are notorious abusers of notation. Part of what mathematicians do is to clean up and simplify the gobbledygook that physicists produce. If what physicists think up were not so significant, mathematicians would be happy to ignore them.

    The reasons for this situation are many, but the main one is that experiment is more important in Physics than formal elegance. Making things up as one goes along is a useful practice, and you're correct that students are usually not aware of it.

    Physics teaching is the art of compressing millenia of thought into a few months' time, and I'm afraid that much of the process of doing Physics is distilled out. I learned the same thing when I TA'd a Calculus class; this subject is one of the most random collections of Mathematical subfields I've run across. There's no structure to the topic except that each piece has proven useful in some area not related to Mathematics.

    [ Parent ]

    How true (none / 0) (#34)
    by adiffer on Wed May 08, 2002 at 05:06:27 PM EST

    Physicists are to mathemeticians what engineers are to physicists. 8)

    At the conferences I've attended, that is exactly what the mathemeticians thought of us. They work so hard coming up with elegant systems that actually work and we butcher them for the sake of practicality.

    If you take the side of the mathemeticians, you will howl at my next installment. Just remember that I know and accept my place. 8)

    -Dream Big.
    --Grow Up.
    [ Parent ]

    dirty engineers (or students, like me) (none / 0) (#37)
    by superflex on Wed May 22, 2002 at 03:50:37 PM EST

    bwa ha ha ha! yes! we destroy your beautiful mathematics! i laugh with glee every time i truncate a Taylor series approximation of a function at the 5th or 6th term because it's "close enough". inverse Laplace/Fourier transforms!? who cares! we've got tables you guys made for us! region of convergence!? bah! you guys can take your real and/or complex analysis and stick it where the sun don't shine!

    [ Parent ]
    Representing objects and properties in Physics | 39 comments (24 topical, 15 editorial, 1 hidden)
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