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andytoh

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andytoh

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- #2

neutrino

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No way. Even though non-mathematicians may not learn the proofs, they still need to learn from a quality source, and more importantly,a pedagogical source. You don't see that in Wikipedia. It is a bunch of articles, written by different people, that are being edited almost on a daily basis. Some articles may be rigorous, while others may be much less so. Wikipedia in most cases (or all?) does not even provide you any insights. You can't say the same thing about a book like Boas'. Even if it so happened that you had no option but to choose a web source, I would recommend a site like Mathworld, Planet Math, or Hyper-Math over Wikipedia.

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- #3

andytoh

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- #4

las3rjock

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That pretty much sounds like a description of the text of Boas or Arfken and Weber...can a physicist learn his math tools from an informal source that gives definitions, qualitative explanations, simple examples, and states the most important results. No exercises, proofs, or rigorous treatment. Just learn the hardcore facts.

- #5

arunma

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- #6

neutrino

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What's the use then? No proofs, no exercises, no use*. Its sounds more like one of those books with integral tables and such.Ok, what I meant was: can a physicist learn his math tools from an informal source that gives definitions, qualitative explanations, simple examples, and states the most important results.No exercises, proofs, or rigorous treatment. Just learn the hardcore facts. Wikipedia was just the first example I thought of.

*To someone who wishes to become a physicist.

- #7

JasonRox

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What's the use then? No proofs, no exercises, no use*. Its sounds more like one of those books with integral tables and such.

*To someone who wishes to become a physicist.

Just extra jargon a crackpot can use in his proofs.

From the mathematical model so-and-so we see that the big bang was contructed through the continuous dynamical so-and-so.

Note: And the funny part is when it comes to a crackpot, is that because he learned on the mathematics on Wikipedia and did no exercises or proofs. He has no idea how to apply. So it's no surprise that when a crackpot puts "mathematics" into his "model" it makes no sense.

- #8

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Compare Wikipedia with (1) Mary Boas's "Mathematical Methods in the Physical Science" and (ii) Arfken's "Mathematical Physics". One would be out of one's mind to dump those two in favor of a very

This fascination and obsession with Wikipedia needs to go out of fashion very quickly.You also have a very strange understanding about "mathematics" and the

Zz.

- #9

Quaoar

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I personally find http://mathworld.wolfram.com/" [Broken] to be a very valuable resource, and much more reliable than Wikipedia.

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- #10

las3rjock

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I consider learning to use a book like Abramowitz & Stegun or Gradshteyn & Ryzhik to be one of the milestones in a physicist's professional development.What's the use then? No proofs, no exercises, no use*. Its sounds more like one of those books with integral tables and such.

*To someone who wishes to become a physicist.

- #11

neutrino

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I consider learning to use a book like Abramowitz & Stegun or Gradshteyn & Ryzhik to be one of the milestones in a physicist's professional development.

I didn't say it wasn't. :) We are discussing a milestone that comes before one starts using such resources. In a sense, it's like learning to play the violin and learning to play a tough musical piece on the violin.

- #12

radou

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I hate to say it, but nothing beats a textbook.

You don't need to hate to say it, since it absolutely true.

- #13

andytoh

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So now I ask if physicists can use an informal source to learn the math tools, a source that avoids the rigour and gives the basic facts, results, and a nice general overview. And now you guys are saying that it's not enough, you must study from a textbook, contradicting the first answer.

- #14

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So now I ask if physicists can use an informal source to learn the math tools, a source that avoids the rigour and gives the basic facts, results, and a nice general overview. And now you guys are saying that it's not enough, you must study from a textbook, contradicting the first answer.

Since when is a rigorous study of the TECHNIQUE implies one way or the other?

Think of a tradesman building a house. Do you think it is fine to grab someone off the street, tell this person what each tool does, and then let him go build a house? If you think this is fine, I'd like to build your next house, and I'm CHEAP!

You have to LEARN how to use mathematics properly. Mathematics is not a subject in which you can simply sit back and read! It requires SKILL. You need to have a FEEL for the mathematics to know what to do and what not to do. These techniques should almost be automatic by the time you have to use it in solving a problem. You do not get such skills simply by reading!

For some odd reason, you simply refuses to look into one of the mathematical physics texts that I've mentioned here and previously elsewhere. Why don't you? You seem to have such difficulty grasping what really is required as far as mathematical skills goes for physicists. Why won't you open these texts and see for yourself to what extent is the mathematics skills and knowledge that is needed here? You could have saved a lot of time and effort by simply satisfying this curiosity yourself.

There IS a LARGE SPACE in between "Learn proofs from ground zero" to "learn mathematics simply by reading Wikipedia". I can't believe that you only think that there are only these two extremes that exist.

Oy!

Zz.

- #15

AlephZero

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And Wikipedia is an incomplete "dictionary" with lots of typos...

Wiki is OK for quick reference, provided you know enough to spot the mistakes - at least the truth of maths propositions are not a matter of opinion, unlike some other parts of Wiki. But it's not a teaching tool, and not intended to be one.

- #16

nrqed

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So now I ask if physicists can use an informal source to learn the math tools, a source that avoids the rigour and gives the basic facts, results, and a nice general overview. And now you guys are saying that it's not enough, you must study from a textbook, contradicting the first answer.

Doing physics is a bit like playing violin. The physics is analogue to th emusic produced and the maths are analogue to the instrument being used, the violin. It is NOT enough to read about what a violin is and the basic idea of how it is used to play music if you want to become a violonist! You have to PRACTICE. It's as if you are talking about becoming a violonist just by reading about the principles of how a violin is played on Wikipedia. If you are then handed a violin, you will not get anything worthwhile out of it this way! You would have to practice for thousand of hours before being good at playing. The same thing for maths in physics. You have to do thousands of exercises and calculations before you start mastering enough the maths to be able to actually use them to do physics.

- #17

Crosson

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You have to do thousands of exercises and calculations before you start mastering enough the maths to be able to actually use them to do physics.

This is simply not true, a few well thought out exercises are often sufficient to be able to work out any future cases which one encounters.

very dubious and unverified source that Wikipedia is.

We are talking about Math, why should we be concerned with figures of authority? If an equation from wikipedia contains errors, big deal, you can see them and you can fix them when things don't make sense, this is an important skill for physicists. Anyone who blindly obeys Arfken without mentally testing the formulae for sensibility is in danger of making an error, just as is the case with Wikipedia.

If we are talking about students, then who cares if what they learn is incorrect in some minor detail? Will their skills evaporate when the detail is corrected? Unlikely, in fact any time spent concentrating is good for the student, even if the object of their concentration contains elements of nonsense/incorrectness.

This phenomenon of established authority figures bashing wikipedia has got to stop. Physicist are no longer human computers, and absolute correctness need not be such a high priority as it was in the last generation, those details can easily be checked in any case that "actually matters".

To the OP, I would answer that yes, one can gain the knowledge of a working physicist with an undergraduate education from wikipedia alone. This is because (in America) the undergraduate experience is merely backround information to prepare one for on the job training.

In the same vein, I know professors of Mathematics who have far less general knowledge then would a student of wikipedia, and whose research is a sham designed to maintain a career built off of what they got out of their graduate advisor. In this sense, Wikipedia is better than good enough for some mathematicians.

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- #18

andytoh

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After making a side by side comparison of wikipedia and mathworld, I find wikipedia to be much more thorough in content, examples, and links. I don't know why people here are bashing out at wikipedia so much. Is it because wikipedia is for the general public, while mathworld is not?

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- #19

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After making a side by side comparison of wikipedia and mathworld, I find wikipedia to be much more thorough in content, examples, and links. I don't know why people here are bashing out at wikipedia so much. Is it because wikipedia is for the general public, while mathworld is not?

Are you hijacking your own thread?

If you wish to talk about the "validity" of wikipedia, please join the existing threads in General Discussion.

Zz.

- #20

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We are talking about Math, why should we be concerned with figures of authority? If an equation from wikipedia contains errors, big deal, you can see them and you can fix them when things don't make sense, this is an important skill for physicists. Anyone who blindly obeys Arfken without mentally testing the formulae for sensibility is in danger of making an error, just as is the case with Wikipedia.

Are you saying what I think you are saying? Are you putting texts such as Arken on the SAME level on the same topic that you find in Wikipedia?

If we are talking about students, then who cares if what they learn is incorrect in some minor detail? Will their skills evaporate when the detail is corrected? Unlikely, in fact any time spent concentrating is good for the student, even if the object of their concentration contains elements of nonsense/incorrectness.

I'm sorry, but this is nonsense. Any instructor can tell you the pain and suffering one has to go through in correcting wrong information and impression that a student has gained.

This phenomenon of established authority figures bashing wikipedia has got to stop. Physicist are no longer human computers, and absolute correctness need not be such a high priority as it was in the last generation, those details can easily be checked in any case that "actually matters".

This is highly dubious. It is the DETAILS that differentiate between a superficial knowledge of something and understanding something well. And what exactly would one use to "check" these details, since you have dismissed "authority figures".

To the OP, I would answer that yes, one can gain the knowledge of a working physicist with an undergraduate education from wikipedia alone. This is because (in America) the undergraduate experience is merely backround information to prepare one for on the job training.

Right.. and we really don't care if your background information is correct or not.

In the same vein, I know professors of Mathematics who have far less general knowledge then would a student of wikipedia, and whose research is a sham designed to maintain a career built off of what they got out of their graduate advisor.

This is absurd. You are using anecdotal instances and exceptions, and turning them into a rule.

Zz.

- #21

AngeloG

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Once you get into specific areas of Physics; each his it's own separate language to go with it essentially. Such as Calculus is really the "language" of classical/general physics. But later down the road you may use tensors, you may use different things. You really can't get this from Wikipedia.

- #22

andytoh

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Once you get into specific areas of Physics; each his it's own separate language to go with it essentially. Such as Calculus is really the "language" of classical/general physics. But later down the road you may use tensors, you may use different things. You really can't get this from Wikipedia.

I disagree. I first studied tensors years ago. Then couple of years later I studied tensors again and was confused at how different it was. I was never given an explanation of the reason for the difference, but accepted it nevertheless. Only last year did it all make sense to me, thanks to wikipedia:

"There are equivalent approaches to visualizing and working with tensors; that the content is actually the same may only become apparent with some familiarity with the material.

The classical approach

The classical approach views tensors as multidimensional arrays that are n-dimensional generalizations of scalars, 1-dimensional vectors and 2-dimensional matrices. The "components" of the tensor are the values in the array. This idea can then be further generalized to tensor fields, where the elements of the tensor are functions, or even differentials.

However, to count as a tensor, the arrays need to transform correctly when the reference co-ordinate system is changed. This transformation is a generalisation of the relationship which holds for vector components, and is similarly an expression of the independence of the underlying entity from the reference frame in which it is expressed.

The modern approach

The modern (component-free) approach views tensors initially as abstract objects, expressing some definite type of multi-linear concept. Their well-known properties can be derived from their definitions, as linear maps or more generally; and the rules for manipulations of tensors arise as an extension of linear algebra to multilinear algebra. This treatment has attempted to replace the component-based treatment for advanced study, in the way that the more modern component-free treatment of vectors replaces the traditional component-based treatment after the component-based treatment has been used to provide an elementary motivation for the concept of a vector. You could say that the slogan is 'tensors are elements of some tensor space'. Nevertheless, a component-free approach has not become fully popular, owing to the difficulties involved with giving a geometrical interpretation to higher-rank tensors.

The intermediate treatment of tensors article attempts to bridge the two extremes, and to show their relationships.

In the end the same computational content is expressed, both ways. See glossary of tensor theory for a listing of technical terms."

- #23

mathwonk

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i thought the question was " can a physicist learn?" and wanted to hear the opinions.

JUST KIDDING GUYS! I KNOW PHYSICISTS ARE SMARTER THAN US PURE MATH TYPES.

no need to tap dance on my head, but it is allowed.

JUST KIDDING GUYS! I KNOW PHYSICISTS ARE SMARTER THAN US PURE MATH TYPES.

no need to tap dance on my head, but it is allowed.

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- #24

andytoh

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"There are various equivalent ways of defining the tangent spaces of a manifold. While the definition via directions of curves is quite straightforward given the above intuition, it is also the most cumbersome to work with. More elegant and abstract approaches are described below.

Definition as directions of curves

Suppose M is a Ck manifold (k ≥ 1) and x is a point in M. Pick a chart φ : U → Rn where U is an open subset of M containing x. Suppose two curves γ1 : (-1,1) → M and γ2 : (-1,1) → M with γ1(0) = γ2(0) = x are given such that φ o γ1 and φ o γ2 are both differentiable at 0. Then γ1 and γ2 are called tangent at 0 if the ordinary derivatives of φ o γ1 and φ o γ2 at 0 coincide. This defines an equivalence relation on such curves, and the equivalence classes are known as the tangent vectors of M at x. The equivalence class of the curve γ is written as γ'(0). The tangent space of M at x, denoted by TxM, is defined as the set of all tangent vectors; it does not depend on the choice of chart φ.

To define the vector space operations on TxM, we use a chart φ : U → Rn and define the map (dφ)x : TxM → Rn by (dφ)x(γ'(0)) = (φ o γ)'(0). It turns out that this map is bijective and can thus be used to transfer the vector space operations from Rn over to TxM, turning the latter into an n-dimensional real vector space. Again, one needs to check that this construction does not depend on the particular chart φ chosen, and in fact it does not.

Definition via derivations

Suppose M is a C∞ manifold. A real-valued function f : M → R belongs to C∞(M) if f o φ-1 is infinitely often differentiable for every chart φ : U → Rn. C∞(M) is a real associative algebra for the pointwise product and sum of functions and scalar multiplication.

Pick a point x in M. A derivation at x is a linear map D : C∞(M) → R which has the property that for all f, g in C∞(M):

D(fg) = D(f)·g(x) + f(x)·D(g)

modeled on the product rule of calculus. These derivations form a real vector space in a natural manner; this is the tangent space TxM.

The relation between the tangent vectors defined earlier and derivations is as follows: if γ is a curve with tangent vector γ'(0), then the corresponding derivation is D(f) = (f o γ)'(0) (where the derivative is taken in the ordinary sense, since f o γ is a function from (-1,1) to R).

Definition via the cotangent space

Again we start with a C∞ manifold M and a point x in M. Consider the ideal I in C∞(M) consisting of all functions f such that f(x) = 0. Then I and I 2 are real vector spaces, and TxM may be defined as the dual space of the quotient space I / I 2. This latter quotient space is also known as the cotangent space of M at x.

While this definition is the most abstract, it is also the one most easily transferred to other settings, for instance to the varieties considered in algebraic geometry.

If D is a derivation, then D(f) = 0 for every f in I2, and this means that D gives rise to a linear map I / I2 → R. Conversely, if r : I / I2 → R is a linear map, then D(f) = r((f - f(x)) + I 2) is a derivation. This yields the correspondence between the tangent space defined via derivations and the tangent space defined via the cotangent space."

- #25

hrc969

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I don't know what books you looked at but from the ones I have, Kuhnel's Differential Geometry, Lee's Introduction to smooth manifolds, Abraham,Marsden and Ratiu's Manifold, Tensor Analysis and Applications all have discussions about some of the several definitions, 3 or 4 different ones each. Abraham's book refers to Spivak's for more information. I have also seen this in several of my Riemannian geometry books (though only as a comment, but that's still better than not pointing anything out.) You probably need to get better books.Here's another example. I studied the tangent space of a manifold from 3 different textbooks, each presenting it in different ways, which confused the hell out of me. Of course, no explanation was given for the different presentations...until Wikipedia explained it to me:

Also the professor for my Manifold theory course went over this as well. He even warned us on the syllabus that the concept of a tangent vector is often the most difficult in the course. Then again this was one of the better geometry professors at my school, so I'm sure that made a difference.

You may find that some of the articles on wikipedia are OK, maybe some are even good. But you can probably always get a better explanation from a good textbook and almost always a better explanation from a good professor (who studies this field).

EDIT:Let me add that if a physicist or mathematician wanted to learn about several complex variables, say in order to later study complex or kahler geometry, they could not do so by going to wikipedia.

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- #26

arevolutionist

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- #27

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I disagree. I first studied tensors years ago. Then couple of years later I studied tensors again and was confused at how different it was. I was never given an explanation of the reason for the difference, but accepted it nevertheless. Only last year did it all make sense to me, thanks to wikipedia:

Look, you ASKED, and a number of us have given you the answer. If you don't care about it and still think you can be a physicist with using only Wikipedia, then I am not going to try to save you from yourself.

Good luck!

Zz.

- #28

Astronuc

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:surprised :surprised :surprisedCan a physicist learn his math tools from wikipedia alone?

Good analogy.

And Wikipedia is an incomplete "dictionary" with lots of typos...

Wiki is OK for quick reference, provided you know enough to spot the mistakes - at least the truth of maths propositions are not a matter of opinion, unlike some other parts of Wiki. But it's not a teaching tool, and not intended to be one.

Wikipedia is should not be used as a primary learning tool for the novice. I reiterate what others have already stated - get ye some good texts books which have been peer reviewed and subject to quality control. That's not to say there aren't errors, but there is less likely errors in a controlled source than in an uncontrolled source that can be edited by anyone.

You've more or less answered your question. Would you have understood the material in Wikipedia without prior study of the math? No single source is adequate.andytoh said:I studied the tangent space of a manifold from 3 different textbooks, each presenting it in different ways, which confused the hell out of me. Of course, no explanation was given for the different presentations...until Wikipedia explained it to me:

- #29

AngeloG

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A lot of these people try to disprove the basic laws of physics and other things. I've seen people try to argue that these laws are wrong and incorrect. And many of you also see these types of documents & posts =p. Many of their arguments fail because of their math or their general thinking.

- #30

neutrino

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Or the lack of either.Many of their arguments fail because of their math or their general thinking.

- #31

fasterthanjoao

- 729

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I've tried, on occasion, to pick up new techniques through this avenue - it doesn't work. Whilst I note this, I also must say that I do believe there's a certain number of levels on which Wiki can contribute. Of course there's the obvious refreshers - no doubt that this is a valuable resource for difficult problems - I would say that upper undergraduate level problems should *only* be observed when you already have an idea of how it works.

For low level undergraduate work, whilst the same may apply, generally the Wikipedia pages are notably more comprehensive and easier to follow - mostly because Wikipedia by nature stores separate problems in different pages. After covering enough physics/mathematics, you'll certainly note that this isn't the way things will be learned.

The solution to uncountable numbers of physics problems is a result of the application of various techniques - thus to fully understand a single issue, one must understand various others.

Finally, I feel not the need to mention much about the fact that Wikipedia is lacking in the most important part of a physicists work, the problems! Throughout most of my undergraduate time, there were at least several courses that I struggled to follow reading lecture notes along (I'd personally be very surprised if this wasn't the case for most people) - problems provide the application and real-life situations you need to get that extra level of understanding.

- #32

theperthvan

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I used wikipedia the other day to refresh myself on the photoelectric effect

- #33

Crosson

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Are you putting texts such as Arken on the SAME level on the same topic that you find in Wikipedia?

Not two things are the same, Z, for if they were their would be one thing. And besides this, no two things in the physical world, much less the social world (utuility as a physics reference), are ever equal.

Yes, Arfken is better then wikipedia; it is even 100$ better, as the price difference between the two indicates. But this is only to say that Arfken is good, not that wikipedia is bad. If the choice for a particular topic is between wikipedia and nothing, than wikipedia is the clear winner, even if some articles contain errors.

I'm sorry, but this is nonsense. Any instructor can tell you the pain and suffering one has to go through in correcting wrong information and impression that a student has gained.

Students like to moan and complain whenever possible, no instructor should embrace this. If you are really having trouble, try explaining to the student why their are misconceptions about the topic, this makes them feel smarter then the author who was wrong and so they respond well, and forget to complain.

This is highly dubious. It is the DETAILS that differentiate between a superficial knowledge of something and understanding something well. And what exactly would one use to "check" these details, since you have dismissed "authority figures".

And I maintain the details are learned on a case by case, in the field, sink or swim method. Not from school learning, which really only has the purpose of familiarizing ourselves enough to be comfortable.

Right.. and we really don't care if your background information is correct or not.

Like I said, once someone is confortable with magnetic fields and laplaces equation in general, they will find it easy to learn/relearn the Garnett treatment of cylindrically symmetric magnetic coil configurations as applied to the equipment they work with.

This is absurd. You are using anecdotal instances and exceptions, and turning them into a rule.

I don't understand, you think existential generalization is absurd?

Let [tex]Sx[/tex] be the statement "x is a shoddy proffessor". Then if my professor is named [tex] p [/tex], then I am using the deduction that:

[tex] Sp \Rightarrow (\exists x) (Sx) [/tex]

- #34

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Not two things are the same, Z, for if they were their would be one thing. And besides this, no two things in the physical world, much less the social world (utuility as a physics reference), are ever equal.

Yes, Arfken is better then wikipedia; it is even 100$ better, as the price difference between the two indicates. But this is only to say that Arfken is good, not that wikipedia is bad. If the choice for a particular topic is between wikipedia and nothing, than wikipedia is the clear winner, even if some articles contain errors.

I disagree. Since you seem to think that anecdotal evidence is valid, then I can bring out many examples of anecdotal evidence out of Wikipedia in which nothing is better than wrong information. I have pointed out a long time ago about the errors in the Accelerator Physics section (which someone later on got wind and "corrected" it). So using my anedotal evidence and using your logic, I can make an "existential generalization" to deduce that the whole of Wikipedia is crap.

If you think this is illogical, look at what you're doing.

Students like to moan and complain whenever possible, no instructor should embrace this. If you are really having trouble, try explaining to the student why their are misconceptions about the topic, this makes them feel smarter then the author who was wrong and so they respond well, and forget to complain.

But you seem to think that instructors have all the time in the world to babysit a student's misconception. Considering that most physics instructors have to (i) deal with the subject matter to be covered (ii) often have to teach the mathematics at the same time, the last thing they need is to correct misconception that should never have happened in the first place IF the students had paid attention to more legitimate sources.

Having taught undergrad intro physics class myself, AND discussion with many physics instructors, I find that this is something that makes very inefficient use of the lessons, especially when it shouldn't happen in the first place. You, on the other hand, find nothing wrong with it.

And I maintain the details are learned on a case by case, in the field, sink or swim method. Not from school learning, which really only has the purpose of familiarizing ourselves enough to be comfortable.

Like I said, once someone is confortable with magnetic fields and laplaces equation in general, they will find it easy to learn/relearn the Garnett treatment of cylindrically symmetric magnetic coil configurations as applied to the equipment they work with.

Not if what they familiarized themselves with were wrong! Being comfortable with faulty knowledge is the worst thing a student can ever have. What it sends is the message that mediocrity is tolerated and that superficial knowledge is sufficient. Nothing could be further than the truth.

I think it is highly irresponsible for you to suggest that one can learn the mathematics all one needs to become a physicist from Wikipedia alone, especially when you have zero evidence of that being done successfully. You were too free with your speculation and had no qualm in turning them into definite statements. Considering that there ARE students in here who do pay attention to what is being said in this forum, I cannot believe that you never even consider the consequences of your actions.

Unless you have sufficient evidence of such a thing being done successfully as per the issue in the OP, I consider such statements as overly speculative and subject to our global Guidelines.

Zz.

- #35

andytoh

- 359

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I never meant for two science advisors to be arguing like this.

Perhaps I should have rephrased my opening post. Since my other thread "Should a physicist study math proofs" led to the conclusion that physicists don't have the time to study math so rigorously, I was wondering if they could they give themselves a crash lesson on a new math tool from wikipedia if they did not have the time to learn the new math tool from a textbook and do exercises from it. Also, in the opening post I was making the assumption that Wikipedia's content is accurate.

Perhaps I should have rephrased my opening post. Since my other thread "Should a physicist study math proofs" led to the conclusion that physicists don't have the time to study math so rigorously, I was wondering if they could they give themselves a crash lesson on a new math tool from wikipedia if they did not have the time to learn the new math tool from a textbook and do exercises from it. Also, in the opening post I was making the assumption that Wikipedia's content is accurate.

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