User talk:Catherine Woodgold

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Welcome

Tasks: start a new article • add basic, wanted or requested articles • add definitions • add metadata • edit new pages

Welcome to the Citizendium! We hope you will contribute boldly and well. Here are pointers for a quick start, and see Getting Started for other helpful "startup" links, our help system and CZ:Home for the top menu of community pages. You can test out editing in the sandbox if you'd like. If you need help to get going, the forum is one option. That's also where we discuss policy and proposals. You can ask any user or the editors for help, too. Just put a note on their "talk" page. Again, welcome and have fun!

You can find some more information about our collaboration groups if you follow this link CZ:Workgroups.You can always ask me on my talk page or others about how to proceed or any other question you might have.

Kind Regards, Robert Tito |  Talk  17:48, 4 April 2007 (CDT)

Economics

As for Jan Pen's book "Modern Economics" its economics is not as modern as the title implies; most of it is an updated re-explanation of what had been already published. If you like the subject, try STIGLITZ, you can read some articles online for free:

• STIGLITZ, Joseph. More Instruments and Broader Goals: Moving Toward the Post-Washington Consensus. The 1998 WIDER Annual Lecture. Helsinki, Finlândia, 07/1/1998.
• STIGLITZ, Joseph E. There is no invisible hand. London: The Guardian Comment, December 20, 2002.

Articles badly in need of proof reading: Economics, History of Ancient Economics, Keynes, Paul Samuelson, Asimakopulos.

To understand the basic principles of Economics

• ECONOMICS 100 ONLINE. Department of Economics at the University of Toronto<copyright K.J. Rea, 2000-2003 all rights reserved>. (A great "primer" to understanding the basic principles of Economics).

The article Economic Theory which should deal with those topics is still not written on CZ. To understand the basic principles of Economics meanwhile I suggest the reading of ECONOMICS 100 ONLINE by the Department of Economics at the University of Toronto. It is a gret "primer" for helping anyone to understand Economics. (contents copyright K.J. Rea, 2000-2003 all rights reserved)

Economics has been completely re-arranged...

Many of your suggestions have been incorporated. The article has been sub-divided. Please feel free to edit any of it. J. R. Campos 11:06, 10 April 2007 (CDT)

Hélas ! Finally somebody is writting on Economic Theory; we already have Supply and demand !

You are very welcome

Please feel free to edit whatever you feel is worth editing. Your editions definitely improved the level of my articles J. R. Campos 11:20, 15 April 2007 (CDT)

Infant growth and developmeny

Really appreciate your correction of spelling errors. On the other hand, please discuss changing of sentences. Of course the baby can be hurt unless the head is molded, but if the mother did not walk upright she could easily have a pelvis that provided a larger opening, and although that needs to be made clearer, changing the wording simply to the "baby emerges" loses the concept entirely. Similarly the way the muscle process sentence is now written it may sound better, but the meaning is not correct, it appears as if the muscle and bone have some kind of conscious arrangement with each other. I know that sentence was lousy, as I said, I was writing it rough. Could you kindly put your suggestions for a better phrase or sentence on the talk page rather than just changing the article? thank you, Nancy Sculerati 14:44, 15 April 2007 (CDT)

It's ok to "be bold" and edit articles. If the new edit loses some meaning, it will get modified further and improve the sentence even more. keep writing!! -Tom Kelly (Talk) 15:42, 15 April 2007 (CDT)

When in doubt, take it to talk. Stephen Ewen 16:52, 15 April 2007 (CDT)

Hm, it seems Nancy and Tom are disagreeing here. I think they are both right, however. Particularly in the context of a well-developed article like Biology, Nancy is right to say that, if what might have seemed to be a copyediting change actually changes the meaning of a sentence, it is better to make suggestions on the talk page. I do this myself all the time, and I highly recommend it. Tom, however, is right to imply that it is possible to take this practice to an extreme. It's hardly as though you need to get permission for every edit. Often, maybe usually, it's better simply to go ahead and make the change. If people didn't do this quite often, nothing would ever get done!

It's an art, not a science. --Larry Sanger 16:54, 15 April 2007 (CDT)

Yes, I agree with Dr. Larry Sanger. The other thing to consider is that Dr. Nancy Sculerati would have improved the sentence later -- She is one of the most active writers on CZ and helps edit/copy edit many, many articles. She has a great command of the English language. Everyone is very busy and we often write draft versions and get back to correcting them later. It's great when people contribute when we are away, however. I was just trying to keep spirits high! Go team, "break" (common American-sports hundle closing expression) -Tom Kelly (Talk) 17:36, 15 April 2007 (CDT)

I can get touchy, and I apologize, myself. thanks for reaching out, Nancy Sculerati 10:02, 18 April 2007 (CDT)

Life is alive

Life has now moved along so that content editing is possible. Yes I do recognise version 1.1 is still not actioned, but it can be. Actually it would do good for you to start talking and doing changes for version 1.2. It would make people realise why your proof argument which is very similar to mine opinions is worth implement at least in part, or as an equivalent policy. In any case don't hold back, but my advice is to make small suggestion and concentrate one one part of Life at a time. But also do the research. I do know about limit cycles and chaos theory, and attractors, but what is need is specif example where they have been applied to life. The actual understanding of say, metabolism is hardly up to the ambitions of the mathematicians and computer modellers. I suspect they are concepts for other articles. We need also bridges to the primary biology literature. David Tribe 20:05, 21 April 2007 (CDT)

complex number comments

I tried to reply to your thoughtful comments on Talk:Complex number with inline indented comments. I'm not sure how well it came off. Greg Woodhouse 21:12, 22 April 2007 (CDT)

Approval Editor Assistant

Catherine, I don't know if it would interest you to assist me as a copyeditor? I need someone reliable to copyedit me, and to handle list announcements. Are you interested? Nancy Sculerati 19:28, 24 April 2007 (CDT)

Au contraire

Your suggestions and edits to the articles I've been working on have only improved them. I'm grateful for your input. Greg Woodhouse 23:02, 28 April 2007 (CDT)

About Primes

Hi Catherine and thanks for a reply :) I do see that the introduction only uses a symbol for mutiplication and is not difficult to follow. Of course everyone has an individual opinion. I would myself, remove any symbols from the introductory paragraph. If 3 dot 3 had to appear, I would use the words themselves, 3 times 3 equals nine, in the introductory paragraph. As the article developed, I would define and then use more symbols until a dedicated section toward the last of the article was just filled (from a newbies view) filled with symbols. I didn't know myself that prime numbers are an important part of cyphers and codes and internet technology and found that fasinating reading. But Ididn't need mathmatical proof to understand the concept laying below it. :) You know, on one hand is proof. On the other hand is the concept being talked about. I walked into the open doors where it said, "what's the use of prime numbers" and won't walk all the way over to the other side of the gymnasium where the proof guys are butting heads about symbology. lol Terry E. Olsen 10:42, 29 April 2007 (CDT)

'e' or 'a'

You may be right, but since Sébastien (sp.?) is a French name, I guess I kind of assumed it was an 'e'. Greg Woodhouse 08:18, 1 May 2007 (CDT)

well-defined

Actually, well-defined has a fairly precise meaning. Suppose we define Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbb{Z}_2} as the set of equivalence classes of integers where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} and $b$ are said to be equivalent if Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a - b} is even. Then, if we choose a representative Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a_1} of the class containing Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} , we know that there is some Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} such that Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a - a_1 = 2n} . If we choose anotherf representative, say Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a_2} , there must be an Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m} such that aFailed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle - a_2 = m} . Now, fix a Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b} . Since

$(b-a_{1})-(b-a_{2})=a_{2}-a_{1}=(a-2m)-(a-2n)=2(n-m)$

the difference between Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b - a_1} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b - a_2} is also even or, said differently, they belong to the same equivalence class. This is just another way of saying that the difference of $b-a$ is independent of the represntative we choose for the equivalence class of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} (and similarly for Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b} ). In other words, subtraction is well-defined - it doesn't depend on any arbitrary choices. Greg Woodhouse 18:10, 1 May 2007 (CDT)

well-defined take 2

Suppose we have complex function, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle say f(z) = z^2} and we want to know its integral along the unit circle Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C} (a closed path in a region where the function is differentiable). In order to do this, we need to select a function that parametrizes Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C} . One such function is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \gamma(t) = e^{it}} where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t} ranges from Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0} to $2\pi$. This is one way of parametrizing the unit circle, but by no means the only one, it is an ecample of an arbitrary choice. But having made this choice, we can write

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int_C\nolimits z^2\, dz = \int_0^{2\pi} \gamma(t)^2 |\gamma\,'(t)| dt}

The integral on the right is just an ordinary (real) integral which we can evaluate (it turns out to be 0). But what if we had chosen a different parametrizations, say Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \gamma_1} ? it turns out that Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle it doesn't make any difference} , that's what the funny looking |\gamma\,'(t)| in there is for. Intuitively, this makes sense, too: If the parametrization "slows down" we'll be picking up "more" data points (in a finite approximation, that is) the derivative will be smaller, and the two effects cancel eachother out, making the actual integral independent of the parametrization. But this is something that must be proved, and in so doing we would be showing that the integral is well-defined - there is no ambiguity in the purported definition.

Now, you asked about something else. The natural numbers (positive integers) have the property that any subset $S\subset \mathbb {N}$ has a least element. This is often expressed by saying that the order on the natural numberrs is well-founded. The property of being well-founded is different from the concept of something being well-defined.

I don't know if this helps, but being well-founded is a mathematical property, it is something that can be said to be true or false about an ordered set like Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (\mathbb{N}, <)} , but "well-defined" is a meta-mathematical concept. It isn't something that is true or false about the objects we study in mathematics, but it is something that is true or false about statements we make in the language we use to talk about mathematics. Meta-mathematics is just a fancy term for talking about mathematics.