User:SamHB/old user page

This is the user page from my first life, April 2008 to December 2008. Many links are of course incorrect.

I am suspending my activities for the duration of BRichtigen's block. SamHB 18:16, 27 December 2008 (EST)

{{welcome|SamHB}}

Math and Science

Shortly after registering at Conservapedia, I saw, in "recent changes", a change by User:CSGuy about Talk:Laplace's equation. Perhaps unwisely, I jumped right in and promised to fix that, adding two more notes there.

But before proceeding with anything, I want to know whether I will be doing the right thing. It seems that CP at one time had, as a major goal, the creation of encyclopedic articles aimed at high-school age (homeschooled and otherwise) students. Looking around, I see four very prolific contributors to this field back in early 2007 or so:

• Jaques (contribs)
• CScience (contribs)
• Noodles (contribs)
• Pixologic

But they are all gone, and no one seems to be minding the store these days. Is there some policy reason for this? Are articles of this type not something that CP is currently interested in?

I note also that there seems to be some kind of viewpoint that frowns upon complex numbers, as seen by poking around in the various mathematics articles. Is this true? If so, that would be quite unfortunate, because I wouldn't be able to put in the fact, which I consider very educational at the level of ambitious high-school students, that the real and complex components of complex analytic functions satisfy Laplace's equation.

SamHB 20:10, 2 May 2008 (EDT)

IP Proxies

My situation is somewhat similar (but not identical) to Deborah's: I have to use proxies. So, to paraphrase Deborah, Please don't block me.

Now it turns out that I have already been blocked once because of a proxy conflict:

23:40, 4 May 2008 Karajou (Talk | contribs) blocked "AnthonyT (contribs)" with an expiry time of infinite (sock of banned vandals ArnieS, FrankD, SamHB, NormanTebbitt)

If I were more thin-skinned about such things, I would be offended by Karajou referring to me as a vandal, in violation of the civility guideline. Under the circumstances, it appears to be nothing more than an incorrect assumption that the use of proxies constitues vandalism. I have never seen Deborah ever commit vandalism. Nor have I.

I may start a discussion/debate page on this subject, if I ever figure out how to start such pages. The attitude toward IP proxies appears to be badly misguided and outdated, and doesn't seem to be helping Conservapedia at all.

SamHB 14:29, 7 May 2008 (EDT)

Further thoughts on IP blocking, and blocking in general

After a lot of looking through block logs, talk pages, users' contributions, vandal edits, and various controversies, it has become clear that the policy of blocking any appearance of duplicate IP addresses is counterproductive, and a total waste of effort.

In fact, I think the entire blocking policy is being done in a nonproductive way, but that's the subject of a much longer essay in the future. But people might want to ask:

• Is the current way sysops operate actually effective in stopping vandalism?

• Is arguing over the statistical methodology leading to the conclusion that people in show business have a higher incidence of breast cancer distracting from more productive activities?

Getting back to IP blocks: They are completely counterproductive. Look through the contribution logs of the "vandals" that were accused of being socks of me -- AnthonyT, ArnieS, FrankD, and NormanTebbitt. They never committed vandalism (well, one of them used an off-color word.) Nor did I, nor did Deborah. They are not socks of me. I have no idea who any of them are.

The IP blocking policy is ostensibly in place to prevent people, who have been blocked based on the content of their edits, from evading the block by creating another ("sockpuppet") account and continuing what they were doing. A check of Wikipedia shows that they also have a policy against sockpuppets, but that it is only invoked when there is actual evidence of sockpuppetry. Such evidence is based on content and other factors, not on IP addresses.

Here in the 21st century, people use varied IP addresses for an enormous number of reasons. The internet is used from cell phones, "internet cafes", airports, corporate firewalls, and many other places that make it hard to draw conclusions about a person's identity. Drawing conclusions about who a person is based on the IP address from which they access the internet is just wrong. Anonymity is everywhere. One may not like it (the police and FBI sure don't), but it's a fact of contemporary internet life. Even the apparent policy that one has to use one's own name to create an account at Conservapedia is futile. You can't censor or police the internet!

As if that weren't bad enough in general, there is now a booming business of "anonymizing proxies" designed to get around censorship. These appear to have started as a way of circumventing the Chinese government's attempts to censor the internet. A couple of years ago I could find only about 5 such. There are now thousands, playing cat-and-mouse games with corporations, schools, and anyone else who tries to censor the internet. You can't censor or police the internet!

It appears that what connects me to AnthonyT, ArnieS, FrankD, and NormanTebbitt is that we used the same public proxy at one time or another. You can't censor or police the internet! Banning people for using the same IP address (or for saying things that sysops don't like) bans all the wrong people. Just look around at the block logs.

SamHB 22:36, 14 May 2008 (EDT)

Writing Plans, Writing Assignments, and more Mathematics

(Hi, Andy!)

It is my understanding that one is supposed to submit a "writing plan". I don't know where one submits it, so I'm putting mine here. It is also my understanding that sysops may give "writing assignments". I don't know how that is done, but feel free to put it here. Yes, here, on my user page, not the talk page. I give my permission for people to discuss things with me here.

Part of the writing plan was given above, relating to Laplace's equation. I still await instructions on that. There are a few more things I have noticed recently, relating to math. As before, I come at this from the standpoint of creating educational articles accessible to Junior-High or High-School-age people, whatever their actual educational circumstances.

• The mathematical series article, even after a sysop corrected one spelling error, still has 15 more, and 3 grammatical errors, and many statements that I question the mathematical correctness/appropriateness of. It doesn't explain how the geometric series formula works, it doesn't define alternating series correctly, and it doesn't explain their convergence criterion. These are all things that should be accessible to the target audience.
• I agree more with Andy than with DanielB on the fight over the fundamental theorem of calculus, but DanielB does have some good points. It could use more work.
• The gradient article is just wrong. Using the word "gradient" as a loose synonym for "derivative" is wrong. The gradient is a vector operation. This may not be accessible to our entire target audience, but it will be accessible to some, and we should explain it properly.

SamHB 22:23, 21 June 2008 (EDT)

You have good ideas, and we welcome educational contributions. My objection to DanielB's edits are to the extent they remove information that may be useful to a student.--Aschlafly 23:40, 21 June 2008 (EDT)

My attempt to contact Andy

The following email was sent to DeanS, while I was blocked, on July 8, 2008. I do not know whether it was ever forwarded to Andy. I apologize for the unpleasant tone of this—one says things in private email that one might not say publicly. But it appears not to have gotten through, so here it is.

[Start of email]

Dean:

Please send this to Andy. He has his mail disabled. Sorry to bother you with this, but that seems to be the way it's gotta be. I'm blocked.

Andy:

The question has come up in the "Can you contact me privately?" section of your talk page (from Jinxmchue) about the legitimacy of some rather technical edits that have been made recently. He admits to having had only "Calculus in my junior year of high school", and wants more expert advice.

Well, I can provide that advice. But I've been blocked by Ed Poor. So you're going to have to wait for a month.

In the space of 6 days, Ed Poor (with a little help from Karajou) has decimated the ranks of people trying to help out with math and science articles. (Actually, worse than decimated, if one takes the true meaning of the word. "Devastated" would be a better term.)

It appears to be quite rare for 6 experts of the caliber of

• Mathoreilly
• DanielB
• LemonPeel
• SamHB (myself)
• Fantasia
• Wandering

to be trying to help Conservapedia at the same time, but this was the lucky state of CP recently. CP had an opportunity to make great progress in this area. Admittedly, not everything was polished very well at the time of the disaster, but these were good people. I, for one, am proud of my suggestion of "advanced" templates for these articles. I thought we could actually make an educational resource that people could find their way around in, and derive great enrichment from. Not all people would get the same enrichment, of course, but with articles carefully written by experts and appropriately graded, we could do a good job.

But Ed has destroyed all that. And destroyed it amidst claims of "I have taught SAT math and I earned AP credit for calculus" and "I have a year of high school physics and a year of college physics". Those boasts are ludicrous relative to the people he was blocking! Those people were real experts! Ed needs to defer to them, and make constructive comments on their efforts, and on how well those efforts are succeeding relative to his understanding. People like these don't come by very often!

Now there are lots of things that I would object to about some of these people's contributions, and I understand that some of them have been blocked for other infractions. And some (including myself) may have been less deferential than we should have been. I don't have time to track down all the details, and I'm not going to defend all of them. But I can say that:

• Mathoreilly and LemonPeel really seem to know their stuff.
• I do too, of course :-)
• While I've had some problems with DanielB (you may recall my discussing them with you several days ago), he also seems to know his stuff reasonably well. And he did create the templates that I had suggested. He also admitted that they may not be perfect, and he solicited suggestions. I can make those suggestions. But not for a month.

If you care about the status of Conservapedia as an educational resource, you should do this:

• Get Ed to back down. I realize that you place great value on sysop loyalty, but he is being way too destructive.
• Restore the following pages that Ed has deleted: Natural logarithm and Radioactivity. I can tell you that those are topics that high school students can understand when presented correctly, as they were in my high school. We can fix them. But I need to see them. Just deleting them is simply destructive of Conservapedia's aims.

It would also be good to get an explanation from Karajou of his infinite block of Mathoreilly: "(Inserting false information: Mathoreilly needs to learn his math back in grade school, and UCLA needs to give him his money back until he does.)" This seems unduly abusive. I can't find the false information, though admittedly there is a lot to look through. I may have missed something. Perhaps he can help me out. Also, I wonder if he could provide the source of his claim that Mathoreilly needs to re-learn grade-school math, or what the UCLA reference was about. Neither of those statements is consistent with my information. And the loss of Mathoreilly is a singular disaster.

Sam.

[End of email]

An Open Letter to Ed Poor

Ed:

I hope you are well rested from your month-long vacation from people trying to improve CP's math and science educational articles.

Dare we say "save CP as an educational resource"? That characterization is quite apt, because the educational articles in this area have fallen into a deplorable state of disrepair, and the powers that be seem to be badly neglecting this important part of CP's mission.

I can assure you that I am well-rested. I have spent the month in deep and somber reflection and contemplation of my actions, as one is supposed to do when blocked. I have also surveyed the devastation, and have come up with a large number of examples of really bad writing, a few of which I have listed in the next section. Some of the bad writing was introduced quite recently (within the last month, while I was blocked and couldn't do anything) and was not reverted or repaired. It would seem that there are no active CP contributors who are qualified or motivated (I don't know which) to maintain these articles. Because of this, the quality of the math and science articles has actually declined over the last month, in addition to the problems that occurred (integration, derivative, integral, gradient, manifold, radioactivity. etc) in the days leading up to that. This is not what "building an encyclopedia" or "making substantive contributions" should mean.

One of the things I did in the last month was to check the state of educational knowledge of the relationship between "radiation" and "radioactivity", an issue that you seem to have been perplexed by here. The McGraw-Hill Children's Dictionary (ISBN 1-57768-298-X) is a resource that I would judge to be aimed at 10-year-olds, at least 6 years younger than what I think CP's target audience should be. The blurb on the back cover indicates a target audience of "elementary school through middle school". I believe that means 8- to 13-year-olds.

Their entry for radioactivity is:

The giving off of energy as a result of the decay of unstable atoms.

Uranium has a high level of radioactivity.

Their entry for radiation is:

The waves of energy sent out by sources of heat or light, or by a radioactive material.

She wore a hat to protect her skin from the radiation of the sun.

Many people are concerned about radiation from nuclear waste.

And yet the changes that you made to the page indicated that you didn't want to deal with the topic even at that introductory level. Furthermore, you made it impossible for anyone else to deal with it, by deleting the page and by blocking people. As a result, CP's page on radioactivity is not even up to the standards of the McGraw-Hill Children's Dictionary. And everyone is afraid to touch it, as though the page itself were radioactive.

In addition to the pages that were damaged by your actions of about a month ago, some more pages have deteriorated in the last month, of which I will list some below. This would not have happened if you had not driven away so many good contributors:

• Mathoreilly
• DanielB
• LemonPeel
• myself
• Fantasia
• Wandering

I have had to watch helplessly as pages were subject to inept edits.

(By the way, I'm not endorsing everything that these people did. But they were good people with good ideas, They deserved better treatment.)

It Takes a Tough Man to Make a Tender Chicken (with apologies to Frank Perdue)

Writing educational math and science articles, even at the elementary school level, requires an enormous amount of expertise, knowledge, and skill. Just knowing the subject matter at the level being taught isn't enough. One must know how to present it in a way that is both pedagogically correct for the intended audience and meticulously correct on the facts. The example below regarding "center" is a very simple example of getting it wrong.

Conservapedia had a particular influx of real experts about a month ago, and they were all driven away.

Your mischaracterization of my goals and actions makes a bad start. I never opposed those who were trying to improve math and education articles. Rather, I found that too much of the edits were misleading or confusing readers.

Articles should be accessible to homeschoolers. They need a simple introduction, and then can build on the basics to discuss advanced topics. Launching right into graduate-school or PhD. level verbiage from the start is a blatant disregard of policy and is not an improvement of anything. You may as well drop the pretense now, or you simply won't be allowed to contribute to this project.

--Ed Poor ^Talk 23:43, 8 August 2008 (EDT)

I never characterized, or mischaracterized, your goals. I do not speculate on the goals of people I do not know well. The closest I came to saying something about your goals was "indicated that you didn't want to deal with the topic [radioactivity]" It is a fact that you didn't deal with it. It is a perception on my part that the reason was that you didn't want to. If that perception was wrong, and your not dealing with it was for some reason other than that you didn't want to, I apologize.

Now I did characterize your actions. I said that you, with help from Karajou, drove away 6 contributors by blocking them. That was not a mischaracterization. It was a fact.

"I found that too much of the edits were misleading ..."

I fully agree with you! (Believe it or not, I am on Conservapedia's side, and your side when you are helping, which you often, but not always, do.)

"[articles] need a simple introduction, and then can build on the basics to discuss advanced topics"

Yes! Yes! Yes!!!! I agree fully!

"Launching right into graduate-school or PhD ..."

I agree!. I fully sympathize with this policy. But why did you put this complaint on my user page? I never did any of that. I believe that my contributions were correct, lucid, and properly pitched at the target audience. I am proud of them. Go and see for yourself.

"You may as well drop the pretense now ..."

I don't understand this. What am I pretending? Do you think I am pretending to have some expertise that I don't have? If so, you are wrong, and I am offended.

Articles that need improvement

• Center—"a point that, on average, the points of the shape are equidistant from"? If you take the average of a set of measurements, you will get just one number. Of course the result will all be the same! This is muddled thinking. A correct definition is a little more complicated, but not too much so.

• Eigenvector and Eigenvalue—Believe it or not, these concepts can be explained in a sensible, albeit elementary way, to ambitious high school students.

• Quantum mechanics—More difficult to do well, but we really can do a lot better, if you let people work on it.

There are a number of others; I won't bore you with the details. One of them was edited by someone with impressive status at CP, in a manner that seems to me to be parody, or, at the very least, not serious.

Restoring material

So what do I want from you? Ideally, I'd like you to apologize for your actions, unblock the remaining people, and indicate that you (and others) will obtain an expert consensus before deleting edits or blocking accounts in the future. But if this is not something that you are able to do, I will understand.

But I really would like you to make available the material that you deleted from Radioactivity and natural logarithm. It seems that you not only reverted the entire contents of these pages, but you deleted the entire edit history (and, ine case, the entire page), so that no one can see the former content. Please make that former content available, either by restoring the former history and then editing the current content on top of that, or by making the former content available elsewhere. Here on my user page, my talk page, your page, a subpage of something, email; anywhere. That way, I may be able to make a good decision how to proceed.

Whether I will actually do anything is another matter. If I'm going to be blocked and/or have my work deleted, there's really no point, is there?

SamHB 19:59, 5 August 2008 (EDT)

Another Open Letter to Ed Poor

Ed:

I see that you have blocked my friend and colleague DiEb. There's essentially no one left. I'm not going to contribute further. This is just an impossible place to work. I can not figure out what your vision for educational math and science articles is, or how you plan to get there, but it obviously doesn't include the 6 people named above, or DiEb.

I have done a huge amount of looking around at the various math articles, during my recent sabbatical and since then. I'd like to share my observations, and suggest how you can make things better.

A recurring claim, both here and, especially, at that other site, is that you are an ignoramus and a bully. I don't agree. After very careful reading of your edits, it is clear that you do know the material, and do have good judgment (see my comments above) about pitching it correctly to the target audience.

• Sorry, I'm going to have to violate the civility policy, and I'm going to say things that could be considered to be characterizations of your motives. I'm also going to say unpleasant things about Foxtrot. I apologize for this, but that's the way it has to be. You can block me or not—I won't be back.

I believe that you have good ideas, but you also have a tendency to bully people, and you let the latter interfere with the former. You could have done so much, but the bullying side of your internet/wiki personality (I have no idea what you are like personally; we'd probably get along fine) kept getting in the way. This is particularly sad in view of the fact that you have so much wiki experience here, at WP, and elsewhere. You could have made the educational offerings superb.

There are many places where you were on the right track, with good ideas and making good comments, and then you needlessly blew someone away. You could have just discussed the issues on article talk pages and user talk pages, encouraging people to write articles consistent with you vision. And, as I have said before, your vision is good. There was a recent case ([1]) in which you did offer helpful advice and guidance. Why didn't you do more of that, and less bullying?

There are many other places where you could have made constructive edits, or given constructive advice to others:

• Series (I discussed this above; you could have looked at it.)
• Fundamental Theorem of Calculus (ditto)
• Gradient (ditto)
• Radioactivity (Can we stop the bickering, reversions, and blocks, and restore the article, and go from there to make it a high quality article?)
• Natural Logarithm (ditto)

A good example of things going wrong is the Line segment article. I completely understand, and agree with, what you wanted. But "I suspect sabotage"?? There was no sabotage there! Nor was it, as Foxtrot claimed, a misplaced parenthesis. I was a serious misunderstanding, by Foxtrot and others, of the distinction between the geometric concepts of a line or line segment, and the arithmetic/algebra/calculus concept of what the real numbers are and why we call them the "real line". You knew that, and I knew that. You could have straightened out the mess. You could have taken Foxtrot aside and expressed your concern. Or you could even have asked me (writing assignment!) to fix it. I was busy cleaning up his mess (and it was parody) at boolean value. I knew about the line segment problem, and was going to get to it.

By the way, I notice your recent statement that you scored in the 99th percentile in the math SAT.

• There's no point in saying that; on the internet people can't check such things, so statements like that just come across as foolish bluster.
• A better way to impress people, and the only way that works on the internet, is to write well. "By their fruits ye shall know them." It took me a while to figure out that you can write well. Others never saw that, and considered you ignorant. You could have shown your positive side.
• I hope you can appreciate that many of the 7 of us also scored in the 99th percentile. As well as the advanced math and physics achievement tests, AP calculus and physics, MAA competition, Putnam competition, GRE, oral exams, thesis defense, etc.

Getting back to constructive things you can do, and that you are going to have to do without anyone's help, I would suggest that a good place to start would be to look at Foxtrot's contributions and his planned agenda. Sorry for the personal remark, but he is not a good writer at all. His center article is just garbage. And his boolean value edit was, well, "Father of logical truths"?

Then finish the Limit_(mathematics) page that DiEb and I were working on. You'll see that I did the "limit as finite X is infinite" section, but didn't get to the "limit at infinite X is finite" section. Then explain convergent sequences in terms of that. Then go to the Series_(mathematics) page (another real disaster) and connect the two concepts. Be sure to give a very careful explanation of the distinction between, and connection between, a sequence that converges to a number, and a series whose partial sums comprise a sequence that converges to a number. Then clean up the material about convergence criteria—it's full of errors and not explained well in any case.

While you are there, you might want to introduce the remarkable (to high-school students) fact that a series made up of rational numbers can converge to an irrational number. Use the fact that non-integral square roots are irrational—the thing from the ancient Greeks. (I wrote up a draft of this section a couple of weeks ago, but it will never see the light of day.) And that you can define the real numbers this way. (You and I know that as the construction by Cauchy sequences.)

While on the subject of defining the reals, go over to the Dedekind cut part of Real analysis and fix up all the errors there. It's a disaster.

Oh, and you might want to restore and fix natural logarithm and radioactivity. Just do it.

Well, that's it. Good luck. Try to play "good cop" more, OK?

I won't be contributing any more, so you don't need to block me. You are invited to show restraint.

SamHB 23:32, 26 August 2008 (EDT)

Note to self

{{Template:Math-e}}

e for early HS

m for mid HS

h for late HS or early university

a for late university/grad

My mathematics sandbox

I'm back from my 3-month vacation (1 month at the suggestion of Foxtrot, and 2 months of boycott.)

Since I'm on probation, I assume that I am not permitted to edit any mainspace articles or talk pages, so I will be doing my work here, in "sandbox" pages. If anyone in authority thinks these are acceptable for copying to the mainspace, please let me know. Please don't just copy stuff yourself—I won't get recognition in the edit history, and I'll never get out of jail.

I'm having trouble getting the nifty math equations to display. They look OK in the preview, but not in the finished product. Similar things in math pages elsewhere don't have this problem. Is it related to this being in the user page space?

Here is a test:

$a=\rho \ \cos \theta \,$

$b=\rho \ \sin \theta \,$

$\rho ={\sqrt {a^{2}+b^{2}}}\,$

$\theta =\tan ^{-1}(b/a)\,$ (with a small amount of ambiguity)

It looks fine in the preview, of course.

Sure enough, it looks fine here also. The problem is because it's a subpage. Sorry.

Complex number

User:SamHB/Complex number.

A huge rewrite, that I think puts complex numbers into the appropriate perspective in math, science, and technology. Previous writing on this subject seemed to present it in a way that I found somewhat dismissive. I have demoted some material, though I don't think I have removed anything outright. The reason is that the powers that be really don't like removal of stuff. I consider some of the material in this page to be irrelevant to a pedagogically proper presentation, and would like to take it out. I welcome discussion. Right here in the castle; it's OK. Or on the talk page. SamHB 14:33, 28 November 2008 (EST)

Complex analytic functions

A new article, to expand more on complex numbers. There is a mainspace article on this, though it is really a stub.

Laplace's equation

Another article. Something I started a long time ago; my first attempt to get into math articles.

Mathematical paradoxes

New article (Well, there is an extremely short thing at paradox, but it doesn't come close to doing justice to this topic.)

The main reason for this is to help put into perspective the "absurd result" discussion going on in the Talk:Axiom of Choice page.

Dense Subset

A rewrite of the existing article. This arose from a challenge posed to Ed Poor. See User_Talk:Ed_Poor#Dense_subset.

Function

Improvement over existing article; shows connection to "bijection", for example.

Continuity

Rewrite of the existing article. Like "Dense Subset" above, it uses multiple grading templates within one article. Note: Until the "calculus" page is improved, I can't really make the third section make much sense.

Group

Rewrite. The existing article was long on obscure examples and short on useful ones. NOTE: This contains some references to things that are probably at too high a level for a high-school-level treatment, such as unitary groups, SO(3), and eigenvectors. This material was put in under the "cultural enlightenment" doctrine—that it is OK to tantalize the students with things that they won't fully understand. See the discussion of Kepler's laws and isotopic stability at User_talk:ElizabethK.

Limit

The article I was working on when the unfortunate event of 28 Aug 2008 overtook me.

Cauchy sequence

Rewrite. The previous article missed the point. The point is subtle.

Dedekind cut

New/rewrite. The previous material on this was in the real analysis page, and was hopelessly wrong. The "foundations of real analysis" were not "shaken", nor did Dedekind cuts "undercut the assumption of the continuity of the real line, by cutting at gaps between points". Dedekind cuts specifically maintain continuity and density; they do not create gaps. Also, they have nothing to do with "non-elementary methods" (complex numbers), or the axiom of choice. The real analysis page, like many pages, needs an overhaul.

Bijection

Improvement over existing article.

Injection

New.

Surjection

New.

Countable

Improvement over existing article. There is considerable overlap with a "cardinality" article, and a serious question of what material should go into what article. But, for now, I've put all relevant information here.

Hodge star

I'm not endorsing this page at all! It is way over the level of what should exist here at CP. But, if we have it, it should not wikilink from the cotangent bundle to the trig function.

SamHB 14:33, 28 November 2008 (EST)

On Complex Numbers and Light Bulbs

It has been suggested, at critical thinking in math, that the ratings of light bulbs can illustrate the irrelevance of complex numbers to real-world issues. This is in fact an uncannily bad choice of analogy, because light bulbs are commonly operated on alternating current, and the analysis and design of AC circuits is one of the areas in which complex numbers are used most successfully.

At an operating frequency of 60 Hz, light bulbs do not exhibit much phase shift, that is, much inductive or capacitive reactance, but the effects still exist. Let's go through some of the many ways in which electrical engineers measure things in terms of complex numbers.

• What is commonly called resistance at DC, that is, the ratio of voltage over current, becomes the complex quantity impedance, because the voltage and current may not be in phase with each other.
• Impedance, the true ratio of voltage over current, is a complex number.
• The real part of the impedance is called the resistance.
• The imaginary part of the impedance is called the reactance.
• Depending on the sign of the reactance, it is characterized as capacitive reactance or inductive reactance. Capacitors and inductors are electronic components designed to exhibit these reactances in fairly pure form.
• The reciprocal of the impedance, as a complex number, is the conductance.
• The real part of the conductance is called the admittance. Because of the properties of complex division, it is not the reciprocal of the resistance.
• The imaginary part of the conductance is called the susceptance. It is not the reciprocal of the reactance.
• Because of phase differences, the power actually consumed by a device may not be the product of the voltage and current. For this reason, devices may be rated in volt-amperes, or in watts. Because of the low frequency involved, a 60 watt light bulb is also very nearly a 60 volt-ampere light bulb.

SamHB 19:05, 25 December 2008 (EST)

Want Math?

I am suspending my activities for the duration of BRichtigen's block. SamHB 18:24, 27 December 2008 (EST)