Conservapedia - User contributions [en]

Conservapedia:Critical Thinking in Math

2009-05-16T19:31:59Z

Robert: (still) interested in this class

"Critical Thinking in Math" is an experimental course with four independent purposes in mind:

*sharpen the analytical skills of students and improve their math [[College Board]] scores

*awaken an interest in [[mathematics]] by students who did not realize they had extraordinary aptitude for math, the future [[Bernhard Riemann]]s

*encourage adults to keep their minds sharp through mathematics, and fend off mental decline

*help parents who would like to teach math to their [[homeschooled]] children

The experiment is to use only fundamental or elementary techniques to accomplish the above results. No tools beyond about 9th grade math are required, and motivated students younger than 9th grade will not have difficulty with the concepts.

This course seeks the contributions of both teachers and students to make it as effective as possible. It will begin in September. Possible topics include:

*a comparative look at different techniques of proof

*major problems that remain unsolved using elementary techniques

*a look at the history of the development of math

*an analysis of what skills [[College Board]] exams test, and how to improve those skills

Please feel free to add other topics and suggestions, and add your name below as a teacher or student interested in this field:
--[[User:Aschlafly|Aschlafly]] 16:08, 5 August 2007 (EDT)

== Draft Curriculum ==

*different methods of proof: [[constructive proof]], [[elementary proof]], induction, contradiction, existence, [[infinite descent]]
*defining and redefining key concepts: [[integer]]s, [[infinity]], [[prime number]]s, [[proof]]
*controversy about proof by contradiction
*17 different ways to prove that there are an infinite number of [[prime number]]s
*[[transcendental numbers]] - how do we know they exist?
*Goldbach's Conjecture and Fermat's Last Theorem
*Unsolved problems: proving that there are infinitely many [[twin primes]]
*[[Brun's constant]]
*Problems solved only with proof-by-contradiction: always a prime between n and 2n (n>1)
*[[perfect number]]s
*[[additive factoring]]
*[[prime number theorem]]
*Types of math problems presented in [[College Board]] exams, [[math contests|American math contests]] and UK math contests [http://www.wpr3.co.uk/UKMT/jmc.html][http://www.wpr3.co.uk/UKMT/imc.html][http://www.wpr3.co.uk/UKMT/smc.html]
*Interesting problems in number theory and Euclidean geometry
*greatest mathematicians in history, and why
*Axiom of Choice, why it has been controversial, and its use in Wiles' proof of Fermat's Last Theorem
*Set theory in general
*Kurt Gödel's incompleteness theorems are interesting; they are applicable not only in maths and logic, but also move into philosophy.
*Hilbert's program (although of course the above renders null its aims!)
*Formal mathematical logic
Students on the course
*I would like to join this. Is it alright if I live in the UK? Your profile suggests that you live in the US, but I am always eager for maths. [[User:AungSein|AungSein]] 18:13, 5 August 2007 (EDT)

:: That's fantastic. Of course you're welcome in the UK. You have great colleges there, and produced some fantastic physicists. Please help build a curriculum (see above). Lord willing, maybe we can make some inroads into some unsolved problems.--[[User:Aschlafly|Aschlafly]] 19:29, 5 August 2007 (EDT)
[[category:mathematics]]
::: Well I come from Burma, but the colleges and university there are good. Your point about unsolved problems is good, too - have you heard of the folding@home project? It is a different concept, I know, but perhaps relevant - maybe what one brilliant mathematician might struggle at, us many lesser minds might gain insight into! I would also recommend for point 3 the UKMT papers [http://www.wpr3.co.uk/UKMT/jmc.html][http://www.wpr3.co.uk/UKMT/imc.html][http://www.wpr3.co.uk/UKMT/smc.html] - I do not know about how it is in the USA, but they are typical here. [[User:AungSein|AungSein]] 20:06, 5 August 2007 (EDT)

:::: Your additions to the above curriculum are superb! Thanks much, and thanks also for the links to those U.K. tests. I just printed one out am reviewing it. Questions look challenging but doable, which is what we want. Lord knows that students can really improve after practicing on lots of those types of tests. We also have high school contests in the U.S. here: [[Math contests]].--[[User:Aschlafly|Aschlafly]] 20:37, 5 August 2007 (EDT)

::: AungSein, a second student in this class took the UKMT Junior contest you cited, and she marked 17 correct, 5 wrong, and 3 non-answered. How did you do on that test?--[[User:Aschlafly|Aschlafly]] 21:54, 6 August 2007 (EDT)
*I'm interested in this math critical thinking class too. --[[User:Luke314|Luke314]] 16:38, 9 August 2007 (EDT)

:: Fantastic! Welcome and Godspeed. Please click "Watch" on this page so that you can easily see updates as September approaches. This will be a great learning experience. Feel free to make suggestions on the curriculum.--[[User:Aschlafly|Aschlafly]] 16:42, 9 August 2007 (EDT)

*I'm interested also, as a teacher. (Credentials on request, of course.) Is this class going to happen? What I see here doesn't look very well-subscribed. Is there another page somewhere, listing details of the class? Details of the Curriculum? Discussion of same? Teaching the axiom of choice or Gödel's incompleteness theorems really correctly sounds like quite an ambitious undertaking, but I'd like to give it a try. [[User:Robert|Robert]] 20:42, 23 August 2007 (EDT)

:: That's great, Robert! We don't have a lot of students yet but it is still only August. We plan to start mid-September and I welcome your input on the curriculum. I expect the interest in this to grow as it has in the American Government course (now up to 45 participants). Much will be accomplished by this math course for the immense benefit of the participants. Godspeed.--[[User:Aschlafly|Aschlafly]] 23:08, 23 August 2007 (EDT)

*I am also interested in participating in the project as an adult student. [[User:StevenW|StevenW]] 20:46, 7 October 2007 (EDT)

*I'm just wondering. How can things like axiom of choice, Fermat & Wiles, open problems, etc, can be covered. They say that nothing above 9th grade math is required. Will there be two different classes? [[User:Rincewind|Rincewind]] 11:58, 4 November 2007 (EST)

*I'd love to join, I'm just a bit confused on the requirements in terms of homework, editing, et cetera. [[User:GlobeGores|GlobeGores]] 18:07, 19 December 2007 (EST)

I'm interested in joining the course by I'm not sure how it all works. Can someone steer me in the right direction?- [[User:Schaefer|Schaefer]] 21:57, 20 December 2007 (EST)

*I'm really interested in this. Any idea of when it's due to start? [[User:KTDiputsho|KTDiputsho]] 14:53, 15 April 2008 (EDT)
*What is the "controversy about proof by contradiction" that you mention? It's news to me that there's any controversy about one of the standard tools of a mathematician. [[User:Googly|Googly]] 19:47, 6 August 2008 (EDT)

:: You'll learn lots of new things here, if you keep an open mind. When resorting to proof by contradiction, it is impossible to know if the result is due to the falsehood of the proposition or an undetected contradiction in the math itself.--[[User:Aschlafly|Aschlafly]] 20:25, 6 August 2008 (EDT)
:::Errors in the mathematics can cause an incorrect conclusion in any kind of proof. What's so special about proof by contradiction? -[[User:CSGuy|CSGuy]] 20:44, 6 August 2008 (EDT)
:::On an unrelated note, is this class still supposed to happen? It's been over a year since it was announced. -[[User:CSGuy|CSGuy]] 20:46, 6 August 2008 (EDT)
:::::: Sorry Aschafly, but your second sentence is just not correct. Are you teaching this Critical Thinking in Maths course yourself? If so, I'd say you've got some pretty muddled ideas which you need to straighten out before you let yourself loose on students. There's nothing at all second-rate about a proof by contradiction. [[User:Googly|Googly]] 20:47, 6 August 2008 (EDT)
::::::: Proof by contradiction can be unsatisfying because often it leads to unconstructive proofs of important statements. For example, [[Euclid]] used proof by contradiction to show there are infinitely many prime numbers, but that doesn't tell us what they are, or even give an infinite set of them with some formula like <math>2^n -1</math>. Another example: there is a [[transcendental number]] in the [[reals]]. If you prove this as suggested in the transcendental number article by using [[cardinality]], you'd never actually have a transcendental number to work with. It's far more useful to actually show a number like <math>pi</math> or ''e'' is transcendental and not use contradiction to do it. -[[User:Foxtrot|Foxtrot]] 20:43, 8 August 2008 (EDT)
:::::::: Proofs are proofs, not formulas or examples. [[Euclid]]'s proof by contradiction that there are infinitely many primes is a perfectly good answer to the question "Are there infinitely many primes?" It's a terrible answer to the question "What are they?" or "What's the 10,000,000th prime?" but that's not what Euclid set out to prove. <math>pi</math> and ''e'' are very useful numbers but showing that they are transcendental doesn't tell you much about any other transcendental numbers any more than knowing that 101 is a prime number tells you whether there are an infinite number of primes -- for that you need a proof and a proof by contradiction is 100% adequate. [[User:AdrianDelmar|AdrianDelmar]] 22:49, 8 August 2008 (EDT)

::::::::: Your argument starts with your conclusion, "proofs are proofs." In fact, esteemed [[mathematicians]] have always held some forms of proofs to be superior and preferred to others. [[Paul Erdos]], for example, felt with good reason that an [[elementary proof]] is superior.

::::::::: In light of [[Godel]]'s revelation that math may contain a contradiction, proofs by contradiction are particularly disfavored. One can never know logically whether the proof simply stumbled into an underlying contradiction in the math, rather than proving the proposition.--[[User:Aschlafly|Aschlafly]] 23:23, 8 August 2008 (EDT)

:::::::::: Elementary proofs may certainly be superior and more satisfying -- [[Paul_Erdos|Paul Erdős']] elementary proof of the [[Prime Number Theorem]] is a very good example -- but that doesn't make proofs by contradiction insufficient or controversial. If you are referring to [[Gödel's incompleteness theorems]], his revelation was not really that math may contain contradictions but that a formal system cannot be both consistent and complete, meaning essentially that a consistent formal system will contain statements that it cannot prove true or false ''within its own system.'' The proof by contradiction that <math>\sqrt{2}</math>. is an irrational number relies on the consistency of the axioms about numbers in use and doesn't come close to worrying about the completeness of the system. <math>\sqrt{2}</math> would not be irrational only in a system with different axioms.

:::::::::: Googly's original question was simply "What's the controversy?" Is this it? Proof by contradiction, Hilbert's program and Gödel's incompleteness theorems are all already on the draft curriculum. Whether elementary proofs are better or not isn't really a controversy. Is there something else? [[User:AdrianDelmar|AdrianDelmar]] 09:57, 9 August 2008 (EDT)

::::::::::: So you seem to agree that not all types of proofs are absolutely identical in rigor. Or do you? [[Elementary proof]]s are plainly preferred and more rigorous than, say, proofs that rely on the [[Axiom of Choice]]. If it is possible to prove something without relying on the [[Axiom of Choice]], then that approach is preferred. Surely you don't doubt that [[Paul Erdos]] would have confirmed as much.

::::::::::: You haven't rebutted the criticism of proofs by contradiction. As I said, it is impossible to know as a matter of logic whether the contradiction is due to the math or the falsity of the proposition.--[[User:Aschlafly|Aschlafly]] 17:53, 9 August 2008 (EDT)

:::::::::::: If a proof isn't rigorous then it's not really a proof, and there is nothing not rigorous about proof by contradiction. A proof that uses contradiction might not be rigorous, but any kind of proof can fail to be rigorous. The axiom of choice is irrelevant.

:::::::::::: Take a look at this [http://www.homeschoolmath.net/teaching/proof_square_root_2_irrational.php proof by contradiction] that <math>\sqrt{2}</math> is irrational. Where is the unseen underlying contradiction? That something times two is an even number? That the product of two even numbers (and therefore the square of an even number) is an even number? That a fraction consisting of two even terms is not simplified to its lowest terms?

:::::::::::: Are you thinking of [http://mathworld.wolfram.com/IntuitionisticLogic.html Intuitionistic Logic]? [[User:AdrianDelmar|AdrianDelmar]] 18:29, 9 August 2008 (EDT)

::::::::::::: You're not addressing my basic point, which I've repeated twice now, so I probably won't pursue this discussion further at this time. Godspeed to you.--[[User:Aschlafly|Aschlafly]] 18:34, 9 August 2008 (EDT)

:::::::: I wonder if you aren't confusing contradiction and counterexample. Today I was reading ''Poincaré's Prize'' by George Szpiro and came across this passage about Poul Heegard finding a counterexample to Poincaré's proof of the duality theorem (p. 85):

:::::::: <blockquote>Let us recall that according to the theorem, the ''k''-th Betti numbers must be equal to the (''n-k'')-th Betti number. Heegard constructed an example of a three-dimensional manifold -- an intersection of a certain cone with a cylinder -- whose Betti numbers are (1,1,2,1). This contradicts the duality theorem. Finding a counterexample to a theorem can mean either that the counterexample is wrong, or that the theorem's proof is wrong, or that everything is based on a misunderstanding. In this case, it was the third alternative...</blockquote>

:::::::: A counterexample is much more "unconstructive" that a proof by contradiction, in the sense that a counterexample simply shows that the proof as stated isn't right, but doesn't say that it couldn't reformulated as Poincaré and other mathematicians went on to do for the duality theorem. -[[User:AdrianDelmar|AdrianDelmar]] 19:14, 20 August 2008 (EDT)

I can think of at least 6 things you could say about a proof that might affect your perception of its rigor, quality, simplicity, or elegance:
#Does it use contradiction?
#Is it constructive? (only applies to theorems that say "there is a ....")
#Does it use complex numbers?
#Does it use the axiom of choice?
#Does it use mathematical induction?
#Does it involve provability or decidability within some logical framework? That is, does it relate to Gödel's incompleteness theorem?
The topic of this thread is supposed to be item 1, but it has twice gotten sidetracked, once into item 2, and once into item 6. It turns out that one can easily separate item 1 from the others. The field of "elementary" calculus has many theorems that use "pure" contradiction, unpolluted by any of the other factors. As an example, take the theorem
:Limits, when they exist, are unique.
This theorem uses the epsilon/delta formulation of limits. I won't go into the details here (I plan to put it into the limit page). But the outcome of the theorem is that
:If f(x) approaches both W and Z as a limit, with <math>W \ne Z</math>, one can set <math>\epsilon = |W-Z| / 3</math> and get a contradiction.

Does that prove that the limit is unique? Well, it proves that '''it is not possible for the limit not to be unique'''. Put another way, '''you can't find two different numbers, W and Z, both of which are limits'''.

One is free to say that such a proof is less satisfying than a really direct proof. What the proof by contradiction method is saying is that
:If you prove that it is not possible for proposition P to be false, you have proved that P is true.
Where, in this case, P means "limits are unique".

One is free to question or object to the above syllogism. At some point it comes down to the "law of the excluded middle" or intuitionistic logic. There are two things I would say about that:
*While this issue is of some interest at a deep philosophical level, all mathematicians accept proof by contradiction on a practical level, in its application to the many theorems of mathematics.
*One could pursue this question in the Critical Thinking in Math course, but it would probably take the students down a different path from the stated goals of the curriculum, and would not likely be appreciated by the audience. It might be suitable for a completely different course. Sadly, I think there would be little interest in such a course, when there are so many fascinating things in the current curriculum.

[[User:SamHB|SamHB]] 22:15, 20 August 2008 (EDT)

*You say: "No tools beyond about 9th grade math are required, and motivated students younger than 9th grade will not have difficulty with the concepts." I think 9th-graders will struggle with Goldbach, Wiles, Hilbert... [[User:Googly|Googly]] 21:09, 6 August 2008 (EDT)

*Regarding the lengthy discussion above, can I point out that non-elementary proofs, particularly if they are elegant, are especially valued by mathematicians because they draw together areas of knowledge which were previously thought to be unconnected. Elementary proofs, i.e. proofs which only draw on a small body of related concepts, don't do that - they may be easier to follow but they don't have the excitement of "sparking across the creative gap". [[User:KennyMac|KennyMac]] 19:04, 11 September 2008 (EDT)

::But non-elementary proofs link these subjects in a non-elementary way, which casts some doubt if they are really connected. If they are ''real''-ly connected, then the link should be evident using real numbers and without resorting to complex numbers, or the Axiom of Choice or any of these other "additions" to mathematics that do not reflect the real world. The one good that I can attribute to a non-elementary proof is that it will make mathematicians search for an elementary proof of the same theorem. With some ingenuity they may find one, as Erdos and Selberg did with the Prime Number Theorem. -[[User:Foxtrot|Foxtrot]] 23:03, 12 September 2008 (EDT)

:::Complex numbers don't "reflect the real world"???!!! I'm so staggered by this statement, I simply don't know what to write! Electricity, economics, biology... there's not much we can understand ''without'' complex numbers. [[User:KennyMac|KennyMac]] 17:49, 13 September 2008 (EDT)

::::Have you ever plugged in a <math>60\sqrt{-1}</math> watt light bulb? Isn't [[current]] always a real value, same with money, spectroscopy values, bacteria populations, etc. Taking integrals to compute things only needs integration over real values. Protein folding and DNA can be studied using real manifolds, etc. Pretty much the entire subjects can be understood entirely in the setting of real numbers and real geometry. The only time that complex numbers enter into "computations" is because they were artificially introduced there. Just because people teach you to use complex numbers doesn't mean it's necessary (and usually, it isn't). -[[User:Foxtrot|Foxtrot]] 19:04, 13 September 2008 (EDT)

:::::Foxtrot, have you ever solved a wave function ''without'' complex numbers? Waves and oscillations appear everywhere in nature. (By the way, I like your statements about guns and the death penalty on your talk page. Glad to see there's a bit of sense in those directions among CP contributors!) [[User:KennyMac|KennyMac]] 19:50, 13 September 2008 (EDT)

:::::If I remember right (and it's been some time), I used complex/imaginary numbers in electrical engineering, systems analysis, signal processing, vibration analysis, etc. - as [[User:KennyMac|KennyMac]] said, pretty much anything with a wave or oscillation. (As we used to say in my engineering classes, imaginary electricity can kill you.) DC current is real, I'm not sure AC is. (Watts are power, not current.) Are you saying these subjects can be covered without complex/imaginary numbers? Again, it's been a while, but that seems odd to me. If that's the case, why is it taught with complex numbers? --[[User:Hsmom|Hsmom]] 20:13, 14 September 2008 (EDT)

::::Hsmom, your recollection is exactly right. Complex numbers are heavily used in a wide variety of scientific and engineering disciplines.
::::The statement about <math>60\sqrt{-1}</math> watt light bulbs is particularly baffling. Complex numbers are universally used in the analysis of AC electricity such as that which powers our light bulbs, though the reactance effects are admittedly minor at 60 Hz. See [[User:SamHB#On_Complex_Numbers_and_Light_Bulbs]].
::::[[User:SamHB|SamHB]] 19:12, 25 December 2008 (EST)

*I would like to join this course. Is there a set date for the start? [[User:Nahomadis|Nahomadis]] 10:12, 9 October 2008 (EDT)

*I'm still wondering if this is ever going to happen. -[[User:CSGuy|CSGuy]] 16:25, 12 October 2008 (EDT)

::Unlikely. But I'm in. [[User:BrianA|BrianA]] 10:10, 21 October 2008 (EDT)

* I think that denying the value of reduction ad absurdum is blasphemous, since the Bible makes abundant use of it. The Book of Ecclesiastes and Paul's letters, for example, use this method. [[User:Sunda62|Sunda62]] 17:20, 5 November 2008 (EST)

*Still wondering if this is going to happen, since it's now nearly 18 months since it was supposed to start. -[[User:CSGuy|CSGuy]] 12:56, 3 March 2009 (EST)
:*Just checking again. If this isn't going to happen, the link should probably be taken off the main page. -[[User:CSGuy|CSGuy]] 17:59, 9 March 2009 (EDT)
::* Please do not keep asking here. You have asked three times now! I am sure I am not the only one who is developing some of this material off-wiki, to send to Aschlafly for consideration.
::* If anyone is interested, I might upload it as well. [[User:BHarlan|BHarlan]] 18:17, 9 March 2009 (EDT)

*I'm extremely interested in this course, and perhaps even in participating in teaching it, and in the preparation of material for it. I'd be very grateful for any materials you might have that you would be willing to upload, mail to me, or discuss. You also say
::I am sure I am not the only one who is developing some of this material off-wiki ...
:I'd be very interested in knowing who else might be working on this, and what materials they are developing. If you can post their names, or have them send me mail, that would be very helpful.

:I offered my services in presenting this course, some time ago, though Andy's comment [http://www.conservapedia.com/index.php?title=Conservapedia_talk:Critical_Thinking_in_Math&diff=289241&oldid=287822 here] suggests that he was not fully satisfied at the time. With any luck, things will go better this time around. [[User:Robert|Robert]] 15:31, 16 May 2009 (EDT)

Talk:World History Lecture Eleven

2009-05-16T19:21:40Z

Robert: /* 20th century science */ new section

I noticed this spelling, Guomindang; can we make redirects like Kuomintang, or such, or how do you wish to handle things like this? Thanks. [[User:RobS|RobS]] 13:48, 9 March 2007 (EST)

Who's Andy Schlafly? How about some bibliographic info? [[User:Testing|Testing]] 15:40, 19 March 2007 (EDT)
:He made the site...--[[User:Elamdri|Elamdri]] 15:44, 19 March 2007 (EDT)

''Stalin established a brutal totalitarian state, whereby he dictated all aspects of life and used violence to destroy any opponents. A secret police aided Stalin in his vicious execution of all opponents.''

And none of this happened under kindly Uncle Lenin? [[User:Pachyderm|Pachyderm]] 10:29, 30 August 2007 (EDT)

Why does it not mention that Warren G. Harding was one of the most corrupt presidents ever? And that he is regularly ranked among the worst presidents by most historians?

: Do you think Harding was almost as corrupt as recent Democratic Administrations???--[[User:Aschlafly|Andy Schlafly]] 12:38, 1 April 2009 (EDT)

::Almost as corrupt? try far more corrupt. He had multiple affairs before and during is time in office. he paid one of his mistresses $50,000 not to reveal the affair. his administration was a den of nepotism. he appointed personal friends to important positions such as head of the veterans bureau. His nepotistically appointed friend Charles Forbes, head of the veterans bureau, stole $200 million from the federal government, and his attorney general Daugherty was found to have profited from illegal shipments of alcohol. so yes, i'd say his corruption and that of his administration FAR exceeded that of any recent democratic administration!!!!{{unsigned|JBryant}}

::Well????

::: Are you sure you aren't trying to describe some of the problems in the Clinton Administration???--[[User:Aschlafly|Andy Schlafly]] 09:59, 13 April 2009 (EDT)

::::Are you sure you're not trying to dodge the question???????????????????????????
listen, I"m no fan of Clinton or the democrats. I think that all presidents, liberal AND conservative need to be held accountable for their actions. I think that it is revisionist to not include Harding's shortcomings. I know that if he had been liberal, you'd be all over his affairs and other such corruption. I'm just asking that you be fair and balanced in terms of talking about corruption. is that too much to ask? [[User:JBryant|JBryant]] 11:13, 15 April 2009 (EDT)

: No, you're wrong in suggesting that a quality world history course would waste time on [[gossip]] about Harding if he had been liberal. This is a quality history course. Read the National Enquirer if you have a need for gossip.--[[User:Aschlafly|Andy Schlafly]] 11:50, 15 April 2009 (EDT)

== Theory of Relativity ==

This section is full of strange mistakes. Are we permitted to edit the lectures here so that the students get accurate science instruction? For example, the Theory or Relativity does not care whether the speed of light changed over time. It probably has not changed, but the theory has no preference either way. Also, why does the author state that the Theory of Relativity has nothing to do with the atom bomb or any other technology? This statement lacks any point or precision. It' not true that the theory of relativity has nothing to do with technologies we use today. Also the Theory of Relativity does not reject "Newton's Theory." It merely modifies certain Newtonian kinematics, as for very high velocities. Also, the Theory of Relativity has nothing to do with moral relativism. Why does the author keep saying it does? It is a scientific theory, not a theory of morality. I am interested in assisting with this project if it is open for participation! [[User:ShmuelB|ShmuelB]] 12:24, 16 April 2009 (EDT)

: The truth is welcome. Falsehoods, even popular ones, are not. Your comments are historically or factually incorrect, unfortunately.--[[User:Aschlafly|Andy Schlafly]] 13:17, 16 April 2009 (EDT)

== Postulates of Special Relativity ==

I clarified one postulate, i.e., ''The speed of light is the same for all observers, no matter what their relative speeds.'' That seems to be an improvement over ''the speed of light never changes''...

This section - especially in its disparagement of Einstein's work - is something you don't find in any common textbook on the history of sciences. Therefore, I'd wish that A. Schlafly would include some sources to bolster his claims.

Unfortunately, such a (in my eyes, mainly unjustified) critique of the importance of the theories of relativity invokes memories of the ''German Physics''.

[[User:ClementB|Clement ♗]] 09:30, 17 April 2009 (EDT)

:It is '''inappropriate''' to compare scientific skepticism about materialist science to Naziism.
:If you find me ten articles that accept the theory of relativity and use it to make historical claims, I can show you ten articles that accept that the speed of light is constant. Do you think that is some sort of coincidence?
:I do not think it is a coincidence. [[User:BHarlan|BHarlan]] 16:03, 17 April 2009 (EDT)

:: I don't find any substance in either of the above comments. If you have a specific factual improvement to the article, then let's see it. Otherwise, let's move on.--[[User:Aschlafly|Andy Schlafly]] 19:00, 17 April 2009 (EDT)

@Aschlafly: My ''specific factual improvement'' of the article is a change of your wording (''the speed of light never changes'') of one of Einstein's postulate of the theory of relativity.
Here a some versions which I looked up over the last days:
*'''Wolfgang Pauli''' ''Theory of Relativity'', 1958, p. 5: ''The velocity of light is independent of the motion of the light source''

*'''Robert Resnick''', '''David Halliday''' ''Fundamentals of Physics'', 7th ed. 1996, p. 1254: ''The speed of light in vacuum has the same value in all inertial frames, regardless of the velocity of the observer or the velocity of the source emitting the light''

and from a source you seem to trust:

*'''[http://www.merriam-webster.com/dictionary/relativity Merriam-Webster]''' ''the speed of light in a vacuum is constant and independent of the source or observer''
None of these - and many others - implies that the ''speed of light never changes''. They stress the point that the speed of light is independent of the motion of the source or the observer - and I think that's the rather baffling, exciting part for everyone who is confronted with this postulates for the first time.

None of those states that ''the speed of light never changes'', but they emphasize the mind-baffling (at least for everyone who is confronted with this theory for the first time) fact that the velocity of light is ''independent of the motion of the light source''.

The phrase ''the speed of light never changes'' is at least unfortunate as it implies that the speed of light has never changed since the begin of the universe. But the postulates doesn't require this, the same theory would hold with a speed of light of 300 km/h instead of 300,000 km/s...

@BHarlan: ''If you find me ten articles that accept the theory of relativity and use it to make historical claims, I can show you ten articles that accept that the speed of light is constant.'' I honestly don't know what you want say here...

That said, I hope you'll approve that I change the lecture to the version of Wolfgang Pauli.

[[User:ClementB|Clement ♗]] 14:07, 20 April 2009 (EDT)

:Pauli did not use it, in the quote you supply, to make historical claims. I maintain my promise of ten for ten, and I caution you against attacking the conservative worldview by prevaricating on what "historical" means. [[User:BHarlan|BHarlan]] 15:21, 20 April 2009 (EDT)

::I stated above that I won't touch the ''historical'' aspects of the lecture, but only the ''scientific'' ones. So, I rectified or - if you prefer - improved a scientific statement. That has nothing to do with a certain ''Weltanschauung'', that's just a question whether a formulation is used in physics or not.
::I think that Aschlafly will accept a formulation which is similar to the one used at Conservapedia's article on the [[Theory of Relativity]].
::[[User:ClementB|Clement ♗]] 15:55, 20 April 2009 (EDT)

::''addendum'' It isn't my lecture. But it isn't an essay, neither, and the page is not protected. Due to the very nature of these lectures, any change should be done after consideration. The quotes above should show that I tried to be painstakingly diligent. That said, I will change the lecture '''again''', and I like to ask you, BHarlan, for a source of the first version of the postulate - if you have the intention to undo my edit, that is... [[User:ClementB|Clement ♗]] 16:02, 20 April 2009 (EDT)

Aschlafly, I've to admit that I'm not glad with the current version (''the speed of light can never be increased''). It's not a general accepted version of the postulates, and differs greatly from the examples I gave above. I don't know why it seems to be necessary to find a new, somehow unique formulation of these century-old postulates. One doesn't take much liberty with the phrasing of ''Newton's axioms'', and one shouldn't with ''Einstein's postulates'', neither.
But as you obviously want to show some creativity, I won't argue any longer.
[[User:ClementB|Clement ♗]] 08:01, 21 April 2009 (EDT)

: Clement, where did your accusation that "you obviously want to show some creativity" come from??? It's bizarre.

: I'm looking for the clearest explanation of the postulate. I don't think your version is any more historically accurate than mine, and yours is far more difficult for history students to understand. Good teaching is about .... clear teaching. It does not allow confusing students with contorted, confusing statements.--[[User:Aschlafly|Andy Schlafly]] 08:56, 21 April 2009 (EDT)

:: Sorry, that wasn't meant as an accusation, that's just an observation: instead of using a formulation of Einstein's postulates which is to be found only with small alterations in most textbook on physics - and even in the Merriam-Webster, you prefer your own wording. That's creative.
:: [[Pauli exclusion principle|Pauli]]'s version in not only more ''historically'' accurate, it is more ''scientifically'' accurate. Of course, the whole concept is baffling. So it may be a little bit more difficult to understand - but you have bright students! And it can be understood correctly.
:: BTW, you will find scant scientists or educators who judge Pauli's statements as contorted or confusing.
:: [[User:ClementB|Clement ♗]] 14:05, 21 April 2009 (EDT)

::: I wasn't offended by your "observation", but found it to be inexplicably bizarre. I articulated the postulate, then you replaced it with a far more complex and non-historical substitute, and then I simplified it into something clearer. Your response was a petulant accusation, without even addressing the substance my improvement. Are you saying the more concise, clearer formulation is wrong? I can't even tell what your view is.--[[User:Aschlafly|Andy Schlafly]] 15:42, 21 April 2009 (EDT)

:::: Until now, the history of the formulations of the postulate in the lecture reads like:
::::# the speed of light never changes (original by Aschlafly)
::::# the speed is the same for all observers (no matter what their relative speeds) (Clement B.)
::::# the speed of light never changes (reversion by BHarlan)
::::# the speed of light is independent of the motion of the light source (Pauli's version inserted by Clement B.)
::::# the speed can never be increased (second version of Aschlafly)

::::Your formulations are shorter, but neither more concise or clearer. Furthermore, I don't know how you can label W. Pauli's version as non-historical?
::::In his article ''Zur Elektrodynamik bewegter Koerper'' - ''About the electrodynamics of moving bodies'' (Annalen der Physik, 1905, p 891), Einstein wrote
:::::'' 1. Die Gesetze, nach denen sich die Zustände der physikalischen Systeme ändern, sind unabhängig davon, auf welches von zwei relativ zueinander in gleichförmiger Translationsbewegung befindlichen Koordinatensystemen diese Zustandsänderungen bezogen werden.''

:::::''2. Jeder Lichtstrahl bewegt sich im ,,ruhenden“ Koordinatensystem mit der bestimmten Geschwindigkeit V , unabhängig davon, ob dieser Lichtstrahl von einem ruhenden oder bewegten Körper emittiert ist. ''

::::This would be the historic origin of the postulates. A translation:

:::::''1. The laws which describe the change of the properties of physical systems are independent of a steady translation of the coordinates in which this changes are described''

:::::''2. Any ray of light moves in «stationary» coordinates with a certain velocity V, regardless whether this ray was emitted from a stationary or moving body''

::::So, from the very beginning you find the same idea which Pauli describes concisely and clearly : '''the speed of light is independent of the motion of the light source'''

::::[[User:ClementB|Clement ♗]] 16:18, 21 April 2009 (EDT)

::::: This is an interesting and informative discussion. But Einstein said that the speed of light always moved with a "certain velocity." That is very similar to my first formulation. Pauli, who had nothing to do with the development of relativity, is saying something different. Under Pauli's formulation, the speed of light may vary. Not so under Einstein's.--[[User:Aschlafly|Andy Schlafly]] 17:53, 21 April 2009 (EDT)

:::::: Einstein speaks of a ''certain velocity V'' - ''eine gewisse Geschwindigkeit V''. This is his way to introduce an abbreviation (''V'') - you'll find similar formulations in the work of his contemporaries. In his whole essay he doesn't touch the question whether this certain velocity V has changed over time.
:::::: The main point - as it is stressed in so many textbooks - is that the speed of light is independent of the movement of the source. Think about it: It's really mind-boggling as it contradicts our intuition! I haven't met a pupil who wasn't intrigued by this, especially if you explained the ''Gedankenexperimente'' ...
:::::: To be petulant for another time: Frankly, I don't think that you can produce a better formulation than that of W. Pauli.
:::::: [[User:ClementB|Clement ♗]] 18:09, 21 April 2009 (EDT)

::::::: Clement, you're not responding to my points, and you've resorted again to a petulant mode. Do yourself a favor: open your mind and think more for yourself, rather than simply repeating what someone else said. Suit yourself, but I'm moving on to others. Thanks and Godspeed.--[[User:Aschlafly|Andy Schlafly]] 18:23, 21 April 2009 (EDT)

:::::::: And may I give you an advise, too? Sometimes it is good to listen to those great minds who actually had the ideas in the first place. Thinking for yourself is all fine and dandy, but sometimes, it seems to be the sensible thing not to ignore a century of textbooks.
:::::::: [[User:ClementB|Clement ♗]] 18:41, 21 April 2009 (EDT)

::::::::: If your approach is to rely on authoritative, time-tested sources, Clement, then '''why haven't you been quoting the Bible during your many edits to this site'''? Instead, you seem very selective in which sources you quote, and as BHarlan pointed out first below, you don't even seem to interpret your own selective sources correctly.--[[User:Aschlafly|Andy Schlafly]] 20:33, 21 April 2009 (EDT)

ClementB, doesn't "a certain velocity V" imply that Einstein is saying that the speed does not change during the scope of the problem?
For instance, if I say "If a certain man V is President for two full terms, V may not be elected to a third term" or "There is a certain function f such that if a car is traveling at a certain velocity V that is less than the escape velocity, then it will fall to Earth in less than time f(V)", then the variables are not changing over the scope of the problem, no? And since some problems take place over very long periods of time, the velocity is assumed not to change over that whole period, no? And doesn't that imply that the speed of light is constant, no matter how far your twin travels? [[User:BHarlan|BHarlan]] 18:26, 21 April 2009 (EDT)

:::::::::: The Bible is my source of inspiration. I keep it out of my science or history classes, though.
:::::::::: Yes, I'm selective in my sources: on science, I quote scientists. I'm humble enough to know that I can't improve the insights of the greatest minds of the last century, but I am confident that I can understand what they were talking about. If you read the quotes above with an open mind, you'll find that your wording of the postulates is lacking: it covers at most half of the original of Einstein, and leaves out the baffling part. You scold me for respecting to much ''what someone else said''. May I quote Sir Isaak Newton: ''If I have seen further it is only by standing on the shoulders of giants.''
:::::::::: I think it is prideful to refuse to climb on these shoulders, and to remain willfully in the shadows of the giants.
:::::::::: And may I say that you offered no quote, neither Biblical nor scientific, for your version of the postulate? I got the impression that you thought it up by yourself. But which sources did you use?
:::::::::: BTW, BHarlan talks about a conclusion drawn from the postulates, not the postulates themselves.
:::::::::: [[User:ClementB|Clement ♗]] 07:25, 22 April 2009 (EDT)

::::::::::: Perhaps you "keep" the Bible "out of" many fields of inquiry, not just science and history (and why censor the Bible from history???). I've never seen you quote or mention the Bible in any of your numerous edits here. You seem to quote everything and everyone ''except'' the Bible.

::::::::::: You've never explained why you think the lecture is incorrect with respect to its current formulation of the relativity postulate. I'm not even sure you do disagree with it, except that you say it is not how Pauli (who had nothing to do with relativity) described it. I have explained why Pauli's description is inadequate: his description ("the speed of light is independent of the motion of the light source") does not expressly preclude somehow increasing the speed of light. Yet the formulas for relativity do assume that is impossible.--[[User:Aschlafly|Andy Schlafly]]

::::::::::::* ''Pauli's description is inadequate'' That's quite a surprise:
::::::::::::* Ever since this 1921 article on relativity in the ''Encyklopaedie der mathematischen Wissenschaften '', Pauli is seen as a kind of expert. This article was praised by A. Einstein himself - and many others (Born, Heisenberg, Sommerfeld). It's one of the most widespread elaborations of the theory, and that's why I quoted it in its English translation
::::::::::::* It's not a description. It's a formulation of the ''postulates of relativity''
::::::::::::* That the brilliance of the postulates: they don't have to state everything ''expressly'', a lot of things are follow ''implicitly''
::::::::::::* These ''formulas for relativity'' are conclusions from the postulates.
::::::::::::[[User:ClementB|Clement ♗]] 16:19, 24 April 2009 (EDT)

::::::::::::: Clement, there's no substance in your replies. You're just imitating and copying. This is a site for thinking. Please address the ''substance'' of my comments above. [[Last wordism]] is disfavored on this site.--[[User:Aschlafly|Andy Schlafly]] 18:33, 24 April 2009 (EDT)

<- unindent: ''Please address the substance of my comments above.'' Fine.
* ''Perhaps you "keep" the Bible "out of" many fields of inquiry, not just science and history (and why censor the Bible from history???).'': I said that ''I keep it out of my science or history classes'', I don't censor it from history.
* '' I've never seen you quote or mention the Bible in any of your numerous edits here.'' I didn't quote the Bible, but I mentioned it - as I do now
* ''You seem to quote everything and everyone except the Bible.'' The Bible doesn't say much about the history of Prussia, the political parties Orwell belonged to, or the Theory of Special Relativity. You haven't quoted the Bible on these issues neither. At the moment, I try to treat Conservapedia as an ''educational'' source, not a ''spiritual'' one.
* '' You've never explained why you think the lecture is incorrect with respect to its current formulation of the relativity postulate.'' If you want to state Einstein's postulates, you should try to represent them truthfully, i.e., use a wording which is accepted in physics. We're talking about something quite elementary, so a look in a text book should help. '''You still haven't given any source for your formulation of the postulates'''. Your formulation: the ''speed of light can never be increased'' doesn't prevent that a static observer '''A''' and a moving observer '''B''' measure different quantities for the speed of light. It only implicates that these measurements doesn't differ from their own earlier - or later - done measurements.
* '' I'm not even sure you do disagree with it, except that you say it is not how Pauli (who had nothing to do with relativity) described it.'' Pauli is nowadays most popular for his exclusion principle. But to say that ''had nothing to do with relativity'' is downright comical.
* '' I have explained why Pauli's description is inadequate: his description ("the speed of light is independent of the motion of the light source") does not expressly preclude somehow increasing the speed of light. '' First, it isn't a description, it's a widespread formulation of Einstein's postulates. Second, yes the postulates don't ''preclude expressly'' that the speed of light increases. As BHarlan stated above, that's a conclusion of the postulates.
* ''Yet the formulas for relativity do assume that is impossible.'' What ''formulas for relativity'' are you referring to?
Yes, I copied your edits above. I tried to address any statement of your edit. As for substance: Calling Pauli's work inadequate, and stating that he had ''nothing to do with the theory of relativity'' - though he wrote one of the most prominent articles on this subject made me cringe.
In a discussion, someone will always have the last word - at least temporarily. But you'll have the last word on the article, as I won't alter it against your will.
[[User:ClementB|Clement ♗]] 00:10, 25 April 2009 (EDT)

:Clement:

::<math> t = \frac{t_{0}} {\sqrt{1 - \frac{v^{2}}{c^{2}}}}</math>

:I don't know why you keep avoiding the obvious: the theory of relativity ''does'' plainly assume a maximum fixed velocity for light, known as ''c''. If you don't believe me, then plug in a velocity ''v'' greater than ''c'' and watch what happens to the above equation.

:As to the Bible, why do you avoid it so much? I cite it repeatedly in my history course, but I haven't seen you cite a passage from it yet despite all your commentary about history. Do you ever cite a specific passage from the Bible? I'd like to see just one example.--[[User:Aschlafly|Andy Schlafly]] 19:59, 25 April 2009 (EDT)

::''Whoever digs a pit may fall into it; whoever breaks through a wall may be bitten by a snake. Whoever quarries stones may be injured by them; whoever splits logs may be endangered by them. If the ax is dull and its edge unsharpened, more strength is needed but skill will bring success. '' (Ecclesiastes 10:8-10)

::'' If you don't believe me, then plug in a velocity ''v'' greater than ''c'' and watch what happens to the above equation.'' But, as you said, in the formula for time dilation, ''c'' represents the speed of light. Plug in a velocity greater than 300,000,000 km/sec for ''c'' and see what happens! Nothing much....

::I said above: Your formulation: the ''speed of light can never be increased'' doesn't prevent that a static observer '''A''' and a moving observer '''B''' measure different quantities for the speed of light. It only implicates that these measurements doesn't differ from their own earlier - or later - done measurements.

::In fact, that's my biggest rub with your formulation.

::The existence of a ''maximum fixed velocity for light'' (though not it's quantity) is a consequence of Einstein's postulates '''if they are stated correctly'''.

::[[User:ClementB|Clement ♗]] 22:39, 25 April 2009 (EDT)

:::My restated postulate that the "speed of light can never be increased" does preclude the scenario you describe, whereby a static observer increases the observed speed of light with the assistance of a moving observer. This is expressly precluded by my restatement of the postulate.

:::But your postulate about "independent of the motion of the light source" does not preclude increasing the speed of light beyond the ordinarily observed "c". Indeed, some relativists now insist that "c" need not be the ordinarily observed speed of light, but can be any assumed upper bound on the speed of light, and might be much greater than "c" as traditionally defined. My postulate is what underlies the above fundamental formula of relativity; your postulate requires redefining "c" in the above formula.

:::Your biblical quote is a good start but it's unclear what it means, if anything, to you. Do you ever ''apply'' the Bible in your quest for the truth? Do you earnestly seek the truth?--[[User:Aschlafly|Andy Schlafly]] 23:36, 25 April 2009 (EDT)

::::If your formulation of Einstein's postulates is superior Pauli's formulation (as quoted by me), why do physicists around the world use Pauli's version in text books, articles, etc. ? Why did Einstein, Sommerfeld, Born, etc. endorsed Pauli's article, where he stated the postulates the way I do? Is yours a new insight into the world of special relativity which all the physicists of today seem to have missed?

::::I'm sorry that you found the biblical quote unclear.

::::[[User:ClementB|Clement ♗]] 00:29, 26 April 2009 (EDT)

::::: Rather than answer my two simple questions, or be substantive, you resort to a question rant. Surely you don't think Pauli's formulation is perfect, and incapable of improvement. No, your real position seems to be that a ''conservative'' cannot possibly improve on it!--[[User:Aschlafly|Andy Schlafly]] 19:23, 28 April 2009 (EDT)

:::::: Two answer your two questions:
::::::*Do you ever ''apply'' the Bible in your quest for the truth? - '''Yes'''
::::::*Do you earnestly seek the truth? - '''Yes'''
::::::Now, here are mine:
::::::*Do you try to ''apply'' the Bible to physics?
::::::*Do you think you are the one to improve Pauli's formulation of Einstein's postulates substantially? The same formulations which are around for a century and used by physicists around the world? Endorsed by the leading scientist of his time? Please, do yourself a favor, and ask some actual physicists what they think about your version...
:::::: [[User:ClementB|Clement ♗]] 00:03, 29 April 2009 (EDT)

== Regarding Trotsky ==

While I was perusing the site last night I happened across the section eleven homework assignments and was curious as to which mottoes by John Smith and Trotsky were being referred to in one of the questions. I checked out the lecture and found the section in question and I believe there is a problem with context involved.

Whereas the Englishman Captain John Smith famously stated in the early days of the Jamestown settlement,
“He that will not work shall not eat, ”Trotsky’s famous motto was this: “Those who do not obey do not eat.”

For one, the John Smith quote seems to indicate that "He that will not work, shall not eat" is a phrase coined by John Smith. It might be good to give proper attribution to the Bible, which is where the thought originated.

Also, regarding the Trotsky quote: ''Trotsky’s famous motto was this: “Those who do not obey do not eat.”'' This indicates heavily that Trotsky advocated such a thought process and that this sentiment was inherent to the birth of communism. This is false. While communist dictators throughout the world have proven belief in this sentiment through atrocious acts of government, it was in no way Trotsky's belief or line of thinking nor was it expressed in the origins of communism as a political and economic theory. While claiming to espouse a saying more akin to "He that will not work, shall not eat", it was in fact '''Stalin''' who most embodied the phrase “Those who do not obey do not eat.”

Now I am certainly not going to make an argument for communism here, it is simply not a functional system of government, I will say that Trotsky as a historical figure has been improperly quoted via lack of significant context. Trotsky voraciously opposed the totalitarian government of Stalin which was the reason for his exile and assassination. “Those who do not obey do not eat.” was Trotsky's response to the 1936 constitution of the U.S.S.R. including the phrase :

In the U.S.S.R. work is a duty and a matter of honor for every able-bodied citizen, in accordance with the principle: "He who does not work, neither
shall he eat."

“Those who do not obey do not eat.” was Trotsky's condemnation of Stalin's methods and was what Trotsky believed to be Stalin's true "motto".

On a lighter note: It may be interesting to your students that after Trotsky's assassin buried a pick-axe in his skull, The sixty year old man remained conscious and actually fought his attacker with an axe sticking out of his head. Trotsky didn't die until the next day. I've always found that interesting. --[[User:NicholasT|NicholasT]] 08:25, 24 April 2009 (EDT)

: Interesting comments. Thanks. But Trotsky was a communist, just not a supporter of Stalin. Did Trotsky believe his motto? I would think so. Also, I'm not sure from where in the Bible you think John Smith's motto came. Godspeed.--[[User:Aschlafly|Andy Schlafly]] 08:47, 24 April 2009 (EDT)

::NicholasT explained how this wasn't Trotsky's motto, but the motto of Stalin as seen by Trotsky. He made it clear that Trotsky didn't endorse this motto
::In lecture 12, you state that Orwell fought in Spain ''against both the communists and Franco’s fascists''. But Orwell was member of a Trotskystic group. So, Orwell ''was'' a communist, wasn't he? [[User:ClementB|Clement ♗]] 09:10, 24 April 2009 (EDT)

:: Regarding the bible verse: ''"He that will not work shall not eat"'' can be found in Paul's second letter to the Thessalonians [http://www.biblegateway.com/passage/?search=2%20Thess%203:10;&version=31;2 Thessalonians 3:10]

::As for Trotsky: I may have not expressed myself well enough. ''"Those who do not obey do not eat"'' was no one's famous motto. The official motto of the Soviet Union under Stalin was ''"He who does not work, neither should he eat"''. Trotsky wrote a book in 1937 entitled "The Revolution Betrayed" in which he condemns Stalin's use of brutality within the state as an oppressive regime. In it he cites specifically Stalin's act of advising local organs to not give work to anyone sympathetic with Trotsky. Trotsky goes on to state that the lack of employment options led to followers of his philosophy lacking money, and in turn food, and leading to starvation. Trotsky says the the old motto of "who does not work shall not eat" had been replaced by Stalin with ''"Those who do not obey do not eat."''.

::My main point is this: ''"Those who do not obey do not eat."'' was not Trotsky's motto or Stalin's motto. It is a statement from a book Trotsky wrote just before his death. Trotsky claimed it to be Stalin's new motto as a point of rhetoric in an argument against Stalin's brutal methods, specifically against the Bolsheviks and supporters of Trotsky. ''"Those who do not obey do not eat."'' might be what happens when a communist dictator is in command, but as far as Trotsky is concerned it was a specific reference to Stalin's starving out of his followers and Trotsky believed it to be the wrong way to run a government. --[[User:NicholasT|NicholasT]] 10:49, 24 April 2009 (EDT)

::: The points above about Trotsky and Orwell are interesting, and I've spent some time without success trying to confirm t. Unfortunately, you don't provide any support for your claims. There's no doubt that Orwell fought against the communists, and that changed his view of them. There also seems to be no doubt that Trotsky said what the lecture states. The very, very subtle distinction between drawn above does not change the essential substance of the lecture, even if the claims are true.

::: I welcome a supported, well-written improvement on the lecture, but not something that would tend to confuse students with hairsplitting and debatable distinctions. Thanks and Godspeed.--[[User:Aschlafly|Andy Schlafly]] 15:15, 24 April 2009 (EDT)

:::: The lecture says Trotsky used the phrase as his personal motto. Nicholas says that he used it as a way to summarize and criticize his opponent, Stalin. That's not a subtle distinction - Nicholas and the lecture report precisely opposite versions! So it's probably worth "getting to the bottom of" if indeed the lecture contains a serious inaccuracy. [EDIT]: This seems to be the source: "[http://www.marxists.org/archive/trotsky/1936/revbet/ch11.htm The Revolution Betrayed]" by Leon Trotsky, Chapter 11. The quote, a little more than halfway down, reads:

::::::...during the “purgations” in the last month of 1935 and the first half of 1936, hundreds of thousands of members of the party were again expelled, among them several tens of thousands of “Trotskyists.” The most active were immediately arrested and thrown into prisons and concentration camps. As to the rest, Stalin, through Pravda, openly advised the local organs not to give them work. In a country where the sole employer is the state, this means death by slow starvation. '''The old principle: who does not work shall not eat, has been replaced with a new one: who does not obey shall not eat.''' Exactly how many Bolsheviks have been expelled, arrested, exiled, exterminated, since 1923, when the era of Bonapartism opened, we shall find out when we go through the archives of Stalin’s political police.
::::I have to say that this supports Nicholas's reading of it, since Trotsky is using the phrase to describe Stalin's reign of terror, and definitely sees the altered adage as a Very Bad Thing. [[User:Carillonneur|Carillonneur]] 15:51, 24 April 2009 (EDT)

::::: No, the lecture does not say that "Trotsky used the phrase as his personal motto." The lecture says it was Trotsky's motto (about the communist regime). I'll add the parenthetical to avoid misinterpretation.--[[User:Aschlafly|Andy Schlafly]] 15:58, 24 April 2009 (EDT)

:::::: Orwell was a member of the POUM (Workers' Party of Marxist Unification ). He wrote a book about it, ''Homage to Catalonia''. That's hardly obscure. [[User:ClementB|Clement ♗]] 16:05, 24 April 2009 (EDT)

== 20th century science ==

There are a number of comments I'd like to make about the science / technology section of this lecture. That is the only part I'm going to address; the rise of "modern physics" (quantum mechanics and relativity) happens to be something I take great interest in. Some of my comments are rather trivial, like the way Freud died, but some are, in my opinion, quite serious, to the point of being untrue, or at least seriously misleading to the point of appearing deceptive.

:But first, you have challenged other contributors making comments on the talk page for lecture 9 to take your midterm exam. Accordingly, I have created a "modern physics" midterm [[User:Robert/Physics Exam|here]]. In the spirit of good fun, I challenge you to take it. And, of course, feel free to adapt any of these questions into your exams.

Here are my comments:

*"The most notable accomplishment in science was the discovery of quantum mechanics ..." You should qualify it as "accomplishments in ''20th century'' science". I realize that this lecture is about the early 20th century, so the context should be clear, but the sentence looks funny without that qualification. Also, you should mention that there were ''two'' theoretical achievements in the early years of the 20th century: quantum mechanics and relativity. Those two together are considered to be the rise of "modern physics", perhaps the most important physics watershed in history. You may consider them very different, and you may assign much greater importance to one than the other, but the fact is that they are taken together whenever one writes the history of "modern physics".
*"ultimately produced about a dozen Nobel Prizes" About a dozen? Much more than that, I'd say. I don't have the list in front of me (it could be looked up easily), but I'd guess that most physics Nobels have been related to quantum mechanics and subatomic behavior.
*"basis for the entire computer industry today" I'll have more to say about that below.
*"Enrico Fermi, a devout Christian" I don't know for sure, but that may be a stretch. From what I've read, he was raised in a not-very-observant Catholic family, and was not very observant himself. He may have been an agnostic. But I'm not an expert on this. You could very well have better information.
*"Quantum mechanics formed the basis later for the discovery of very small transistors, which today form the integrated circuits in every computer and electronic device." More below. It is, in any case, somewhat redundant with an earlier statement.
*"relativity was proposed based on mathematical theory rather than observation" Well, quantum mechanics was also based on mathematical theory (statistical mechanics) rather than observation. No one observed quantum effects in a recognizable way until well after Planck's "quantized oscillator" theory. Of course, Planck's observations about statistical mechanics were ultimately based on observation (no area of physics can be formulated completely in a vacuum), but the same can be said of relativity -- it was based on observed invariance of Maxwell's equations, etc. The two theories actually had quite similar origins, as mathematical theories designed to explain effects that were quite esoteric in comparison with the usual way scientific theories are made (dropping balls from the Tower of Pisa, for example.)
*"the expression arose that 'space is curved.' But experiments later proved that space is flat overall." Totally misleading and/or wrong. The curvature of spacetime as the source of gravity is firmly established, and has been for decades. The way this is popularized is unfortunate, but the statement you made seems to be exploiting the imprecision of the curvature in the popular imagination. It then seems to imply that space isn't curved after all. This is just wrong, if not outright deceptive. The two effects are completely different. The scientists using supernova data to determine the overall curvature of the universe know full well that ''local'' curvature is real, and is the source of gravity.
*"Nothing useful has even been built based on the theory of relativity" More below.
*"Einstein's work had nothing to do with the development of the atom bomb, contrary to popular opinion." Largely true, and you are to be congratulated for debunking some nonsense. (I even have a book about the Manhattan Project claiming that Einstein was at Los Alamos!) But "nothing to do with" is too strong a statement. I'm not sure just how the sentence should be phrased.
*"validity of that particular award [Hulse/Taylor, I presume?] is questionable" Is this really a controversy you want to get into? Are you questioning the research or results of Hulse and Taylor? Can you cite that? Is it relevant to the history of 20th century physics?
*"Many things predicted by the theory of relativity, such as gravitons" Not true. Relativity never predicted gravitons. They arose from later attempts (still ongoing) to unify relativity with quantum mechanics. As you know, Einstein never participated in those attempts, and wasn't very accepting of quantum mechanics.
*"Many observed phenomena, such as the bending of light passing near the sun or the advance of the perihelion in the orbit of Mercury, can be also predicted by Newton's theory." '''Absolutely untrue'''. The two theories give different values for the bending of light; and the determination of which value was correct (not whether it bends at all) is what Eddington was seeking. We all know that Eddington handled the situation in a way that wouldn't pass muster today, and pointing this out was the right thing. But subsequent observations, that are accurate and unimpeachable, confirm the relativity value or 1.75 arcseconds. There is a lot of confusion in the lay literature about whether classical mechanics predicted any bending at all, and, consequently, just what Eddington was looking for. You have a chance to clear that up. But the existing article seems to muddy the waters, rather than clearing them.
:Furthermore, Newton's theory '''does not predict (anomalous) perihelion precession'''. Absolutely not at all. Now one might think that one could fudge the exponent (2) in the inverse square law, but
:*That wouldn't be Newton's theory. Newton set the exponent to 2.
:*It doesn't work in any case. The anomalous precession fraction is 3 v2/c2. Connected with the velocity as a fraction of the speed of light. It is, without question, a relativistic effect.
:General relativity is the only credible theory explaining this, and has been right from the start.
*"Eddington supposedly retorted, 'Who's the third?'" This is a very widely misunderstood anecdote. You say nothing about what he meant. Please put it into the context, so that people can understand what it was about, and not continue with their lack of understanding.
*"many seized upon the theory of relativity to apply it in a vague way to morality and social issues" Could you please say "wrongly seized upon"? I know you believe that seizing upon this is wrong; you can help put this foolishness to rest.
*"There remains enormous political support for the theory of relativity that has nothing to do with physics" Really? Does this have to do with the "vague morality and social issues" business? You seem to be implying that by putting it in the very next sentence. Do you really believe that congressional appropriations on LIGO, for example, are based on some notion that it will promote moral relativism? Can you cite evidence?
*Big bang vs. steady state -- good.
*Freud -- minor nit: Is there a point to saying that his death was assisted by a physician? If your intent is to show that doctor-assisted suicide did not originate with Dr. Kevorkian, and that it was going on at least as far back as 1939, please say so, with appropriate statistical data. As it is, one anecdote doesn't really say much. BTW, a far more telling anecdote relating to 20th century science would be the death of Max Planck's son.

=== When is technology "based on" something theoretical? ===

Some statements in the lecture, cited above, attempt to draw a clear distinction between quantum mechanics, with an apparently huge number of practical applications (including the entire computer and semiconductor industry) and relativity, with none at all. It is extremely misleading to say that quantum mechanics can be credited with producing transistor technology. So much so that a reader might come away from this lecture having been deceived into thinking that quantum mechanics is "more important" than relativity. They are both extremely important. But they are both '''theoretical''' advances. They give us insights into how the universe works. In retrospect, those insights are, of course, crucial to everything we do. Including transistors.

Consider this:

*Quantum mechanics tells us how electron orbitals work, and hence how all chemical reactions work. Without chemical reactions, we would have nothing.
*Relativity tells us how gravity works. Without gravity, we would have nothing. Relativity also tells us how electromagnetism works. This is the basis for the "electrical revolution" of the 19th and 20th centuries.

But people have known about chemical reactions (for example, fire) since long before 1900, and people have known about gravity since long before 1900. Fire, and all the inventions dependent on it, is now known to be explained by quantum mechanics. Space travel, to name one thing out of millions, depends on combustion. Do we credit quantum mechanics for that?

Similarly, without gravity, we would not be in orbit around the Sun. We would have none of the benefits of being close to a star. In fact, neither the Sun nor the Earth could have formed. Do we credit relativity for that?

Furthermore, the electric and magnetic forces are unified by relativity. Magnetism could be thought of as just a relativistic consequence of the electric force. Therefore, all electric motors and generators, for example, use relativity as the underpinnings of their operation. Do we credit relativity for that? Of course, Maxwell knew nothing about relativity when he formulated his equations. He did not know that they took the form that they did because of relativity. But the cavemen didn't know about the quantum-mechanical underpinnings of fire.

We can credit quantum mechanics, and relativity, '''after the fact''' for all these wonderful things. But most of them were developed without direct use of these theories. There are a few inventions (SQUIDS, for example) that directly, intentionally, and knowingly depend on quantum mechanics. But most use it indirectly. The semiconductor properties of Germanium and Silicon were known long before the details of the "band theory" solid-state quantum mechanics were worked out.

Putting it another way, one can fabricate a transistor without knowing the details of quantum mechanics, just as one can upload gravitational time dilation information to GPS satellites, or turn on a fan, without knowing the details of relativity.

[[User:Robert|Robert]] 15:21, 16 May 2009 (EDT)

User:Robert/Physics Exam

2009-05-16T19:10:04Z

Robert: The exam!

This is a "midterm exam" on the rise of "modern physics" (ca. 1900), intended to accompany [[World History Lecture Eleven]]. It is presented in the spirit of good fun.

==QUANTUM MECHANICS==

(Multiple choice, choose one) What observation led to the insight that light is emitted in discrete quanta?

:A. photoelectric effect
:B. Stern-Gerlach experiment
:C. "ultraviolet catastrophe"
:D. Geiger-Marsden experiment
:E. Rutherford experiment
:F. Franck-Hertz experiment
:G. Bohr model of the atom
:H. Davisson-Germer experiment

(Multiple choice, choose one) What observation led to the insight that light is absorbed in discrete quanta?

:(as above)

(Multiple choice, choose one) What observation led to the insight that light carries energy in discrete quanta?

:(as above)

(Multiple choice, choose one) What observation led to the insight that electron energies in an atom are in discrete quanta?

:(as above)

(Multiple choice, choose one) What observation showed the wave nature of actual physical particles?

:(as above)

(Multiple choice, choose one) Which of the experiments listed above was assigned to some newcomers to the laboratory, as a sort of "throw-away" exercise?

:(as above)

(Multiple choice, choose all that apply) The Pauli exclusion principle applies to what types of particles?

:A. Leptons
:B. Hadrons
:C. Fermions
:D. Gluons
:E. Bosons
:F. Photons

(short answer) Ernest Rutherford made a famous statement involving tissue paper. To what was he referring?

(short answer) What happened to Erwin Planck, son of Max Planck?

(medium answer) Describe the contributions of Planck, Bohr, and Schrodinger, and give the approximate dates of each.

(Honors essay) Briefly describe the eight experiments/observations/insights listed above.

==RELATIVITY==

When Arthur Eddington made his famous statement, (referring to the number of people who understood general relativity at that time) "I'm wondering who is the third", what was the question/statement to which he was directly replying?

:A. "Is it really true that General Relativity is so complicated that only three people understand it?"
:B. "Isn't it true that you, Einstein, Poincare, and Lorentz are the only people who really understand this? And yet they say that the number is actually only three."
:C. "Don't be modest, Eddington."
:D. "You and Einstein obviously understand this. Anyone else?"

The actual event at which Eddington made that statement was the discussion period following a lecture/seminar. Who was the speaker at that lecture?

:A. Einstein
:B. Minkowski
:C. Eddington himself
:D. Lorentz

(short answer) Taking at face value the assertion that three people really understood general relativity at the time, who were those people?

Aside from general relativity, which of the following is '''NOT''' among the then-credible hypotheses advanced in the late 19th century / early 20th century to explain the anomalous perihelion shift of Mercury?

:A. Unobserved solar oblateness
:B. An unknown moon of Mercury
:C. A velocity-dependent term in the equation of gravity
:D. Geometric change in Mercury due to the FitzGerald contraction
:E. An unknown small planet
:F. A finite speed for the propagation of the gravitational force

(short answer) What is the difference between Einstein's formulation of relativistic length change ("the FitzGerald contraction") and FitzGerald's own formulation?

(short answer) What result of relativity led researchers to believe, prior to measuring it, that the fission of the Uranium nucleus would release enormous amounts of energy, ''even by the standards of other known nuclear processes''? How was this calculation done? What was the resultant energy?

(short answer) One pre-Einstein hypothesis to explain the null result of the Michelson-Morley experiment was that the Earth dragged its local aether with it. What observations refuted that?

User:Robert

2009-05-16T19:05:01Z

Robert: Point to the "physics exam".

I have created a "just for fun" exam on modern physics, intended to accompany
[[World History Lecture Eleven]]. It is [[User:Robert/Physics Exam|here]].

Conservapedia talk:Critical Thinking in Math

2007-09-14T00:27:10Z

Robert: Request status change to student.

I have a number of comments on the proposed curriculum. Much of this relates to the difference between something that might be titled "mathematical topics in popular culture" and "critical thinking in mathematics". The latter requires very careful presentation, with adherence to the axiomatic method and the understanding of correct proof procedures. This concern applies particularly to the material on the Axiom of Choice and the Gödel incompleteness theorem.

I believe that there is at least a 10-year gap in educational achievement between 9th graders (even future Riemann's!) and some of the things mentioned. We couldn't say anything about the Axiom of Choice or Wiles' proof that wouldn't be dumbed-down to the point of worthlessness, and, IMHO, not what we want for this class.

I am not aware of any a controversy about the method of proof by contradiction. It is so totally ingrained into the subject matter of mathematical proof that nothing further needs to be said. I still remember being taught about it, in 9th grade, before we did any "real" math.

While we are discussing the 17 proofs of the infinitude of primes, we might discuss the fact that there are over 300 proofs of Pythagoras' theorem. Including one by President James Garfield!

The "transcendental numbers - how do we know they exist?" is not the way I would put it. I assume you are referring to the Cantor "diagonal" construction, layered on top of a Dedekind or Cauchy construction of the reals. But there's actually a lot of tedium in the proof that the reals can be represented by decimal expansions. Do you want to gloss over that and just use the "intuitive fact" that the reals correspond to the decimals? But I have another problem: "How do we know they exist?" has a sort of mystical ring to it, particularly because of the connotations of the word "transcendental". The same thing construction could be used to prove the existence of irrationals, without the mystical baggage. They're uncountable too. And there is a very clever and approachable proof from the ancient Greeks about the existence of irrationals, that does not rely on countability arguments or diagonalization. Or do you genuinely want to use the transcendentals because the ancient proof can't be used?

"Problems solved only with proof-by-contradiction". As above, I consider the method of contradiction to be so fundamental that I'd be reluctant ever to say that somethng can be proved '''only''' that way. Better: In the introductory explanation of proof by contradiction, using the "always a prime between N and N+1" theorem, or the "infinite number of primes" theorem, as an example to motivate it.

Definition of the integers. Do you really want to do a Peano-postulate program here? As in Landau's "Foundations of Analysis"? I don't think people in this age group will actually appreciate that the tediousness of this is worth it. (Of course, '''we''' know that it's worth it, but '''they''' donn't.) Also, a Dedekind-cut construction of the reals would actually contain material that the students don't already "know", in that it shows, for example, that the square root of 2 really exists. But of course, skipping over the integers and going straight to the reals is somewhat unesthetic! The students already "know" the result of the Peano program, they just don't realize that they don't really know it.

"Interesting problems in number theory and Euclidean geometry". Yes! There's a lot of really cool, engaging, and surprising material in geometry, above and beyond its use to show the axiomatic method. Geometrical inversion, for example.

"Axiom of Choice ... Wiles' proof". I have a problem with this. There's really very little we can say about AC, and even less about Wiles' proof, that would be accessible. The simplest places that I know of in which AC appears are the Tychonoff Theorem and the construction of sets that are not Lebesgue measurable. Not what I would want to do in a course like this.

The Gödel incompleteness theorem, and the Church or Turing analysis, are extremely tedious to go through if they are to be understood properly, and take a great deal of background that high school age people won't be able to get through. Once again, we would have to dumb it down to the point of worthlessness. Though there '''are''' presentations of what is effectively Russell's paradox, which is related, and that are accessible and compelling.

There are other things that can be covered that are very good for high school students: projective geometry, conic sections, vectors, matrices, operators, eigenvectors/values, function spaces, introduction to differential equations using eigenfunctions, complex numbers in electrical engineering, Fourier series, inner products, geometrical inversion, ....

: You raise some good points. Thank you. I will response as soon as I can. In Christ, --[[User:Aschlafly|Aschlafly]] 01:14, 7 September 2007 (EDT)

: In further response, first in a general way, I do not subscribe to the view that more abstraction is better. Unfortunately, many of today's top college math progams graduate studens who haven't a clue about [[number theory]], unsolved problems, or issues in math that were controversial only a few decades ago. Proof by contradiction was disfavored, for obvious reasons, by many mathematicians as recently as 30 years ago. That you're completely unaware of it merely underscores the need for this course. It's healthy to step back and evaluate a field from a critical perspective. This is not by any means yield to popular opinion. Quite the contrary, it is to inject a degree of accountability . In Christ,--[[User:Aschlafly|Aschlafly]] 00:52, 9 September 2007 (EDT)

::Well, I'm chagrined and disappointed by this, but I'm always willing to admit my ignorance and learn new things. So please change my status from instructor to student -- I'm still very much interested in this. Also, can you recommend any books that can fill me in on some of these issues? [[User:Robert|Robert]] 20:27, 13 September 2007 (EDT)

Conservapedia talk:Critical Thinking in Math

2007-09-07T00:41:08Z

Robert: Discussion of curriculum

Conservapedia:Critical Thinking in Math

2007-08-24T00:42:12Z

Robert: /* Draft Curriculum */