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Barbara:

"Unfortunately, to this day a statement such as one's love for geometry has the feel to me of something I might hear from ET about life on his planet. (I remember reducing Joan Mitchell Blumenthal to literal tears of frustration as she tried vainly to explain some theorem to me; however hard I tried to understand, my mind seemed to snap shut the moment I saw those squares and triangles on paper.) But I did love deductive logic, because I saw its purpose and it fitted my purposes.

"At UCLA I took a course in logic from Hans Reichenbach, a famous logical positivist -- and Phil, this is relevant to our discussion of integration --who did something quite wonderful. He presented the class with murder mysteries, which we had to solve by the use of deductive logic. It was fun, it was instructive, and it tied logic to reality."

1. My real love in mathematics is not deductive logic and proof, but inductive reasoning. I was tinkering around out of curiosity one day in my senior year in high school. I wondered: why is the double and the square the same number for 2, but not for any other number? I made some columns of numbers that included the numbers themselves, their doubles, and their squares and stared at them a bit, trying to see a pattern. Shortly, a pattern actually did leap out at me. By comparing the numbers in the columns, I saw that the square of any number is the same as the square of the next smaller number PLUS the double of the next smaller number PLUS 1. I had actually inductively discovered what we all learn in algebra as (x+1)-squared = xsquared + 2x + 1.

Through the years, by indulging my curiosity about other issues in math, I have made other discoveries of this sort -- plus one that I don't think anyone else has ever discovered. I've perused the literature and find no trace of it. I discovered a new method for generating "Pythagorean triplets", which are sets of three whole numbers that work as sides of right triangles. The one method I have ever seen discussed in texts and journals was discovered over 2000 years ago by the Greeks and Babylonians, but mine is a distinct method, and it works better in some ways than the traditional one. Also, I know it's valid, because I later proved it deductively by applying the binomial theorem to the Pythagorean equation. If I'd done that to start with, I'd have had a result, but I wouldn't have had the faintest idea what to do with it. It was only because I started with brute arithmetic facts and tried to discern a pattern among them that I realized I was on the trail of a useful generalization or principle (my method for generating Pythagorean triples).

This kind of mathematics is what George Polya writes about in his books on math. It is the creative, discovery-oriented side of math. It deeply appeals to hunter-gatherer types such as myself. :-)

2. There are commercially available books that teach algebra, geometry, and calculus in a much more metaphor-rich, literary style. Borders carries them (or did several years ago, when I first noticed them). They look like a lot of fun, though dry, techno types would probably turn up their noses at them. I personally think that technical material should be tailored for people according to their thinking styles and personalities. Intuitive-thinking types (NTs in Jungian/MBTI lingo) don't need no stinking metaphors, man! But Intuitive-feeling thypes (NFs) thrive on such stuff, and it would actually make arid subjects as math more accessible to them, if they had a motivation to learn it.

REB

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> I remember reducing Joan Mitchell Blumenthal to literal tears of frustration as she tried vainly to explain some theorem to me; however hard I tried to understand, my mind seemed to snap shut the moment I saw those squares and triangles on paper.)

Barbara, I can explain anything from algebra or geometry to anyone. You're not going to force me prove this to you at the summer conference, are you? :-)

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More on recovering Objectivists:

I've observed a pattern with a lot of them, so frequent that I gave it a name - post-Objectivist wild oats syndrome. It was endemic in the first few years after the Branden excommunication.

Intellectually-inclined people virtually always go through a phase of granting serious attention to fairly silly skeptical and solipsitic notions, as when they ask whether they exist or not. Most get this out of their system at eighteen or nineteen. Some, though, were too dogmatically Randroid at that age, and they go through it, to everyone's embarassment, a decade or two later. It's like stories one hears about people who went steady with the same partner all through high school and got married not long thereafter. Five, ten or twenty years later they find themselves divorced and playing the field for the first time, looking ridiculous as they do.

Peter

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I haven't run into that many "recovering Objectivists" over the years.

I never expected to become one (sort of). When I joined the Unitarian community, it was lot like how I always imagined Objectivism was or could be, in the flesh.

The Fountainhead and Atlas Shrugged were very liberating to me, especially at first. I think that's the typical reaction.

I never saw anything in any of the books that suggested that you need to be an arrogant, superior prick. Yet, that's what happened to me and I didn't pay attention to that for a long time; to me it was simply sticking to principles. Had to work on that for more than a minute.

The reason I looked for something else is because, while Obectivism satisfied (and in many respects continues to do so) most needs, it simply did not satisfy, for me, my spirituality. In this way, I felt very empty.

What I did was more of an integration than a departure.

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Rich,

I don't want to hear it. You are our resident RECOVERING OBJECTIVIST. No more rationalizations.

Up on the block. Come on! Get on up there!

WE ARE GONNA DISSECT YO ASS, BRO!!!

Gotta see what makes you tick.

//;-))

Michael

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MSK-

Heck, why not? I was resident heretic at SOLO for awhile, I can take it!

There was a lot of funny stuff there, as you know. But I thought one of the funnier was when I explained that the UU church is pluralistic, including atheists. Of course the next question was whether I was "one of the atheist members or not."

It just got all twisty after that, man... I just couldn't get individual religious consciousness through to some of them.

rde

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> I discovered a new method for generating "Pythagorean triplets"

Roger, sort of away from the topic of this thread, but there are math websites where teachers and experts answer questions, make comments. If you submitted or posted it there, you might find out if it's original.

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I wrote:

I discovered a new method for generating "Pythagorean triplets"

Phil commented:

Roger, sort of away from the topic of this thread, but there are math websites where teachers and experts answer questions, make comments. If you submitted or posted it there, you might find out if it's original.

It's true that I have complained about thread hijacking or rampant topic straying over in the aesthetics folder, but that is a dedicated folder for the topic of aesthetics. I was under the impression that it was OK to be loose and informal and free-wheeling in the "Living Room." Is that not so?

I appreciate your suggestion about the math websites for Q&A &c. I may follow up and do just that.

TWIMC, some of my math essays are posted here:

http://members.aol.com/REBissell/indexmmm.html

In particular, the one about "x to the zero power" grew out of comments I made back in 1995 to David Kelley's online epistemology seminar. Someone had asked what was the meaning in reality of zero exponents. To my chagrin, I noticed that in some later lecture series (perhaps "Induction in Physics and Philosophy"), Peikoff was giving one of his students a pat on the back for his "brilliant" explanation of the meaning of zero exponents. I can't help but wonder...

REB

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I have thoroughly enjoyed reading the thoughts expressed on this tread. Thanks everyone.

One of the critically underdeveloped aspects of a philosophy for living life as an Objectivist is the concept of friendship. There is much more discussion of hero-worship and of romantic love in Ayn Rand's work, but there is little discussion of friendship. This is rather strange, since friendship and our desire to respect the heroic and our desire for romantic love are at least closely related. I will only sketch some of my concerns about the effect this has on Objectiivists and their forum behaviors and its implications for the development of a broad Objectivist movement here. I think this will be the subject of my next essay on my blog.

When I read Atlas Shrugged, I loved it. I really enjoyed the heroes and everthing about them. Sometimes the longer sections on the villians dragged a bit for me. The principal other disappointment for me was the fact that Eddie Willers was left to die in the crumbling world.

Eddie Willers is not a super-hero like John Galt or Hank Readen. Though one wonders that Hank had a place in Galt's Gulch even after his long guilt over not loving his wife, while Nathaniel Branden has no place in ARI Objectivism. But back to Eddie. He was a childhood friend of Francisco D'Anconia and he was always Dagny's friend. Whenever she needed assistance, he was there to do his best. After innumerable meals with John Galt, how could he not have been a friend? He had a good sense of life and he was a practical man. He loved Dagny. Now, if you know a very decent person well and you share a love with him for something or someone, isn't that person likely to be a friend?

With civilization rapidly collapsing, knowing that those most associated with the vanishing heroes will be most in danger, knowing that Eddie was reasonably successful in his work and therefore had possessions the looters were bound to steal or kill for, knowing that soon after returning to the world, the railroads would have to be rebuilt and Dagny would need help, you would not leave your friend Eddie behind. If you would, you are a real low-life. Yet, for some reason, presumably her great focus on hero-worship, Ayn Rand left Eddie to die. No one who thoroughly understands the key principles of Objectivism and lives those principles fully in their lives would do this. It is not rational and it is not consistent with our principles.

If we worship the heroic in man, we have to respect the good in man. The equivalent hero to John Galt has probably never lived. I, for sure, have never known him. One of the great fears that many Objectivists have is that they would not be invited to Galt's Gulch. I, for one, would not be. Now, if you love heroes, it is very disappointing for most people not to measure up. If Objectivism says we must all be John Galts or very close to a man of that stature, then Objectivists will feel they have failed. Failure is hard to face and a philosophy that ensures failure does not make a good philosophy for living life.

This realization makes many Objectivists very insecure and that insecurity looks for very unprincipled ways to reassure itself. One way is to make oneself a hero-worshipper by worshiping the goddess Ayn Rand and seek acceptance by other worshippers in a parallel to the acceptance so many Christians and other religious people seek from others. Another way is to substitute a knowledge of Ayn Rand's writings and viewpoints for one's own and become immersed in that. Then no one, of the religious group, can say that one is unworthy, at least as long as you only quote Ayn Rand.

If we are to end the bickering in Objectivism, people need to have the means to develop a greater sense of security in being themselves. They need to respect Eddie Willers and give him their friendship. Most people who cannot respect him, will not be able to respect themselves. We need to realize that heroes come in many sizes. We need to appreciate the heroic acts that many people do and rather than constantly griping that they are not always heroes, we need to encourage them with praise for those acts that are heroic. We need to make room for Eddie Willers. We also need to make room for Nathaniel Branden.

No mass acceptance of Objectivism will ever occur until Objectivists offer more people encouragement for maximizing the best in them. If Galt's Gulch only has room for John Galt, Francisco, Dagny, and their equivalent, the Objectivist movement will remain small and nasty. This does not need to be the fate of Objectivism. There are many wise and nice Objectivists. There need to be many more and they need to become at least as visible as the insecure cultist type of Objectivist.

Such people are not really the real thing since they are not rational, do not think independently, do not sufficiently value achievement to risk making the mistakes that inevitably come with pushing the boundaries of our knowledge, and do not have well-developed self-esteem. Being an Objectivist is not simply parroting Ayn Rand's views. To be an Objectivist, you must be able to think rationally and independently. You must also be able to develop a strong understanding of your own individuality and a mastery for managing your own life. Our lives and the world we live in are tremendously complex. Ayn Rand, prodigious though she was, did not figure it all out for us. She told us to do that for ourselves. On our own, though having learned much from her, we will make mistakes, as she did. We must learn from our mistakes and hers, accept that we will make mistakes, and accept that others will also. This is an unavoidable part of life and we should not allow it to keep us from living our lives.

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> We need to appreciate the heroic acts that many people do and rather than constantly griping that they are not always heroes, we need to encourage them with praise for those acts that are heroic...No mass acceptance of Objectivism will ever occur until Objectivists offer more people encouragement for maximizing the best in them.

Very well put, Charles. There's a strong tendency to have a Platonic rather than an Aristotelian standard of perfection among Objectivists: If you ever make a mistake, you're evil or an evader and not worthy of praise or support or admiration.

> One of the great fears that many Objectivists have is that they would not be invited to Galt's Gulch.

I need to inform you that John Galt has read your post and has just emailed me to extend you an invitation to the Gulch. (If you are attending the summer TOC conference, I can hand you the actual invitation in person.) Unfortunately, he told me I either needed to do more writing or help him market his static electricity motor, so I'm still on probationary status.

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My last note was a first draft on some ideas I have had in the back of my mind for a very long time. It was near dawn when I started it and after dawn when I finished and realized I was in great need of the dinner I had never had. Somehow, I failed to really close the loop on the importance of better developing the concept and practice of friendship among Objectivists. It needs more work and will get more work.

Phil,

Thanks for the comment and the humor. I got a good laugh out of it. I thought Hank was counseling John to withhold the invitation until I had developed Anderson Super Material. Did they give up on that and just say, "Well, he would at least be useful doing our lab analyses for us."?

I really wish I could afford to go to the TOC Summer Seminar, but I am paying loans for sending 2 daughters to college and my laboratory has required a great deal of investment lately. If that were not enough, my Dad has been in increasingly bad health, so what little time I can get away from the lab, I want to spend with him and my mother in Oklahoma. Maybe the summer of 2007 will be different. When I have gone, before Kirsten went to college, I loved it. It was wonderful being among so many good and interesting people.

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Charles, you wrote: ". . . for some reason, presumably her great focus on hero-worship, Ayn Rand left Eddie to die. No one who thoroughly understands the key principles of Objectivism and lives those principles fully in their lives would do this. It is not rational and it is not consistent with our principles."

I can tell you what Rand said about why Eddie Willers was not invited to join the strikers in Galt's Gulch. (And note that the Valley was a haven only for the people who had gone on strike.) She said that the Valley was for giants of intellect and achievement, and not merely for "good" people. Eddie was intended to be the average man at his best. Further, Eddie's fate was intended to convey that such a man can survive and prosper in a world run by Dagny, Rearden, and others like them, but in a world run by the James Taggarts, he was doomed to perish.

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Barbara,

I understand that this is what Ayn Rand must have had in mind. It is certainly true that Eddie Willers would prosper only in a world with men of greater intellect and ability than he had. However, the collapse and the end were far along and chaos had taken over. Real people care about the good people they know. Besides, Eddie was much better than average. He was not very philosophical and he was not a giant, but he had earned everyone's respect and friendship. While one can symbolically treat Eddie as he was in the novel, people with rational values would not do that to the real person who had been a part of their lives. It was only necessary to give him a hideaway, maybe not even in Galt's Gulch, for a few weeks or months. Eddie was of value, but the message really is that he was not of much value. People who enjoy life form real attachments to the good people who have long been close to them. Eddie had always been close to Dagny and had done his best to serve her well. How could she leave him behind without remorse? Hadn't he ever become woven into her life?

Barbara, if you had run Taggart Railways, could you have left Eddie Willers behind without feeling pain specifically for the loss of Eddie Willers? I could not have and I feel no remorse that I could not have. I do not think this is an irrational thought. The bonds that we form with good people who are not intellectual giants are rationally important to us. In this world, let alone the more deteriorated world of Atlas Shrugged, good people are not to be taken for granted.

Of course the world of Atlas Shrugged is the stylized and symbollic world of a novel and it lives for a purpose. It is not real life. But most Objectivists forget this. Perhaps rather than objecting to Eddie being left behind in the novel, I should just remind everyone that in real life we should not leave him behind. We need to at least make the distinction between these worlds.

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On other forums, some people wanting to point out what Barbara Branden pointed out above would have started something like,

"You are a presumptuous dimwit to think you have any business re-writing Atlas Shrugged."

Of course, this is true. To add to this, I have made the point before that the world created for the purpose of the novel Atlas Shrugged is not the same as the real world. But in this context and at this time I was not thinking of that, though I should have been. The point in the last paragraph of my last note should have been central to the longer note on Eddie Willers above.

Thanks for your more constructive note Barbara. It reminded me of the context I was forgetting in this case. It is a context a lot of Objectivists forget even when they are too worshipful to suggest re-writing the novel.

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Charles,

I started laughing reading your defense of Eddie Willers. I wanted to yell out, "Rand wasted the dude. Deal with it! Get over it!"

But you are right. Eddie is not a real person. He is a symbol (selectively recreated from reality).

Your comments about the callousness of Dagny on leaving him behind without remorse is a good reminder that Dagny also is not a real person. People should not emulate her attitude toward Eddie. She was more fleshed out, but still she was selectively recreated from reality. She did not represent full reality - particularly not full psychological reality. (Although she did kind of have a way with heroic men...)

Your comments also are a reminder that Atlas Shrugged is about philosophy - especially where making rational choices are involved - not about psychology (which is present, but very secondary and sketchy). The fate of Eddie Willers works on a philosophical level for depicting society, but not on a psychological one for depicting how a person acts and feels towards friends.

btw - The kind of dimwit who holds Atlas Shrugged to be the Holy Bible of Objectivism will be hard to find around here. I don't speak for Barbara, but from what I have learned of her, I imagine her response was to provide you some information to help you get over your exasperation. I might be wrong, but I think she was trying to give you some comfort by giving you a reason why your friend Eddie bit the big one (you really did come off as upset), not "set you straight on the facts" like our dear dimwits would.

Michael

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Many of the people close to me, loved by me, and important to me are no more intellectual and achieving giants than Eddie Willers. Of course, it would be wonderful to be surrounded by such giants, but that is not the pattern of our real lives. Eddie Willers is important to me.

Yes, I agree with your observations on the distinction between the characters of the novel and our friends in real life. It is very important for Objectivists to be careful to make these distinctions themselves. They should be careful not to expect that their wife will be Dagny Taggert. Though I must say that I find her very appealing, I would add a few characteristics before taking her as a lover. Whoa, there goes that rampant ego again!

On your comment that I came across as upset, was that in regard to my long dawn rant or was that with respect to my reply to Barbara Branden? For the reasons in my first paragraph above, I have always had concerns that might register as upset in the first case. If you speak of my reply, any upset I may have had was with myself for forgetting the context of the novel and I hope that that did not spill over into my reply as being upset with Barbara. I was not upset with her, though I may have put her on the spot to reply about how she would act in real life and maybe I should not have done that. But, that is really the question here, isn't it? I did take her comment as an attempt to answer my dilemna and it was useful in reminding me of the role of symbols. I never thought that she meant in any way to be other than constructive. I really do appreciate her comment and in the context of what I can expect she knows about me, there is no reason for me to think that she should have known that I would simply benefit from a reminder of the context of the novel versus real life.

As big as my ego is, I nonetheless have no business re-writing Atlas Shrugged. My comments on that were just my effort to keep my perspective real and to point out that Barbara's constructive response was in contrast to the unconstructive response I might easily have had elsewhere! I love Atlas Shrugged still, even though it is less than a complete blueprint for living one's life! Unfortunately, some people do not remember that and they think they are the authenitic Objectivists. Other people observe that it is not and they say that therefore Objectivism is not a philosophy for living life. They are wrong, but this is because living the Objectivist life is not fully contained in the novel. We all have to apply the principles to our own lives with continuous rational, independent thought. This then tends to make us really individualistic and unruly people!

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Charles,

The written word sure has its limitations. You did not come off as upset against Barbara. You came off as upset (to me at least) because your friend Eddie Willers bought it. You didn't want Eddie to die and you were upset that he did. And his friend Dagny didn't give two hoots.

I wanted to convey that I thought Barbara was giving you a shoulder to cry on, that's all.

(I better stop before I get in trouble...)

Michael

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Charles: "Barbara, if you had run Taggart Railways, could you have left Eddie Willers behind without feeling pain specifically for the loss of Eddie Willers?"

I could not have left him behind -- period.

You did not at all put me on the spot, and I did not think you were offended at me. I understand what bothered you, and I consider it a wholly legitimate concern. I'm glad if my explanation of how Rand saw the issue in the context of her fiction was helpful to you.

You say you will be writing about friendship on your blog. I hope you will also publish it here. I agree that it's a very important subject, which Objectivism -- and Objectivists -- have not dealt with, and an article on the subject should lead to very interesting discussions. In my view, some friendships can be as important as romantic love.

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The scene that really angered me was the one in which Galt refuses to let Francisco tell Hank that Dagny was still alive after she'd crashed in the valley. Nathaniel says in his memoir that he was bothered by that, and Ayn said something about worrying that Galt would look wishy-washy if he made an exception for a person not on strike. I thought it was too cruel to countenance and made Rand look as if she was stretching a point way too far. The line "Pity, Francisco?" I sometimes think of in mockery, answering, "Hell, yes."

Ellen

___

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BTW, Eddie Willers did not die. Last I heard from him, he said that he rides his horse to go places now, and that he likes it even better than before when he used to travel by train.

He is merried to Cheryl, she didn't not die, hers was a faked suicide.

CD

ps.

He also said that people are punished with death penalty, not only if they commit a crime, but also at the first sign of improving their life at someone else’s cost . You are allowed to invent things, only, if you will work as any person would for your inventions, other wise you must keep the inventions to yourself.

For instance, you cannot built a ship if you will not navigate with it. You cannot open a restaurant if you would not cook, you cannot be a president if you would not fight in first line during a war etc…

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*laugh* Thanks for the epilogue Ciro. I too was never fond of the cavalier abandonment of Eddie in AS. However, it didn't bother me as much as killing off Taggart's wife (or Andrei after he found reality in WTL).

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It is a pleasure to have the company of nice and intelligent people, especially when they are also Objectivists who can understand my values and share so many of my interests. Thank you all for the ideas discussed here and also for the comfort you give me simply by existing.

Barbara,

I was pretty sure that you would not and could not leave Eddie behind. Thanks for your personal confirmation that we share values and live our own lives in a more complete way than the characters we love and enjoy so much in Atlas Shrugged. Our real lives are more complicated than those of characters whose role is to clarify a few, albeit important, issues. This complexity helps to make us richly individual. I think you understand this well and I am looking forward, with fascination, to learning more about your thoughts.

Thanks for the interest in and encouragement for writing more on friendships. I cannot claim to be especially expert on the subject, but I think about it and wish others would think more about it. Like you, I think that a good friendship is of comparable value to romantic love. Specifically, Objectivists should value friendships more than many do. In forming and maintaining a friendship, many, hugely many, of our values become involved. A good friendship is the result of many shared values, the investment of our most limited resource, time, and a great way to make the best in ourselves more visible. As we have a loyality to our values, we should certainly have a loyalty for our friends. If we do not, then our grasp on our values, so entangled in a friendship, is very fragile.

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Ellen,

I also found that I strongly felt Hank Rearden's agony due to Dagny's disappearance. I thought that Galt should should have let Francisco tell him to, but that also leads a bit into a dilemna then about what does Hank do in response to the knowledge that she is OK, but he cannot know where she is and who she is with. That one would have created a real problem with the plot. Still, this is another dramatic case of how our real life values and emotions cannot necessarily be fully embodied in a novel developed to clarify the philosophical issues relating to the heroic in man.

I am very much enjoying reading your comments. You seem to have a free and easy way of saying what is on your mind. This could make you a loose cannon by itself, but you also seem to have a good grasp on reality. It is fun being around you.

Aaron,

I suppose we could say that Cheryl should have understood how bad James Taggart was before marrying him or at least earlier than she did. The failure to understand can have terrible consequences. Or, maybe we should say that OK she made a mistake and now she should put it behind her and taken advantage of what she had learned to live a better life by leaving him. Then we should be angry at her for killing herself instead.

I was angry when she died. I was angry at Taggart and his destructive nature, I was angry at Cheryl for killing herself and not fighting on, and I cried. This is probably just the way I was supposed to feel.

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To me, Eddie and Cheryl were the closest to real life people in Atlas Shrugged. I identified with them the most. As a matchmaker, I would have fixed them up. I wanted to see them make it to the end and emerge heroic, but alas....

Kat

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The idea of matching them up sounds good to me! Too bad neither of them had a future.