woolcutt

Concerning free will, I recommend John Conway's six part lecture series, hosted on Princeton's servers, on his proof of the "free will theorem".

The examples are often chosen to be bizarre intentionally so that you are forced to focus on the relevant material: the underlying LOGIC of the sentence at hand. That the logic should apply equally well to sensible situations should be obvious, but by masking out the possibility that you are using intuition, the instructor can have some guarantee that you have actually learned the material covered in the course.

Haha. If you value the relationship and you find yourself on the receiving end of a pained smile when you are looking for a favor (or however it comes up) and try shelving those plans for a while if you can and find something else to do. Think about the situation and talk it over later and see if you're really putting that person out or not. It takes a bit of finesse, however, to read a situation--there is a lot I'd do for my SO that might put me in a bit of a grumbly mood temporarily, but I can look long term enough to know that it's worth it (but the MINUTE it's not--out the door!).

Good luck! Checking out the first podcast as I type.

I would hazard the following guess: his expectations of what life at Goldman would be like were not met and perhaps a well-paying job did not offer him the self-satisfaction he thought it would. Corporations, viewed as a large machine, often restrict expression (via dress codes, protocols, standardized equipment, etc...) to achieve the larger (selfish) goal of profiting the company. If you are prepared for corporate culture the transition is no big deal, if you don't like it you are free to do something else! Again, just a guess at his meaning :/ Edit: The "interviewer" is the one who seems to be doing the proselytizing!

I think that the short quote "Life is the standard of value" is a nice way to put all three of those together. Values are necessarily held by a valuer, yet to maintain one's life (the valuer) there are certain rational requirements that must be met (food, shelter, etc...). So one must hold one's OWN life as a value (self-esteem) if one is to avoid simply drifting by at the whim of the moment which may lead to making irrational decisions.

As an Objectivist I've learned to keep my eyes open for all kinds of opportunities and it's really given me a great perspective on a proper work ethic. I enjoy "being busy" because I know that I'm working to make a good life for myself and where a lot of people may complain about long hours and wasting their time I know that I'm being productive and can enjoy my time--even when the going gets tough. So when this opportunity for a weekend job rolled along I had to hop on it. I am now officially a balloon artist. The past month I've squeezed in training in the off hours and now I know about 30-40 different creations and I work with a small local business (just three of us right now) doing performances at festivals, music events, trade shows, etc... This on top of a full-time job and studying for the actuary exams keeps me mega busy, but as much fun as it is to go out and make crazy balloon creations for people it's worth it! PLUS (and I include this purely out of marvel at my own situation) once I'm done with the on the job training I'll be pulling in more than $50 / hour doing balloon gigs, so it totally fulfills all my "objectivist greed" for the almighty dollar! Haha! P.S. I'm not a frequent poster, but am a frequent reader of the forums... thanks for lot's of entertaining reading!

Thanks for your input. I think I'm just going to see out the semester like usual. I still disagree with the university's policy, but I'm not calling the shots. I'll shortly get over myself, lol.

Well as for still working here, I can't claim omniscience of all events - I just found out about this recently. I want to finish whatever work I said I'd finish and then I'm out of here. I know this makes me seem petulant, but well, maybe I am in this. I just don't like the "I'll scratch your back if you scratch mine" attitude applied to academics. That the department is desperate to hold onto PhD candidates is just as good a reason to maintain the standards as to bend the rules to keep a few struggling students. The exams are not just classwork, they are a necessary part of acquiring the degree. I never have cared about the result of a classwork exam nor my grade for a course. In three years of graduate school I've checked my GPA twice: after my first year and last night. I have a 3.97 - HA! Lowering the standards for this exam represents a significant decrease in the value of the degree overall. Unfortunately, as the university seems to be the only venue to practice and teach higher mathematics it would appear that I'll have to tolerate some kind of silly politics anywhere I go. BTW: I'm not really going to go through with this pipe dream. But I thought you all might get a kick out of the story.

It's a rare occasion where we are given a chance to emulate our heros, but I believe I have such an opportunity: I began graduate school with a great passion for my subject intending to pursue a PhD in mathematics. One of the great hurdles of doing this is passing the PhD qualifying exams of which there are two at my university. I spent fully a year (okay maybe it was more like nine months) studying for the exams and passed them on my first attempt. This was an extremely demanding task, but I am proud of my achievement and time spent. This past year the professor I really wanted to work with was unavailable and I spent my time taking classes tangential to my interests and in private study. A handful of other graduate students attempted the exams in that time and didn't do so well, however, rather than fail these students the administration saw fit to give these students a second chance and a week to take the exam home and complete it with any resources they had on hand. Some of these students required even a third attempt (second take home!) to complete and finally pass the exam. I feel that this diminishes the value of my achievement, and this and other factors are contributing to me considering a change of school and even possibly a change of career. Currently I teach a relatively low-level course trying to save some money for whatever is to come in the months ahead. I've been toying with the idea of giving the students a surprise optional take-home final exam worth 100% of their grade, which would most likely take and therefore most likely all earn A's for the course. Passing 50 odd students with A's would be an unusual outcome for the course, but I feel it nicely mirrors my situation and sends the appropriate message to administration. It can only help the students pass the class and they would all most likely be elated. The class is a terminating course, meaning that it satisfies no prerequisites for advancement at the university, so I would not be inadvertently setting up any students to fail in a class ahead. What do you think guys, is this my (mini) Howard Roark moment?

Basically my food policy the past couple months has been to only buy foods which I can identify all the parts of. This heuristic leads to buying simpler foods and ultimately cheaper foods. I have sort of "gone granola" which I realize may not be a popular choice here, but like other people have mentioned whole grains are cheap. I buy lot's of food bulk out of bins rather than packaged whenever possible which will ultimately saves me money. I'm on a tight budget and so buying healthy food on the cheap is a big priority which originally led to me eating this way. The weight loss (with an added exercise routine) and extra energy will keep me eating this way for years to come.

I wanted to share this picture I generated using Mathematica and Photoshop. This picture uses facts about the distribution of the prime numbers to control a cursor around the screen and draw the following picture: I realize that it looks kind of post modern, but I see it more as a bridge between the type of imagery that goes on while I'm thinking about mathematics and what would be appreciable visually to those non-mathematically inclined. I study mathematics and am pursuing a graduate degree at the University of Hawaii. I add a little bit of random noise to the motion for aesthetic purposes (while preserving the primary mathematical structure). I allow the thickness of the line to diminish and the color to pass through the spectrum as it moves about to get the picture you see above. Apart from the aesthetic decisions I made, this picture is actually very precise in the sense that if someone stumbled across the same pattern and developed the same algorithm they would generate essentially the same picture. This type of work is engaging for me because I perceive generally the final form right from the start, but I don't know exactly how it will turn out, because I can't do the calculation with thousands of prime numbers in my own mind before hand. If people are interested I am happy to discuss this picture further and will share similar pictures in the future if people are interested.

I disagree. To me your criticism sounds like the universe would be limited precisely by what is knowable by the human mind. This smacks of subjectivism. Indeed the world exists outside of the human mind and it is knowable. Bacteria were magic vapors before the microscope, sub-atomic particles were figments of mathematics before the right technology came about to observe them. It's conceivable that the extension of the human mind through technology could proceed ad infinitum OR that the fine structure of the universe eventually stops. My point was that it is an interesting question to ask yourself which of these is the case. There is of course no satisfactory answer (either you discover more or you don't, but your lack of discovery doesn't imply non-existence). Eventually you tire of the game and eat a burrito, and hope you did something productive amongst your speculation.

By definition of existence it would include everything even the potential stuff "past the edge". An interesting alternative to consider is to partition existence into two types: those things which are observable by humans and those which are not, and ask the question "what is the extent of the unobservables?" That direction necessarily ends in futility, but is not immediately ruled out by the definitions. Indeed, perhaps the fine structure of the universe is composed of particles which we will never be able to perceive the individual nature of as we do photons and atoms. The difference here lies of course in that we haven't posited existence outside of existence, merely existence outside the realm of human observation.

I agree. This post also reminds me of how it is possible to construct sentences and questions that are essentially meaningless. For instance "how big is the color red?" or "just how holy is that pine cone?" Vague queries such as this serve a philosophic purpose--in particular identifying vague statements!--however, for serious philosophic discussion we need to be able to weed these out of our discourse.

A friend of mine asked me to explain the immorality of altruism to him. He is basically a socialist at heart, and so societal altruism is really really important to him. I'm looking for some help in making four or five good points. I'm not particularly good at debate, and since I have convinced myself of this a while ago, haven't thought much about "Objectivist Apologetics" the past couple of years. So I could use some pointers! In particular some help from similar experiences would be nice, such as identifying and establishing a workable common definition (we're obviously not going to agree on that), and building up a case from there. Thanks!

--my two cents-- Fantastic movie! I agree with a lot of the other opinions posted and its too bad that the movie hasn't done better in theaters. I have to share my favorite quote which went something like this: "Do you want to take command of this ship?!?!" "Yes!!!" "Well... you can't." That cracked me up I especially agree with JMeganSnow, the villain's quote at the end was a fantastic way to end the show!

You don't have to represent it without sin and cos (but you can!). Its not like this new book is going to destroy any old relations or formulae--it will only aid in the development of new mathematics. If you learned your sines and cosines fantastic! I have a strong feeling that when we wake up tomorrow, the old formulae will still check out. But there is nothing mystical or necessary about scratch marks on paper--only the relations they represent (necessary, NOT mystical). To be bound by tradition is, well, archaic.

Ugh, the debate goes on. If people have trouble dealing with repeating decimals, what is the state of NON-repeating decimals? We all know that the circumference of a circle of radius r is 2 * Pi * r But Pi = 3.1415926535... To maintain logical consistency the people who believe that infinite decimals DO NOT specify real numbers but rather some limiting process would have to believe that the circumference of a circle gets larger and larger the more decimal digits of Pi we used because there is no number exactly corresponding to Pi since it just exists as an ephemeral limit of some process. Of course this patently contradicts a circle as a single finite object.

It would appear that the benefits of the new system are two-fold. Doing away with the Trigonometric functions allows students to solve equivalent problems and eliminates the pedagogical difficulty of explaining what the trigonometric functions are. This not a breakthrough as it stands, but a nice refinement of the system. The interesting application to higher mathematics (which DOES have the potential to influence new research) is that since the fundamental tools of Rational Trigonometry are polynomials instead of infinite power series, we can use them to analyze the geometry of different mathematical objects besides the real number plane. Polynomials are fundamental to all field structures, but power series may be more meaningful in one field than another (i.e. may have a limit in one field but not another). Of course I haven't had a chance to read this part of the book... So I don't know exactly how far the author intends to push this analogy.

I too have read the first chapter and as I am teaching part of a Trigonometry class here at UH will claim to have some expertise in the field. The beauty of this new system is that any of the old formulas involving the relatively arcane trigonometric and inverse trigonometric functions are done away with. The point was NOT to do away with squre roots and irrational numbers (which is unfortunately suggested by the name "Rational Trigonometry"), but to do away with complicated functions like Sin(x) and ArcTan(x) which are hard to explain to someone without the use of calculus and power series. For instance its hard to calculate the value of ArcTan(19/20) without a calculator (in fact would be very difficult to explain to the average trigonometry student and almost impossible to explain the concept of why that calculation works), but this calculation does come up in relatively simple trigonometry problems. [Note: I have in mind the method of approximation by power series, if my particular example is easily worked out by hand forgive me] The book replaces the concepts of "distance" and "angle" with "quadrance" and "spread". Instead of deriving formulas involving distances and angles (i.e. Laws of Sines and Cosines), the book shows us the relations between quadrance and spread which turn out to be (relatively) simple polynomial equations. This means that instead of using approximations, students can use the quadratic formula (something that is pretty easy to understand) and get EXACT ANSWERS. This alone would be such a boon for the average TA grading papers (like me), and would save hours of time hunting through HW scrawl looking to see if a wrong answer is the result of not understanding the concepts or a rounding error early on in the problem. Thats my two cents, I like the first chapter and look forward to reading the rest. There are implications for much of higher mathematics too, but I only wanted to comment on the "basic" trigonometry aspect right now.

A small (but hopefully growing) crowd Are you from Hawaii as well?

Howdy! I just moved to Honolulu, I'm living in the Kaimuki area and I'm a grad student in Mathematics. I posted a similar topic last night and someone pointed me in your direction. Perhaps we could meet up for coffee sometime?

No, I'm on Oahu too, currently living on the east side of Honolulu in an area called Kaimuki, though I'm considering looking for a new place to stay. Thanks! I might have to look up Legendre sometime.

This is a topic I have seen on numerous other Internet forums, though I've never seen this level of accurate (philosophical) analysis before. I am not going to add any further comments towards solving the dilemma beyond what TomL quoted me as saying in our chat, but needless to say there are several levels at which we can fruitfully analyze this problem and I thank the other posters for shedding light on (the philosophic) aspects of identity and translation I had not considered. I do propose that at this point we split the thread into two: one for discussing the philosophic analysis of the problem and one for people who are still not convinced that within the context of real analysis that .999... = 1. As a side note, I have mentioned this topic to a handful of other (math) graduate students and a couple professors that I work with and almost without exception they say something equivalent to "who DOESN'T know that point nine repeating equals one?" (although chuckles and head nods were also a common response). Best regards