Thinking again

Part of this gets into some kinda advanced math. This post is more about my own introspection than it is about math, but part of the story is how excited I was to learn something, so it seemed relevant to put what I learned that was so exciting. I try to explain most of it in simple terms, and in easy to understand ways, but I don't know how good I actually am at that. So I will let you know when the super-mathy part starts and ends so that if you are scared you can skip it. But if you're feeling brave, I encourage you to try to read it. If I didn't explain it well enough, (or, for those of you who know what I'm talking about, if you find an error (I am doing this post from memory and learned this stuff over a year ago)) let me know and I'll try to explain/correct it. I don't claim to be perfect, but I do claim to strive for improvement, and any polite, constructive criticism is welcome. :-)

So I need to figure out what I'm going to do. First, I will examine where I have been.

I have always liked science and math for at least as long as I can remember. I like knowing how things work, and where they come from.


In high school, looking at colleges, I needed to figure out what I wanted to study. I figured probably some kind of science since those, along with math, were almost always my favorite classes, not counting various kinds of music classes. (Though I also have always loved music, I didn't feel it was the right *career* for me, though I had every intention of playing music forever.) Out of my science classes, I found a basic division of the natural sciences into three categories: chemistry, biology, and physics. The physics class I had felt extremely straightforward to me, so I wasn't sure how exciting it could be in college. So I stuck the other two words together and came up with biochemistry and decided to try it.

So I got to college, and studied biochemistry. I took Organic Chemistry, which was not presented in a way that was interesting to me. I would have loved it if they had presented it like "Here's this cool stuff that these things do and how it works." But instead, almost everything was about *how to make* things out of other things. Questions on the tests would be of the form "You want to make X. You have Y, Z, and W. Draw each step of the process, including the required temperature and all byproducts and their percentages of each step." I don't really care how to make things. I just want to know how they work.

At the same time, I was in a seminar class where we got to read papers recently written by biochemists. Over the course of half a semester, we read two papers. Though I am well aware that two data points are not ideal for finding statistical patterns, I was starting to feel like everything the biochemists were doing is the same. There is some gene or protein they study, they find a mutated form of the gene (or the gene that codes for the protein), put the mutated gene back into something (usually a plant, yeast, or bacteria), and see how it affects them (by survival rate and, in the case of plants, also the shapes they grow in). And while I love to read about the things we learn from these experiments, I concluded that if I had to do them day in and day out for years, I would become very bored.

So by the middle of my second semester, I knew biochemistry was not for me. Meanwhile, my physics class was taught by a very energetic instructor (who unfortunately left at the end of the year) and I was reminded of how excited I was about the physics I knew despite its straightforwardness. So I decided to try physics next.

Due to issues with what version of what class can count for which major, after changing my major to physics I had to take my third version of first-year physics. It was a lot of fun, and I enjoyed every bit of it, even if it was nearly all familiar, except with more calculus and derivations. I decided to try to find some work as an undergrad in my newly-chosen field. After asking around in the department, I found that one of the professors had a meeting weekly with some students that were helping with designing the LHC. This seemed to be the closest I would get to particle physics. I was warned that the field was pretty popular with the machine about to be turned on, but that I was welcome to attend the meetings anyway to hear what the others were doing.

And so I did. Each week, some student from the group (some I knew were undergrads, but some of the ones I didn't know might have been grad students. I am still not sure) would spend the hour talking about what they've been doing and what they plan to do next. I did gather a little about which particles decay into which other particles, most of which I have since forgotten, but that part was very interesting to hear. Most of the time, though, was spent describing how to come up with simulations, or how to put some piece of the machine together. The simulations would be used to show what "should" happen if certain deviations from the Standard Model were true, so that we would recognize the difference when we get the data back from the machine once it's turned on. Once or twice there would be someone telling about what electronic gizmo they were attaching to what other one, and how they would arrange the parts in space so as to use less wire so the information wouldn't have to travel as far and thus get there faster.

The most interesting thing I learned at these meetings, and the only thing I really remember clearly, is that the hardest problem in designing this machine was figuring out how to throw away information fast enough. The sensors would be taking in information several orders of magnitude faster than it was physically possible to record it. So they needed to throw away enough that they could write the rest. And they needed to figure out how the computer would tell what to keep and what not to, and how to tell fast enough for it to be worth it.

The other most important thing I learned at these meetings, is that that wasn't what I wanted to be doing. Again, too much of it was about how to make things, and not enough about how things work or might work. I realized that if I wanted to do physics, I would only really be happy with theoretical physics. Playing with pretty equations on chalkboards *coming up with* the things the experimentalists will test with the gigantic machines they build. But there isn't really that kind of physics work for undergrads, and it sounded like even a significant way through grad school you don't even get to that part of physics.

But I could play with pretty equations on chalkboards *right away* if I changed to math. The kinds of things I wanted to do with it would be pretty much the same between math or physics, with the exception that physics would have "stuff" in it, whereas math would be just the math itself. This was not a distinction important to me at the time. So again, I changed my major, and now considered myself a mathematician (in-training).

So now I was taking more math classes. One of them was Real Analysis. The first thing we did was to define the real numbers.

----------~~~~~~~~~WARNING: MATH EXPLANATION SEGMENT~~~~~----------

I was already familiar with the concept of making numbers out of other numbers, so that in and of itself wasn't new. I remembered when I first learned about negative numbers, where you get them from taking a big number away from a little number, and that the positive numbers with the negative numbers and zero were called integers. I remembered later where when dividing numbers instead of keeping a remainder, we cut it into even pieces and we had fractions. The integers with all the fractions were together called rational numbers. Then there were exponents and roots. At first, we could only take square roots of square numbers, that you got from taking a rational number to the second power. But then they said, yes you can, those numbers are just irrational. The rational numbers together with the irrational numbers are called real numbers. But you can't take square roots (or any even numbered root) of a negative number, because any real number squared is positive (because negative times negative is positive). But then, again, they said, actually you can, they're imaginary numbers, and together all these numbers so far are complex numbers. It does go a little farther than that, but I haven't yet actually used any of those numbers outside the complexes.

So in real analysis we, as would seem appropriate, began by defining the real numbers. We did this by constructing them from the rationals. I don't remember that particular construction very well, but there is another one that we learned later. This may or may not make sense to those of you who don't do much math, but if you ask, I'd be happy to try to explain again the parts that don't make sense.

So if you list a bunch of numbers in a row, you can call the list a sequence. A sequence can have the numbers in any whatever order you want. Usually it is written with commas between the numbers and curly braces on the ends. So I could have the sequence {1, 2, 3}. Or {1,2,3,4}. Or {2,2,3,1}. Or {1,3,2,2}. All of these sequences are different, because order matters in a sequence.

Sequences don't even have to end. They can go on forever. These are infinite sequences. They sometimes have a pattern, but they don't have to. Sometimes, a sequence might do this thing called converging. When a sequence converges, there's this special number, called its limit. In a converging sequence, you can choose any distance from the limit, no matter how small, and there will always be some place in the sequence where all the numbers after that will be at least as close to the limit as the distance you chose. No matter how small of a distance you choose, this is true. This is what it means for a sequence to converge.

The most obvious kind of converging sequence is when all the numbers are the same, or when all the numbers after a certain point are the same. This is allowed. But if you allow more than just integers, for example if you allow all rationals or all reals or all complexes in the sequence, the sequence might converge without ever actually reaching the limit. This topic is sometimes scary for people the first time they come across it, but sort of the reason it's able to work is because between any two numbers there's another number. (This isn't true for integers, so for a sequence with only integers, if it converges, after a while it reaches the limit and stays there. Like {3,2,1,1,1,1,1,1,....} where all the rest is 1. That would converge to 1.)

But sometimes you have sequences that sort of converge, except that the limit doesn't actually exist in the number set you're using. Like if you only have rational numbers, you don't actually have the square root of 2, but you can make a sequence that looks like it would converge to it. This is called a Cauchy sequence. A Cauchy sequence happens when no matter how small a distance you choose, after enough of the sequence has gone by, no more of the numbers will be farther apart from that distance. Every sequence that converges is also a Cauchy sequence, but not always the other way around. Like if we have a Cauchy sequence of rational numbers converging to pi {3, 3.1, 3.14, 3.145, 3.14159,...} it is always getting close to pi, but since we are only allowing rational numbers to be in our sequence, we can't actually say that pi is the limit. But if we chose some rational number to call the limit, we would be wrong, because there would be some rational number even closer to pi that would be in the sequence. But it is still a Cauchy sequence, because the numbers are still always getting closer to each other.

So now we're ready to build the real numbers out of the rational numbers. The set of rational numbers is called Q. Why Q? I'm not entirely sure, but I think it comes from the word "quotient" since the quotient is the answer to a division problem, and fractions are all the same thing as division problems. And they can't use R for rationals, because it's already taken for the real numbers. So anyway, at the beginning, let's pretend all we have is Q, the rational numbers. And we have this other set R that doesn't have anything in it yet. Now we make a bunch of sequences. We make all the sequences. Which is a lot because not only do we have infinity numbers to put in them, we can have the sequences be as long as we want. So now we have all the sequences.

Now we take one of the sequences, and check, is it a Cauchy sequence? If it is not a Cauchy sequence, we throw it away. We don't need it anymore. If it is a Cauchy sequence, we ask, does it have a rational number limit? Is there some rational number which the sequence is always getting closer to? If it does, we put that rational number into our new set R. Then we throw away the sequence because we're done with it. But if it does not have a rational number for a limit, we decide to let that sequence represent some number that will be its limit. This limit is not rational, but we just declare it to exist. (Kind of like when we learned about negative numbers. We just declared them to exist.)

We go through this process for all the sequences, until we have exhausted all of the sequences of rational numbers. Technically, we can't do them only one at a time, even if we went forever, because there are more of these sequences than there are counting numbers. (This is not true of the rationals. You can count them, though it would take forever. But you can't count our sequences even if you had forever to do it. Some infinities are bigger than others. While I would be glad to explain this further, it is less relevant to my story, so I won't explain here unless asked.) So we sort of do the whole thing at once.

So now we've got this set R. Some of the numbers we already knew, they were rational and already existed. Some of them are not rational and so far are just described by these sequences. We make other notations for them since decimal expansions of them, no matter what base we use, will never end or repeat themselves. One of these is pi. One of them is the square root of two. R is the set of all the real numbers.

-------~~~~~~~~~END OF MATHY SEGMENT~~~~~~~~----------

So this really cool mathy thing was really exciting to me. I learned how to make the real numbers out of the rationals. I had some vague notion of how to make the rationals out of the integers, and the integers out of the counting numbers. So naturally, my next question was "Where to the counting numbers come from?" Pretty much whoever I asked, though, pretty much all they'd give me is some vague reference to set theory. So basically, set theory is to the rest of math what math is to all the natural sciences. (For what I mean by that last bit, see this awesome comic.)

So I decided I wanted to learn set theory. But... the math department doesn't have any set theory classes. But I remembered hearing somewhere that certain systems of logic have been proven equivalent to set theory. So I decided to sign up for a logic class at the next opportunity (which is this semester).

Then one weekend I ended up at this awesome math conference, and at the dinner there we were talking about stuff, and I mentioned my ambition to learn where all of math comes from, by which I mean, how it is all constructed from the smallest parts possible. Then one of the people at the table said that's pretty much exactly what the Bourbaki books are. I had never heard of them, so I asked more about this seemingly-magical series of books that promised to be exactly what I'd been looking for for months.

So a long time ago, there was this guy Euclid, who wrote a bunch of stuff about what it means to prove something, and for a proof to be rigorous. And people were like "That's awesome! We should make sure that everything we know, we actually know it!" But they hadn't been practicing for very long, and there were still things that they just assumed. Like counting numbers. They just existed. Why? Because how can they not exist? It just didn't make any sense to them.

Then, several hundred years later, we're in the early twentieth century. People are doing math with things that aren't numbers. Basically anything they can think of in a way like they think about math, they're calling it math. They have these things called sets. Sets are really exciting. You can put anything in sets! You can put sets in sets! You can put sets in sets in sets in sets in sets. And so on. So then, it was only natural to ask "Can you put all the sets in a set?" Well let's see. Let A be the set of all sets. It looks like it worked. Is A an element (one of the things we put in the set) of A? Well, it looks like it. I'm not sure exactly how that one was decided.

But here's a more interesting one. Let B be the set of all sets that are not elements of themselves. *double-take* wait, what? Okay, so if you don't use sets much you might not see right away how weird that sounds. So let's ask a question about B. Is B an element of itself? If B is an element of B, then Be is a set that does not include B as an element. That sounds like a contradiction. Because it is. But if B is not an element of B, then by the definition of B, B is an element of itself. Another contradiction. No matter how we answer this question, we are wrong. Mathematicians don't usually like when that happens. Because if you let a contradiction be true, then you can't keep false things from also being true. And mathematicians like to be able to tell the difference between true things and false things. That's kind of like the whole point.

One of the things that came from this, is that they made more rules about sets. I don't know what all they are yet (but I hope to learn soon!). They added rules so weird things like that can't happen, and so that what's true is true and what's false is false, and we always can tell the difference. (Actually, sometimes there are things we can't know if they're true or false, and we can prove that we can't tell. But at least we don't have things that are both true and false.)

Another thing that came from this is that some people started realizing that as rigorous as we thought we were, we actually took a lot of things for granted. Most of the mathematicians, like Euclid, didn't really mind because the things they assumed were true didn't make any sense to be false. So they didn't really care.

But there were a small handful of mathematicians who decided that they didn't like that. They wanted to know what all the rules were so that they would know for sure that math made sense, at least as far as the rules did, but you can't define making sense based on some rules if you don't know what those rules are. Or how you get everything else from them. But like I said, most of the other mathematicians didn't care and thought it was silly to worry about it. So these few mathematicians that were worried and wanted to fix things got together in secret and published their books under a collective pen-name. Nicolas Bourbaki.

So what they did, was they worked out what was defined in terms of what, and what was constructed from what, and, as best they could, write it all out. All the assumptions, all the definitions, all of everything. They wanted to make the foundations of math as solid as possible.

So, of course, I decided that weekend that I wanted to find these books, and to read them. There are at least nine books. I have obtained the first one. They don't even get around to defining the counting numbers until the third chapter. That's how thorough they are. And this stuff is really dense. Though I'm still an undergrad, most of my classmates in my math classes are grad students. And I had to read the first subsection of the first section of the first chapter twice, and both times slowly, to even know what it was talking about. That's how dense this is. Five pages took a couple hours, at least. Separated by a couple weeks, because reading too much in a row makes my brain tired. So this is not easy stuff at all.

But I want to do it. I want to know where it all comes from, and I have not heard any better strategy than to read these books. It will probably take a long time, but I think I can do it. It will take a lot of work, patience, and determination, but this is what I want to learn. I don't think I will feel comfortable settling down into any particular field until I feel like I know more solidly where it comes from.

So currently, I am thinking I will, at the very least, take a break between graduation and grad school. I am sure my professors will be disappointed and want me to go to grad school, because that's what math students do. But I want to learn where it comes from first. I'm also suspecting that I won't want to stay in the same part of math forever, I'll probably want to drift between them sometimes.

Had I long enough to learn it, here is what I would want to learn. First, I would want to learn where math comes from, starting at the smallest pieces possible. Then from there I would solidly learn everything else that we already know. I might get "sidetracked" partway through this task and decide I want to stay there and figure out new things no one knows yet. I don't know yet. If I do choose a topic I want to do that for, I'll go back to grad school and do the academia thing. Otherwise, I'll just keep learning more and more new kinds of math out of things people have already figured out.

If I run out of math and still have time, I'll start on the natural sciences. Mostly, these are biology, chemistry, and physics. They explain how stuff works. Most of biology comes from chemistry, since all the processes and stuff has to do with how the molecules interact with each other. But then all the chemistry in turn comes from physics, since the way the molecules interact has to do with the electrons and the electromagnetic fields. And sometimes they count "nuclear chemistry" as a kind of chemistry, and that's just the protons and neutrons and the forces that hold them together, which is also physics. And physics is just math with stuff thrown in. So after math, I'll work my way through physics, then chemistry, then biology.

After that, I'll start on the social sciences. Linguistics, psychology, history, things like that. I don't know what all of them are. But they will be next. After that, I'll do more philosophy stuff, and I guess work on my skills at whatever art I can find to learn.

If I manage to live long enough to do all of this, I will have had an extremely long life. I don't think I am likely to ever "run out" of things to do unless I manage to become effectively immortal. But if I have learned all of these things about how everything works ever, I probably will have achieved Enlightenment, or something very similar. So I have no idea what I will want to do then, the state of my mind is likely to by then be sufficiently different that I can't currently comprehend it.

That's not my reason for wanting to learn things. I want to learn things because I want to learn them. I know it sounds like a tautology, but I can't really think of a better explanation. I want to learn for learning's sake. Not so I can be smarter than everyone else or because I think some awesome thing will happen to me if I learn it. Just because learning is what I want to do.

So, to summarize, I want to learn things because I want to learn them. My starting place of choice is set theory, which I intend to learn from the Bourbaki books. So I'll probably end up posting a lot here about what I learn there. But with the shiny new labels I made, you'll hopefully be able to tell which ones those are, so that whether you read them or not, it is on purpose.

Organizing

Hi! In preparation for what might be a flurry of activity, I'm going back and adding labels to existing posts so that when I start having more posts you, the reader, will be able to more easily find those posts which are interesting to you! Yay!

Randomness

Friend recommended Muse. They do indeed have very awesome music. :-)

Oh, yeah! This thing is still here, isn't it?

I know I probably don't have very many (any) readers at the moment. However, this is my statement that I am entertaining the idea of posting more frequently. No promises, but it is a thought.

.imu'omi'e la .jdakrat. .skaryzgik.

mi'e la .jdakrat.skaryzgik. poi fanva je ctuca

I reinvented my name again. This new one means roughly "Pope skaryzgik the Translator and Teacher". It feels more succinct (and I might have a halfway good chance at remembering it now) and hopefully the description portion of it will be accurate in the near future.

Translation update

It's been a while, I've been adjusting to a new schedule, but I (hopefully) will be updating more regularly (frequency is uncertain at this time) soon.

First, I would like to thank those who have helped here and on the lists to tweak my wordings/construct usage to improve the translation, both those whose effects are easily seen and those whose ideas have sparked their ideas. Also, I would like to encourage their continued help as well as the help of anyone else who can spare the time to give some thoughts. I really do appreciate it.

Also, I probably should mention that the text I'm translating is "(K) ALL RIGHTS REVERSED - Reprint what you like", so it seems only reasonable that I have a similar policy regarding my translation of it. So if any of you have ideas and send them to this, those ideas used here will be similarly copyable.

Now, for the point of the message, the translation. I'll start with my revised version of what I already had. The English and my first try are here, so I won't be typing it all again here. But here is my second run through (taking into account the help of others):

.i lo pa botpi be lo vanju be'o
.e lo pa tuple be lo citlanme be'o
.e do ge'esai
ne ne'a mi ge'u
zi'e noi siclu
va'o lonu manku

.i ko na se cirko fi le te ctuca be fo le ka se stura be'o vau
sei sitna be le papi'emumoi be la gutra cukta

Now for the next section of translating. The next part is excerpts from an interview, with a title in front of it. I'm thinking of using a topic-comment construct with a set of tu'e-tu'u brackets around the lines of dialogue. The title of the excerpts is pretty long, though, and I only got a little bit through it. Here's the English of the excerpts title, though:

Some excerpts from an interview with Malaclypse the Younger by THE GREATER METROPOLITAN YORBA LINDA HERALD-NEWS-SUN-TRIBUNE-JOURNAL-DISPATCH-POST AND SAN FRANCISCO DISCORDIAN SOCIETY CABAL BULLETIN AND INTERGALACTIC REPORT & POPE POOP.

Here is the (unfinished, remember) Lojban version as I have it so far. (Yes, I know cutting it off where I did makes it ungrammatical, but that's as far as I got today. Comments (in English) will follow.)

ni'o piso'o le za'e paurselsku be le za'e nunreisku be la .malyklips. poi citmau bei fo

(That looks like even less in typing than it does in my notebook.... In my defense, I would like it noted that I spent a lot of time reading the chapter about text structure.) So I tried {paurselsku} for "excerpts", thinking of a place structure along the lines of: x1 is an excerpt/partial quote of x2 (speaker) said to original audience x3. Although I didn't need the x3 here. I then figured if I wanted a lujvo for "interview" that {nunreisku} could work, if it had a place structure of: x1 (event) is an interview of x2 (interviewee) about x3 (topic) by x4 (interviewer). But when I put it through jboski, it seemed that {nunreisku} already had a place structure, which was different than I wanted, so I knew that I would really need the {za'e} there, unless I can find another word for "interview" which would serve my purposes without needing it.

Thank you again for your help! .i ki'esai

First Piece of Translation

Here's the first piece of my attempted translation of the Principia Discordia. I still haven't decided on what to use for the title. It has been recommended that since the English title is a play on the Principia Mathematica, a book that sets out some axioms of some parts of math, that the Lojban title should be a play on the Complete Lojban Language (sometimes referred to more shortly as the Big Red Book), the book that sets out all the rules of Lojban (which is similarly logical), or one of its many names. I want to start with a piece that's a little bit simpler, so I'm going to save the title for later, but if anyone has any suggestions, either following this or another strategy entirely, do go ahead and let me know.

I started at the beginning of the Principia. Follows is the English version of what I have so far, followed by my attempted Lojban translation of it, and then some of my own comments about my translation.

A jug of wine
A leg of lamb
And thou!
Beside me,
Whistling in
the darkness

Be Ye Not Lost Among Precepts of Order...
-The Book of Uterus 1;5

.i botpi lo vanju
.i tuple lo citlanme
.i do
.i zvati mi
.i siclu di'o
lo ka manku

.i ko na se cirko fi le te ctuca be fo le ka se stura
.i la gutra cukta pe li pa pi'e mu


I know the lines in the poemy part at the beginning should probably be connected, and are probably more complex than simple observatives, and any help connecting them would be appreciated. Also, I had a little trouble with "The Book of Uterus 1;5". I wanted to use two relative phrases, but that ended up trickier than I expected. If someone has a way of connecting them with a more specific relation than a tanru, that would also be appreciated. Also, any other suggestions to make any of my wordings less awkward or mean closer to the original would be good, the things I pointed out were just specific things I was already thinking about.